Railways. In treating of the construction and mode of working rail- ways, we shall confine ourselves principally, to those which are intended for the transit of passengers and goods, and which are now opening so vast a field for the improvement of the human race; an improvement, in fact, entering into all the relations between man and man, and which no one, be he ever so sanguine, can venture to fix a limit to.

From the middle of the seventeenth century various con- trivances have been in use for decreasing friction on roads, particularly near the collieries in the north, such as laying down tracks of wood and stone for the wheels of waggons; it having been found that the much greater quantity of work performed by horses on these tracks, or, in other words, the less number of horses required to do a given portion of la- bour, more than repaid the expenses attendant on forming the tracks. These, in general, gave way to the flat or tram rail, made of iron; but the improvements were very slow, and at last were only applicable to certain circumscribed locali- ties and materials for carriage.

Possessing little general interest, and chiefly benefiting individuals, the attention they attracted was principally con- fined to the parties immediately connected with them. But how different is the prospect now before us, since we have seen the magnificent creations of George Stephenson? Pack- horses are still the only mode of transit for traffic in many parts of the world; and within seventy years this was the general mode of conveyance for the carrying trade to York- shire and Lancashire from the west of England and Birming- ham. In the year 1830, when the London and Birmingham railway was projected, the expense of constructing it was stat- ed at £6,000 per mile with one line of rails, which were to be worked by horses, and warranted to go eight miles an hour; now the public are complaining of going only twenty miles an hour, and we have a right to expect that, at no very distant period, this velocity will at least be doubled; in fact, at the rate improvements have been advancing for the last few years, we know not where to place a limit of increase in speed.

It is of these splendid creations that we have here to speak. We shall shew the method of conducting a modern railway, from its earliest commencement, through all its various stages in each department, both in and out of doors, up to the pe- riod of its final completion; and shall end by explaining the method of setting it in full operation, pointing out, in each division of the labour, those modes of proceeding which will most conduce to a satisfactory result, and marking those things which practice has shewn should be avoided; collect- ing the contrivances and appliances which have been found useful, from whatever source they may be derived, and set- ting a beacon upon shipwrecks, that they may become other men's landmarks.

When a railway is proposed between any two places, the public want to know how to distinguish between a bubble speculation, got up by a few interested individuals, a crude- ly-formed and hastily-adopted, but really good project, and a line got up with care and attention through all its parts, shewing it to be the result of patient research and of matura- red judgment; and according as inquirers find the follow- ing directions more or less attended to, they may place con- fidence in the scheme which is laid before them.

These undertakings generally begin with a few indivi- duals interested in the line of railway proposed, when the project is honestly intended; but the great mass of original proprietors are men of a speculative and adventurous turn of mind, who enter into these concerns for the mere purpose of making money. If the thing succeeds, and the shares rise to a large premium, as they often do, the original holders realize the profits at once, by selling out, and then apply their surplus capital in other projects, with the same hope of gain. These people, by going out, make way for another class of proprietors, namely, those who look to their shares as a per- manent investment, and hope to make by them a greater annual receipt than they can get in the public funds, or by any other means.

In the earlier stages the directors are generally self-elect- ed. They should be men of local interest, rather than the lions who are too often found in these situations; men who can influence members of Parliament in either house, con- ciliate landholders, get off the shares, &c., and, above all, they should be of regular and businesslike habits. After a few meetings, they will find out what are their respective quali- fications, and can allot themselves into sub-committees ac- cordingly; some to look after the traffic, others the survey- ing, others the share list, others to attend to the canvassing along the line, &c. Almost their first duty will be to choose the secretary, the engineer, the solicitor, and the banker.

On the appointment of the first three much of the future success of the company will depend. The secretary should be a man of firmness and nerve, with conciliatory and gen- tlemanly manners; of a strong habit of body, able to rough it out in travelling, and possessing a stock of scientific and mechanical knowledge. If he is a draughtsman so much the better, and he should have been habituated to command large bodies of men, and be able to make a public speech at a short notice. With these qualifications, habits of order, and plain common sense, he will be a most valuable man.

The engineer must be judged of by the works he has ex- ecuted, either by himself or under the direction of a super- ior; the first, of course, being the most conclusive, but the second by no means to be neglected. Skill and genius may often be very prominent in subordinate situations. Of course, all other things being equal, one who has been employed on railways should be preferred to one who has not. The soli- citor should, if possible, have been connected with a railway bill before, and should have not only ability, but zeal. The advantage of having one who had been connected with a pre- vious undertaking is obvious, and if he has had much expe- rience in parliamentary business, so much the better; a local acquaintance amongst the landowners and residents along the line is also of much use.

We suppose that, prior to advancing even thus far, the pro- moters of the undertaking have travelled between the termini nary in- of the intended railroad, and have ascertained that there are quirles, no engineering difficulties of a marked character; and from our present stage, if the share list be found to fill, we have next to ascertain the nature and quantity of the traffic, first, as to whether it will pay for a railroad at all, and secondly, for what kind of a railroad. These questions should be met openly and honestly, or the consequences will be most disastrous.

The proper way to gain a correct knowledge of the traffic along any given line of country is, first of all, to station a man by day and another by night for two or three weeks, to count all vehicles passing a given number of spots along the intended line, (these spots should be near the principal towns), leaving out the largest terminus, as, for instance, London, and keeping the men on that side of all the respec-

Railways. tive towns which is nearest the largest terminus. For this purpose memorandum-books should be furnished them to note down all that passes. These should, at the end of their twelve hours' beat, be digested into printed forms, where each class is to be placed in its proper column, and any remarks made, if necessary. The forms are then to be daily transmitted by post to the secretary, who should make it his business to ascertain that, by fairs, races, elections, or any other causes of local excitement, the traffic is not in an unusual state. He is then to consider attentively the returns he has received, discriminating that which would be available for the railway in question, from that which would not, and bring the whole series into one general total, under the head of "direct traffic." The men are also to make a return, as nearly as they can, of the number of persons travelling in each vehicle, the quantity of goods in each wagon, van, cart, &c., distinguishing the nature of it, when practicable; also the number of all kinds of cattle passing the road, and where all the various passengers and goods are being conveyed to, as far as can be ascertained.

A similar series of observations must be carried on along the canals, if any, which lead from those parts of the line likely to become available for the intended railway, distinguishing the nature and quantity of the traffic. Most canal-boats are marked at the head and stern with the draught of water; and by finding out what they sink for every half-ton, a sufficiently near estimate may be found of the weight they carry. In certain situations the entries at the custom-house will be useful auxiliaries; the returns from clerks of markets will often materially assist as checks, as will also the rental of the various turnpikes; and no means are to be neglected to obtain a fair and honest statement of the general traffic in actual existence along the proposed line.

The next object is to find out what will be the probable increase on this existing traffic, when it shall be carried so much quicker and cheaper by a railway. The usual method of doing this has been to assume some ratio of increase, deduced from other undertakings of a similar nature, and two to one have been considered rather under than over the truth; but when it is remembered that the increase of passengers, these being the main contributors to a railway, has been, in all proportions, up to eighty to one, it is obvious that this is a very uncertain mode of ascertaining such an essential element.

A much better method of arriving at this point will be to take, with the help of a map, all those stage-coaches which run from places where travellers can go cheaper and quicker by the proposed railway. The numbers of these, their daily journeys and their mileage, can be readily got from the stamp-office returns, printed in Robson's Directory. When these various returns and data of every possible kind have been collected, and information has been brought to bear from every quarter whence it can, by any means, be obtained, the whole must be drawn up ready for calculation, so as at last to exhibit, in the simplest manner in which it can be shown, a tabular result not only of the existing traffic, but also of that which can be affected by the proposed railway under any circumstances, which latter may be called "contingent traffic."

The best mode of computing the data, as above described, is to multiply the distance between the stations by the number of coaches; then by the number of daily or weekly journeys made by each; and then by the number of passengers they may fairly be presumed to carry. By proceeding in this manner, the last results, in this case, can be added in a column, which will give the number of passengers carried one mile, daily or weekly, as the case may be. This, divided by the number of miles there will be on the intended railway, and augmented so as to exhibit the yearly quantity, will give the first step in the inquiry. The same method exactly is to be made use of for the canal traffic, if any, substituting tons for passengers, which is also to be done with the waggons, vans, and other public conveyances.

The contingent traffic, or that which is obtained from the stamp-office returns, is to be handled in a similar manner, only taking care that the various coaches and other vehicles are only taken for that distance which, in all probability, they will go upon the railway. When the whole is reduced, it must be put into money, and will then contrast with the amount of the same quantity of traffic at existing prices.

It is very easy to determine a limit beyond which none of this contingent traffic will, by any possibility, be available for a railway. We shall show how this is done, as it may serve thus far as a guide, so that no place beyond the limit need, of course, be paid any attention to.

In any triangle \(a, c, d\) (fig. 1), let \((ad)\) represent any increment uniformly generated with any given velocity \((h)\), and let \((ae)\) and \((cd)\) represent another increment uniformly generated with any other given velocities \((b)\) and \((p)\). Now all these velocities being in this case comparable with each other, if we represent the different increments by the times in which they are generated, we may show by the respective portions \((ad)\) \((ae)\) and \((cd)\), the progress of any object whose motion is uniform.

Let \((ad)\) represent a part of the road now used between any two towns \((a)\) and \((d)\), let \((ae)\) be a portion of a railroad, and let \((cd)\) be a cross-road joining the railroad \((ac)\) with the turnpike road \((ad)\). Then if the velocity \((b)\) \((p)\) and \((h)\) in the respective times \((e')\) \((f')\) and \((i)\) are such, that,

\[ \frac{e'}{f'} + \frac{f'}{i} = \text{or} = t \]

the point \(d\) would be at the limit, and no person beyond it could travel along \((de)\) and \((ea)\) in order to get from \((d)\) to \((a)\) with advantage.

As a railway may, in general, be taken in comparison with a coach-road, both as to time and price, in the ratio of \(1:2\), price may at once be excluded from the investigation, and time only taken into account; because those to whom time is an object in travelling, by attending to that alone, will evidently reap, along with it, the benefit of cheapness also; and those to whom price is an object, will, in attending to time only, gain that advantage, and in conjunction with it, the minimum of price likewise. Particular circumstances may, in a few cases, modify this; but the general features of the comparison will be as above.

Taking then, the ratio of \(p:b=h:b=2:1\), and considering \(p:h\) to be a ratio of equality, and that for one hour \(h=p=10\) miles, and consequently, \(b=20\) miles, or, in other words, that on the railroad \((b)\), the rate of travelling will be 20 miles an hour, while on the direct road \((h)\), and the cross road \((p)\), the rate will be at 10 miles an hour; we have then only to add the whole of the perpendicular \((p)\) to half the base \((b)\), and subtract the same from the hypotenuse \((h)\), which is got from the stamp-office returns for each town, and the remainder, if any, will be the miles gained by travelling over the two sides of the triangle instead of over the third, and if there is no remainder, that particular town is beyond the limits, and will not be benefited by the railway, consequently, it must be rejected from the traffic returns.

It is well there were no railroads in Euclid's days. We do not know what he would have said to our thus making the perpendicular and half the base equal to the hypotenuse; but such is the practical fact in the question we are considering, and this fact has been exemplified on every railway where the traffic can partly be derived from towns right and left of the line, which is the case almost invariably. We shall give a few instances, taken from the traffic returns of the London and Birmingham railway.

It is required to know whether the coaches running from Bedford to London ought to be included in the returns of Railways. traffic for the London and Birmingham railway, or, in other words, whether the inhabitants of Bedford would go cheaper and quicker to London, by first getting to the London and Birmingham railway, and then proceeding by that route to London, or whether they had better go by the old direct coach road, and vice versa, on their return from London, whether it would be cheaper and quicker for them to go along that railway, and then by a cross country coach to Bedford, or continue to use the old road?

The nearest station for the people of Bedford on the London and Birmingham railway, is at a place called Wolverton; from Bedford to Wolverton (p) is 15 miles, to which add \( \frac{1}{2} b \) half the distance from London to Wolverton, which is 25½ miles, and the total 40½ miles, \( \frac{1}{2} b + p \) is the equivalent distance from London to Bedford, via the railway; that is to say, by travelling along the two sides of the triangle. Now, in the stamp-office returns, it will be found that the direct road (h) is 52 miles, consequently, either in going to London, or coming from it, the people of Bedford would in each case save 11½ miles in equivalent distance, or 1 hour and 9 minutes in time, besides money. It is clear, then, that Bedford ought to be included in the traffic returns of that railway company.

The same question is proposed as to the town of Hatfield. The nearest station on the railway to this place is at Two-waters, and the distance between them (p) is 10 miles; adding to this \( \frac{1}{2} b \), half the distance from London to Two-waters, which is 10½ miles, we have \( \frac{1}{2} b + p \), the equivalent distance via the railroad between London and Hatfield, equal to 20½ miles. Turning now to the stamp-office returns, we find (h) the distance from London to Hatfield by the direct road, is also 20½ miles, and consequently, the two routes being equal, that town ought not to be included in the estimate of traffic.

It is required to know the same thing with respect to the town of Hitchin? Here the inhabitants would join the railway in question at Leighton Buzzard, and we find (p) = 16½ miles, \( \frac{1}{2} b \) = 19 miles, total or \( \frac{1}{2} b + p \) = 35½ miles, whilst (h) = 36 miles; and there would be a consequent gain of half a mile in distance, or 3 minutes in time.

In the case of Oundle and London, the station where the inhabitants of that town would join the railway, is near Northampton, and we have (p) = 26 miles, \( \frac{1}{2} b \) = 32 miles, total or \( \frac{1}{2} b + p \) = 58, whilst, by the stamp-office returns, we have (h) = 81 miles; consequently, there is a gain of 23 miles, or 2 hours and 18 minutes, by thus travelling over two sides of the triangle instead of the third.

It is desired to know, whether the inhabitants of Leicester, in their communication to and fro with Birmingham, and vice versa those of Birmingham in the communication with Leicester, will be benefited by the London and Birmingham railway. Here the point where each party would either join or leave the railway would be Coventry, and we have (p) = 25 miles, \( \frac{1}{2} b \) = 9 miles, total or \( \frac{1}{2} b + p \) = 34 miles, whilst (h) = 36 miles, shewing a gain of 2 miles, or 12 minutes in time.

We will throw a few more examples into a tabular form, as this part of our subject is a very important one, and cannot be too well understood. Care will, of course, be taken, that all the distances are those really existing on the respective roads in question; and it will also be advisable to reject all minute savings from the traffic returns, in order to be under, rather than over, in the estimate.

The best way of commencing to make out the following table, will be to take a map of the railway for which it is to be formed; and this should embrace a considerable portion of the adjoining country. Draw on the map a straight line from the one terminus to the other; this will represent (b) in fig. 1, and from this, lay off at right angles from each of the termini, other straight lines; these will represent (p) in fig. 1. We shall now shew how to ascertain the point in (p)

| Between what places | Distance from the railway to the point of equidistance | Gain in time | |---------------------|--------------------------------------------------------|------------| | Shenley Hill and Watford | 7 | 14 | 3 | | St. Neot's and Blisworth | 26 | 27 | 53 | | Uxbridge and Stanmore | 5½ | 5½ | 11 | | Woodstock and Stoney Stratford | 25 | 25 | 50 | | Stamford and Rugby | 40 | 42½ | 82½ | | Oxford and Fenny Stratford | 27 | 22 | 40 |

from which (h) is to be drawn in each case to the more distant terminus, and then shew the mode of using this figure when thus laid down on the map.

We have given to us by the conditions of the problem:

\[ h = \frac{b}{2} + p, \quad (1) \] \[ p = h - \frac{b}{2}, \quad (2) \] \[ b = \frac{h - p}{2}, \quad (3) \]

and from the relations of a right-angled triangle we have

\[ h = \sqrt{b^2 + p^2}. \quad (4) \]

Substituting in this latter expression the value of (p) from equation (2),

we get \( h = \sqrt{b^2 + h^2 - hb + \frac{b^2}{4}} \),

whence we have \( h = \sqrt{b^2 + h^2 - hb + \frac{b^2}{4}} \),

or, \( h^2 = b^2 + h^2 - hb + \frac{b^2}{4} \),

whence \( 0 = b^2 - hb + \frac{b^2}{4} \),

or, \( hb = b^2 + \frac{b^2}{4} \);

and finally, \( h = b + \frac{b}{4} = \frac{5b}{4} = 1.25 b \),

and substituting this value of (h) in equation (2),

we have, \( p = \frac{3b}{4} = 0.75 b \).

From this we see, that the length of (p) will always be three-fourths of (b), and the length of (h) once and a quarter that of (b).

On the map then, calling (a) (c) the termini, we set off on (p) in four directions three-fourths the length of the straight line (b), and then draw the four lines (h), (see fig. 2,) and we are sure that the four triangles (b, p, h) include every town that can by any means come to our termini to use our whole line, and if the line b was in reality a straight one on the ground, as it is in the figure, the triangles would include Railways: every other town throughout the whole tract of country, the inhabitants of which could avail themselves of the benefits of the railway, therefore, in using our figure, we must make the outer boundary lines (h), respectively curve right or left as the line of railway departs in either of those directions from the straight line (b). The values of (h) may then be found and marked ready for use, as nearly as can be judged, by seeing where the stations would, it is presumed, be ultimately placed; then having ascertained the values of (p) and (h) from the stamp-office returns, or any other equally authentic document, they may in each case be marked against the roads for all the towns which we may see fit to calculate upon for putting or not into the traffic returns, according as their inhabitants would gain or not by using the railway.

It will, on a very slight inspection, be self-evident, that for perhaps three-fourths of the whole space included within the lines (p) and (h), there will be no need of any calculation, except to show the quantity of saving. In the earlier stages, therefore, if it is merely required to know the amount of traffic; but only the doubtful places need be computed, and the rest may be deferred till it is desirable to complete the whole table. It must also be noted, that although a place may be actually without the boundary lines, yet there may not be a conveyance from it to either of the termini, as the case may be, and that the inhabitants, in order to be enabled to travel thither, may have to come to a place within the lines. They are then to be tried for as if they were themselves situated within the lines, and, of course, all towns beyond the termini must benefit, when travelling towards the opposite end of the line.

The effect of railways will be this: They can only be made upon main lines, because such lines will alone pay; the stage coaches will go off these lines when the railway has been a short time in operation, but the same coaches will be employed on cross country roads to feed the railway; and it is a curious fact, that through this operation one more coach was licensed at Liverpool and Manchester the year after the railway opened than there was the year before.

If the above rules be attended to, a tolerably correct knowledge of the traffic to be expected may be obtained, and it is sure not to be an exaggerated one. Whilst this has been going on, the engineer will have been employed in looking at the general features of the country preparatory to surveying and levelling it; and in most cases a man of a practised eye at this kind of work will be able at once to decide on all the principal points along which the line should go. During the same time the solicitor will have been feeling his way amongst the landowners and the occupiers, so that where much dissent is manifested, that property may if possible be avoided. Landholders have been proverbially hostile to railways, and enormous in their demands for compensation, yet they have invariably found that their property has been benefited instead of being injured; and when more land has been required from them, they have asked a higher price on account of that very railway running through their property, whose existence they had in the first instance declared to be a nuisance. This state of things cannot last much longer; but whilst it does, it must be met as far as possible in the above manner.

There are many things to be taken into consideration before definitely fixing on the precise line in which a railroad is to run. Borings should be largely taken to obtain a correct geological knowledge of the various strata. A considerable subsequent expenditure may often be saved in this way. It is of no use to put a penny on our eyes to hinder us from seeing a guinea. Borings may be carried to any depth by sinking a well part of the way, and without this they have been worked to a depth of 760 feet. The nature of the traffic must also be taken into consideration, so that when all other things are equal, the line may be run so as to include particular towns. The population of all the adjacent places should be ascertained and marked on a map; the nature of the various markets and fairs should be examined into and the state of trade; the wants of persons connected with it ought also to be taken into account; the quantity and quality of the existing goods traffic, its nature, and the demands on it with reference to any probable increase; and the capabilities of harbours, if any are within reach of the line, their draught of water, the nature of the protection they afford, their present trade, and the effect of the railroad on that trade. In this, as well as in all other cases, the results of a transition from peace to war, and vice versa, should be well considered, together with the effect of any future line of railway which may become a partially competing one.

The more effectually these inquiries are made, and the more fully their results are honestly put before the proprietors, together with separate estimates for the engineering department and the managing department, so will their confidence in the undertaking increase; and it is a most essential point to place this confidence on a sure basis, so that if any little mishap, which none can avoid, take place, the shares may not be suddenly thrown on the market at a ruinous sacrifice, and the undertaking abandoned, through the projectors not having had the necessary information, to enable them to see that the result of their labours would be a profitable speculation, notwithstanding any trifling losses arising from causes against which perhaps no human foresight could provide.

Railways with two lines of rails in very favourable situations have been completed for £10,000 per mile in England. This however must be taken as the exception, and not the rule. Under very unfavourable circumstances they have cost £50,000 per mile; and of course there will be found an expense per mile at all differences between these two, which may fairly be taken as the extreme limits. Now it is certain, that with a line 80 miles in length, a traffic of 75 tons of goods per day from each end, or 120 passengers per day each way, or with 35 tons of goods and 60 passengers per day each way, the railway, if even constructed for £12,000 per mile, which will rarely happen, would not afford a dividend of more than a quarter per cent, and (our numbers throughout meaning daily each way) it would require 100 tons of goods, or 160 passengers, or 50 tons of goods and 80 passengers, to pay 1 per cent.; 125 tons of goods, or 200 passengers, or 62 tons of goods and 100 passengers, would but little exceed 1¼ per cent.; and it would take 200 tons of goods, or 320 passengers, or 100 tons of goods with 160 passengers, to pay 4½ per cent.

The Americans have such facilities for these constructions, that 1600 miles of railroad have been made in that country (a good deal of it, however, being only single line) at an average cost of only £5081 per mile; whereas in England the mere permanent way alone would amount to £4400 per mile, if the rails were 45 lbs. to the yard, and laid upon longitudinal timbers; £4900 per mile, with rails 42 lbs. per yard, having chairs and cast-iron supports between them, on longitudinal timbers; £5300 per mile, with rails 42 lbs. per yard, on blocks 3 feet apart; £4800 per mile, with the same sized rails on wooden sleepers; £5600 per mile for 62 lb. rails, on blocks 4 feet apart, and £5100 for the same rails on wooden sleepers; £6000 per mile for rails of 75 lb. per yard on blocks 5 feet apart, and £5500 per mile for the same on sleepers. These prices do not include laying the way, ballasting, and draining. Thus we see that the mere cost of the permanent way in the country, averaging £5200 per mile, exceeds that of the whole expense of a complete railway in America; and 75 pound rails on blocks and sleepers, including laying, ballasting, sidings, turnplates, and every expense, has exceeded £8000 per mile.

The mean receipts for five years on the Liverpool and Manchester line give the following proportions: Revenue 100, expenses 55, profits 45; and the expenses have been as high, Railways or higher than 60. The average, however, gives the ratio of revenue to profit at 1 to .45. On the Dublin and Kingston railway the same ratio for 26 months gives 1 to 4344. On the Brussels and Mechlin railway the ratio for 1 year is 1 to .488. On the Grand Junction railway, for 6 months, it is 1:48. On the London and Birmingham, no data exist to form a judgment. There is a very singular coincidence in these ratios on lines so very differently circumstanced, and of lengths varying from six miles to more than 100; but we have not yet acquired any sufficient experience in railway statistics to enable us to speak with confidence on the subject. If every railway would publish yearly its experience, as was so handsomely done in the Liverpool and Manchester for several years, analyzing every source of expense, and reducing them to the ratio per passenger and per ton per mile, we should then soon acquire such a stock of knowledge as would enable all these points to be decided; indeed, of so much consequence are railways now becoming, that the legislature should take up the question, making it a law that returns should be sent yearly, according to a form arranged by some person thoroughly conversant with the subject.

When matters are so far advanced that the engineer can be directed to make out his plans and sections, he will commence by consulting the ordinance map, and by the help of that and his geological knowledge, obtained from the borings and trial shafts, together with his inspection of the wells, mines, quarries, and other excavations in the immediate vicinity of the intended work, he will proceed to lay down at least three or four lines, if some local circumstances do not absolutely limit him to one particular tract of country; endeavouring to cross all streams and rivers as near their source as possible, that being the lowest point; and where hills intersect his progress, aiming at some position where streams run down on either side in the direction as near as possible to his intended line. He should avoid going along the sides of hills, particularly if they are composed of clay or shale, in order to be clear of the unpleasant consequences which slips would give rise to in these strata. He should run through no more seats or ornamental pleasure grounds than possible, and avoid towns and villages where the land would be expensive. He should, as far as practicable, be furnished with lists of the population, the state of trade, and the numbers of the assenting and dissenting owners and occupiers of land, together with the quantity and value of their property. He should have the water analyzed with reference to its fitness for locomotive engines, inquiring into the state of the existing roads and canals, as to the facilities they afford for getting coke, building materials, &c., on to the line; also whether lodgings can conveniently be had for large bodies of men, and whether the necessary labourers and mechanics can be procured at reasonable rates in the immediate vicinity of the line; and generally he should enter into all inquiries necessary to enable him to choose the best line, and construct it at the least cost.

In order to save time and expense, it will be quite sufficient if what are called rough or flying levels are taken of these preparatory lines, for which purpose the mountain barometer will be amply sufficient, if proper care be taken to apply the necessary corrections, and strict attention be paid to comparing it as often as possible, and at stated regular times, with a stationary standard barometer. Cross stations between the lines should likewise be taken, in order to ascertain the lowest point. The rates at which streams run will also assist in giving indications, and the ordinance map may be sufficient authority for distances. He should particularly attend to curves and gradients; a curve of three-quarters of a mile radius, in conjunction with a rise of 16 feet in a mile, reducing the speed of a locomotive to nearly one-half. Where the gradient is good, curves are not of so much consequence. A curve of a quarter of a mile radius on the Bolton and Leigh railway is constantly passed with safety at a speed of thirty miles an hour, but the wear of engines and carriages must be increased.

The whole question of gradients is only beginning to be understood; and we have no doubt that at some future time railways will be made much more level than they now are. There is no reason why in many cases hydraulic locks should not be used to carry the trains up and down different levels, and to do away with the inclined planes. The practical effect of gravity is not well known. We have long had the angle of repose given as 1 in 280. This is correct with some carriages and waggons, but others differ extremely. Care must be taken where two planes meet that they are eased into each other if their difference is much. This is best done by laying a short piece of the line level. We have known an instance in which, at an inclination of 1 in 330, a waggon ran down 4 miles, and acquired a velocity of 8 miles an hour. The question is not at what angle a carriage will just become quiescent, but at what angle will a velocity be acquired which can have a useful practical effect. The Irish railway commissioners have taken this at 1 in 140; whilst on the London and Birmingham railway the Enston extension plane is for a considerable part of its length 1 in 75, the train on it attaining a velocity of 30 miles an hour, and working remarkably well. It is unfortunate, too, that their classification of engines does not contain at all, those in use on that line. The third class is the nearest, but will give much too little as the power of those engines, which go 60 miles an hour up considerable inclined planes. The third class has 11-inch cylinders, 18-inch stroke and 5-feet wheels, the weight being, engine, 8½ tons, tender, 5½.

The principal difference between this class and the engines on the London and Birmingham railway is, that the latter have 5½-feet wheels and 12-inch cylinders. Taking, however, the above third-class engine, and allowing the friction of the engine gear to be 51 lbs., the friction of the engine on the railway 68 lbs., the friction of the tender 49½ lbs., and the atmospherical pressure upon the piston 190.06 inches, reduced in the inverse proportion of twice the stroke of the piston to the circumference of the working wheel, or 533½ lbs., we have a total absorbed power of 702 lbs. before the engine can move, or, which is the same thing, a steam pressure of 702 lbs. is requisite for that purpose. Now the whole power being the area of the piston multiplied by the pressure, say 64.7 lbs., when the steam is at 50 lbs., we get for the whole power of the engine 2337 lbs., or the power to propel the load 1639 lbs., which, even with 9 lbs. per ton friction caused by the load, gives a fraction of 182 tons on a level.

Supposing a load of 88 tons, including the tender, on a level, to be drawn at the rate of 20 miles an hour, and that it has to ascend afterwards a plane of 1 in 140, we have then the absorbed power = 702 lbs.; 88 tons at 9 lbs. per ton = 792 lbs. or 1494 lbs. power of steam pressure required for this load on a horizontal plane. But when the train comes to the inclined plane, the weight of the engine has first to be added, making the load 100 tons, or 224000 lbs., and 1½ of this, or 1600 lbs., is the additional traction required, and taking every 8 lbs. traction to cause 1 lb. additional friction on the engine gear, gives 200 lbs., therefore the whole power or steam pressure required is, up the plane, 3294 lbs., and the velocity being inversely as the pressure, we have 3294 : 1494 = 20 : 9; or the velocity will be reduced to 9 miles an hour; in other words, the time expended in ascending the inclined plane will be more than double that which would be required on an horizontal plane, but as the descending will be performed in the same time as if it was a horizontal plane, and as 1494 : 3294 = 1 : 2·2, the equivalent length of the horizontal plane, the length of the ascending plane being unity, will be 2·2, and the average of the two will be 1·6.

It is upon these data the Irish railway commissioners give tables of the lengths of equivalent horizontal lines to gra- The following table from Mr. Pambour's work will also assist in forming a judgment; it is for engines of 8 tons, the loads being that of the train and tender. The errors here are also on the safe side.

| Gradient | Equivalent horizontal lines | |----------|-----------------------------| | | Ascending | Descending | Mean | | 1 in 90 | 2-66 | 1-00 | 1-83 | | 95 | 2-58 | 1-00 | 1-79 | | 100 | 2-50 | 1-00 | 1-75 | | 110 | 2-36 | 1-00 | 1-68 | | 120 | 2-25 | 1-00 | 1-62 | | 130 | 2-15 | 1-00 | 1-57 | | 140 | 2-07 | 1-00 | 1-53 | | 150 | 1-94 | 1-00 | 1-43 | | 180 | 1-83 | 1-00 | 1-33 | | 200 | 1-75 | 1-00 | 1-29 | | 250 | 1-60 | 1-00 | 1-21 | | 300 | 1-50 | 1-00 | 1-16 | | 350 | 1-43 | 1-00 | 1-13 | | 400 | 1-37 | 1-00 | 1-10 | | 500 | 1-30 | 1-00 | 1-06 | | 750 | 1-20 | 1-00 | 1-01 | | 1000 | 1-15 | 1-00 | 1-00 | | 1500 | 1-10 | 1-00 | 1-00 |

The great disadvantages arising from bad gradients, are capable of being tolerably well estimated by these tables; but the principal evil is the expense which they occasion, since the load to be carried along the whole line must not be heavier than can be drawn by the engines up the inclined planes, or else additional engines must be employed to assist at those places. On some of the American railways, there are planes so steep that sails are made use of in descending them to check the velocity. The Irish railway commission have computed the cost of working locomotive engines with different loads, as in the following table, in which, as in the preceding one extracted from them, the engine may be expected to do more than is stated.

This table, as far as expense goes, can only be considered as an approximation; the steam pressure too, which is taken at 9 lb. per ton, is higher than what is now found to be the case; but it will, nevertheless, shew the relative expense; for instance, if the engine can draw 191 tons on a level, and there are gradients of \( \frac{1}{3} \) on the line of railway, the load, to enable the engine to ascend these, must be only 75 tons, and the ratio of expense will be \( 1.04 - 72 = 32 \), or the increased cost of the engine will be 32 per cent. on its journey, besides, there being three journeys to carry the 191 tons, so that the expense and locomotive power will be quadruple what it would amount to if the line was level, and double what it would be with no incline beyond.

The following table will be useful in calculating gradients:

### Table of Gradients

| Feet per mile | Inches per chain | Ratio of height to length | |---------------|------------------|---------------------------| | | | | | 1 | 0-15 | 1 in 5280 | | 2 | 0-30 | 2 in 2640 | | 3 | 0-45 | 3 in 1760 | | 4 | 0-60 | 4 in 1320 | | 5 | 0-75 | 5 in 1056 | | 6 | 0-90 | 6 in 880 | | 7 | 1-05 | 7 in 754-2 | | 8 | 1-20 | 8 in 660-0 | | 9 | 1-35 | 9 in 586-6 | | 10 | 1-50 | 10 in 528-0 | | 11 | 1-65 | 11 in 480-0 | | 12 | 1-80 | 12 in 440-0 | | 13 | 1-95 | 13 in 406-1 | | 14 | 2-10 | 14 in 377-1 | | 15 | 2-25 | 15 in 352-0 | | 16 | 2-40 | 16 in 330-0 | | 17 | 2-55 | 17 in 310-6 | | 18 | 2-70 | 18 in 293-3 | | 19 | 2-85 | 19 in 277-9 | | 20 | 3-00 | 20 in 264-0 | | 21 | 3-15 | 21 in 251-4 | | 22 | 3-30 | 22 in 240-0 | | 23 | 3-45 | 23 in 229-5 | | 24 | 3-60 | 24 in 220-0 | | 25 | 3-75 | 25 in 211-2 | | 26 | 3-90 | 26 in 203-1 | | 27 | 4-05 | 27 in 195-5 | | 28 | 4-20 | 28 in 188-6 | | 29 | 4-35 | 29 in 182-1 | | 30 | 4-50 | 30 in 176-0 | | 31 | 4-65 | 31 in 170-3 | | 32 | 4-80 | 32 in 165-0 | | 33 | 4-95 | 33 in 160-0 | When, therefore, the flying levels are complete for the three or four lines, as we have before directed, the engineer and manager, or secretary, should bring all their information together, and throwing it into one common stock, select that line out of the whole, which, on the fullest deliberation, appears to be the best with reference to its gradients, geology, commercial importance, and the facilities it affords for soundly and cheaply constructing the necessary works. This subject will of course require deep attention, and the reasons for the selection should be written out in the fullest and clearest manner, for the inspection of any proprietor who may desire to see them, publicity always insuring confidence; and in most cases, it would be best to submit vital points of this kind to a general meeting of the whole body, before proceeding to parliament to obtain an act of incorporation. This would entirely prevent any mistrust.

That these matters require the greatest consideration, will be apparent from the difficulty, delay, and expense of obtaining acts of parliament for railways. The cost of that for the Liverpool and Manchester line, for instance, thirty miles, was about £900 per mile. That for the London and Birmingham, 112 miles, was £72,869, or £650, 12s. per mile; and it is well known that the expense has reached £1,000 per mile on long lines, and that latterly, in every new session of parliament, there have been fresh difficulties thrown in the way of obtaining the necessary acts, till it is now nearly impossible to succeed at all.

There are many very great hardships connected with obtaining an act of incorporation for a railway. Parliament requires that a plan and section of every part of the ground through which the intended line is to pass, shall be lodged with their clerk, and with the clerks of the peace in every county through which the railway goes. This is a very proper regulation, in order that every landholder may be able, by travelling a convenient distance, to have a personal inspection of a duly authorised document, so as to examine the nature and extent of the benefit, or the inconvenience which it may occasion to his particular property; but parliament should at the same time have given the railway companies the power of complying with this wholesome regulation, in the same way as road surveys are made in Ireland, by an order from two magistrates to enter any requisite grounds. This, however, is not done, and therefore it follows, as a necessary consequence, that the proprietors of these undertakings, no matter how beneficial or important sooner to the community at large, are left entirely at the mercy of the landholders, whether they can make their survey or not. We have ourselves known, that when decided opposition has been evinced to the undertaking, the engineers and surveyors have been put to all possible shifts to obtain the necessary data for their plans and sections. Working by night with lanthorns has even been unavoidably resorted to; and in one case, where the proprietor was a clergyman, he was watched on Sunday until he went into his church, and a strong party immediately setting to work, just succeeded in finishing the business as he concluded his sermon.

The facilities of opposing a bill in parliament are so great, that every temptation is held out to do so, especially when the rich harvest to counsel, solicitors, and witnesses, is considered; and as has been well observed by the Irish railway commissioners, discussions are mooted of the most discursive and discordant kinds, relating to all the abstract professional matter in the most distant manner connected with a railway. The principles of curves and gradients are entered into with mathematical precision, and the laws of friction and gravity are investigated; questions about which the counsel and the court are often equally ignorant, the one side seeking to swell the estimates and lower the profits, and the other pulling in the opposite direction, like the bulls and bears on the stock exchange; till at last, probably after the expenditure of thousands, the bill is thrown out, not on its own merits or demerits, but because, perhaps, a notice to the proprietor of five or six yards of a cabbage garden, was left next door by mistake.

The parliamentary rules are now as much too strict, as they were at first too loose. The time when the required plans and sections are to be deposited, is very inconvenient; two years at least being required between the deposits being paid and the act obtained. Thus, at the present time, if any line is wished to be procured, the surveys must be made in the autumn of 1838, the plans must be lodged and the notices given in March 1839, the petition for the bill presented to the Commons in February 1840, and supposing the act obtained the same session, little if any real work can be done until the spring of 1841. The subscription of ten per cent. required on the capital, merely leads to delusion; bankers in general advance the money, and whether the bill succeeds or fails, they get it back with interest and commission, for by the very terms of the order of the House of Commons, it may be paid back to the person advancing it. The public obtain no security against a bad project by this regulation, whilst a good one may be crushed for want of a speculating capitalist. Nobody is benefited in fact, except the banker and the broker; and that this is the process largely employed all are perfectly aware.

If a bill be lost in one session, it cannot be proceeded with in the next without a new contract deed being signed. This is a considerable hardship. The deviation in section is too limited, and should only apply to raising embankments and lowering cuttings; the reverse should be allowed to any extent, and the deviation should be reckoned from the surface of the ground, and not the lateral line. If the same line is kept, the effect would be the same, but by removing to a different level, what may be cutting in one respect may be embanking in another. The limitations in all respects as to deviations may be considered as too strict, and they always have the effect of cramping the company and their engineer; palpable improvements in many cases, have been abandoned on account of the heavy cost of going to parliament for new acts; and others in all probability would never have been made, except that the companies in question were forced to apply for a new act, in order to enable them to borrow more money, and then the improvement is put in along with the rest as a rider.

When the intended line is once decided on, the surveyors should be sent out as speedily as possible; and these are followed by the levellers, who are the engineers. It will be best to survey wide, when you are not quite certain of the exact position of the line; the surveyors give in their plans to the engineers, who proceed to lay down upon them the line as their levelling goes on, taking care as nearly as possible to balance the cuttings and embankments. It will save the engineers a deal of trouble, if where curves are to be run, a man is sent ahead to put in marks at short distances, giving him the measure from the nearest hedge on the plan, which measure he takes on the ground, and sticks in his mark.

It will be best to take ground enough to make the embankments sufficiently wide; if this is not attended to, when they come to shrink, as they undoubtedly will, they become too narrow, and an addition has to be made to their width, which will be found a very troublesome operation, such additions being peculiarly liable to slip.

The survey, with complete plans and book of reference, containing the land for at least three times the width required for the railway, showing every field numbered for each parish, with its owner and occupier, ought not to cost more than L15 per mile. The best plan will be to survey as wide as is intended to apply for a power of deviation in the act of parliament.

Estimates. The next thing is for the engineer to make out his detailed estimates, and get ready his plans and sections to be deposited in parliament, and with the clerks of the peace for the several counties through which the line will pass; he should consult the standing orders of both houses, or be supplied with such extracts as relate to his department. In his estimates there are unfortunately many difficulties; and most people forget the distinction between a railway being completed and opened, and opened and completed. Besides this, let an engineer be ever so much inclined to make a full and clear exposition of the cost of a line of railway, he may plainly see that if he does so the line will never be made, although it would be a profitable speculation. We should recommend, nevertheless, that no other but a correct and fair estimate should in all cases be furnished, in order to compare it with the traffic. For this purpose, every known bridge and viaduct should be separately computed, and ample allowance made for occupation bridges; the land, together with all the earthwork, tunnels, fencing, and permanent way should then be calculated, the secretary furnishing an estimate of the office expenses, printing, stationery, travelling expenses, law, advertising, conveyancing, and all other items of this kind. At least ten per cent. should be added to the engineering estimate for stations, and the machinery connected with them, and a full allowance for engines and carriages. When everything that can be thought of is thus collected together, allow not less than twenty-five per cent. for contingencies; and note that by a mean of nearly 100 railways, the whole number of bridges average 2½ per mile.

In estimating for rock, as this is seldom found except in deep cuttings, it may generally be taken as earth-work, with the necessary slopes. For instance, in a cutting forty-five deep, with slopes two to one, and a base of thirty feet, the sectional area of the opening, and of course the cubic contents of any given length, is four times the area of the cut of the same length with vertical sides, and a price on a rock cutting thus taken out, may be put at four times as much as the earth cutting with slopes, without any increase of estimate. In shallow cuttings this does not hold good; but the excess may safely be thrown on the contingencies, the amount not being great, and the occurrence seldom. In a thirty-feet cutting, the difference is only three times, which may be sufficient when the rock is not very hard, with the saving in land to assist the price; but in a sixty-feet cutting, with slopes of two to one, the quantity is five times that of vertical cutting, and with the saving in the land occupied by the slopes, would make the rock cutting much the cheapest, unless of extraordinary hardness. It will take more time to cut through the rock, length for length, but would not if it could be entered at several places at once. Where land is extremely valuable, it will in many cases be cheapest in a cutting to support the sides with retaining walls, purchasing little more than the absolute width of the railway.

The width of the land required will of course vary with the depth of the cuttings and length of the embankments, together with the slopes necessary to be given; rock, for instance, stands generally vertical, chalk varies from ½ to 1, to 1 to 1; gravel 1½ to 1; the coal measures 1½ to 1. The London clay has been made to stand at 1 to 1, and has slipped at 3 to 1, depending greatly upon the dryness of it when tipped into the embankment. Blue seepy shale has slipped at 4 to 1, for instance, on Bugbrook Downs, in Northamptonshire; and in every stratum there are great variations, much depending on the weather. Bad material in wet weather will often stand at no slope whatever. A double line will have ample width in fifteen yards, allowing two yards on each side for the drainage and fencing. The land required for this amounts to 5,456 acres per mile forward; and if 1-454545 is multiplied by the number of yards in perpendicular height, in any embankment or cutting, at slopes of 2 to 1, it will give the additional number of acres per mile forward, and by a geometrical average, the whole line may be very closely estimated in this way. For example, take a line of 112 miles in length, and 15 yards in breadth, for railway, ditching, and fencing, and averaging in height of embankments and depth of cutting 24 feet or 8 yards, then 5455×112=61096 acres for railway, ditching, and fencing, and 8×1-454545×112=130327 acres, required for the slopes at 2 to 1, this giving a total of 1914 acres, and this mode of estimating may be considered to include the land required for stations and approaches to bridges.

It will be necessary to compute, in many cases, whether a viaduct will not be cheaper than an embankment. The method of doing this will be found in the article Viaduct. Where expense is a great object, timber may be made use of; beams of which, trussed with iron, have lately been introduced instead of arches, and to a great extent in some cases, for instance the Midland Counties railway. On the North Union railway, a timber viaduct is constructed of great height; several similar works are in course of execution in the north of England; and in some of the Scotch railways the system of trussed beams of timber has been applied to very large spans. In many instances, a considerable reduction in the cost of bridges and viaducts may thus be made, especially where the crossings are very oblique, or where the additional height of arches would involve great expense in embanked approaches.

Should money be short and time so valuable as to make the expeditious opening of the line a subject of the first importance, great part of the excavations may be removed at night after the line is open, where they are not required for the embankments. This plan is not, however, to be recommended, and still less so making the embankments less than their full width at first; the additional patch of embankments hardly ever uniting equally with the part first made, but sliding off, and leaving the side of the embankment as smooth as glass.

Expense again may be saved where land is valuable, by iron colonnade viaducts, by which means towns may be entered much farther than is now possible to do without an enormous outlay. The cost of such a viaduct will in general not exceed two-thirds of a brick one of the same height and width; in fact, there are many ways in which expenses may be lowered, and the railway got into work in a speedy and safe manner at a moderate outlay; after which, if the project turns out a successful one, ornament may be attended to, to any extent which may be thought advisable.

In the same manner it should be calculated whether a tunnel or an open cutting will be the cheapest mode of getting through hills of importance. The method of doing this will be shown in the article Tunnel. Where rock There are so many ways of computing earth work, all Railways of them equally accurate, that the choice consists mainly in using the one which occupies the least time. Tables have also been published for taking out the cubic contents by inspection. The following formula, however, which we have arranged for this purpose, is so very quick in bringing out the results, that we have always given it the preference over any other method.

### Table of Earthwork in Cuttings or Embankments 30 feet wide.

| Height | Half width at top. | Area in square yards | Contents in cubic yards, per chain forward. | |--------|-------------------|----------------------|---------------------------------------------| | 1 | 16 | 3444 | 75-777 | | 2 | 17 | 7-110 | 156-420 | | 3 | 18 | 11-000 | 242-000 | | 4 | 19 | 15-111 | 332-444 | | 5 | 20 | 19-444 | 427-777 | | 6 | 21 | 24-000 | 528-000 | | 7 | 22 | 28-777 | 633-110 | | 8 | 23 | 33-777 | 743-110 | | 9 | 24 | 39-000 | 858-000 | | 10 | 25 | 44-444 | 977-777 | | 11 | 26 | 50-111 | 1102-444 | | 12 | 27 | 56-000 | 1232-000 | | 13 | 28 | 62-113 | 1366-444 | | 14 | 29 | 68-444 | 1505-777 | | 15 | 30 | 75-000 | 1650-000 | | 16 | 31 | 81-777 | 1799-110 | | 17 | 32 | 88-777 | 1953-110 | | 18 | 33 | 96-000 | 2112-000 | | 19 | 34 | 103-444 | 2275-777 | | 20 | 35 | 111-111 | 2444-444 | | 21 | 36 | 119-000 | 2618-000 | | 22 | 37 | 127-111 | 2796-444 | | 23 | 38 | 135-444 | 2979-777 | | 24 | 39 | 144-000 | 3168-000 | | 25 | 40 | 152-777 | 3361-110 | | 26 | 41 | 161-777 | 3599-110 | | 27 | 42 | 171-000 | 3762-000 | | 28 | 43 | 180-444 | 3969-777 | | 29 | 44 | 190-111 | 4182-444 | | 30 | 45 | 200-000 | 4400-000 | | 31 | 46 | 210-111 | 4622-444 | | 32 | 47 | 220-444 | 4849-777 | | 33 | 48 | 231-000 | 5082-000 | | 34 | 49 | 241-777 | 5319-110 | | 35 | 50 | 252-777 | 5561-110 | | 36 | 51 | 264-000 | 5808-000 | | 37 | 52 | 275-444 | 6059-777 | | 38 | 53 | 287-111 | 6316-444 | | 39 | 54 | 299-000 | 6578-000 | | 40 | 55 | 311-111 | 6844-444 | | 41 | 56 | 323-444 | 7115-777 | | 42 | 57 | 336-000 | 7392-000 | | 43 | 58 | 348-777 | 7673-110 | | 44 | 59 | 361-777 | 7959-110 | | 45 | 60 | 375-000 | 8250-000 | | 46 | 61 | 388-444 | 8545-777 | | 47 | 62 | 402-111 | 8846-444 | | 48 | 63 | 416-000 | 9152-000 | | 49 | 64 | 430-111 | 9462-444 | | 50 | 65 | 444-444 | 9777-777 |

| Half width at top. | Area in square yards | Contents in cubic yards, per chain forward. | |-------------------|----------------------|---------------------------------------------| | 16-5 | | | | 18 | | | | 19-5 | | | | 21 | | | | 22-5 | | | | 24 | | | | 25-5 | | | | 27 | | | | 28-5 | | | | 31 | | | | 32-5 | | | | 34 | | | | 35-5 | | | | 37 | | | | 38-5 | | | | 40 | | | | 41-5 | | | | 43 | | | | 44-5 | | |

---

*Note*: The table provides the contents in cubic yards per chain forward for different heights and half widths of cuttings or embankments 30 feet wide, including areas in square yards, heights in feet, contents in cubic yards per chain forward, and half width at top. Let \(a\) be the area in square yards.

\(c\) be the content in cubic yards, per chain in length.

\(w\) be the width in feet of the cuttings or embankments.

\(h\) be the height in feet of the cuttings or embankments.

\(m : l\) be the ratio of the base of the slopes to their altitude.

Then the rules applicable to every case will be

\[ a = \frac{wh + mh^2}{9} \]

And as 30 feet is a very general width, if we adapt our formula to that, we have with slopes of 1 to 1,

\[ a = \frac{30h + h^2}{9} \]

And with slopes \(1\frac{1}{2}\) to 1,

\[ a = \frac{20h + h^2}{6} \]

And with slopes 2 to 1,

\[ a = \frac{30h + h^2}{9} \]

And for any other widths and slopes the results will be brought out very quickly, by an adaptation of the general formula. By the particular ones given above, the tables on the preceding page were computed, giving the cubic contents per chain in length, at one view, for every foot in height, up to 50. In the column for the area, the decimals are given to three places of figures, but four places were used in calculating the cubical content. Where a dot is placed after the last figure in the column for the area, it denotes that the same figure goes on in infinitum. In using the column of cubic contents, increase the last decimal figure by 1 when it is above 5.

The columns of "half-widths" in the preceding tables, will enable the engineer to set out his work from the centre pegs as he proceeds. This is done at once, where the country is level, on the cross section; but in sidelong ground a correction will be required, to obtain which, after the half-width has been staked out, the level should be planted over the centre peg, and the height above and below the cross level taken at the points which mark the half-width. It is evident, that for each foot which these points may be above and below the level of the centre peg, one foot must be added to the half-width on the side which is above the centre, and subtracted from it on the side which is below, where the slopes are 1 to 1, and a corresponding alteration at all other slopes; or if we put

\(h'\) be the height above the centre, or depth below it;

\(m : l\) be the base to the perpendicular;

\(c\) be the correction,

\[ c = \pm mh', \]

where \(c\) is \(+\) on the high side, and \(-\) on the low one. This will give a first approximation, and may be repeated if necessary, by levelling to the half-width thus corrected, and proceeding as before, and the cubic contents must receive a similar correction when necessary, our tables presuming the cross section to be on a level. The average height, however, can in almost every case be taken perfectly near enough for every practical purpose.

It is a great pity that the custom has not been generally introduced of taking all the measures in yards and decimals, surveying staffs being marked to \(1\frac{1}{2}\)ths of a yard. This would reduce the calculations considerably; and the reduction of any of them to feet, for plans and sections required in Parliament, or any other isolated purpose, would be infinitely less troublesome than using feet throughout, and having to divide by 9 or 27 for the area and cubic content.

The column of half-widths, when required for any other Railways, slopes or widths than those we have given, may be readily computed by the formula

\[ x = \frac{w}{2} + mh \]

where \(x\) is the half-width at the top, and \(w\), \(m\), and \(h\) as before.

The column of cubic contents, when required for any other width than 30 feet, may be readily found, by using a correction \(e'\) to the cubic contents at 30 feet, which correction is \(+\) when the width is above 30 feet, and \(-\) when below,

\[ e' = \frac{w'h'^2}{27} = w'h...2-4444 \text{ in cubic yards}, \]

where \(w'\) is the number of feet above or below 30, and \(h'\) is the height in feet. The correction is the same for all slopes, taking care to add or subtract it from the cubic contents for 30 feet at the given slope.

With reference to apportioning the work, so that the cuttings and embankments may be equal, regard must be had to the nature of the soil to be moved. For instance, in the London clay it will be found that any quantity of cutting will not make the same quantity of embankment by about ten per cent., whereas in common earth just the reverse takes place, and the cutting will make an embankment nearly ten per cent. greater.

There is a point, which, in the early stage of laying out a railway is too often lost sight of, that ought to be a subject of the deepest consideration; in fact, it is of vital importance to the whole interest of the line in question, and no pains ought to be spared in most fully and rigidly investigating it; and this is, to what extent cutting and embanking can be advantageously carried, that is to say, a line perfectly level, allowing for the curvature of the earth, from one end to the other, being the point of perfection, how near ought this to be approached, looking on the one hand at the first outlay, and on the other at the future gain, in the cost of locomotive power, and repairs of engines, carriages, &c.

We can calculate the cost, for instance, of making a line having no inclinations in any case greater than 1 in 300. With this line we should have a determinate outlay in locomotive power and repairs. The question to be considered then is simply this: If we make the line, instead of having no inclination, greater than 1 in 300, to have none greater than 1 in 500, or 1 in 1000, do we lay a foundation for a yearly saving, when the railway comes into work, sufficiently great to pay us for the consequent first cost of these reductions in the inclinations?

In order to enter properly into this question, experiments must be made for the purpose of determining the cost of locomotive power on the various inclinations, selecting some railway where different engines can be employed on inclines suitable for the case in hand, there being no data in existence, in this country at least, which can with certainty decide this point. The following table, by the engineer of the New York and Erie railroad, may help us a little:

| Ascent per mile, in feet | Gross load in tons, 2880 lbs. each, cwt. | Cost of motive power per ton per mile, in cts. | |--------------------------|------------------------------------------|-----------------------------------------------| | Level | 75-25 | 3-50 | | 10, or 1 in 528 | 49-53 | 4-20 | | 20, or 1 in 264 | 37-35 | 4-90 | | 30, or 1 in 176 | 27-24 | 5-95 | | 40, or 1 in 132 | 20-22 | 7-28 | | 50, or 1 in 105-6 | 17-04 | 8-19 | | 60, or 1 in 88 | 13-92 | 9-66 | | 70, or 1 in 75-4 | 11-31 | 11-41 | This table, giving principally impracticable gradients, will only serve to show us that the ratio of expense is an increasing one, the first differences being respectively 0.7 : 0.7 : 1.05 : 1.33 : 0.91 : 1.47 : 1.75.

If we admit, till we can obtain better data, that altering our gradients from 1 in 250 to 1 in 500, saves two-tenths of the expense of locomotive power, and that reducing it to a level instead of leaving it at 1 in 500, saves two more tenths, we can easily see what the effect of that would be.

The number of tons carried, as given in the table, is not decreased according to the law of gravity alone, but contains another element, most probably the result of experience on the road in question. Suppose then that on the road we are about to construct we may expect to work seven trains per day each way, with passengers, there being ten carriages in each train, averaging four tons each, and two trains each way with goods, in ten wagons per train, averaging goods and waggons five tons each, and going at the rate of ten miles an hour; also let the railway in question be one hundred miles in length; then at a cost of £304 per day, the passengers being taken at eighteen in each carriage at £1.4d. each per mile, and the goods at £1.6d. per ton per mile, at which price it is known they can be carried, we may presume, that if, instead of having an inclination of 1 in 250, our road was level, we should decrease these expenses four-tenths, or bring them to about £152 per day, or £66,430 per annum. Thus presuming the above to be correct, we should be saving money, if our road could be made level at an additional expense of one million.

Each particular railroad must of course form a separate case, but we are persuaded it will generally be found that a large outlay will be justified in approximating to a level as near as possible; and where the line is entirely so, the cuttings can always be cleared of water, by sloping the side draining down each way, from the centre till they arrive at the nearest water course, where as usual they will deliver their contents. Our practical knowledge of this subject of reducing railways to a level is founded on such slight data, that a careful set of experiments in order to show the way more fully into such a question is very much wanted; and we question whether hydraulic locks will not be found to save a considerable expense in difficult situations, bringing the trains from one level to another, by which means railways may be made through tracts of country which would otherwise never pay for the necessary outlay.

When the contracts along the line are fairly at work, one of the first knotty points which the directors will have to decide on, is, the width of the rails, their shape, the length of their bearing, and the form of their chair. The width between the rails has only lately become a subject of dispute; nearly all the railways prior to the Great Western, having been laid down 4 feet 8½ inches apart. Mr. Brunel has extended it to seven feet; the Irish railway commission recommend six feet two inches; several of the Scottish railways are laid down at five feet six inches; in fact, the variations run from four and a-half to seven feet.

The question of the stability of the carriages on the railway may be left out of consideration in looking at this matter, because the machinery will always require sufficient space between the wheels to insure this. Now, as four feet eight inches and a-half are found to be enough for the good performance of an engine, which, with five and a-half feet wheels, will go on a level upwards of 60 miles an hour; as with five-feet wheels, Marshal Soult, on his visit to Liverpool just after the Queen's coronation, was taken over 10¾ miles of favourable ground on the Grand Junction Railway within 10 minutes; and as an engine has gone 60 miles an hour on the London and Birmingham Railway up an inclined plane, is it wise or prudent to make any change at all, and will any additional speed, which may be gained by increasing the width of the rails and the diameter of the wheels, compensate for the greater expense and the outlay which will constantly be required to keep the road in order on account of the increased weight? This will receive light from the experiments on the Great Western, but will not be finally decided until it be tried on the Irish or some other railways, as Mr. Brunel's rails are altogether different from most others in use. The plan recommended by the Irish railway commissioners, of putting the rails farther apart but not widening the carriages, merely making the wheels run outside the bodies, is a good one in some respects; but it would add to the expense of the works considerably, and the result would be exceedingly questionable.

It must not be forgotten, that, where a different width from that in common use is adopted, the railway on which it is used becomes isolated. None but its own carriages can travel on it, and they can travel on no other line. This alone will, in most cases, be a serious objection. For our own parts we should say, let well alone; wait for more experience; we are yet infants amongst railways, and we ought not to innovate on that which has been proved to do well, until we become giants. The majority of opinions, however, are beginning to lean towards some increase in the width, although there is every diversity in the quantity which practical men think necessary. Certainly the machinery under the boiler is compressed into its minimum space, and more room for it would be a great advantage, if it does not induce an incommensurate loss in other ways.

With respect to the form of the rail, it can be proved that a fish belly has greater strength, weight for weight, than any other. A 60lb. fish belly at three-feet bearings, rolled with a lower web, would be the best form of all; and this has been effected, as the original Liverpool and Manchester rails had partially this shape. The question, however, must be looked at in conjunction with the length between the supports. We have given below those forms most approved of in practice, and have added that in use on the Great Western Railway, which is however light, and does not stand well, three feet having been the original distance of the bearings.

Fig. 3 is the old Liverpool and Manchester rail, laid down at three-feet bearings; weight thirty-three lbs. per yard, with square joints. This rail was rolled with a lateral swell at the bottom, which on one side was continued the whole length, but on the other did not quite reach the chair. One side of the chair was cast with a cavity, into which the lateral swell fitted, and the opposite side had a nearly similar opening, in which was driven an iron key, shaped like a wedge, which, entering in a longitudinal direction, not only forced the swell into the cavity which was formed to receive it, but by this means, at the same time, kept the rail down in the chair.

Fig. 4. Leslie's patent rail, in which he sought to gain a still more powerful mode of keeping the rail down in the chair, by having his key tapered vertically as well as longitudinally, so as to act as a wedge downwards, as well as in the direction of its length; whilst, at the same time, the necessary expansion and contraction is allowed to take place. A key on each side has also been used with this form of rail; still, however, the keys were always found to work loose. Losh had also a projection rolled on the bottom of his rail; at the part which lies in the chair, where a corresponding cavity was cast to receive it, so that the effect of expansion or contraction would have a tendency to raise the rail in the chair, and thus wedge it tighter. The upper part of the notch for receiving the key in the chair was also formed with a slight curve, to allow of a small motion in the block, and the rails were made with a half-lap joint, formed not by cutting the middle rib of the rail, but by setting it back, so as to preserve its whole strength. They were laid down at three feet bearings, and weighed forty-four lbs. per yard, but of course were not restricted to that, or to any other weight.

Fig. 5. The London and Birmingham fifty pound fish-bellied rail. This was laid down at three-feet bearings, and the half-lap joint formed by setting back the middle rib instead of cutting it, in the same way as Losh's rail. It was keyed down by a pin going through the side of the chair in a direction sloping downwards. The end of this pin went into a notch in the side of the rail, at its lower parts; the pin was forced tightly in by an iron key acting through the chair, and also through a hole in the pin, by which it was driven both in and downwards; and the end of the key being split, was then opened, to prevent it being shaken loose. Mr. Stephenson has a patent for this chair. The rails did not rest on the bottom of the chair, but on a loose piece of iron, the lower part of which was the segment of a circle, and the upper part flat, and of the same width as the middle rib of the rail; and this worked in a circular cavity in the chair, so as to allow a motion when deflection took place in the rail. These rails had no bottom webs.

Fig. 6 is the St. Helen's and Runcorn rail, with a bottom web, having a semicircular base. These rails are forty-two lbs. per yard, and were laid down at three-feet bearings. A wedge on both sides is used, which acts downwards as well as sideways, from the opening in the chair to receive it being narrower at the top than at the bottom.

Fig. 7 shews the parallel rails laid down on the Grand Junction, and London and Birmingham railways. The left hand one is sixty-four lbs. per yard on the London and Birmingham, and sixty-two lbs. per yard on the Grand Junction. The right hand one is the London and Birmingham seventy-five pound rail. Rails of this kind are laid on seventy-five miles of that railway, and were intended to be at five feet bearings, but proved a complete failure at that distance, which had to be reduced to three feet nine inches. The left hand one was intended to be at four feet bearings. These rails were both laid down contrary to the opinion of the engineer, Mr. Stephenson, and have entailed a vast expense on that company. They have wooden wedges.

Fig. 8 is the Great Western rail, laid on longitudinal timbers, and forty-four lbs. per yard. Felt is laid between the rail and the timber, and the former is fastened down with screws. It has been found deficient in strength for the heavy engines used upon that railway.

Fig. 9 has been frequently adopted on railways formed with longitudinal bearings. It is spiked down to the timbers, and requires no chair. The weights have varied from thirty-five to sixty lbs. per yard. Sometimes the spikes have not gone through holes in the rail as in the figure, but have been driven in just outside each edge of the rail; in which case they are made with large heads, which come down and clip the rail firmly to the timbers.

The London and Birmingham Railway Company, after a long discussion, decided to try four and five feet with a parallel form instead of a fish-belly, which, requiring one-third more height in the chair, had, in addition to other disadvantages, that of being more liable to wring the chair from the block, which is found in practice to take place directly as the height of the chair. The block is also more loosened in the ground by a high chair, and the continual repairs arising from this loosening, amount to one-half the wages expended in repairing the way in general; hence every means of diminishing such a heavy item, which can possibly be devised, should be put in practice. As usual, where all was theory, there were considerable diversities of opinion. Those who wish to enter more at large on this subject, may consult Professor Barlow in favour of lengthening the bearings, and Lieutenant Leconant against it. As the matter has had a fair trial, it is only necessary here to state the results.

On the Primrose Hill contract, which was laid with four- The flexure produced by this weight perpendicularly has also this bad effect, that the engine and train are constantly ascending an inclined plane in practice, although the railway is considered as level, and of course where the railway has an inclination, that inclination will be proportionally increased. This was first pointed out by Professor Barlow, and is an important fact; for on the short planes between each block or sleeper caused by the deflection of the rail, the gain in descent is so insignificant, that it may be entirely neglected; consequently the engines and carriages are constantly going up an inclined plane between each support of the rails equivalent to the central deflection divided by twice the distance between the supports. This is, from calculation, ascertained to be as follows, viz.:—

| Bearing distance | Deflection | Equivalent Planes | Increased Power required per ton | |------------------|------------|-------------------|---------------------------------| | Ft. In. | Inches | | | | 3 9 | .024 | 1 in 3000 | .75 lb. | | 3 9 | .037 | 1 in 2432 | .92 lb. | | 4 0 | .041 | 1 in 2341 | .95 lb. | | 5 0 | .064 | 1 in 1875 | 1·20 lb. | | 6 0 | .082 | 1 in 1756 | 1·30 lb. |

Although the deflection of rails will generally be different from the above, and the increase of power required to surmount the consequent planes will also require considerable modification to suit the action of locomotive engines, which depend upon so many other circumstances besides the action of gravity; yet the fact remains the same, namely, that with deflection there is a consequent loss, and the subject deserves much more consideration than it has received, especially as we know that fish-bellied rails do not fail in the middle, but about eight inches from the supports. A rail ought not to act as a spring; but as this to a certain extent must be the case, it should be made to do so as little as possible. A spring should only be used to get over an obstacle where one must be met, but if the rail acts as a spring it creates an obstacle where none existed before. We must also remember that when deflection becomes permanent, fracture begins, as we break a thing we are not strong enough to pull asunder, by bending it backwards and forwards. In fact, the experiments on deflection have hitherto been such that they have merely served to unsettle all opinion, and to place one set of deductions in opposition to another. The mode of estimating this element by two wheels on an axle, loaded at their peripheries, and oscillated on the rails, is one which well deserves attention. In all cases, the firmer the rail is fixed to the chair, as respects rising in it, the less will be the deflection. Of course it must always have a motion in the direction of its length to allow for expansion and contraction, the force of which will vary in good or tolerable iron from nine to six tons per square inch of section.

The expansion of a fifteen-feet rail may be taken at .00126 inches for each degree of Fahrenheit, and as it will not be safe to take less than 90° for the range of our climate, this gives .1134 inches for the total, or .0567 at each end of such a rail.

In order to understand the action which takes place in the case of a deflected rail when a heavy weight passes over it, we must know the effect of gravity at the velocities used on railways. For this purpose, if we take three, four, and five-feet bearings as those which seem at present likely to be the limits, the following table will give us the time occupied in going over half the rail in each case; and from this we shall be able to ascertain the effect of gravity during that time. Or putting \(a\) for the velocity in miles per hour, \(v\) for the velocity in yards per minute, and \(v'\) for the velocity in yards per second, we have

\[ v = \frac{1760a}{60} = 29.333a \]

\[ v' = \frac{1760a}{3600} = 4.888a \]

And in the table, taking either of the three right-hand columns, according to the length of bearing, for instance the eighteen-inch column for a three-feet rail, we have the number of inches through which the engine or any other body would fall by the action of gravity in free space, in the time which it takes to pass over 18 inches at the given velocity, by the formula

\[ s = t^2 \cdot 193, \]

where \(t\) is the time in seconds, and \(s\) the space in inches. Thus at 20 miles an hour, with a three-feet rail, where 18 inches are passed over in \(\frac{1}{193}\) of a second, the engine would fall during that time

\[ \left(\frac{1}{193}\right)^2 \cdot 193 = \frac{1}{384} \cdot 193 = \frac{193}{384} = 5, \text{ or half an inch}. \]

Again at 30 miles an hour, with a 3-feet rail, 18 inches of which are passed over in \(\frac{1}{193}\) of a second, the engine during that time would fall

\[ \left(\frac{1}{193}\right)^2 \cdot 193 = \frac{1}{858} \cdot 193 = \frac{193}{858} = 225, \]

or not quite a quarter of an inch.

And denoting by \(t\) and \(s\) the time and space as above, we have conversely, knowing the space an engine would have to fall, for instance, through a bad joint, the distance the engine would pass over without touching the lower rail, by the formula

\[ t = \sqrt{\frac{s}{193}}. \]

Thus when \(s = 225\), we have

\[ t = \sqrt{\frac{225}{193}} = \sqrt{0.01166} = 0.341 = \frac{1}{29.3} \]

on a second, in which, at 30 miles an hour, we find by the table the engine would pass over 18 inches of the lower rail without touching it, describing in its fall a parabola modified by the effect of the springs on the engine.

This has been put to the test of experience by bending a rail nearly half an inch, and then painting it. An engine and train of carriages were then run over it, none of the wheels of which touched the paint for 22 inches. This affects a railway in three ways. First, when the engine has to fall, through a bad joint, the rail which it leaves being higher than the rail it is coming upon, the increased momentum from the fall will here occasion a larger deflection than ordinary, and a consequent inclined plane against the engine, from the time it comes on the rail till it passes the next chair. Secondly, when a rail is permanently bent, where the resistance on the second or rising part of the rail will be less than in the first case. And thirdly, when the rail is simply deflected by the weight of the engine, and restores itself to its original level when that weight has passed; here the effect will be least of all, the rail taking the form of a receding wave before the wheel, and a following wave after it.

In the second case, where the rail is permanently bent, the formula for the space the engine would fall will be

\[ s = \frac{H}{L} \cdot 193t^2, \]

where \(H\) is the height of the plane, and \(L\) its length, \(s\) and \(t\) being as before. For instance, if the head is \(\frac{1}{193}\) of an inch in a 3-foot rail, we have

\[ s = \frac{1}{180} \cdot 193 \cdot \frac{1}{858} = 0.0125 \text{ of an inch, at 30 miles an hour, and } s = \frac{1}{180} \cdot 193 \cdot \frac{1}{384} = 0.0278 \text{ of an inch at 20 miles an hour, or } \frac{1}{193} \text{ of an inch at 20, and } \frac{1}{858} \text{ of an inch, at 30 miles an hour, would be descended by the engine by the effect of gravity, in the same time that steam and gravity together take it along 18 inches of the rail.}

Let us next suppose we have steam enough to carry the engine along at a velocity so great, that gravity will not bring it down the \(\frac{1}{193}\) of an inch perpendicular, whilst steam carries it along the 18 inches horizontal, we shall find this velocity to be at and above 44 miles an hour, for it takes \(\frac{1}{193}\) of a second for a body to fall one-tenth of an inch by the effect of gravity, and \(\frac{1}{193} \cdot 18 \text{ in. } = 3500 \text{ ft. } : 44 \text{ miles}; \text{ hence at 44 miles an hour, and at all velocities above it, the engine, after arriving on the rail, bent one-tenth of an inch in the middle, and forming two planes, will no longer touch the rail till after it has passed the middle of it, and velocities of 60 miles an hour have been attained.}

In the third case, the engine does not go down a plane, as above, but has to make its own curve through its weight, deflecting the rail. The necessity then of knowing the laws of deflection is such, that no idea can be formed of the effects these important matters will have on the economy of railroads; yet we have up to the present day positively no data to go upon, which will lead us at all near the truth; and railways are constructing, at a cost very little short of seven millions, without the means having been taken to put such essential points as these out of the pale of doubt and uncertainty, which could be done by a few well conducted experiments. We know, for example, that in an iron bar, if \(l\) = the half length, \(x\) = any variable distance, \(y\) = the corresponding depth, and \(\Delta\) = the sine of the elementary deflection, the sum of the deflections when \(x = l\) is

\[ \int_{0}^{l} \frac{x^2 \Delta}{(a + bx)^3} \text{ for a parallel bar, and } \int_{0}^{l} \frac{x^2 \Delta}{(a + bx)^3} \text{ for a fish-bellied rail, in which latter expression } a = \text{ the least depth, and } b = \text{ the difference of the depths divided by the half length.}

In some cases, where we have good experiments, the mode by which they have been calculated, in order to generalize and render available their results, is inaccurate, and the effect may be shewn by the following table, giving the deflection of rails, with three tons' weight on the mid- of them, each column deduced from the same set of experiments, differently computed, and varying to an enormous degree.

| Length of bearing in inches | a | b | c | d | e | f | g | h | |---------------------------|-----|-----|-----|-----|-----|-----|-----|-----| | 39 | .024| .036| .03 | .02357| .0272| .0286| .072| .0838| | 42 | .037| .050| .06 | .047 | .0538| .0569| .111| .1707| | 45 | .041| .063| .072| .056 | .064 | .098 | .123| .204 | | 57 | .064| .122| .139| .108 | .123 | .191 | .192| .393 | | 60 | .074| .150| .171| .1385| .153 | .162 | .222| .486 | | 69 | .082| .210| .241| .188 | .216 | .228 | .246| .684 |

Column \(a\) gives the deflections at 3 tons, deduced from the experiments by the experimenter, except for the sixty-inch, which is derived from the fifty-seven inch bearing. Column \(b\) gives the deflections derived from the formula given by the experimenter as the results of the same experiments. Column \(c\) gives the deflections from this formula, recomputed by another person. Column \(d\) gives the deflections computed from another formula given by the experimenter. Column \(e\) gives the deflections in column \(d\), computed by another person. Column \(f\) gives the mean of columns \(e\) and \(c\), which appears to be the best approximation we have. Column \(g\) and \(h\) give the deflections for 9 tons' weight, the first being derived from column \(a\), and the second from column \(f\), the difference in the longest bearing 69 inches, being nearly 3 to 1.

With this lamentable uncertainty in the data for a deduction of such importance as that of a deflection in the rails causing an engine to be constantly ascending an inclined plane, there is no hope of arriving at any commonly accurate results. For instance, if we take the bearing of 5 feet, which Mr. Barlow gives, as occasioning the ascent of a plane of 1 in 1875, the deflection, with 3 tons' weight, being .064, and substitute for .064 the deflections in columns \(a\) to \(f\) successively, we have as follows:

| By column \(a\) | Deflection | Consequent Planes | |-----------------|------------|------------------| | | .074 | 1 in 1621 | | | .150 | 1 in 800 | | | .171 | 1 in 702 | | | .1335 | 1 in 899 | | | .153 | 1 in 791 | | | .162 | 1 in 741 |

In which there is more than two and a-half to one difference in the results, all of which are drawn from one set of experiments, whilst at the same time the probability is, that the planes ought to turn out less steep instead of being more so.

From the effects which arise in consequence of deflection, it will be well worth considering what advantages are derived from the use of felt under the chair. If the rail was perfectly stiff, then, when the engine came over a chair, and compressed the felt, it would afterwards have to go up an inclined plane, through the rail being depressed at the block it had just passed over; and this would continue to take place till the engine arrived towards the next block, when it would depress the rail again in a similar way, and thus its course would be continually up a partially rising plane, the assistance downwards being almost insensible.

But as every rail deflects more or less, the inclination produced by this cause acts just exactly in the opposite manner to that which takes place through the depression and spring of the felt; for whilst the wheel, from the effect of deflection in the rail, descends during its passage over the first half of the rail, and ascends while going over the second half, the effect which the compression and springing of the felt has upon it, is to make it ascend a plane during its passage of the first half, and to descend during the time it is going over the second half. The felt acting as a spring, however, is exceedingly questionable, although maintained by some persons. Its use will be found to consist more in giving a steady seat for the chair when the block is composed of hard stone, and offering a defence against the grating of the chair on the block, which will otherwise take place, producing a grinding, a loss of surface, and consequently a looseness, which, when once arrived at, rapidly increases.

From the above observations on the effects of inclined planes, we may see how desirable it is to have the blocks and sleepers placed in the most accurate manner, as respects uniformity of height. For we must recollect, that in a three-feet rail, a difference of one quarter of an inch in the height of two adjacent blocks, or, more properly speaking, in the height of the basis of two adjacent chairs, converts that three feet of rail into an inclined plane, rising 1 in 144.

With respect to placing the blocks diagonally, this is a placing of less stable position in the line of rails than when they are placed square, for the resistance of the ground to the sinking of the block, whether conceived to be similar to a collection of springs acting under the block, or a collection of weights acting above it, must in either case be referred to the centre of gravity of each half of the block, considering it as moved by the passing weights about a line drawn through its middle at right angles to the line of the rails; that is to say, in a block two feet square, and one foot thick, there are 12 inches in the direction of the rails, 24 inches across them, and 12 inches in depth, acting on each side the axis of motion when the block is laid square, the surface of each half being 288 inches. Now, any uniform effect on these 288 square inches drawn into the distance of their centre of gravity from the axis of motion, gives for the stability of each half 1728. Any uniform effect on the 288 inches of a diagonal half block will give a less number; for the distance of the centre of gravity from the axis of motion was 6 inches in the square block, but it will be only \(5 \times 65682\) in the diagonal, being \(1 - 3d\) the altitude of the triangle, and hence we have only \(1629 \times 6416\) for the stability in the direction of the rails. The diagonal block will consequently have its maximum resistance to sinking at 45° from the line of the rails, or in the position where stability is least required. Circular blocks have been proposed in order to get equal resistance in all directions, but the gain would not be equal to the extra expense, and the stability, although a trifle more than that of the diagonal block in the line of the rails, is less than that of the square one; for the area, as before, being 567 square inches, \(=785398d^2\), and \(d\) being the diameter, we have \(d = \sqrt{733386} = 27.0811\), and the radius \(=13.5405\), and as the arc is to the chord, so is \(d\) radius to the distance of the centre of gravity from the centre, or \(3 \times 14159 \times 13.5405 : 27.0811 = 9.02703 : 574678\) inches, and \(574678 \times 288 = 1655 = 0.07264\) for the resistance.

We have experimented on the two positions of the blocks, and found that when placed diagonally, there was rather more resistance to lateral motion than when placed square, and they are more conveniently got at to repack in the former position than they are in the latter; but when placed as close as they ought to be, in order to form an economical road, the diagonal position is inadmissible.

It will be seen from the following tables which we have computed, that instead of increasing the bearings from three feet, if we study economy, we should reduce it; and as we have in these tables taken into account all ordinary variations in the elements of expenditure, we must consider it proved that except under very extraordinary circumstances, the nearer the supports are brought together up to the limits here given, the cheaper will the railway be made, ### Table I

**Comparative Cost of Long and Short Rails**

| Length of rail in feet | Price per yard | Price per block | Total price | Price of one yard | |------------------------|----------------|----------------|-------------|------------------| | 2 | 40 | 26-65 | 3 | s.d. | | 21 | 45 | 33-75 | 4 | s.d. | | 22 | 50 | 41-65 | 5 | s.d. | | 23 | 55 | 50-42 | 6 | s.d. | | 24 | 60 | 60-00 | 7 | s.d. | | 25 | 65 | 70-42 | 8 | s.d. | | 26 | 70 | 81-66 | 9 | s.d. | | 27 | 75 | 93-75 | 10 | s.d. | | 28 | 80 | 106-66 | 11 | s.d. | | 29 | 85 | 120-42 | 12 | s.d. | | 30 | 90 | 135-00 | 13 | s.d. | | 31 | 95 | 150-42 | 14 | s.d. | | 32 | 100 | 165-66 | 15 | s.d. |

### Table II

**Weight of Rail when the Prices per Yard are equal**

| Length of rail in feet | Price per yard | Price of rail per yard | |------------------------|----------------|------------------------| | 2 | 17 | 12 0 | | 21 | 17 | 11 4 | | 22 | 17 | 10 9-6 | | 23 | 17 | 10 4-36 | | 24 | 17 | 9 8-31 | | 25 | 17 | 9 5-14 | | 26 | 17 | 9 2-4 | | 27 | 17 | 8 9-88 | | 28 | 17 | 8 6-32 | | 29 | 17 | 8 4-8 | | 30 | 17 | 8 2-12 | | 31 | 17 | 8 0-8 | | 32 | 17 | 8 0-8 | | 33 | 17 | 8 0-8 | | 34 | 17 | 8 0-8 | | 35 | 17 | 8 0-8 |

### Table III

**Effects of one-sixth decrease in the price of iron on the comparative cost of long and short rails**

| Length of rail in feet | Price per yard | Price per block | Total price | Price of 1 yard | |------------------------|----------------|----------------|-------------|-----------------| | 2 | 2 | 9 1/2 | 8 0 | 10 9 1/2 | | 21 | 3 | 6 1/2 | 8 6 | 12 0 | | 22 | 4 | 4 0 | 9 0 | 13 4 | | 23 | 5 | 3 0 | 9 6 | 14 9 | | 24 | 6 | 3 0 | 10 0 | 16 3 | | 25 | 7 | 4 0 | 10 6 | 17 10 | | 26 | 8 | 6 0 | 11 0 | 19 6 | | 27 | 9 | 9 1/2 | 11 6 | 21 3 | | 28 | 11 | 11 1/2 | 12 0 | 23 1/2 | | 29 | 12 | 12 0 | 12 6 | 25 0 | | 30 | 14 | 14 0 | 13 0 | 27 0 | | 31 | 15 | 15 0 | 13 6 | 29 2 | | 32 | 17 | 17 4 | 14 0 | 31 4 |

### Table IV

**Effect of a decrease of one-eighth in the price of a block complete on the comparative cost of long and short rails**

| Length of rail in feet | Price per rail | Price per block | Total price | Price per yard | |------------------------|----------------|----------------|-------------|----------------| | 2 | 3 | 4 | 7 0 | 10 4 | | 21 | 4 | 2 1/2 | 7 5 1/2 | 11 7 1/2 | | 22 | 5 | 2 1/2 | 7 10 | 13 1 | | 23 | 6 | 3 1/2 | 8 3 | 14 7 1/2 | | 24 | 7 | 6 | 8 9 | 16 3 | | 25 | 8 | 9 1/2 | 9 2 1/2 | 17 11 1/2 | | 26 | 9 | 10 | 9 7 | 19 10 | | 27 | 10 | 11 1/2 | 10 4 | 21 9 1/2 | | 28 | 11 | 12 1/2 | 10 6 | 23 10 | | 29 | 12 | 13 1/2 | 10 11 | 25 11 1/2 | | 30 | 13 | 14 1/2 | 10 11 | 28 3 | | 31 | 14 | 15 1/2 | 11 4 | 30 7 1/2 | | 32 | 15 | 16 1/2 | 12 3 | 33 1 |

### Table V

**Effect of a decrease of one-sixth in the price of the rail, and one-eighth in the price of the block, on the comparative cost of long and short rails**

| Length of rail in feet | Price per rail | Price per block | Total price | Price per yard | |------------------------|----------------|----------------|-------------|----------------| | 2 | 2 | 9 1/2 | 7 0 | 9 9 1/2 | | 21 | 3 | 6 1/2 | 7 5 1/2 | 10 11 | | 22 | 4 | 4 1/2 | 7 10 | 12 2 | | 23 | 5 | 3 1/2 | 8 3 | 13 6 1/2 | | 24 | 6 | 3 | 8 9 | 15 0 | | 25 | 7 | 4 | 9 2 1/2 | 16 6 1/2 | | 26 | 8 | 6 | 9 7 1/2 | 18 1 1/2 | | 27 | 9 | 9 1/2 | 10 4 | 19 10 | | 28 | 10 | 11 1/2 | 10 6 | 21 7 1/2 | | 29 | 11 | 12 1/2 | 10 11 | 23 5 1/2 | | 30 | 12 | 14 1/2 | 11 4 | 25 5 | | 31 | 13 | 15 1/2 | 12 3 | 29 7 1/2 | | 32 | 14 | 16 1/2 | 12 3 | 32 1 |

### Table VI

**Effect of a decrease of one-sixth in the price of the rail, and of one-fourth in the price of the block, on the comparative cost of long and short rails**

| Length of rail in feet | Price per rail | Price per block | Total price | Price of 1 yard | |------------------------|----------------|----------------|-------------|-----------------| | 2 | 2 | 9 1/2 | 6 0 | 8 9 1/2 | | 21 | 3 | 6 1/2 | 6 4 1/2 | 9 10 1/2 | | 22 | 4 | 4 1/2 | 6 9 | 11 1 | | 23 | 5 | 3 | 7 1/2 | 12 4 1/2 | | 24 | 6 | 3 | 7 6 | 13 9 | | 25 | 7 | 4 | 7 10 1/2 | 15 24 1/2 | | 26 | 8 | 6 | 8 3 | 16 9 | | 27 | 9 | 9 1/2 | 8 7 1/2 | 18 4 1/2 | | 28 | 10 | 11 | 9 0 | 20 11 | | 29 | 11 | 12 | 9 4 1/2 | 21 11 | | 30 | 12 | 14 | 9 9 | 23 9 | | 31 | 13 | 15 | 10 1/2 | 25 9 | | 32 | 14 | 16 | 10 6 | 27 10 1/2 | ### Table VII

Effect of an increase of one-sixth in the price of the rail, and a decrease of one-sixth in the price of the block, on the comparative distance of long and short rails.

| Length of rail in feet | Price per rail | Price per block | Total price | Price per yard | |-----------------------|---------------|-----------------|-------------|----------------| | | s. d. | s. d. | s. d. | s. d. | | 2 | 3 10-666 | 6 8 | 10 6-666 | 15 10 | | 2\(\frac{1}{2}\) | 4 11-0625 | 7 1 | 12 0-0625 | 16 0-833 | | 3 | 6 0-915 | 7 6 | 13 6-915 | 16 3\(\frac{1}{2}\) | | 3\(\frac{1}{2}\) | 7 4\(\frac{1}{2}\)| 7 11 | 15 3\(\frac{1}{2}\)| 16 8 | | 4 | 8 9 | 8 4 | 17 1 | 17 1 | | 4\(\frac{1}{2}\) | 10 3\(\frac{1}{2}\)| 8 9 | 19 0\(\frac{1}{2}\)| 17 6\(\frac{1}{2}\) | | 5 | 11 11 | 9 2 | 21 1 | 18 0 | | 5\(\frac{1}{2}\) | 13 8 | 9 7 | 23 3 | 18 7\(\frac{1}{2}\) | | 6 | 15 6\(\frac{1}{2}\)| 10 0 | 25 6\(\frac{1}{2}\)| 19 2 | | 6\(\frac{1}{2}\) | 17 6\(\frac{1}{2}\)| 10 5 | 27 1\(\frac{1}{2}\)| 19 9 | | 7 | 19 8\(\frac{1}{2}\)| 10 10 | 30 6\(\frac{1}{2}\)| 20 4\(\frac{1}{2}\) | | 7\(\frac{1}{2}\) | 21 11\(\frac{1}{2}\)| 11 3 | 33 2\(\frac{1}{2}\)| 20 11\(\frac{1}{2}\) | | 8 | 24 3\(\frac{1}{2}\)| 11 8 | 35 11\(\frac{1}{2}\)| 21 7 |

In calculating for any intermediate lengths not in the table, for every tenth of a foot increase in the length of bearing, add 2 lbs. to the weight per yard, and 2\(\frac{1}{2}\)d. to the price per block, in each case to the tabular number, in a line with that length to which the addition is made. Thus, for 2\(\frac{1}{2}\) feet say 44 lbs. per yard, and 8s. 4\(\frac{1}{2}\)d. for the block; and when a different price is taken for the block, increase it \(\frac{1}{8}\)th for each 3 inches of increase in the length of the rail, and proportionally for all other lengths.

The minimum price in Table I. is when the length of bearing is 2\(\frac{1}{2}\) feet, being then 16s. 11-45d. per yard single rail.

Table II. is computed to show that if we take the same proportion for the blocks as in Table I., and at the same time keep the total expense per yard the same at all lengths, we shall have too little money left to get an efficient rail; it is calculated, by turning the price of the blocks in Table I. into the price per yard, and subtracting this from 17s., the remainder will be the price of the rail per yard, which, at 1\(\frac{1}{2}\)d. per lb., will show how heavy a rail can be got for that price. Thus, we see that we can only have 8lbs. more in a five-feet rail than we ought to have in a three-feet; besides which, we cannot get up to our standard, namely, 60 lbs. at three-feet bearings.

Table III. shows the comparative cost with the rails at 1\(\frac{1}{2}\)d. per lb., or L.11, 13s. 4d. per ton, and the minimum laying between 2\(\frac{1}{2}\) and 2\(\frac{3}{4}\) feet of bearing, we shall show how to ascertain where it exactly is, which method answers for the other similar tables. Let us first take 2\(\frac{1}{2}\) feet for the length of bearing, and adding, as before directed, 2 lbs. for this additional tenth of a foot, to the weight at 2\(\frac{1}{2}\) feet, we get 52 lbs. per yard, as the weight at 2\(\frac{1}{2}\) feet, and 3 feet : 52 lbs. = 2\(\frac{1}{2}\) feet : 45-066 lbs. for the weight per rail, which at 1\(\frac{1}{2}\)d. per lb. is 56-382d. The price of a block for a 2\(\frac{1}{2}\) feet length is 108d., and adding 2\(\frac{1}{2}\), we get 110-4d. for the block at 2\(\frac{1}{2}\) feet; and this added to the price per rail, gives 166-732d. for the total price per rail, or nearly 13s. 10\(\frac{1}{2}\)d. Thus, as 2\(\frac{1}{2}\) feet : 166-732d. = 3 feet : 16s. 0-38d., for the price per yard complete of single rail, whereas at 2\(\frac{3}{4}\) feet it is 16s. 0-1d.; hence the minimum lies between 2\(\frac{1}{2}\) and 2\(\frac{3}{4}\) feet, and not between 2\(\frac{1}{2}\) and 2\(\frac{7}{8}\) feet.

Resuming our trial with 2\(\frac{3}{4}\) feet, we have 45 + 3 = 48 lbs. for the weight per yard at 2\(\frac{3}{4}\) feet, and 3 feet : 48 lbs. = 2\(\frac{3}{4}\) feet : 38\(\frac{1}{2}\) lbs. per rail, which at 1\(\frac{1}{2}\)d. per yard, costs 4\(\frac{1}{2}\). The price of the block at 2\(\frac{3}{4}\) feet is 102d., and adding 3\(\frac{1}{2}\)d. we get 105-6d. for the block at 2\(\frac{3}{4}\) feet; that added to the price of the rail, gives a total of 12s. 9-6d., and as 2\(\frac{3}{4}\) feet : 153-6d. = 3 feet : 192d. or 16s. 0d., whereas the price at 2\(\frac{3}{4}\) feet is 16s. 0-1d. In the same way we may repeat the calculation till we arrive at what extent of accuracy we choose.

Having seen the effect which lowering the price of iron has, we know that by raising it, we should find it cheaper to put the blocks close together than our first table indicated; thus, if iron is 1\(\frac{1}{2}\)d. per lb., we have for 2-feet rails 3s. 10-666d. as the price of the rail, and 11s. 10-666d. as the price of the rail and block complete, which gives us 17s. 10d. as the price per yard, whereas with 2\(\frac{3}{4}\) feet rails it would be 4s. 11-0625d. the rail, and 13s. 5-0625d. for the rail and block, or 17s. 10\(\frac{1}{2}\)d. per yard. Table IV shows the effect of cheaper blocks on the total cost at each length of bearing; it begins at 7s. per block, and increases 5½d. or 1½d. for each 3 inches of increase in the length of the rail. The price of rails will never materially differ in any part of England, the freight being the principal variable quantity, but the price of blocks will alter in a very great degree, and the effect of this may be shown; take, for example, 2s. 8d. as the price of one for a two-feet bearing, and we know they have been procured cheaper; adding to this, as we have done before, 2s. for the other items connected with the block, we get 4s. 8d. as the price of a block complete, and the price of the rail being 3s. 4d., the total price is 8s. per rail, or 12s. per yard. In the same way we have 12s. 6d. per yard at 2½ feet bearings; 13s. 1d. at 2½ feet; 13s. 7d. at 2½ feet; 14s. 2d. at 3 feet; and 18s. 11d. at 5 feet; hence in a railway 31 miles long, we shall find the saving, by having the blocks at two feet apart, L.75,293, viz.

| Distance | Cost | |----------|------| | 31 miles at 5 feet | L.206,937 | | " 2 feet | L.130,944 |

L.75,293

And as an useful approximation to this calculation, we may take each farthing per yard increase of cost in the total price per yard of single rail, to give L.73,333 per mile of double line, or in the above instance, there being 332 farthings between 12s. and 18s. 11d., we have 73,333 × 332 × 31 = L.75,474.

As we are obliged to place our supports close together, to get a minimum cost when the blocks are less in price than the cost we first assumed, so we shall find that when greater, we must increase their distance. For instance, if a block for a two-feet bearing costs 9½d., the cost per yard of block and rail complete will be 18s. 6d.; at 2½ feet, 18s. 4½d.; and at 2½ feet, 18s. 4½d., the minimum being between 2½ and 2½ feet.

We have next to see what will be the effect when the rail and block are both either greater or less than in Table I. This divides itself into three branches; first, when they decrease or increase in an equal ratio; secondly, when the rail decreases or increases in a greater ratio than the block; and, thirdly, when the block decreases and increases in a greater ratio than the rail.

In the first case, the ratio of the price per yard will remain evidently the same as in Table I. Thus, if both rail and block are reduced in price ½th, we shall have at 2 feet, the price per yard, 14s. 18½d.; at 2½ feet, 14s. 16½d.; per yard; and at 2½ feet, 14s. 2½d.; hence the minimum is as before at about 2 feet 2 inches, and the same will hold under any other increase or decrease, the ratio in rail and block being equal.

For the second case, when the rail decreases in price in a greater ratio than the block, Table V shows the corresponding effect, and the minimum will be found again at about 2 feet 2 inches, for at that distance we have 44 lbs. for the weight of the rail per yard, or 32-267 lbs. for the weight per rail, which at 1½d. per lb. is 40-334½d.; for the block, if 25 of a foot, increases the price 5½d., then 2 of a foot will increase it 4½d., which added to 8½d., the price at 2 feet, gives 88-2½d. for 2 feet. Hence the total price of rail and block is 10s. 8½d., or 14s. 7½d. per yard, which is rather less than at 2½ feet.

It will be found, in like manner, that the effect of an increase of price in the same ratio will not affect the minimum; for example, with an increase of ½th in the price of the rail, and ¼th in the price of the block, we have at 2 feet the rail 3s. 10½d., the block 9s.; total, 12s. 10½d.; or 19s. 4d. per yard. With 2½ feet, the rail will be 59-065d., the block 114-75d.; total, 14s. 5½d.; or per yard, 19s. 3½d. With 2½ feet the rail will be 72-915d., the block 121-5d.; total, 16s. 2½d., or per yard 19s. 5½d.; and with 2½ feet, we have the rail 56-465d., the block 113-376d.; total 14s. 1½d.; or per yard, 19s. 3½d., or rather less than at 2½ feet.

For the case where the rail increases or decreases in a less ratio than the block, Table VI shows the comparative effect on the minimum, which is here at about 2 feet, with a decrease in the prices; for trying 2½ feet, we get for the rail 40-334½d., the block 75-6½d.; total, 115-934½d., or per yard, 13s. 2½d.; and at 2½ feet, we have for the rail 36-75d., the block, 73-8½d.; total, 110-53½d., or per yard 13s. 1½d.

When there is an increase of ½th in the price of the rail, and ¼th in the price of the block, we have for 2 feet bearings, the rail, 46-665d., the block, 120d.; total, 166-665d., or per yard, 20s. 10½d.; for 2½ feet, we have, rail, 59-0625d., block, 127-5d.; total, 186-5625d., or per yard 20s. 8½d.; for 2½ feet, the rail is 72-915d., the block, 135d.; total, 207-915d., or per yard, 20s. 9½d. Hence the minimum is at 2½ feet; for at 2 feet the rail is 61-715d., the block, 129½d.; total, 190-715d., and the price per yard, 20s. 8½d.; and at 2½ feet, the rail is 56-465d., the block, 126d.; total, 182-465d., and the price per yard, 20s. 8½d.

We have now only left the cases where the price of the rail increases, while that of the block decreases; the effect of this is shown in Table VII; and when the price of the rail decreases, while that of the block increases, this is given in Table VIII. In Table VII, the minimum expense is at the distance of 2 feet, and in Table VIII, at 2½ feet, this being the greatest distance yet obtained; hence cheap rails and very dear blocks are the only conditions which will warrant a distance at all approaching to those now in use; 2½ feet appearing to be the limits under any ordinary prices, and in general only 2½, while in some instances 2 feet only should be taken, in order to lay down a railroad at the minimum expense, as far as the cost of the permanent way is concerned.

In Table VIII, we do not know on which side of 2½ feet the minimum expense will be; we shall therefore, in order to complete the inquiry, investigate this as we have done in the other cases. Taking, then, 2½ feet, we get 52 lbs. per yard for the weight, or 45-065 lbs. per rail, costing at 1½d. per lb. 56-332½d.; for the block we have as 25 feet 7½d.; 1 foot = 2½d., or 10s. 8½d.; total, 185-132½d., or per yard, 17s. 9½d., being rather more than the price at 2½ feet. Trying now 2½ feet, we have 48 lbs. per yard, or 38-8½d. per rail, costing 48½d., and for the block 119d., the price at 2½ feet plus 4½d., the proportion for 15 feet, or 123-2½d.; total, 171-2½d., or per yard, 17s. 10½d., which is more again than at 2½ feet; the minimum price will therefore be very near 2½ feet, but rather more if anything.

It now remains for us to show, why the particular rate of increase and decrease in the size of the rail and block, which we have given in the tables, has here been assumed. And, first, of the blocks. Every person, when calculating this effect of prices for any particular railway, will of course take into consideration the cost of rails, blocks, and sleepers for the railway in question; and as the rate of increase we have given, viz. one-fourth in the price of the block chair, and all appurtenances complete for each foot increase in the length of the rail, is more than what is necessary rather than less, and as a decrease in the price of the blocks will lead to shortening the rails still more, it will be seen that any error will be on the safe side. It will most probably be found in practice, that whatever the distance between the supports may be, the same absolute surface should be preserved in every case; for although it has been said that each block, be its distance what it may, has but to support a certain weight passing over it, yet this is not a correct mode of reasoning, because it has to support that weight for a longer time, when the distance between each Railways is increased, which is the same thing as having to support a greater weight. For instance, with blocks five feet apart, if we only took them at four square feet each for the intermediate ones, and five square feet for the joints, we should have 183040 square feet, supporting the train for one hour, at a velocity of twenty miles per hour, whilst the same sized blocks at three-feet bearings would afford 281600 square feet to support the train for the same time at the same speed, being a difference in favour of the short bearings of 98560 square feet, or more than one-third. Our increase in the table is rather less than would be required to preserve the same absolute surface.

With respect to the increase in the weight of the rails which we have taken, viz. sixty lbs. per yard at three-feet bearings, as a standard, and adding or subtracting five lbs. for every three inches of increase or decrease, we can only state that we have taken this from an attentive consideration for some years of the practical effects exhibited by the rails now in use on various lines. A mathematician will say, this is following no known law. It is not, and we firmly believe that to attempt to lay down mathematical laws for the dimensions of rails would be perfectly premature, in the present state of our ignorance on this subject. Before this can be done, a complete and satisfactory set of experiments must be made, to settle the many points now in dispute; and so much depends on the form of the rail, and the quality of the iron, that the weight and dimensions must be left to the judgment of the engineers of the respective lines, who, having their characters for ability at stake, will be influenced in every possible way to take all the necessary steps for coming to a right conclusion, and when in doubt, they will of course resort to experiment, every penny spent in which will in all probability save many pounds.

To assist in computing similar cases to those which we have above given, we may observe, that each farthing per lb. in the price of iron gives L2. 6s. 8d. per ton, and each pound per ton gives £428571, &c. of a farthing for the price per lb.; hence, multiplying the number of pounds and decimals of a pound in the price per ton by £428571, will give the price per lb. in farthings and decimals.

In computing the relative strength, &c. of the various rails, the following table will be useful:

| Length of rail | Square. | Cube. | |---------------|---------|-------| | 30 | 900 | 27000 | | 33 | 1089 | 35937 | | 36 | 1296 | 46656 | | 42 | 1764 | 74088 | | 45 | 2025 | 91125 | | 48 | 2304 | 110592| | 57 | 3249 | 185193| | 60 | 3600 | 216000| | 69 | 4761 | 328509| | 72 | 5184 | 373248|

| Depth of rail | Square. | Cube. | |---------------|---------|-------| | 3½ | 12-25 | 42-875| | 3¼ | 14-0625 | 52-74375| | 4 | 16- | 64- | | 4½ | 18-0625 | 76-765625| | 4¾ | 20-25 | 91-125 | | 5½ | 22-5625 | 107-171875| | 5½ | 25- | 125- | | 5½ | 27-5625 | 144-703125| | 5½ | 30-25 | 166-375| | 5½ | 33-0625 | 190-10937|

Our experience is yet so small, that various opinions exist even amongst those best informed, as to the proper form and weight of the rail and chair, and the size of the blocks and sleepers; and there is no doubt that in a few years a material alteration will take place in all these things. Until the present time, however, there has been nothing but change both in rails, chairs, and keys, and in the distance between the supports. Every rail should be tested before it is received from the contractor, and it should be always remembered that too much care cannot be taken with the permanentway materials. All the expense incurred in earthwork and masonry is only a means to an end, viz. the permanent road. We recommend the fish-bellied rail as possessing weight for weight, the most strength; and this would be increased by rolling them with a lower web. How much depends on the manufacture will be apparent, when it is stated that no less than thirty rails broke on the Liverpool and Manchester railway, in the fortnight ending on the 21st January 1837.

The question of expense, as far as the present mode is concerned, is a simple problem of maximum and minimum; and it has been so treated in the preceding tables, algebraic formulae having been omitted, to make them more generally useful. But there seems to be little doubt that with a 60-pound rail on three-feet bearings, and a block one foot thick, containing five cubic feet of stone, the increase we have given for longer bearings will not be considered as too much, when we recollect that the block has not only to support the rail, but has to sustain it against lateral deflection. When the blocks merely sink, the unusual motion of the engine and the carriages will at once detect it, and the proper remedy must be resorted to; but it might easily happen that the rails would be laterally deflected without its being observed until the train was thrown off altogether, particularly when it is taken into consideration that the carriages are still matter of experiment, and that the play of the wheels between the rails and upon the axles is not by any means a fixed quantity, and also that the whole weight of the engine acts laterally, whereas vertically that weight is divided.

A breadth of from 2 to 2½ inches for the top of the rail, seems admitted by nearly all parties to be sufficient; less would induce considerable wear on the engine and carriage wheels. The wear of rails on the top surface may be taken at one-thirtieth of a pound per yard per annum, and the total loss of weight at one-ninth of a pound per yard per annum; but more accurate experiments are yet required on this head, particularly as to the top surface wear; and the curious fact is yet unaccounted for, that rails laid on the ground, or keyed into chairs on blocks, but not run over by engines or carriages, oxidize considerably more than those which are used.

Six feet between each line of rails, seems also generally adopted as a convenient width; but this, of course, depends in some measure on the width between the rails, and the construction of the carriages. Should the plan of placing the wheels outside the carriages be generally adopted, a less width between the lines may suffice, but the distance would not bear to be much decreased. The width of embankments outside the rails should at least equal the width between the rails, so that, when the engines or carriages get off the line, their wheels will be so confined between the rails, that the outer one will not get off the embankment. The mode of action when an accident of this kind happens, appears not to be well understood. We frequently hear of engines being expected to drag their trains off the embankments; but this is a thing unlikely to occur often; for when an engine gets off the rails, it will generally strike so hard against the blocks and sleepers, that its velocity, independently of the shutting off the steam, or reversing the motion, will very quickly be lessened. When this takes place, the train, by its momentum, either forces the engine farther along, or, if it strike it at an angle, which is generally the case, throws it over on its side; and it is from this momentum of the train that the damage proceeds. Intermediate carriages getting off are the cause of much less danger. From the weakness of the present axle-guards, however, these generally break when the wheels strike the blocks or sleepers; and there is a great want of strength in the second and third-class carriages. We have known four of these, fortunately empty, crushed into toothpicks when a collision took place.

The following formula will enable manufacturers of fish-bellied rails to fit their rolls to any required size of rail. Thus, for three-feet lengths of bearing, In figure 10 Let \( r = CD \) be the radius of the rolls EF and \( ma \). \( d = \text{maximum depth of rail} \). \( d' = \text{minimum depth} \). \( e = CB = \text{distance of real and false centres} = \frac{d + d'}{2} \). \( z = \text{the angle LCD} \). \( g = 2re \). \( k = r^2 + e^2 \). \( x = \text{the abscissa in inches} \). \( y = \text{the ordinate in inches} \). \( h = BL \).

We then have \( h = \frac{2r + d + d'}{2} \), and \( y = h - \sqrt{k + g \cdot \cos z} \) in the first quadrant of the roller, or from \( 0^\circ \) to \( 90^\circ \), or from 1 to 9 inches in a three-feet rail, and \( y = h - \sqrt{k - g \cdot \cos z} \) in the second quadrant, or from 9 to 18 inches; but \( z = \frac{2r \cdot 3.14159}{360} \cdot 10x = 1^\circ \cdot 10x \); hence \( y = \sqrt{k + g \cos \left( \frac{2r \cdot 3.14159}{360} \cdot 10x \right)} \) for every inch of \( x \), or \( y = h - \sqrt{k - g \cos \left( \frac{r \cdot 6.2831852}{360} \cdot 10x \right)} \), or \( y = h - \sqrt{k - g \cos (r \cdot 0.0174533 \cdot 10x)} \).

The rolls EF and \( ma \) should be both equal, and likewise equal to the required length of the rail between the bearings, which, as the above formula stands, is 3 feet, but having the length, breadth, and depth of any required rail given, the size of the rolls may be determined; for their circumference will always be equal to the given length of rail between the bearings, viz. 3, 4, or 5 feet, as the case may be, and all the rest is got from the above equation, which is general for all sizes, by merely noting, that when the length is any other than 3 feet, \( \frac{180}{a} \cdot z \), must be substituted for \( 10x \); where \( a \) equals the number of inches of half the length of the rail between the sup- ports. Thus, for instance, for a five-feet rail the part in the final equation within the brackets will be \( (r \cdot 0.017453 \cdot 6x) \). The natural cosines are to be used, and \( g \) is to be applied although the cosine may \( = 0 \).

A fish-bellied rail, 50 lbs. to the yard, and with depths of 5 inches maximum and 3-8 inches minimum, compared with a parallel rail of the same weight, and the depth due to that weight, namely, 4-4 inches, each laid at three feet bear- ings, and having the thickness of their ribs and the form of their heads exactly similar, will be deflected, as the numbers 1881 for the fish-belly, and 2282 for the equivalent parallel; that is to say, a thickness of iron of about 3-10ths of an inch, must be added to the parallel rail in order to make it equal to the fish-belly. This proposition will nearly show the gain obtained by the use of fish-bellies for all the usual lengths of bearing, and may be taken at 11 to 9, since, in all cases, it is stiff- ness which is so essentially required. Mere strength will always be had with the sizes now generally adopted; and it is consequently against deflection which we have to guard, at the same time looking to economy, and not ex- pending immense sums of money unnecessarily, as has been done in purchasing rails much heavier than are re- quired. So much, however, depends on the quality of the iron, that we would strongly recommend every rail to be thoroughly tested when received from the manufacturer, and the results in each case registered. This would soon enable such a valuable collection of facts to be made, as that all hypothesis would cease; whereas, hitherto, there have been such discrepancies between experiments made by persons of the first eminence, that, practically, the sub- ject is involved in as much uncertainty as ever.

Wooden sleepers, which should be laid on all embank- ments till they are thoroughly consolidated, ought to be wide and long, and it will not be found too much to give them ten feet in length and one foot in width for a three-feet bearing, having a proportional increase and decrease at any other bearing. The cheapest way will be to buy the sleepers in the round, and have them ripped in two by cir- cular saws of about three feet in diameter, or even more, and withal the teeth broken off except every third or fourth. This will prevent the saw from choking; and, in a great meas- ure, from heating, which occasions the instrument to buckle, as it is termed. The boring of the blocks should also be done by machinery before they are delivered to the contrac- tor, and a proportional decrease be made in his charge for laying the permanent way; and if the company do not per- form this part of the work, the contractor will find it much to his interest to set up a machine for himself, if his con- tract exceed half a mile in length.

Various have been the opinions respecting the kind of joints by which the rails are connected, or, more properly rails, speaking, respecting the shape of their ends; but this di- versity of opinion ought not to have existed, and has only been a consequence of our want of experience on the sub- ject. It stand to reason, and has been found to be a fact, that butt joints, that is to say, when the ends of the rails are at right angles to their length, will always occasion a shock in passing over them, even if ever so well fitted; and if, as is too generally the case, no regard is had to the tempera- ture in laying the way, wide gaps will be found at each joining, particularly in winter. Half-lap joints are much preferable to butts, and greatly diminish the shock, but are still liable to objection; in the first place, through their weakening the rail; and, in the second, for still giving a very unpleasant jar to the carriages, although in a less degree than the butts. If they are laid right and left, as shown below, it will improve them for diagonal joints. The form of joint we should recommend is given in fig. 11,

Fig. 10.


Fig. 11.

---

In which the arrow shows the direction of the train. The slope of the joint must be placed exactly contrary upon the other line of rails, so that the wheels never meet the pointed end of the rail, but always run off. It then needs no other care, than that the point should of the two be the most prominent towards the wheel, and, if it is not so, the joining rail should be taken down a little with a file.

Treenails should be made of good heart of oak, well seasoned, until thoroughly dry, or of African teak, straight- grained; and each treenail should be cylindrical, one inch and a half in diameter, and six inches in length, having a cir- cular hole, half an inch in diameter, and six inches in length, bored through the centre for the insertion of the iron spike to fix the chair. They are sometimes made by being turned Railways in a lathe, and are also done by being passed through a cutting knife; but by whatever process they are brought to the required shape, regard should in all cases be had to the grain of the wood, which should in every instance be completely followed. The most usual way of contracting for these is, at so much per thousand, stating the place of delivery; but if a steam-engine be used to make wooden keys, it can also work lathes for the treenails, which, in that case, will be no cost, except for labour, as, in cutting up planks for the wedges, plenty of waste pieces will be found to make the treenails. A plan has grown into use on some railways, of dropping the treenails loose into the hole of the block, and then driving the spike in and splitting them; but this is not so good as driving them in tight. Oak spikes have formerly been much used, and have been known to last twenty years; we should not, however, recommend them, with the rate of speed that has now been attained.

The best form of chair is a subject requiring deep consideration, and on which engineers of eminence are by no means decided; we have, therefore, given several drawings of those which are most approved. The leading distinctions are, whether the rails have been keyed in by iron or by wood. The latter method, indeed, is almost indispensable when the rails have lower webs; for, as it would by no means do to have the chair following the shape of the rail, as in that case it must always be detached from the block whenever it is required to take the rail out of it, this consequence ensues, namely, that the opening in the chair must be as large as the lower web of the rail. A chair of this kind, with its wooden key, is shewn in fig. 12.

In every mode of keying it must always be remembered, that the intention is merely to keep the rail down in the chair, and not to attempt to confine it from longitudinal motion. The right way of making these wedges is an essential thing, and should be done by the company. The original mode was to purchase oak plank, thoroughly seasoned, and of the thickness required. If it be not seasoned in the most complete manner, it will not answer; but this process may be hastened by steaming it in a tank, with a pressure of about 12 lbs. on the square inch. When it is thoroughly seasoned it should be removed into a drying-house, having hot air flues under the floor, made of iron pipes, where all moisture must be extracted; and when thoroughly dry, it is cut into the proper scantling, and into thirteen-inch lengths, each of which when complete is cut into two for joint chairs, or three for intermediate chairs. They are first prepared by joiners to the right shape for going through the cutters; a joiner will prepare about 100 in a day. The cutters are composed of four blocks of iron, fixed one over the other, with openings between each of about one inch, sloping downwards. In the centre of the three lower blocks are steel cutters, the lower one being exactly the shape of the key, and the others above gradually larger. The key is put in at the top, and forced through by a lever about seventeen feet in length, brought down by a chain and crab winch, with eighty teeth in the wheel and ten in the pinion. Three men will work this, and in ten hours will cut 500 pieces, thirteen inches long, to the required shape. The shavings come through the spaces between the iron blocks, and by the gradual cutting, each one taking off a part, the knots in the wood go through without breaking, and the key comes out perfectly smooth.

The next process is compressing them, which is done by forcing them through an iron block, ten inches thick, with twelve holes in it, 3-16ths of an inch smaller than the key at the lower part, and tapering to the top to admit the key. They are forced through by the ram of an hydraulic press, worked by two pumps, one of an inch and a-half in diameter, the other of one inch, the diameter of the ram being nine inches, and the safety valve loaded to about nine hundred tons. Four men work the large pump, and two the small. They will get through 900 per day. A little rough grease is first rubbed over them. They are then cut into two or three, or more, in the proper proportion, according to the relative number of joints to intermediate chairs, and packed up in bags, care being taken to keep them in a dry place.

This method of manufacture has been much improved by the erection of an engine on the London and Birmingham railway, by which circular saws, running from 900 to 1100 revolutions per minute, rip the plank into scantling, and afterwards cross-cut the thirteen-inch lengths. Two more cutters were adapted on the top of the other four, but gradually larger. These took in the thirteen-inch lengths without their going into the hands of the joiner; and the key was forced through by a plunger working up and down, by a guide and parallel motion on the end of an iron beam. A similar plunger force them through the compressing box; and 1100 were completed in ten hours. A part of the power may also be applied to drill the stone blocks for the permanent way. The cost of the whole, with the necessary shops, amounted to about £1,500; but the keys may be made for £8 per thousand, if a cheap pattern be adopted. The circular saws also cut up the waste wood into treenails, which were bored by a lathe adapted to that purpose, the whole being worked by steam. It is found to save the labour of fifteen men. When this sort of chair is used, it will occasion a great saving of time and trouble, if all the chairs are either made by one contractor, or every one gaged before it is received; for if there be the least difference in the size, it requires a different set of cutters, and a different compressing block for each sort, besides giving a great deal of trouble to the men employed in laying the way. The same remark applies to the rails. The best way is to take plenty of time, by beginning early. Find a respectable man, and let him have the whole job, at a sum varying with the price of iron.

In iron keys there are many more ways of shaping them. The accompanying drawing (fig. 13.) shews a very good one, where the rail has a web on one side of the bottom only, and the other side of the chair is notched to receive an iron pin. The only objection ever urged against iron pins is, that they are apt to get loose. This might be obviated by splitting the end which enters first, and opening it when driven home. If this be done, the other end should have a head, so that a clawed crowbar could be applied in order to draw it out.

The annexed drawing (fig. 14.) shews another good form, invented by Mr. Robert Stephenson, where the rail is confined by two bolts having angular ends, which enter a small score in the rail, and are keyed home by iron keys with split ends; the key hole in the chair, and that in the bolts, being so proportioned, that the effect of keying up is to press the end of the bolt against the rail. In these chairs there is a moveable piece of iron, the bottom of which is circular, and the top flat, laid in a properly-formed receptacle in the bottom of the chair; and on this the rails rest, so as to give perfect ease to any motion produced by flexure. Mr. Buck's chairs (fig. 15.) are well spoken of. The wedge is driven against the rail by a vertical key. The accompanying drawing (fig. 16.) shews another good form,

Fig. 15. Fig. 16.

in which an iron ball takes against the rail, and is keyed close up to it by a longitudinal key. The joint chair is laid down, not at right angles with the rails, but diagonally, and is cast with a split end, rather smaller than the rail. It has therefore to be chipped to get the rail in.

There is however a great loss on all these chairs, through their being made of cast iron. This occasions numbers to be broken in fixing and keying. To prevent this, wrought iron chairs may be made, by rolling the iron into the required form in lengths, and then cutting up the lengths into chairs by shears; after which they may be drilled and completed.

A chair upon a universal joint has been patented, so as to allow the rail to accommodate itself to the sinking of the block; but it has not been adopted on any railway that we are aware of. The inquiries necessary under these and other heads, as the works increase in their number and magnitude, will be best met by the directors dividing themselves into sub-committees under the various necessary branches, which is always advantageous, as long as there is one managing head to bring all the parts to bear upon a common focus.

Points and crossings are things which require considerable attention; and great care should be taken that they are laid down on a plan which combines simplicity with safety. Where one line intersects another, and the crossing is a fixture, or as it is called, a through-crossing, no more will be necessary than to bolt the sleepers well together, and pay rigid attention to the adjustment of the rails; but where it is requisite to have the power of going either on one line or the other, as at a siding, the matter becomes more difficult, and the mode of doing so may be considered as far from settled, opinions being still very various.

The oldest form is the common switch, where, upon one side of the line of rails, is a bar, moveable on a hinge, capable of being laid into either the main line, or the line of sidings. (Fig. 17.) Abreast of this is a fixed check rail,

Fig. 17.

the main rail being bent, and having a nick in it (a) for allowing the flange to pass when the carriage is not to shift its line. The left hand half of the figure exhibits the same thing for the opposite line of rails. A check rail must also be placed at each point, so as to ensure the train going upon the required line when the switch is placed in the proper position. The switch is generally moved by a horizontal bar or rod of iron connected with it, which is drawn in and out the required distance by an eccentric, at the opposite end to that which is connected with the switch. This eccentric is attached to a vertical rod, coming up about three feet inside an iron standard, and it is turned at the top by means of a lever key which can be taken off at pleasure, and which no person should be allowed to touch except the switchman. This form, although the oldest, is a very good one, and is very easily understood and managed. There is, however, a very cheap and good plan of moving them, instead of an eccentric. This is a vertical lever, which draws them backwards and forwards, the handle springing against an arc with notches to receive it in each position. This might be placed inside the switchman's sentry-box, where it could be locked up if he was unavoidably absent, and no one could touch it.

Another form, also much approved of, is what is called the check-rail, to distinguish it from the former, which is called the switch-rail. In the check-rail there is a moveable bar to both sides of the line of rails. These are moved simultaneously, by the eccentric being connected to each of them by a cross bolt. The action of the check-rail and the switch-rail has this difference, that it takes place on different sides of the flange, the check-rail acting on the outside of the flange, and the switch-rail on the inside. The check-rail is not so good as the switch, nor is it so easily understood. It is shewn with its eccentric in Plate CCCCXX. Fig. 1 is the slide rail in plan, fig. 2 the elevation, fig. 3 the elevation of the eccentric, fig. 4 the point, and fig. 5 the general arrangement.

Another form which has been much adopted, is Curtis's slide rail. This has a double bar upon each side of the line of rails, is moved by an eccentric like the others, and is very effective, but expensive. In fact, they all answer the purpose, but the slide rails require signals, which we shall hereafter describe. But this is not the case with the others. Opinion seems now coming back to the old switch rail, modified by making the switch part of it considerably longer, and having it kept in the right position for the main line, by a weight or spring, so that when the train is to go on the siding, the switchman has to hold the switch all the time the train is passing. This is objectionable. But the construction has an advantage which overbalances anything which can be said against it; namely, that it will be opened by the wheel of the engine, if purposely put wrong, so that the train can by no possibility get off the line of rails, unless it is actually wedged immovably in the improper position. This is susceptible of further improvement. As it stands, it is the subject of a patent, but we question whether it could be sustained.

We have seen a very cheap, simple, and effective switch on the Great Western Railway, adapted for peculiar situations, where fixed crossings would be disadvantageous. This consists of a switch moveable at the middle by a pivot, instead of at the end. This connects two lines in either direction, but is not to transfer trains from one to the other. Whichever plan may be adopted, we should recommend one set to be made rigidly accurate, and then that templates should be formed from these as a guide for all the others. No method but this will ensure the correctness of the whole; and crossings being always dangerous, they should never be used if it can be helped, except on a station. There is still a difference of opinion amongst engineers whether the rail should be inclined or not. The gain and loss may be thus stated. The advantages consist principally in preventing so much wear both on the tire of the wheel and the rail, but chiefly the former, for when the rail is upright, the wheel, theoretically speaking, is only in contact with it on a line having hardly any breadth. This is found to wear away the wheel very fast, and the rail likewise suffers a loss on the side where the contact takes place; besides which, the wear approximates the tire of the wheel more and more to the shape of a cylinder instead of a cone; and the rail also partially adapts itself to this action, in each case, through the abrasion of the working lines. In addition to the increase in repairs, through these causes, the wear is to a certain extent unequal, and an irregularity is produced which consequently leads to an unsatisfactory performance between the engine and the rails. But this is avoided by inclining the rail so that it receives the wheel on nearly the whole of its bearing surface; and 3-8ths of an inch in 11 inches is the inclination of the blocks on the London and Birmingham railway.

The disadvantage consists mainly in this, that if the wheels do bear on the whole of the surface, say two inches, there must be a constant rubbing action going on, arising from the unequal velocities with which the outer and inner tire of coned wheels revolve, and this will of course be equivalent to dragging the whole train for a certain distance with every one of the wheels locked. Let us see what this dragging will amount to.

Let \( d \) be the greater diameter of the coned wheel, and \( d' \) its lesser, each in inches; taking the bearing surface at two inches, and supposing that in this breadth the two diameters differ half an inch, both which suppositions are in excess, we then have

\[ \frac{d-d'}{2} = 3.141593, \quad \text{or} \quad (d-d') = 1.570796 \]

for the rubbing at a mean in each revolution of the wheel, and the length of this revolution will be

\[ \frac{d+d'}{2} = 3.141593, \quad \text{or} \quad (d+d') = 1.570796. \]

If we take \( d=604 \) inches, and \( d'=594 \) inches we get \( (d-d') = 1.570796 = 5 \cdot 1.570796 = 785398 \) inches, which is the quantity of dragging for each revolution, the length of which will be \( (d+d') = 1.570796 = 120 \cdot 1.570796 = 188.49552 \) inches, we then have this proportion,

\[ \frac{523598}{785398} = \frac{1760}{264} \]

Hence, the dragging of the whole train will be 264 inches per mile, or 733 yards in 100 miles for each wheel. This, at first sight, appears considerable, but in practice it will be much less. The data have been taken large to show the limit of this action, and the whole bearing surface is not practically in contact with the tire of the wheel, arising from the various imperfections inseparable from the manufacture of both wheels and rails, particularly the latter, although it must be allowed that the better they are made, the more dragging will take place; and likewise the more the surfaces come into contact, the greater will be the effect of shocks from bad joints and other imperfections. Still our opinion tends to inclining the rail.

It appears absolutely necessary in railroad engines and carriages, that the wheels should be keyed to the axles, the wheel and axles both turning round together; several attempts have been tried to introduce fixed axles, but although the greatest care has been taken in the manufacture, both in boring the hole in the nave, and turning the axle, yet a lateral shaking has always been found to take place, throwing the carriages off the rail on very moderate curves.

The quantity of inclination which the cone of the wheels should have, will, strictly speaking, depend on the radius of the curve. But, as half an inch on 3½ inches in width, or 1-7th of the width is found to be practically advantageous, in keeping the flanges of the wheels from rubbing against the rails in straight lines; and, as by raising the outer rail, the effect of gravity may at any given velocity be made to neutralize the centrifugal force, that inclination of the tire of the wheel may be adopted, except in very extraordinary cases. With this slope, and a wheel of three feet in diameter running on a line of rails 4 feet 8½ inches in width, with a play of one inch, Mr. Pambour gives the following table of the elevation necessary in the outside rail:

| Radius of the curve in feet | Surplus elevation of the outside rail | |-----------------------------|-------------------------------------| | | At 10 miles an hour | At 20 miles an hour | At 30 miles an hour | | 250 | 1·14 | 5·60 | 12·99 | | 500 | 0·57 | 2·83 | 6·56 | | 1000 | 0·29 | 1·43 | 3·30 | | 2000 | 0·15 | 0·71 | 1·65 | | 3000 | 0·10 | 0·47 | 1·10 | | 4000 | 0·07 | 0·36 | 0·83 | | 5000 | 0·06 | 0·28 | 0·66 |

To enable this calculation to be made for any other inclination, or suitable curves to be made where the inclination is determined, we shall explain the method of investigating the subject.

The resistance on curves is of two kinds, one from the carriage having to turn on the rail without any corresponding play on the axle, thus producing a dragging of the wheel, which takes place on that which is going over the inner part of the curve; and, secondly, that which arises from the centrifugal force, and which causes a friction to take place between the flange of the wheel and the rail. To correct these, the inclination of the coned wheel, the radius of the curve, the velocity and the elevation of one side of the line of rails, must have definite relations, and the wheels must have sufficient play between the two rails to admit the centrifugal force without being able to induce the second resistance, yet under given conditions to correct the first.

To arrive at this result, whilst the outside wheel of the carriage describes the arc \( mm' \), (fig. 22,) the inside one must describe the arc \( nn' \) terminating at the same radius; the working circumference of the wheels must therefore be represented by these arcs, and putting

\( D=\) diameter of the outside wheel, \( D'=\) diameter of the inside wheel, \( r=\) the ratio of the circumference to the diameter, we have

\[ \frac{mm'}{nn'} = \frac{\pi D}{\pi D'} \]

Also, as the two arcs are terminated by the same radii, we have

\[ \frac{mm'}{nn'} = \frac{mo}{no'} \]

and if we put the radius of curvature (\( rr' \)) and the half breadth of the road \( e \), the above proportion will become

\[ \frac{mm'}{nn'} = \frac{r+e}{r-e} \]

or

\[ \frac{D}{D'} = \frac{r+e}{r-e} \]

and

\[ D-D' = D\left(1-\frac{r-e}{r+e}\right) = \frac{2eD}{r+e} \]

which gives the difference necessary in the diameters of the curves.

Railways—wheels, in order to produce the required effect; and in order to know what lateral play must be had, if we take the inclination of the tire at \( \frac{1}{a} \), we find this to be

\[ \frac{1}{2} a (D - D') \]

and substituting for \( D - D' \), its value found above, we have the lateral motion equal to

\[ \frac{aeD}{2(r+e)} \]

We have now to obtain the necessary displacement by means of the centrifugal force, and for this purpose putting \( r = \) radius of curvature,

\( V = \) velocity,

\( m = \) mass of the moving body,

\( g = 32 \frac{1}{3} \), or the accelerating force of gravitation in 1 second,

\( f = \) the centrifugal force produced on the curve,

we have \( f = \frac{V^2}{r} \),

but \( P = \) the weight of the same body, we have

\[ P = gm, \]

or

\[ m = \frac{P}{g}, \]

and

\[ f = \frac{PV^2}{gr}; \]

making a foot in each case for the unit of space, and a second for the unit of time, we get the measure of the centrifugal force represented by its proportion to the weight \( P \).

Thus on a curve of 500 feet radius, at a velocity of 20 miles an hour, or 29-25 feet per second, we have

\[ f = P \cdot \frac{29-25^2}{32 \cdot 500} \]

or about \( \frac{1}{6} P \), the effect of which force in the direction of the radius, will of course be to press the carriages against the outside rail till the flange of the wheel stops them; and the elevation of the outer rail must be such that the centrifugal force is so balanced by the natural tendency from gravitation, by which the carriages would slide towards the inner rail, that the coned wheel corrects the effect of curvature without producing a friction on the flange,

calling \( y = \) the elevation of the outside rail,

\( 2e = \) the breadth of the way,

the inclination of the plane on which the carriage wheels are placed, will be

\[ \frac{y}{2e}, \]

and the gravity of a body weighing \( P \), will be

\[ \frac{Py}{2e}, \]

and this force tending to bring the carriages towards the inner rail while the centrifugal force \( \left( \frac{PV^2}{gr} \right) \) occasion them to approach the outer one, the height \( y \) of the outer rail above the inner one, if we wish the carriages to run in the middle of the rails, must evidently be taken, so that

\[ \frac{Py}{2e} = \frac{Pe^2}{gr}, \]

in which case we have an equilibrium between the two forces. But we require a tendency outwards to correct for the curvature, putting this \( = \mu \), we get

\[ \mu = \frac{aeD}{2(r+e)} \]

If we suppose this lateral displacement to have taken place, the inclination of the plane on which the carriages will be, Railways, is

\[ \frac{y}{2e-\mu}, \]

whilst, at the same time, from the coned form of the wheels, the tire having an inclination \( \frac{1}{a} \), this lateral deviation to the extent \( \mu \), has produced a difference of height in both wheels amounting to \( \pm \frac{\mu}{a} \); that is to say, the outer wheel will be raised \( \frac{\mu}{a} \) and the inner wheel lowered \( \frac{\mu}{a} \), and the result or total inclination \( \frac{2\mu}{a} \) will have to be added to that which has been produced by the difference between the height of the rails, hence, the outer wheel will be raised

\[ \frac{y + \frac{2\mu}{a}}{2e-\mu}; \]

and as the base between the bearing points is \( 2e-\mu \), the carriage will be on a plane equal to

\[ \frac{y + \frac{2\mu}{a}}{2e-\mu} \]

consequently to establish the equilibrium between gravitation and the centrifugal force required in practice, we must have

\[ \frac{y + \frac{2\mu}{a}}{2e-\mu} = \frac{PV^2}{gr}, \]

whence

\[ y = \frac{2V^2e + V^2a - 2agr}{gr} = \frac{2V^2e}{gr} + \frac{V^2a}{gr} - \frac{2\mu}{a} = \frac{eV^2}{gr} \left( 2 - \frac{aD}{2(r+e)} \right) - \frac{eD}{r+e}, \]

by which formula the table of surplus elevation for the outer rail has been computed, and of course the value of the radius of curvature, or any other element may be found, the others being given. As an example of the calculation, let us take the inclination of the wheel, or \( \frac{1}{a} = \frac{1}{2} \); the velocity \( = 29-25 \) feet per second; the breadth of the way \( = 4 \) feet \( 8 \frac{1}{2} \) inches, or \( = 2-3542 \) feet, \( D = 3 \) feet, when properly situated on the rail, and \( r = 500 \) feet, we then have

with \( g = \frac{193}{6} \),

\[ y = \frac{23542 \cdot 29-25^2}{193 \cdot 500} \left( 2 - \frac{7 \cdot 3}{2(500 + 23542)} \right) \frac{23542 \cdot 3}{500 + 23542} = \frac{23542 \cdot 8555625}{96500} \left( 2 - \frac{21}{10047084} \right) \frac{70626}{5023542} = \frac{23542 \cdot 8555625 \cdot 6}{95500} \left( 2 - 0.0209006 \right) - 0.014059 = \frac{23542 \cdot 5133375}{96500} \cdot 1.9790994 - 0.014059 = \frac{12084991425}{96500} \cdot 1.9790994 - 0.014059 = 0.125233 \cdot 1.9790994 - 0.014059 = 0.247848 - 0.014059 = 0.233789 \text{ feet, or } 2.8 \text{ inches.} \] We have here supposed \(a = \frac{1}{7}\), or the inclination of the tire of the wheel to be \(\frac{1}{7}\); but it is evident this must be such, that no rubbing of the flange will be produced on any curve on the line. We obtain this from the equation

\[ \mu = \frac{aeD}{2(r-e)} \]

We first establish the play between the rails. Allow this to be two inches, or that the flanges of the wheels in their regular position are 1 inch from the rails; then \(a\) must never be quite equal to 1 inch, and if we give \(r\) in the last equation above, its numerical value for the worst curve on the line, and to \(a\) its limit, a small quantity less than half the play of the wheels, we obtain the value of \(a\), which we must use on that line, as follows:

\[ a = \frac{2e(r+e)}{cD} \]

For instance, with half the play = 1 inch, or 0.833 feet and \(r = 0.9\) inches, or 0.75 feet, we have \(a = \frac{75.3525}{7.0626} = 10.669\)

or the inclination of the cone \(= \frac{1}{10.67}\) of a foot; observing that if we have only one or two bad curves, we must examine whether we may not admit a little rubbing on them for a corresponding gain on the good ones. This investigation will show how necessary it is that the play of the axles on the carriages should be as small as can possibly be, or the effect of the coned wheels will be completely deranged.

This is a matter which is much too little attended to in practice.

There is nothing in a railway which demands such serious attention as the stations, both as to their numbers, position, and the mode of constructing them. The number and situation will of course be mainly determined by the nature and extent of the surrounding population; and the first step should be to get a good map of all the places within the sphere of the railway, and to mark upon it the population of each place from the last parliamentary census; bearing in mind, that taking, for the present, railway-travelling to be twice as fast at half the cost of coach travelling, that a very wide portion of country will receive the benefit of a long line. We have explained this before; but that it may be perfectly understood, we shall shortly advert to it in a different shape.

For instance, suppose a line 100 miles long, and a person 50 miles at right angles to one end of it, who wants to go to the other end. If he travelled in a stage-coach along the hypotenuse of the triangle, he would go about 112 miles, say at 4d. per mile, his total cost would be L1.17s. 4d., and his time expended about 11 hours. On the contrary, if he came first to the terminus of the railway nearest him, and then went along the railway to the other terminus, he would have first 50 miles in a stage-coach at 4d., or 16s. 8d., with an expenditure of time equal to 5 hours, and then 109 miles by the railway at 2d., or 16s. 8d. more in 5 hours, the total time being 10 hours, and the total expense L1.13s. 4d., consequently he would save 4s. in money, and 1 hour in time, by taking the longest road.

There is no doubt but that the greater the number of stations, the more the travelling will increase; for it has always been hitherto found that the quick and cheap transit by a railway has not only increased the already existing traffic, but has actually created it where no traces could be found of it before. The nature of the produce, and the state of trade should also be taken into account in determining both the number and the situation of the stations.

The minor stations along the line may be divided into two classes. The first might consist of merely one room, serving for office and waiting-room, where nothing but passengers and small parcels are sent either up or down. Such stations would do for small villages or points where only a limited traffic is expected. We do not, however, recommend these, although they are used on several railways. All passengers pay alike, and they are therefore entitled to the same accommodation. The other class should be a house containing an office, waiting-room in common, or which is better, one for each class of passengers, ladies' waiting-room, and two rooms for the inspector of police to reside in, a small office for the police, and a porter's room. To this would have to be added, if water was required to be pumped, a steam-engine, and the requisite room for the engineer, a locomotive engine-house when necessary, and a covered space for holding spare carriages, trucks, horse-boxes, &c., together with the requisite sheds, and an office for the goods department.

The entrance to the station should be protected from the weather, so that when carriages drive up, the passengers can alight under shelter, and there should be a platform next the railway, about the same height as the carriage floors, so that the passengers can walk into the railway-carriages without having to climb up the steps. Arrangements should be made, for the passengers who are going into the carriages to go all upon one side, and those going out should get out from the other side; for which purpose the entrance should be on one side of the railway, and the exit on the other side. A light roof should be thrown over both lines of rails and their stages; in fact, the passengers should be entirely under cover from the time of leaving the vehicles which bring them to the station, till the time the train takes them away. This occasions very little expense, and is a great addition both to health and comfort.

For such a station two clerks would be required, one for passengers, parcels, and private carriages, the other for goods. The mode of conducting the business we shall advert to in its proper place. An inspector, and about four policemen, with porters, according to the extent of the traffic, would probably be sufficient; the whole should be well lighted up with gas, if it can be conveniently got; and it would much conduce to the comfort of the passengers, particularly ladies, if a decent female attended in the waiting-room, and had for sale pastry, biscuits, or sandwiches, with lemonade and ginger beer.

Great care should be taken at each out-station, that the following things can all be simultaneously performed, viz. First, that the train can be setting down passengers on the one side who are going to remain; secondly, taking up passengers on the other side who are going on; and this on both lines; thirdly, that the engine can be taking in coke and water, and also raking her fire, for which purpose, a small coke store should be built close to the water crane, and an ash pit properly excavated in the requisite position; and, lastly, that horses and private carriages can be in a situation to enable them to be attached to and detached from the train, at the same time as the other things enumerated above are being done. It will also be requisite, that the same care be taken at the goods' station, but goods' waggons should also be able to be attached to and detached from passengers' trains, as they will often be useful, when the traffic in passengers runs a good deal one way, in completing the load of the engine, and economising the outlay in locomotive power.

To explain how this is to be done, let us suppose a line of railway running north and south, and that the east line of rails is that by which the trains arrive when going from north to south, and the west line of rails is that by which they arrive when going from south to north. For the east line of rails, the water crane should be so far to the south of the station, that with an average number of carriages in the train, when the tender is under the crane, the middle of the train is opposite the station house. The position of the crane fixes that of the ash pit and coke store. The passengers alighting get down from the west side of the carriages, and go out from the west side of the railway. The passengers who are getting up, do so on the east side of the carriages, and come to the carriages from the east side of the railway.

The horses and carriages which are to leave the train, must, of course, be at the end of it. These, when detached, are to be run back, or to the northward, where a turnplate should be fixed to take them up by the cross line, to the spot where they are to be landed. This spot, which should be a third line of rails farther east, should be so far to the northward of the station house, that a siding can be run from the third or extra line of rails into the main east line, so as to be clear of the end of the train; and on this siding should be the embarked carriages which are to join the train. On the west side of the railway, there should be another additional line of rails, with a cross line from it to the place where the carriages are embarked. Along this line the goods may be brought. It will be readily seen that all the required objects will be effected by this arrangement.

For the western line, the water crane should be sufficiently to the north of the station, to allow the centre of an average train to be opposite the station-house, when the tender is under the crane. The ash-pit and coke-store arc, as in the previous case, regulated by the position of the crane. The passengers who are leaving the train, get out on the eastern side of the carriages, and leave the railway also on the eastern side. The passengers who are to join the train are waiting on the western side, and get into the carriages on that side. The horses and carriages which are to leave the train, are run back to the southward, past the siding from the west additional line by which those come on which are joining it, and are brought back to that siding, when clear of the carriages joining the train. By the siding they get on to the west additional line, and going to the northward, are taken across as soon as the train has left, and are disembarked at the proper spot.

Goods joining or leaving the train are managed exactly in the same way. Those which are to leave it being run back on the main line, till past the siding by which those come into the main line which are to join the train; and when these are clear, those which left the train are to be brought to the siding, and run into the goods' station. Proper waiting rooms for the passengers should, of course, be provided on each side of the railway, and their exit and entrance will be by stairs, either up or down, as the station is situated on an embankment or in a cutting. A foot-bridge may sometimes be thrown across with advantage.

There is such a decided convenience in having all stations on a level, that we should strongly recommend them to be placed so wherever it is at all practicable, even if there is some little sacrificed in another point of view; but this is a matter which will, in general, be so completely governed by the localities, that it may not be possible, in many cases, to attain it. When this happens, however, great care must be taken to make the approaches wide, and of a gentle slope.

As the works proceed towards completion, so many causes will arise to engage the engineers and directors, even without the occurrence of any particularly great accidents, that on all the leading questions time should be taken by the forelock. Springs of water, rock, and quicksands, will be met with where least expected perhaps, and the constant exertion of every talent will be required towards the close of the works. Good drainage will be most wanted when least at command; and work done with wet materials will be always slipping. Many times have embankments made of wet clayey earth slipped at all kinds of slopes; and although hundreds of cubic yards of dry material have been tipped on to them, they have been swallowed up and totally disappeared, whilst, at last, the only remedy to be found was weighting the slip itself with a sufficient quantity of earth to enable it to bear the embankment above.

When rock occurs at any height up the sides of an excavation, advantage may sometimes be taken of it to decrease the expense, by cutting only a sufficient width for the railway, and having no slope to the earth below the rock, but building up retaining walls from the railway below when bottomed out to the rock above, or what is called undersetting, an example of which may be seen at the great Blisworth cutting on the London and Birmingham railway. (See Plate CCCCXXVI. figs. 2, 3, 4.)

It will often happen that many parts of the permanent way are laid prior to its being possible to open either end of the line for traffic. These had better be kept in repair by the contractor; but when the line is once opened, or any part of it, for the purpose of travelling, it will be much the best way for the company themselves to keep it in order, taking especial care that the contractor repays them a proper price for so doing. The consequences of any accident by the engine or carriages getting thrown off the rails are so frightful, that no attention and expense can be thought too great which can prevent such an occurrence. We have seen instances in which carriages have undergone so complete a smash, that not a square foot of plank could be picked up anywhere.

A set of plate-layers consists of nine men for turnplates; twelve for laying rails; five for repairing the way; and six for laying in points and crossings.

To each set, the following tools will be required:

- 2 chisel-ended crowbars for drawing spikes. - 1 point-ended crowbar for moving rails, the point being put in the ground. - 1 claw-ended crowbar. - 1 cuddly or three-legged stand for the levers, so called from the name of the inventor. (Fig. 19.)

Fig. 19.

2 gauges for the distance between the rails. (Fig. 20.) 1 spirit level. (Fig. 21.)

Fig. 20. Fig. 21.

1 beetle, 6 inches diameter and 20 inches long, for drawing down sleepers. (Fig. 22.) 4 punning rammers. (Fig. 23.)

Fig. 22. Fig. 23.

2 adzes for trimming the sleepers to receive the chairs. (Fig. 24.) 2 levers. (Fig. 25.)

Fig. 24. Fig. 25. He should be very careful in bringing his engine down to the head of the train, where the connection should be made by a man specially appointed for the purpose. He should leave his condensed steam cock open as long as he can, being very cautious that it is shut just before the time of departure. During the journey he, in conjunction with his fireman, should keep a vigilant look-out for all signals of danger, watching each policeman as he approaches him till he has made his notification that all is in security along his part of the line. He must be attentive to stopping the train at the places ordered, and that he does not exceed the regulated speed, considering correctness of arrival his greatest aim, and consequently making up as far as he can in one part of his journey for any unavoidable detentions which may have arisen in other parts.

He should be very attentive to his water-gauge, and test it, whenever he thinks it necessary, by his guage-cock. This, however, should be done as little as possible if he have confidence in the water-gauge. He should never use his pumps without turning his pet-cocks, and ascertaining by them that every thing is working properly for the injection of the water; particularly when one pump has got out of order, that if anything should happen to the other he may instantly stop the engine and examine both of them, the necessary tools for which should be in his tool-box. He should always when practicable take the opportunity of pumping in water when going down inclinations, or at other favourable times. He should attend well to his rakings, and should be careful not to put on too much coke at once, unless he is very strong in steam; he should be constantly alert to the signals from the guard of the train, and ready to stop it in the shortest possible time when ordered to do so. The guard should have a check-string to the arm of the engine-man, and a flexible hollow tube should be fixed from the guard's carriage to the engine, through which the men can converse, which the noise of the engine and train will otherwise render difficult.

After completing his journey, and placing his engine near the engine-house over the ash pit, he should see the fire carefully raked out, and if his engine requires blowing off, he should take it to the proper place for doing so, and then apply for the necessary assistance to place it afterwards in the engine-house. But if it should not require to be blown off, he must of course proceed to the engine-house as soon as his fire is out, and having placed his engine in security, he should make his report to the foreman of all circumstances relative to the journey, and of any defects in the line, or in the engine, that he may have noticed, and the correct cause of all detentions which may have taken place. The engine should be examined and cleaned by proper persons appointed for that purpose; but this should not supersede the necessity of the engine-man personally investigating, before he starts on a journey, that every thing is in correct order. A great deal of expense in cleaning engines, as well as in their wear, would be saved by using a tarpaulin covering down each side from the boiler, to protect the machinery from rain. The engine-man should also have a fencing from the wet over the place where he stands.

The resident engineer who takes charge of the line when opened, should draw every thing by requisition from the storekeeper. The overseer should, in the first place, make out his weekly pay-bill, which should be checked by the time-book of the respective timekeepers; and when signed by the engineer, it should be forwarded to the audit-office, and the pay sent down to the booking-clerks of the adjacent stations, who should pay the men in the presence of the overseer, each man signing his name to attest the reception of the money. The necessary clerks and draftsmen for this part of the engineering department should also be paid weekly in the same way.

We have never yet seen a good mile mark on a railway; Mile marks The object apparently being merely to comply with the act of Parliament, certainly not to let the passengers see the miles, for the marks are generally so short, that all persons in the middle seats of the carriages have no chance whatever of seeing them. What we should recommend would be light iron posts having a box on the top. The box may be made triangular in its ground-plan, (Plate CCCCXXV. fig. 5,) and be about one foot in height, the apex of the most obtuse angle facing the railway. This angle should be so obtuse as merely to allow room in the box to hang a small lamp, and the two sides which form this angle being made of glass, should be painted or ground, except the figures, which are left clear. These shew the miles by day, and the nearest policeman lighting the lamp, they are also shewn at night. Or the planes forming the sides of the triangle next the railway may be of sheet iron, with the figures cut out of it, and merely that portion covered with glass; in either case the head must have a lid moving on a hinge. The height of these should be just half way up the carriage windows. In the cuttings, the post should be very short, and the mile mark set back on the slope. On the embankments it will be proportionally longer. It may have holes, or other ornaments, cast in its base, serving for steps to get up to light the lamp; or this may be done with projecting rings, and a slide may be made to receive coloured glass as a signal of any accident.

When such mile marks as these are not adopted, and it is desired to know the velocity of a train at night, this may be readily done whenever the blast pipe of the engine sounds sufficiently loud to be heard, which is generally the case in most engines. The way to ascertain the speed at which the train is going, will be to count every fourth puff from the blast pipe in ten seconds, this giving one revolution of the driving wheels, and the speed will be had by the following table:

| Blast pipe | Velocity—miles. | Velocity—miles. | |------------|----------------|----------------| | Number of fourth puffs in ten seconds. | Wheels, 5 feet diameter. | Wheels, 5½ feet diameter. | | 15 | 16-06 | 17-67 | | 16 | 17-14 | 18-85 | | 17 | 18-21 | 20-03 | | 18 | 19-28 | 21-21 | | 19 | 20-35 | 22-38 | | 20 | 21-42 | 23-56 | | 21 | 22-49 | 24-74 | | 22 | 23-56 | 25-92 | | 23 | 24-63 | 27-10 | | 24 | 25-70 | 28-27 | | 25 | 26-77 | 29-45 | | 26 | 27-85 | 30-63 | | 27 | 28-92 | 31-81 | | 28 | 29-99 | 32-99 | | 29 | 31-06 | 34-16 | | 30 | 32-13 | 35-34 |

The rapidity with which the cylinders of steam are expelled through the blast pipe, would at any common velocity prevent every puff being counted; but a very little practice will render the counting of every fourth one exceedingly easy, and the rate of going may always be found to the nearest half mile, by those who have only tried this method three or four times. A still easier method, although it will not generally be quite so accurate, is as follows: For five-feet wheels, count the number of fourth puffs in ten seconds and three quarters, and these will be the number of miles per hour the engine is going; and for five feet six wheels, count the number of fourth puffs in eleven seconds and three quarters. The exact number of seconds is 10-7 Railways, and 11-78. The method by the tables however is the best.

Paved crossings on a level with the railway are things to be avoided by all means whenever it is practicable to do so; but as some cases will arise where they cannot be done away with, we must render them as little liable to danger as possible. We have given drawings of these, (figs. 29, 30, and 31,) and an approved form of chair (fig. 28), which holds the rail, and also the two protecting irons, which should be laid next to the rails, in order that the wheels of those vehicles which cross the railway may not impinge upon the rails and injure them any more than can be helped. The whole crossing should be well paved with the usual road stones, and there must be strong gates on each side. These gates must be constructed so that when shut they may close up the road on either hand, and when open, may form a barrier across the railway.

The subject of lamps forms one to which attention is required, and we should recommend all railways to make a red light at night and a red flag by day, the symbols of danger. A green light should be placed at each station at the spot where the engine-man should slacken his speed, and a red light at the point where he is to stop. The police should have hand lanthorns, with a white glass and a red one, which latter can be turned round in an instant, whenever any thing obstructs the passage of the railway; and the light held up at any train approaching, on seeing which the train is immediately to stop. A green glass may also be added, the signification of which would be, proceed with caution; the train should then come slowly on and ascertain the reason for the signal.

For lighting the insides of the carriages, the roof lamps, contrived by the writer of this article, and patented, are the best. The frame is circular, about six inches in diameter, and about nine inches in height; the bottom is formed of a ground glass saucer, which is let through the roof of the coach, the top being protected by a box; on the inside is a small fountain lamp, on an improved principle, which is very nearly shadowless; the whole of the lamp body being above the frame, and the connection between them consisting of a tube of an inch in thickness, which tube should always be turned towards the carriage door. These give a soft mellow light, by which the passengers may easily read.

Point signals should be made in the following manner. The sliding rail, which forms the communication from one line of rails to the other, and which is moved by an eccentric, turned by a lever handle, should have, on the other side of the line, an iron rod from the rail, going into a box at its end with a pinion on it. This pinioned end of the rod turns a rack when the sliding rail is moved, which rack is contained in the box, and is fixed to a vertical rod, moveable in an upright post, similar to a lamp post, through the top of which, about four feet in height, the upper end of the rod comes out for about six inches, and is in this part made square. On this square part there is put a lamp by night, to show a white light when the points are right, and a red one when they are wrong; so that whenever the sliding rail is moved, it of necessity turns the light round, and cannot fail to place the different colours in front of the line of rails to which the signal is meant to apply.

In the day time the lamp is removed from the square, which, however, is not necessary, and the same signal is made visible by two circular hoops covered with canvas, one being painted red and the other white, and one being fixed on the top of the other at right angles to it; or the hoops may be one inside the other, at the same height and at right angles, nothing more being necessary than that the signal should be such that when combined in this way, the sliding rail can never move without the signal also moving, which should show white when the points are right, and red when they are wrong. These things, however, will never be properly correct till the engine itself is made to turn the points, which has often been tried, and is considered as having failed, but may certainly be done with ease and effect.

Self-acting alarms, with gong-shaped bells standing upright and fixed about twelve feet high to a wall, should be supplied to each station, and they should be wound up by men stationed at them, who may also act as policemen. These alarms are for the purpose of giving notice to the station-people of the arrival of a train. Two minutes are sufficient time in ordinary cases, and, with active men, one would suffice, and proper regulations must be established to ensure this space of time. On the train arriving at the proper spot, the man stationed at the alarm pulls a trigger, which allows a weight to descend. This turns a wheel, and this wheel works a pinion, to which is attached an eccentric, which gives motion to the clapper from side to side, and the alarm is struck by the hammer in the usual way, the man stationed at it being at liberty to attend to any other business the instant he has pulled the string. A large station-bell is also useful to summon all the persons to their posts at unusual times, in order to receive any unexpected trains, and for many other reasons. A bell should also run from the station office at the out-stations, to summon one or more porters inside the office.

A good means of preventing accidents would be, to have the engine-man in the front of the engine. If anything could ensure care, this would, the generality of engine-men being quite foolhardy; a defect which will never be remedied till we have a distinct class of men educated and brought up for engine-men from their youth, to whom should be given such a salary as would bring in young men of respectability.

In Plate CCCCXXV, fig. 3, we have given a plan of an invalid carriage, capable of containing four invalids and their four attendants. (a, a) are the seats for the passengers, one on each side of the first and second bodies of the carriage being for the invalid, and the opposite one, lengthways of the carriage, being for the attendant. When the invalid wishes for the use of the closet, he comes out by the door (b) into the middle part of the coach (d), which is a gallery with a raised roof, as in fig. 2. There are three portable water-closets (c) in this carriage, or the middle one, if thought more desirable, may be merely an urinal; the centre one, to whatever purpose it may be converted, is arrived at from the gallery by the door (e), and the right and left-hand clo-

sets by the doors (f) (f) respectively. The ventilation here would be very perfect, and no inconvenience whatever could arise to any one of the passengers. An attendant belonging to the railway company could attend on all the passengers remaining in the gallery (d) till his assistance was required, for which purpose a bell might be hung with pulls in each compartment. By this arrangement double the number of invalids could in each case be accommodated with a passage.

The following are the engines in use on the London and Birmingham railway, and which were made by Mr. Bury of Liverpool. The description here given applies to both the passenger and goods' engines, except when otherwise stated.

The two cylinders are to have an 18-inch stroke, those of the passenger engines being 12 inches, and the goods' engines 13 inches in diameter, with single slide valves, brass spring pistons, and cast iron packing; the cover of each cylinder having one oil cup. The boilers are made of the best Yorkshire plates, either Bowling or Lowmoor. The fire-boxes are of the same material, and are welded so as not to have the rivets or lap exposed immediately to the action of the fire. They are 3-8ths of an inch thick, the back plates half an inch, the outside of the fire-box and the backplate 3-8ths of an inch, and the rest of the boiler 5-8ths of an inch. Full-sized drawings are furnished to show how the plates are to be worked; the plate for the tubes at the smoke-box end is half an inch thick, and a lead plug, 5-8ths of an inch in diameter, is riveted in the crown of the fire-box.

The tubes are two inches in diameter inside, and are secured with steel hoops at the fire-box end, and iron hoops at the chimney end. These hoops are made to a given gauge; and the tubes are of the best rolled brass, No. 14 wire gauge thick; the arrangement as well as the exact size of the tubes being regulated by a template.

The engines have four wheels; those for the passengers are 5½ and 4 feet in diameter, and those for the goods are each pair 5 feet in diameter. Each wheel has a cast iron centre; and the spokes are of wrought iron, accurately fitted into the nave. The tire consists of two thicknesses, the inner being 3-4ths of an inch when finished, of the best Staffordshire iron, well secured to the end of the spokes by riveting; the ends of the spokes having been previously turned in their exact position. The outside tire is made of the very best Bowling or Lowmoor iron 1½ inches thick when finished. When the outside of the inner tire has been well riveted to the spokes it is turned; and the inside of the outer tire having been accurately bored, so as to secure a perfect fit, it is then shrunk on, and the outside turned and finished. The naves are bored out, and the axles turned to fit; they are secured on by two steel keys, one inch square, at right angles with each other. The goods' engine wheels are connected on the outside by a rod, with a ball pin at one end, and a parallel pin at the other. These engines have also a damper to their blast pipe.

The crank axles are made from Backbarrow iron, cut out of solid blocks, and finished according to full-sized drawings. The straight axles are made of the very best scrap iron. The framing of the engine is of wrought iron accurately fitted. There is one pump attached to each cross-head, and made of good tough brass, the suction pieces being connected by Macintosh hose pipes, with screw coupling joints next the engine. The eccentrics are fixed on the crank axles in the mode shown by drawings. The steam and exhausting pipes are of copper, No. 12 wire gauge in thickness. When these engines are made by other persons, templates and full-sized working drawings are given out, from which no deviation whatever is allowed without Mr. Bury's approbation, so as to secure all parts of the engines matching each other.

The top of the fire-box has a copper cover, No. 16 wire gauge thick, secured to the wooden covering on the lower

part of the fire-box and body of the boiler, by screws two inches apart. The wooden covering on the fire-box is finished to \( \frac{1}{2} \) inch thick, and is made fast to the boiler by two hoops; and round the fire door it is lined with thin sheet iron under the hoops; the sheets being 6 feet long, and 2 feet 3 inches broad, with a hole cut out for the furnace, and secured at the ends by screw nails 2 inches apart, to prevent the fire from burning the wood casing on the boiler. The casing on the barrel of the boiler is secured by four hoops, with a strip of brass under the fore-end hoop, about 2\( \frac{1}{2} \) inches in breadth, to cover the ends of the lining and the rivet heads at the junction of the barrel of the boiler, and the smoke-box. The boiler is wrapped in at least three thicknesses of flannel all over.

The lagging on the boiler is put together with iron feathers \( \frac{1}{2} \) by \( \frac{1}{2} \); the boiler is covered over the lagging with thin sheet lead, about 3\( \frac{1}{2} \) feet broad along the top of the barrel. The smoke-box is No. 7 wire gauge thick, and the chimney is No. 13 wire gauge. The cover on the lock-up safety valve is of brass, secured to the boiler; there is a brass frame round the door of the smoke-box, and a brass handle to the small door in the middle of the large one.

All the pins of the joints are of steel, and hardened when practicable, but if not, they are steeled and hardened, and the working parts of the engine, which are of iron, are case-hardened. In making the boilers, the sharp edges of the rivet holes are taken off on both sides, and the rivets and rivet heads made to correspond. The engines are furnished with a wooden guard, and two leather buffers stuffed with cotton flock; and there are a draw-bar, draw-pin, and loop in the centre of the wooden guard, to connect them to the tender. They have three water guage cocks, and a glass water guage, with a lamp stand; also a whistle, and a number plate on each side of the boiler; and they are furnished with a complete set of screw-keys.

All the screws in all the engines correspond, for which purpose, either master taps, or sets of stocks and dies, at the option of other makers, are furnished them by Mr. Bury. They receive two coats of paint, and are finished with two coats of the best varnish. They are guaranteed for one month, or 1000 miles, during which trial, no other work is allowed but the tightening of cotters, and the very best workmanship and materials that can be produced, are in all cases rigidly insisted on.

The framing of the tenders is of well-seasoned oak, or ash timber, thoroughly secured with iron knees and bolts, having an iron box, No. 7 wire gauge thick, underneath, to carry the coke, which box is secured to the wooden frame. The tank contains 700 gallons of water. The wheels are of cast-iron, turned to receive a tire of either Bowling or Lowmoor iron, bored out to secure a perfect fit, and finished to \( \frac{1}{2} \) inches thick. The axles are 3\( \frac{1}{2} \) inches in thickness, of the best hammered scrap iron; and the journals are 2\( \frac{1}{2} \) inches in diameter, case-hardened, with brass bushes and oil box.

The steadingment for the axles consists of two plates, one outside, and the other inside the framing; both of them being bolted through the framing, and secured together below, by a piece of iron between the plates for steadying the axle bushes. These are made completely parallel, and the bushes fitted into these so as to move up and down, but in no other direction. The tenders have buffers, a spring to which the load is attached, and also four springs by which they are supported, one over each oil box.

The tank is No. 10 wire gauge thick, having two brass cocks or valves, and rod handles with bushes for the top of the rods; also two copper pipes, 1\( \frac{1}{2} \) inches in diameter, for carrying water from the tender to the engine. The tender frame and tank have two coats of paint inside and out, and two coats of varnish. They are fitted up with a brake, and furnished with a complete tool box; a wire sieve in the main hole of the tank to prevent dirt or water from getting into the tank; and two Macintosh hose pipes, one to each suction piece, with the necessary connexion to attach them to the engine.

When water requires to be pumped from the tender into the boiler of the engine, previous to the starting of the train, it is the usual practice to run the engine backwards and forwards for a short distance, in order to work the force pumps. This increases the wear and tear both of the engine and the road, besides inducing a liability in a crowded station of running foul of something, if great care be not taken. The following contrivance will obviate the necessity of this inconvenient method of filling the boiler. A square pit should be sunk in some convenient part of the line, selected with reference to its intended use. This pit should be large enough to admit a pair of three-feet wheels fixed on an axle similar to the carriage wheels. There should be no flanges, and a part of the circumference of these wheels should come up through the rails, which must be cut so as to admit them, additional chairs being put in to support the ends of the rails. This part of the circumference of the wheels thus becomes a part of the railway, the wheels being made to lock at pleasure; but when the engine requires to pump water into the boiler, it must be brought with its driving wheels directly on those in the pit, and these latter being then unlocked, the steam is let gradually on, and the pumps worked as long as is found necessary to fill the boiler, without the engine advancing from the exact spot in which it was first placed, the only effect produced by the driving wheels of the engine, being to turn round the wheels fixed in the pit. When the boiler is filled, the pit wheels are locked, and the engine proceeds to the performance of her assigned duty. How much more advantageous this mode of filling the boiler is, will be readily seen, particularly when it is remembered that if engine-men are not looked well after, they will oil the driving wheels and the rails when in the engine-house, and then letting on the steam, fill their boiler by means of the wheels slipping round on the rails. We have often seen this carried to such an extent, that streams of sparks have been struck out by the attrition. When no better plan can be obtained, the engine should have one end lifted by screw-jacks, till the driving wheels are off the rails, and the steam may then be let on without any damage being done.

The Caliban engine, made by Sharp, Roberts, and Company, of Manchester, drew 80 tons up an inclination of 1 in 180, on the Grand Junction Railway, for 3\( \frac{1}{2} \) miles, at 13\( \frac{1}{2} \) miles per hour, at a steam pressure of 50 lbs. per square inch, and with a consumption of coke of 480 lbs. The average of 14 trips of three quarters of a mile each, up 1 in 90, from Euston Square to Camden Town, on the London and Birmingham railway, with the great engine made by Robert Stephenson and Company to work the trains up the inclination till the fixed engine was ready, amounted to 15 miles an hour, with 70 tons, viz. 14 carriages and 148 passengers, at a steam pressure of 50 lbs. per square inch. The average of 12 trips of 24\( \frac{1}{2} \) miles, up 1 in 440, on the Grand Junction Railway, with six engines, three made by Robert Stephenson and Company, and three by Sharp, Roberts, and Company, was 23\( \frac{1}{2} \) miles per hour, with a weight of 58 tons. The coke consumed was 864 lbs., and the steam power 48 lbs. per square inch; this coke, however, was very bad. The average of 14 trips of 23 miles, up 1 in 440, on the London and Birmingham line, with No. 16 engine, built by Mr. Hawthorn of Newcastle, was 22 miles an hour, with a gross weight, including the tender, of 70 tons. The coke consumed was 486 lbs., and the steam pressure 48. The engine No. 7, on the London and Birmingham line, built by Mr. Bury of Liverpool, went 10 miles in ten minutes, 3rd October 1838, with only one cylinder working, namely, from Hampton to Birmingham, being for 4\( \frac{1}{2} \) miles, up 1 in 660, 3\( \frac{1}{2} \) miles, up 1 in 1370; the rest of the way was level, and the time included the getting up and slackening down the speed. Whilst such machines as these can be turned out of hand, we may rest satisfied, although considerable improvements will doubtless be yet made; great difference of opinion still existing respecting the proper size of the driving wheels, which may either be made larger to give an increased speed, or keeping the speed the same, the piston may move with less velocity, either of which is a desideratum. The crank axle may also be done away with, as Dr. Church has exemplified in his engine, or by other means, or it may be cut out of solid iron. At present, too, the steam whistle, which can be heard several miles in a still day, is only made use of to warn persons of the time when the engine is approaching them. How much better would it be to have two of these with totally distinct sounds, one to be used on the arrival line, and the other on the departure line? Each would then not only perform its present office as an alarm, but would form the most complete fog and night signal that could be desired, and would at all times, in the densest fog or the darkest night, give perfect notice whenever two engines approached each other, on which line each was travelling, and thus prevent almost the possibility of a collision.

There has so seldom been an instance of a locomotive engine boiler bursting, that it is perhaps hardly necessary to advert to such an accident. We know only of two amongst the tubular boilers. One happened lately on the Liverpool and Manchester Railway, apparently from the boiler being used till the rivets got so worn, that they were weaker than the tubes. The fire-box end of the boiler was blown out, and the above is the only way of accounting for it, as tubes must always bear a steam of 50 lbs. on the square inch. Of course when new, they bear considerably more, and their form gives every advantage to their strength, the pressure on them being inwards, whilst on the boiler it is outwards. It is also known that the safety valve was held down. The second instance occurred on the Brussels railroad. In this case, the lock-up safety valve was found to be loaded to 105 lbs. upon the square inch; and it had also been screwed down more on one side than on the other. These valves are held down by a series of elliptical springs, which move on a guide rod passing through their centres. When they are not screwed down equally on both sides, their position becomes diagonal, and they jam on the guide road instead of working easily, as they do when rightly managed. Safety, in all the usual cases, is insured by having a fusible plug on the top of the fire-box, composed of four parts lead and one part tin. This will melt before any danger can arise, and the steam will rush into the furnace. The late American experiments on this head may be consulted with advantage; but the mystery has not yet been unravelled. We have had an open vat burst in Meux's brewery; and in two instances boilers have been suffered to get quite cold. The man-hole has then been opened, and a person has gone inside, but soon afterwards, in each instance, upon their introducing a lighted candle, explosions took place, and they were in both cases killed. Gas generated by boilers getting red hot, and absorbing the oxygen, has been supposed to be a leading cause; this, however, is exceedingly doubtful. If such be the case, it might be well to try protecting them by means of another metal. It would also be a good thing to rotate the safety valve, which is locked up from the engine-man, by machinery, to prevent any improper adhesion, and by using a mercurial steam gauge, nearly all blowing-off at the safety valve might be avoided, which now often amounts to one-fourth of the generated steam. The boiler tubes, as now made, are capable of running 30,000 miles. The want of adhesion so much talked of, is found to be nonsense, and if there had been any, it would only be necessary, as the writer of this article suggested several years ago, to connect a galvanic magnet with one or more of the axles, to act on the rails, by which means, with the addition of only a few pounds, an adhesion equivalent to the weight of two tons could be produced at each axle, being capable also of acting or not at a moment's notice. But there is always found to be sufficient adhesion, except sometimes in foggy weather, at first starting; when once in motion, the train acts as a fly-wheel. We have no hesitation in saying, that electro-magnetism will at no distant day compete with steam as a motive power, and successfully.

We are yet, however, very ignorant not only of the powers steam, but even of the nature of steam. No one can satisfactorily prove whether it is a mechanical division of water, or a chemical decomposition. The currents which take place in water whilst it is heating, and which are reversed when it cools, are not yet taken sufficient advantage of, and there are many other facts which require examination. It is well known, that if we put on our bare hand, an iron kettle of water boiling rapidly we feel no sensation of heat, but the moment the ebullition ceases, we feel a gradually increasing warmth, which is greatest at the edge of the bottom. When the bottom, well cleaned, is placed almost in contact with the bulb of a thermometer, it will only raise it $8^\circ$ or $10^\circ$ in thirty seconds, or about $40^\circ$ in five or six minutes, although the water, at the expiration of that time, will be at $90^\circ$ higher. With an earthenware pot, the difference is very great, the thermometer rising $100^\circ$ in thirty seconds, instead of $8^\circ$ or $10^\circ$. A drop of water placed in a metal vessel, at a white heat, is very slowly converted into steam, whilst at a lower temperature its conversion is so rapid, as almost to resemble an explosion. At the high temperature, it will spin round, and will take nearly a minute to evaporate, during which time, if it be turned into the hand, it will barely feel warm.

The experiments made by the committee of the Franklin Institute of Pennsylvania, are well worth consulting on these subjects. It is there shown, that a drop of water on polished copper, at the temperature of $445^\circ$, took $210$ seconds before it was converted into vapour. It was evaporated in the smallest time, at a temperature of $292^\circ$, at which it took three seconds. But when the copper, instead of being highly polished, was highly oxidated, the temperature of maximum evaporation was at $348^\circ$, and the time required to convert the drop into steam only one-fourth of a second, or as $12$ to $1$; whilst in iron the temperature suffered but little variation, whatever was the condition of the metal, except it was very highly oxidated, the iron having its highest evaporating points in this case about $35^\circ$ above copper in the same condition. The time varied nearly in the ratio of the conducting power of the metals, or about $2\frac{1}{4}$ to $1$, the copper requiring the least.

At $20^\circ$ to $40^\circ$ above the point of maximum vapourisation there is a perfect repulsion between the drop of water and the heated metal, the former rotating in all directions, without wetting the metal. When larger quantities of water were used, the point of maximum vaporisation was much higher; which renders it evident that locomotive engines have yet to be considerably altered, before they can work at the greatest advantage. The same experiments shew, that water injected, either hot or cold, into an engine boiler, heated to bright redness, produced no hydrogen, but that the resulting gas was nothing more than atmospherical air, deprived by the heated metal of more or less of its oxygen; that is to say, nitrogen more or less pure, according to the quantity of oxygen which has been absorbed.

The nature of the most advantageous alloys for the fusible plugs of locomotive or other high-pressure boilers, has plugs been carefully examined by the same committee, and the following table is deduced from their observations, the stationary point being that of congelation.

The proportions are by weight throughout. The stationary points are not given for the ten latter alloys, but the decrease in temperature by which they became "hard solid," on the surface we presume, was as follows, viz. $25^\circ$, $24^\circ$, $20^\circ$. The practice of putting two engines to a train is not considered so good as dividing the train into two, and putting one engine to each. Whatever may be the objections to the latter plan, those who argue in this way assert that no two engines will have their wheels mathematically accurate as to size, and if they had, still their rate of working, depending as it does on so many elements, would always prevent their velocity being precisely the same, except for a short time, by mere chance; and when this is not the case, a most destructive rubbing immediately takes place. When two are working together, for instance, with driving wheels 5 feet 6 inches in diameter, the circumference will be 17-2787 feet, and at a speed of 40 miles an hour, which is 211200 feet, or 3520 feet per minute, equal to 5866 feet per second, these wheels must revolve 12223 times in an hour, or 20371 times per minute, equal to 3395 times per second.

Now, if we only take half this velocity, or 20 miles an hour, or 105600 feet for the one engine, and 19 or 21 miles, or 100320 and 110880 feet respectively for the other, we have at once a rubbing motion of no less than 5280 feet per hour, or one mile in twenty, with a rubbing instead of a rolling motion. In fact, the rubbing will always be equivalent to the difference between the velocities of the two engines, and the loss of power, the wear and tear; and the injury to the machinery by the extra steam which must be brought on all the working parts, if the above be true, may readily be imagined. A self-registering counter, fixed to ascertain the number of strokes, would easily settle this point; to do which, it must trace the work of each engine on paper, similarly to the self-acting anemometer of Mr. Osler of Birmingham. But for our own parts no proof is required. We are certain it is not the case, and that the speed of both engines becomes equalized almost immediately after they start; that engine which would travel the fastest, doing the largest proportion of the work, and thus relieving the pistons of the other, by drawing her along at her own rate, as she would, in fact, if the steam were shut off altogether. A strong man and a weak man working at a winch is an exactly similar case.

Before long there is no doubt that signals will be established along all considerable lines of railway. The use of them is sufficiently obvious, and they might be turned to profit also, by conveying messages of all kinds, at the rate of so much per word; they would thus, instead of being a cost to the railway company, become a source of emolument. Communications throughout a length of 100 miles, when they can be made at one signal from each station, would be transmitted in about a minute and a quarter, and any ordinary message out of the usual course in about half an hour; a telegraph would be prevented from working by the weather, about two months a-year in the aggregate.

There is nothing so easy as to make a telegraph book; in fact, it is only numbering a dictionary, and the thing is done, book. In fact, hundreds of messages may be sent on the usual address of a newspaper, without the possibility of the post-office being at all aware of anything of the kind being carried on. In the case of a railway, each head of the different departments should send in lists of the various messages most likely to be wanted, and these could be added to, as time develops what is required.

The original expense of such a thing would probably be about L260 each station, and the annual expense about L77 per station; to which would have to be added the salary of the superintendent, clerks, and a few supernumerary men. Their great use renders them most desirable things. For instance, an accident happens to an engine ten miles from an engine station. The telegraph would send out another engine in a minute, with any commonly good look-out; whereas, to send on foot would require two hours, thus deranging the time of all the succeeding trains. As another instance, a train starting from one end to the other of the line, perhaps leaves 50 passengers at some intermediate town; the telegraph might immediately make this known to the clerk of that station, who, if he had few passengers ready for the train, could prepare goods' waggons to put on, so that the engine should not go with half a load; a matter of great importance, for the power absorbed by an engine before it can put itself in motion, being one-third of its whole power, it follows that the relative expenditure of power per ton per mile, is nearly six times greater with a load of 10 tons than it would be with a load of 100 tons.

When accidents do happen upon railways, they may generally be expected to be extremely serious, and no means should be left unprovided, for immediate assistance being dispatched; even an advice carriage, which might be worked at 20 miles an hour, would be but a slow method, compared with a telegraph, for instance, if medical assistance, or what is more likely, surgical assistance, was wanted. In many cases, it will be highly advantageous, particularly in a pecuniary point of view, to run trains at different velocities, passing each other by means of sidings, the expense of locomotive transport increasing so much with an increased velocity. This desirable method will no doubt eventually be much practised. It would be almost impossible without a telegraph.

The effects of high wind upon a train, especially a side-wind, which binds the flanges of the wheels against the rails, and very much impedes the velocity, as well as increasing the wear and tear, renders it a desirable thing to have its force measured at all the principal stations, so that whenever it exceeds a certain standard, to be determined by experiment, a second engine may be sent out to assist the train. The most complete instrument for this purpose is the anemometer, invented by Mr. Osler of Birmingham, now used at the Philosophical Institution of that town, at Plymouth, and in other places. This also combines so many other arrangements, as well as that for measuring the force of the wind, each of which it transfers by machinery to paper, that it is in fact the heavens registering themselves, and for a cost of about L50 leaves nothing to desire.

For railway purposes merely, a more simple contrivance will be sufficient, although the cost will not be very materially decreased, if it be fitted up with the requisite attention to convenience as well as accuracy. For instance, if a vane with a long tail, high above the top of the engine-house, and having at its point end a board one foot square, be fitted up in the following manner, it will be sufficient for all the wants of the locomotive department. The vane should be fixed on a hollow pole, which should turn with it and descend through a tube down to about five feet of the floor of the engine-house, where there should be a horizontal dial-plate, on which should traverse a pointer fixed to the vane-pole. This pointer would always indicate the direction of the wind; and in order to ascertain its force, the board, one foot square, on the pointing end of the vane, should act on a spiral spring, and work a drum by a wheel and pinion, communicating by a cord, with a similar drum at the bottom of the vane-pole, where a vertical dial-plate should be fixed, on the outside, and opposite to the lower drum, on which a hand traversing round the vertical dial-plate would shew the force of the wind.

According to the power of the engine, and the nature of the usual traffic, experience will soon point out when a second engine ought to be dispatched; and a table being formed for each point of the compass for this, should then be invariably acted on at all times, unless other local circumstances occasioned any alterations in the general average of the loads.

To estimate the force of the wind, we have, by the experiments of Dr. Hutton, a plane surface of one square foot, at a velocity of 20 feet per second, suffering a resistance of 12 ounces; and as it varies very nearly as the square of the velocity, we have in pounds, calling $f$ any other force, and $v$ the velocity,

$$\frac{3}{4} \cdot \sqrt{\frac{f}{v}} = 20 \text{ feet} : v \text{ feet},$$

and as the number of feet per second, multiplied by $\frac{6818}{2}$, produces the number of miles per hour, the above becomes, for miles,

$$\frac{3}{4} \cdot \sqrt{\frac{f}{v}} = 13.636 : v \text{ miles}.$$

or $$\frac{1732}{2} \cdot \sqrt{\frac{f}{v}} = 13.636 : v,$$

or $$\frac{866}{2} \cdot \sqrt{\frac{f}{v}} = 13.636 : v,$$

whence the velocity in miles per hour is

$$\frac{13.636}{866} \cdot \sqrt{\frac{f}{v}} = 15.746 \cdot \sqrt{\frac{f}{v}} = v,$$

and we have also sufficiently near

$$f = \frac{v^2}{248}.$$

Hence we obtain the results given in the following table:

| Velocity in miles per hour | Force of wind in avoirdupois pounds | Velocity in miles per hour | Force of wind in avoirdupois pounds | |---------------------------|-----------------------------------|---------------------------|-----------------------------------| | 10 | 0·4 | 50 | 10·1 | | 15 | 0·9 | 55 | 12·2 | | 20 | 1·6 | 60 | 14·5 | | 25 | 2·5 | 70 | 19·7 | | 30 | 3·6 | 80 | 25·8 | | 35 | 4·9 | 90 | 32·7 | | 40 | 6·5 | 100 | 40·3 | | 45 | 8·2 | | |

and for every useful purpose, the force may be had within $\frac{1}{4}$th of the above by using this simple formula,

$$f = \frac{0·04v^2}{248}.$$

So much has been said about the inconvenience and danger of tunnels, that it is necessary, whilst there are yet so many railways to be called into existence, to state that there is positively no inconvenience whatever in them, except the change from day-light to lamp-light. This matter was clearly investigated and proved upon the London and Birmingham railway, a special inspection having been there made in the Primrose-hill tunnel by Dr. Paris and Dr. Watson, Messrs. Lawrence and Lucas, surgeons, and Mr. Phillips, lecturer on chemistry, who reported as follows:

"We, the undersigned, visited together, on the 20th of February 1837, the tunnel now in progress under Primrose-hill, with the view of ascertaining the probable effect of such tunnels upon the health and feelings of those who may traverse them. The tunnel is carried through clay, and is laid with brick-work. Its dimensions, as described to us, are as follows: height, 22 feet; length, 3750 feet; width, 22 feet. It is ventilated by five shafts, from 6 to 8 feet in diameter, their depth being 35 to 55 feet.

"The experiment was made under unfavourable circumstances; the western extremity being only partially open, the ventilation is less perfect than it will be when the work is completed; the steam of the locomotive engine was also suffered to escape for twenty minutes, while the carriages were stationary, near the end of the tunnel; even during our stay near the unfinished end of the tunnel, where the engine remained stationary, although the cloud caused by the steam was visible near the roof, the air for many feet above our heads remained clear, and apparently unaffected by steam or effluvia of any kind; neither was there any damp or cold perceptible.

"We found the atmosphere of the tunnel dry, and of an agreeable temperature, and free from smell; the lamps of the carriages were lighted; and in our transit inwards and back again to the mouth of the tunnel, the sensation experienced was precisely that of travelling in a coach by night between the walls of a narrow street; the noise did not prevent easy conversation, nor appear to be much greater in the tunnel than in the open air.

"Judging from this experiment, and knowing the ease and certainty with which thorough ventilation may be effected, we are decidedly of opinion that the dangers incurred in passing through well-constructed tunnels are no greater than those incurred in ordinary travelling upon an open railway, or upon a turnpike road, and that the apprehensions which have been expressed, that such tunnels are likely to prove detrimental to the health, or inconvenient to the feelings of those who may go through them, are perfectly futile and groundless."

The above will, of course, set the question at rest, especially as the Leeds and Selby tunnel, only 17 feet in height, and 700 feet in length, is found to produce no inconvenience; and as any persons may now try the experiment themselves. on longer tunnels than even that at Primrose-hill. We may instance the tunnel near Kilsby, on the London and Birmingham railway, which is 2425 yards long, and traversed without the slightest inconvenience or sensation of cold or damp; the change experienced being merely that from sunshine to shade, and from daylight to lamplight, and this latter only in those seasons of the year when the days are considerably longer than the nights.

The quantity of friction in well-formed carriages we consider as certainly not more than 8 lbs. per ton; but as about 9-3 lbs., or \( \frac{1}{10} \)th of the weight, will perhaps be a more general average, we here give a table for the total resistance arising from gravity and friction, calculated from the following formula:

\[ G + F = \sin I + \frac{H}{L} + \frac{F}{L} \]

where \( G \) is the effect of gravity, the weight being taken as unity, \( I \) the inclination of the plane, \( H \) its height, \( L \) its length, and \( F \) the friction, the numbers in the table being the values of the right-hand member of the equation.

### Inclination of the Plane Equal to 1 in

| Inclination | Load in tons for each ton adhesion | |-------------|-----------------------------------| | 0 | 0 | | 10 | 0.04167 | | 20 | 0.054167 | | 30 | 0.06757 | | 40 | 0.08107 | | 50 | 0.09557 | | 60 | 0.11007 | | 70 | 0.12457 | | 80 | 0.13907 | | 90 | 0.15357 |

For any lesser inclination, divide 1 by the length of the plane to a height of unity, or find \( \frac{H}{L} \), and add to the quotient in either case 0.04167.

To use the table, look along the upper column for the hundreds, and down the left-hand column for the tens of the rate of inclination; and at the point of intersection will be found a number which is to be multiplied by the total weight of the carriage and its load in lbs. for the total resistance. Thus for a carriage weighing 8000 lbs., at an inclination of 1 in 560, we have 8000 \(\times\) 0.059524 = 52.6192.

Calling \( W \) the weight of the carriage, the friction alone will vary from \( \frac{W}{550} \) to \( \frac{W}{200} \), according to the care with which it is constructed, and this may be divided into that arising from the wheels on the rails, or the rolling friction, which is a constant quantity, more or less, according to the strength, or the stiffness of the rails, \( \frac{W}{850} \), the remainder being due to the rubbing of axles on their bearings. A great deal depends upon the unguent used, both as it respects quantity and quality. A wheel loaded with from 1 to 4000 lbs., and turned on its axle on a half bearing by a weight and rope, which detached itself after falling 30 feet, leaving the wheel to revolve till its own friction brought it to rest, made 36 revolutions, when nearly deprived of oil, and 278 revolutions when the oil was heaped on that side of the bearing which the circumference of the axle approached as it turned round. The ratio of bearing surface of the axles has also a considerable effect. This should not exceed 90 lbs. per square inch, and the length of bearing should not be much less than twice the diameter of the axles. Under these circumstances, friction on railways will be uniform at all velocities with well made carriages, and will be in the ratio of the weight.

The friction of engines, without any load, and exclusive of the tenders, will be in the average ratio of the diameter of the wheels, and nearly as their weight; \( \frac{8}{5} \) tons, with five-feet wheels, being 15 lb. per ton; with a load, 1 lb. per ton must be added.

The friction of edge-rails to that of plate rails, is as 17.5 to 27.8. The wear and tear of ropes on inclined planes is about \( \frac{1}{4} \)d. per ton per mile; and their friction, either self-acting or with fixed engines, will vary from \( \frac{1}{3} \) to \( \frac{1}{2} \) of the weight of rope wheel and sheaves in action plus the pressure of the rope on the wheel. This quotient will have to be divided by the difference in diameter between the sheave and its pin, and an allowance must be made for any curves in the line of direction.

The adhesion of engines may be taken as at least equal Adhesion to \( \frac{1}{4} \)th part of the weight on the driving wheels. This will of engines enable them to draw in the following proportions for each ton of the weight under the most unfavourable circumstances, and may be much increased when the weather and all other circumstances are in the most advantageous state.

| Inclination | Load in tons for each ton adhesion | |------------|-----------------------------------| | 1 in 4480 | 26.25 | | ... 3360 | 24.21 | | ... 2240 | 23.58 | | ... 1680 | 22.40 | | ... 1120 | 21.33 | | ... 1000 | 20.86 | | ... 900 | 20.37 | | ... 800 | 19.88 | | ... 700 | 19.14 | | ... 600 | 18.31 |

In the common steam engine, the power is as the area of the piston, and the pressure of the steam on it. But in the locomotive engines this is not the case; for the power of raising steam in any quantity, which may always be had in a stationary engine by increasing either the size or the number of the boilers, has a limit in the locomotive, determined by the weight to which the engine must be restricted. The power in this case resides in the capability of the en- The locomotive power is rather more than one-fourth of a penny per ton per mile.

The maintenance of the way upon the Grand Junction railway, for eighty-two miles to Newton, has been let at £244 per mile, including rails, chairs, bridges, and everything. We have no doubt this is amply sufficient. They pay £20,000 a-year to the Liverpool and Manchester company for the use of their line and offices. The Great Western railway, under unfavourable circumstances, has been let at £416 per mile; and the repairs to the London and Southampton line are divided, the company finding all materials, and contracting for their labour only, for which they pay £140 per mile, including the use of tools. But the best data to found any calculation on this varying expenditure, are those contained in the reports published by the Directors of the Liverpool and Manchester railway, for the five half years ending the 30th of June 1834. We shall endeavour to set this calculation in its true light, which has not yet been done. The following are the various items of expenditure, exclusive of interest, with which we have nothing to do.

Liverpool and Manchester Railway expenditure for five half years ending June 1834, exclusive of interest:

- Locomotive power, including new engines........... £67552 - Maintenance of way, including new rails.................. 38306 - Coaching, including compensation for lost goods, repairs, and office expenses.......................... 32628 - Carrying, including waggon repairs, carting, and compensation........................................... 63279 - Stationary engine expenses, including ropes, &c.... 4728 - Police disbursements........................................ 5285 - Engineering department..................................... 2084 - Direction, office expenses, rent, taxes, bad debts, and sundries.............................................. 23842

Total, exclusive of interest................................. £237,704

We have included the cost of new engines in the locomotive power expenditure, as otherwise we should have had to allow an uncertain amount for depreciation. For the same reason we have included the cost of new rails in the disbursements for the maintenance of way; whereas former computers have only included the cost of new blocks and sleepers. In the coaching and carrying departments are included the following items, which we shall afterwards use:

- Coach repairs.............................................. £7957 - Waggon repairs............................................. 6436

Let us now see what duty has been performed for these several amounts of expenditure:

944,113 passengers conveyed in 15,831 trips, or 59.63 per trip = 34½ miles on a level.

For power, Goods, nett, 440229 tons, viz. goods 345463 + coals 189533

Goods, gross, 676065 tons, viz. 440229 + waggons 188669 + empty do. at ¼ = 47167.

For way, Goods, nett, 489614 tons, viz. 440229 + 7411 + 91358

Goods, gross, 751914 tons, viz. 489614 + waggons 209840 + empty do 52460.

For power, Goods, trips, 11702 at 37.63 tons per trip,

For way, .................................................. 13014

The distinction shewn here between the power and the way arises from a small portion of the coals and the Bolton tonnage not being drawn by the company's engines; and hence these have to be omitted in any calculations on the cost of locomotive power, but are retained in the expenses. of keeping in repair the permanent way. The number of trips has also to be augmented by an average allowance for the above tonnage. For computing the expense of the way, we must likewise include the weight of the engines and tenders, say 15 tons each. We then have

Goods........................................... 751914 Engines 13014, at 15 tons.................. 195210

Total weight of goods' trains.............. 947124 Passengers, at 15 to a ton............... 62941 Luggage, at 28 lbs. each.................. 11801 Trains, 15831-16.3655..................... 259082

333824 Engines, 15831 at 15 tons.................. 237465

Total weight of passenger trains.......... 571289 Total load passing on the way.............. 1518413

In the above, we have allowed coach room for 64 passengers per trip, and have taken the weight of a first-class train at 21 tons, and a second class at 12½ tons; the relative numbers of each being at the time we speak of, 13 to 16; hence the average weight of a train is \( \frac{21.13 + 12.616}{13 + 16} = 16.3655 \) tons, and more on longer lines from the luggage being heavier.

We have now to deduce the drawn and the passing weight over 1 mile upon a level, calling the Liverpool and Manchester railway equal to 3¼ miles on a level, when due allowance is made for the gradients.

Drawn weight, 1 mile on a level.

| Trips | Goods, nett | Goods, gross | Passengers nett, including luggage | Passengers, gross | |-------|-------------|--------------|----------------------------------|------------------| | 11702 | 440229-341 | 676065-341 | 74742-341 | 333824-341 | | 15831 | 1518413 | | | |

Passing weight, 1 mile on a level.

| Trips | Goods, nett | Goods, gross | Passengers nett | Passengers, gross | |-------|-------------|--------------|-----------------|------------------| | 13014 | 489614-341 | 947124-341 | 74742-341 | 571289-341 | | 15831 | 1518413 | | | |

We now require the ratio of expenditure for passengers and goods, for locomotive power and maintenance of the way. This has generally been taken in proportion to the number of trips with each, which is clearly wrong. Both the weight and the velocity are evidently functions of the expenditure, taking the drawn weight in estimating the cost of the power and the passing weight for that of the way; and as the cost of passengers and that of goods is not separated, which indeed could hardly be done for the way, we have no guide, and can only make an approximation, by taking the cost directly as the weight and velocity. We have then

For locomotive power

\[ \frac{23324242-15}{11516028-25} : \frac{349863630}{287923200}, \] or as 1:215 to 1.

This gives us in money,

Goods........................................ L.37054.5 Passengers.................................. 30497.5

Total....................................... L.67552

A similar result drawn from the number of trips only, would give for the goods, L.28710, and the passengers L.38842, which is clearly inadmissible; unless we are prepared to say that the locomotive power is used in a most disadvantageous manner, of which we have no evidence. Hence, if we multiply the number of passengers by 0.353585, or, which will be sufficiently accurate, by 0.3536, it will give us the total weight drawn in trains, averaging as those did on the Liverpool and Manchester line at the time in question; or, in other words, there are 2:8282 passengers to a ton gross weight.

In order to apportion the expense of maintaining the way between the goods and passengers, we have,

For maintenance of the way,

\[ \frac{32675778-15}{19709470-25} : \frac{490136670}{492736750}, \] or as 1:1-005.

This gives us in money such a small difference from equal proportions, that we may safely venture to place half the expense on each; always premising, as we have before explained, that the workmanship in the waggon springs, wheels, and axles, is to be considered as of the best description, without which the expense may be almost anything.

The result deduced from the number of trips would have given us the goods' expense to the passengers, nearly as 16:22, an additional proof that this method is very erroneous. We are aware of the difficulties which envelope the whole question, especially in first working a railway, when the embankments settle down and render very expensive repairs necessary, without a single vehicle passing over the road, whilst the more it is used, the sooner it will get in perfect order. Nor are there any data to guide us correctly, as respects the effect of velocity; but from an attentive consideration of the subject, combined with a comparison on many lines, we believe the foregoing method to be that which agrees best with practical results, and with this we must rest satisfied till more experimental knowledge is acquired.

For the locomotive power, the cost of new engines and repairs must now be separated from that of the working expenditure in coke, oil, grease, waste, wages, &c. We shall find this to stand as follows:

Repairs, &c.................................. L.42376 Working expenses............................ 25176

Total....................................... L.67552

This again will divide itself into,

Repairs, &c., Passengers.................. L.19131 Goods....................................... 23245

Total....................................... L.42376

Working expenses, Passengers............. L.11366 Goods....................................... 13810

Total....................................... L.25176

In the same manner we may divide the expense of maintaining the permanent way into

Wages, Passengers.......................... L.19216 Materials.................................... 19090

Total....................................... L.38306

This comes so very near a half, that we may safely estimate it at that quantity, or at one-fourth of the total, as follows:

Wages, Passengers.......................... L.9576.5 Goods....................................... 9576.5

Total....................................... L.19153

Materials, Passengers....................... L.9576.5 Goods....................................... 9576.5

Total....................................... L.19153 Reducing the whole of the preceding items, we get, as in the following Table, the expenditure per ton per mile.

| Cost of the following items on the Liverpool and Manchester railway reduced to a level. | Passengers per ton | Goods per ton | Total goods and passengers per ton | |---|---|---|---| | Locomotive power, | d | d | d | | Total | 6355 | 2-8385 | 0-3813 | 0-5855 | 0-4563 | | Repairs | 3987 | 1-7806 | 0-2392 | 0-3673 | 0-2919 | | Expenses | 2368 | 1-0579 | 0-1421 | 0-2182 | 0-1734 | | Maintenance of way, | d | d | d | | Total | 2332 | 1-7826 | 0-1407 | 0-2721 | 0-1755 | | Wages | 1166 | 0-8913 | 0-0704 | 0-1366 | 0-0878 | | Materials | 1166 | 0-8913 | 0-0703 | 0-1365 | 0-0877 | | Coach repairs | ... | 0-7406 | ... | ... | ... | | Waggon repairs | ... | ... | 0-1017 | ... | ... |

The police expenses are about £75 per mile, including gatekeepers and switchmen; and this would of course be doubled for a night and day line. The portage of the goods at the termini, costs 8½d. per ton, and has been for some time paid at that rate by contract.

As an example of the mode of estimating per ton, and per passenger per mile, the following accounts for the Stockton and Darlington railway will be useful. The traffic on this line consists of coals carried on an average 20 miles per trip, with 63 tons 12 cwt. nett. Goods averaging 12 miles, and passengers the same distance, are conveyed indiscriminately in the same train.

The following statement is for the half year ending the 31st December 1834:

No. of trips with coals equivalent to 20 miles per trip | Trips | 3682-5

The expenses of locomotive power, including the repairs, working, fuel, wages, &c., and interest on capital... £8310 14 9

Which gives per trip | 2 5 1-61

This gives per ton per mile | 0 0 0-4258

In the above is included

Water stations | £126 12 1 Agencies | 81 18 4 Miscellaneous | 294 8 4

Total | £502 18 9

No. of trips of 12 miles, with goods and passengers, 22613 No. of passengers conveyed one mile, 398244 No. of passengers conveyed one trip of 12 miles, 33187

Expense per trip of 12 miles | £0 12 3-35 Expense per passenger per trip | 0 0 1-004 Receipts per trip of 12 miles | 0 18 0-61 Receipts per passenger per trip | 0 0 1-276

Total cost of locomotive power for the half year | £1388 12 10 Total receipts from passengers for ditto, 2041 7 4

The cost for goods and passengers is as follows:

Working the engines | £1207 5 1 Guards and clerks' salaries | 187 2 10 Repairs of coaches | 34 16 3 Miscellaneous | 337 12 2

Total | £1766 16 4

Brought over—Total...£1766 16 4 Railways.

Deduct proportion of expense for some coals drawn by passenger engines | £79 1 6 Deduct for goods 7185 tons, 12 miles at ½ths of a penny per ton per mile | 215 10 11 Expenses in the goods' department | 83 11 1

Expense for passengers only | £1388 12 10

Hence 7185 tons of goods cost per ton per mile | £0 0 0-8337

Being £215,10s.11d.+£83,11s.1d. total cost on | 299 2 0

The performance and cost in locomotive power for five of the principal passengers' and goods' engines during the six months, is as follows:

| Engines | 12 mile trips | Wages, coal, oil, tallow, hemp, &c. | Repairs | Total | |---|---|---|---|---| | North Star | 370 | 74 7 8 | 112 8 3 | 186 15 11 | | Planet | 263 | 44 1 2 | 34 18 1 | 79 19 3 | | Globe | 286 | 27 16 6 | 207 7 9 | 235 4 3 | | Shildon | 193 | 15 8 0 | 136 11 7 | 151 19 7 | | Willberforce | 836 | 170 0 1 | 310 14 10 | 481 0 11 | | Average | 389 | 66 7 10 | 160 8 13 | 226 15 11 |

The performance of eleven of the principal coal engines is as follows, the trips being equivalent to 20 miles each, with 63 tons, 12 cwt.

| Engines | No. of 20-mile trips | |---|---| | Royal George | 293-01 | Locomotive | 222-93 | Coronation | 262-82 | Director | 286-11 | Lord Brougham | 236-07 | Adelaide | 237-56 | Earl Grey | 278-03 | Lord Durham | 249-89 | Experiment | 227-78 | William | 212-46 | Rocket | 217-85 | Average | 247-11

The estimated expenditure per trip of 20 miles with coals, when this railway company worked their own engines, was, for the years 1833-4:

Locomotive power, total | £2 2 7-344 Interest of capital, rent of shops, &c. | 0 3 1-187

The same expense when the power was let to contractors in the years 1834-5 | 2 2 4-48 Water engines, agency, and superintendence | 0 1 5-25

Saving per trip of 20 miles, with 63 tons, 12 cwt. nett, in 24 waggon, | £0 1 10-481 The cost of L2, 2s. 4½d. to the contractor may be divided as follows:

- Engine-man's wages: L0 6 1½ - Fireman's do.: 0 3 0 - Engine bars: 0 0 8 - Coals: 0 4 9¾ - Oil, tallow, and white lead: 0 3 7¼ - Hemp and spun yarn: 0 0 4

Total: L0 18 6½

Interest of capital: 0 1 11 3½ Rent of shops: 0 1 1 8½ Repairs and profit: 1 0 9 11¾

Per trip of 20 miles: L2 2 4½

Or, per mile: - Wages and consumable articles: L0 0 11 12½ - Interest and rent of shops: 0 0 1 8½ - Repairs and profit: 0 1 0 45 6½

Total: L0 2 1 4½

The following is the amount of repairs for two years, 1835 and 1836, to seven engines on the Stanhope and Tyne Railway:

| Materials | Labour | Total | |-----------|--------|-------| | £ s. d. | £ s. d. | £ s. d. | | Preparing engine, cleaning do., adjusting pistons and slides, packing glands, and putting on man-hole doors | 4 9 0 | 73 2 9 | 77 11 9 | | Lifting, stripping, and putting together | ... | 196 16 8 | 196 16 8 | | Carriage, and axle-rod brackets | 21 7 54 | 20 17 6 | 42 11 11 | | New wheels, taking off and keying on | 380 1 5 | 68 4 6 | 448 6 0 | | Connecting rods, straps, keys, brasses, and liners | 2 1 3 | 9 13 | 11 14 5 | | Steam pipe regulator | 6 10 11 | 19 13 | 26 4 16 | | Crosshead, cross bars, parallel blocks and bars | 0 18 7 | 8 1 12 | 8 19 8 | | Pistons | 29 17 6 | 22 9 3 | 82 6 9 | | Weigh shafts, slide spindles and shafts | 24 0 8 | 43 15 10 | 67 16 10 | | Pumps, plungers, glands, gland bolts, clock seats, union pipes, suction pipes, and hose | 103 13 9 | 70 13 7 | 183 7 4 | | Lifting apparatus, with eccentric rods, straps, sleeves, forked lever, clutch ring, and reversing lever | 14 4 3 | 53 13 11 | 67 18 3 | | Side rods, keys, liners, brasses, straps, turning crank pins, and keying on cranks | 8 7 6 | 32 4 3 | 40 11 11 | | Frame with hand railing, spring, spring pins, links, frame ends, buffers, and foot board | 30 18 2 | 76 0 | 1 16 18 11 | | Coupling bar, drag bolt, drag plates, cotters and ferrules | 16 14 7 | 17 6 2 | 34 0 9 | | Fire box | 41 14 4 | 105 18 5 | 152 12 9 | | Tubes, taking out and putting in do., and putting in hoops | 240 17 6 | 47 1 5 | 293 18 11 | | Smoke box, blast pipe, and chimney | 34 10 54 | 98 11 82 | 133 2 2 | | Fire frames and bars | 71 3 8 | 17 9 10 | 89 13 6 | | Cleaning boiler | 0 1 6 | 19 7 5 | 19 8 11 | | Water gauges | 0 15 11 | 0 18 1 | 1 13 0 | | Gauge cocks | 1 13 7 | 11 16 1 | 13 9 8 | | Tools | 11 9 42 | 18 18 41 | 25 7 9 | | Painting engine | ... | 18 5 2 | 18 5 2 | | Tender | 115 2 11 | 108 13 2 | 223 16 14 |

Total: 1166 3 0 | 1194 2 8 | 2360 5 10

Total, per annum: 583 1 63 | 597 1 43 | 1180 2 11

Total per engine, per annum: 83 5 11 | 83 5 11 | 168 11 10

The work performed by these engines in the two years, Railways, was as follows:

| Tees, 1 mile | Tons, 1 mile | |-------------|-------------| | Gross load | Net load | | Two years | 10322616 | 4825309 | | Per annum | 5161308 | 2412654 | | Per engine, per annum | 737330 | 344665 |

The comparative cost of the different modes of transit is, under all circumstances, strongly in favour of railways. For instance, in wagons travelling 2½ miles an hour, the cost of each ton, per mile, for goods, is about 7½d., of which nearly 3d. is the cost of horning. In vans travelling at 4 miles an hour with lighter goods, the expense is nearly 1s. per ton, per mile, the horning costing rather above 4d. of this sum. The expenses of four-horse stage coaches, vary from L4 to L5 per lunar month, per double mile, according as their rate of travelling varies from 8 to 10 miles an hour; their hire and repairs cost 2½d. per double mile; the duty is 3d. per double mile; and the horning is 2s. The coachman and guard are seldom paid except by the passengers, say 10s. 6d. per week for them at the outside; and for tolls and incidental charges 6d. per mile; being a large allowance. The tolls on the Holyhead road, one of the best in England, are not quite 4d. per mile, for a four-horse coach. This gives 1s. 9d. expenses per single mile, while the returns will be 2s. 6d. per mile. From this calculation we have excluded the charge for parcels, &c., leaving it to go, with the allowance for incidentals, to the support of the office establishments. The coaches which ran between Birmingham and London, prior to the opening of the railway, charged L2, 10s. inside, and L1, 10s. outside, the distance being 108 miles, and after the opening, L1, 10s. inside, and 17s. out. Our computation of coach profits we know is under the mark. The cost of this mode of travelling is about 3d. per passenger per mile, or 3s. per ton, taking 12 passengers and their luggage to a ton. In canal carriage, the cost varies from 3d. to 5d. per ton per mile, in the fly boats going at the rate of 4 miles an hour; and by slow boats, from 1½d. to 2d. per ton per mile, at the rate of 2½ miles an hour. The passenger boats, going 10 miles an hour, charge from 1d. to 1½d. per passenger, per mile, or from 1s. to 1s. 3d. per ton of passengers, per mile.

The cost of carriage by railways worked with horses, is Cost when from 1½d. to 2d. per ton, per mile, for heavy, and 3d. to 3½d. worked by for light goods, and from 1d. to 1½d. per passenger, per mile, horses, or from 1s. to 1s. 6d. per ton of passengers, per mile. Those worked by locomotives charge about the same for goods, and rather more for passengers, or from 1½d. to 2½d. per mile on an average. These latter charges however are too high. The resistance by the several modes of transit, is for railways, 8lbs. per ton; canals, 2½lbs. per ton, at 2½ miles velocity, 7lbs. at 4 miles, 40lbs. at 9 miles, and 60lbs. at 11 miles, which is the greatest hitherto attained. Turnpike roads' waggons, 7½lbs.; vans, 7½lbs. at the before mentioned velocities; and coaches, 80 to 85 lbs. at from 8 to 10 miles an hour.

In whatever light we view the question, no other mode of transit can be put in competition with railroads, except Railways, the very slow carriage of heavy goods on canals. But this is not a fair comparison, as speed must be taken into account as well as price; and we have no hesitation in saying that upon well managed and economically-conducted railroads, goods of every kind can be carried, with proper precautions, quite as cheap as by any canal, and with three times the speed at least. A great deal remains yet to be done in this department of locomotive transit, and the question cannot be decided on any railway with certainty, till it has been some time in operation, and the mode of working and maintaining it, and of economising the locomotive power expenses, are reduced to a well regulated system.

Many doubts were entertained, at an early period of the railway system, as to the performance of engines when snow lay on the rails to a depth which on the common roads interrupted the ordinary communications of the country; they have however completely triumphed over this difficulty; a striking proof of which took place on the Newcastle and Carlisle Railway; where the possibility of working the engines, under the above unfavourable circumstances, was put to the test on December 20, 1835, in the deep cutting through the Cowran hills, where the snow had accumulated to the depth of four or five feet; when the Hercules engine came down on the morning of the above day. Numbers of the country people assembled to see how it would act in such an emergency, and to render any assistance which might be necessary. On arriving at the spot, however, the engine dashed right into the drift, clearing its way through, apparently without any difficulty; the snow at the same time flying over the top of the engine chimney, like foam from the broken waves of a violent sea; and notwithstanding this and other similar obstructions, the train came down from Greenhead, twenty miles, in one hour and a quarter, and their times of arrival were properly kept up, whilst all the communications by the ordinary roads were more or less seriously obstructed, if not entirely cut off.

Hence any of the so often proposed plans for sweeping or scraping the rails will rarely be found necessary, much less the plan seriously proposed and patented so late as 1831, of making the rails hollow and filling them with hot water in winter. In the extreme case of rain succeeded by frost, thus forming a coat of ice upon the rails, it will generally be found sufficient to place a waggon, or any other empty light vehicle in front of the engine, which will break up the ice sufficiently to allow of the necessary adhesion. The effect of severe frosts on the road itself will be found of infinitely more consequence, and is an additional reason why drainage should be scrupulously attended to in countries where much cold is experienced. The manner in which frosts acts on common roads, is sufficient evidence of what may be expected on a railroad, if the water is not most carefully carried off from the ballasting.

In America, for instance, where railways were first laid down on blocks, similar to the way they are constructed in England, it was found that their severe winters completely disorganised them; splitting the blocks, throwing the rails out of gauge, and even twisting them so as to render them unfit for the passage of the engines, and obliging the trains to travel at a reduced speed. From these causes, and as it was found necessary to relay the road after each winter, blocks have in a great measure been abandoned, longitudinal and cross sleepers being generally substituted, and laid on broken stones filled into trenches; but the evil is yet only partially remedied. It may, however, in all cases, be set down as a general rule, that where timber can be obtained cheap, it should be used in preference to blocks.

The difference, however, is necessarily so great between the railroads in that country and this, as very much to preclude comparison. Some of theirs are constructed of plate rails 2½ inches wide, by half an inch thick, and weighing from 10 to 17 lbs. per yard; their curves and inclinations are such, from the nature of the country, as to render cross ties more frequently required than they are in English railroads. Continuous stone bearings have also been tried in America; also piles at three feet distance, as supports to the rails, which are spiked down to them without the intervention of any chairs.

Several of their railroads are carried across valleys by means of wooden trestles, well braced together, and assisted by piles; the lower ends of which in soft ground are often left square instead of being pointed, as a means of affording additional stability. These sort of roads are in several cases carried over valleys of such a depth, as to occasion no small surprise to those only acquainted with the substantial embankments of England and most other parts of Europe. It must be confessed, however, that the Americans, in the expense of their railways, beat the old country hollow; and there are many things which we should be glad to see copied from them; we may instance their guards in the front of the engine to remove obstacles from the road, and their long and high carriages.

Some of their lines are worked by horses at the rate of 15 miles per hour; and on the locomotive lines, where the curves are bad, the driving wheels are placed next the fire box, and the front part of the engine is supported on a four-wheeled truck, to which it is attached by a vertical pivot, while the weight rests on friction rollers; this management admits of a motion by which the wheels are in a great measure assisted in their passage round the curves, which in some cases have not more than 300 feet radius, whilst in others they have gradients of 1 in 110, and inclined planes rising 1 in 10.

Another striking departure from the method of constructing these works commonly adopted in England, has been introduced by Mr. J. K. Brunel on the Great Western Railway, with a view to an increase in speed, and also to obtain a more solid road, on embankments particularly. Instead of resting the supports of the rails, that is to say, the stone or wood bearings, whether longitudinal or transverse, on the ballasting, where the repairs to the railroad consist in continually packing more ballast under the bearings, as they subside through the weights passing over them, or from the various other causes which affect them, Mr. Brunel has fixed his bearings at certain points, so that they cannot rise up nor go down, whereas in the usual mode of construction, it has only been attempted to prevent them from going down.

The gauge of the Great Western Railway is 7 feet 2½ inches from centre to centre of the rails, and the width between the two lines is 6 feet. The mode of construction is as follows. (See Plate CCCCXX.) At every 15 feet length along the railway, beech piles are driven into the ground, at 15 feet distance apart, transversely; they are driven from 8 to 10 feet in cuttings, and in embankments, they are in general sufficiently long to go about the same depth into the original ground on which the embankment stands. These piles are formed to the proper length, and driven in, without any being cut off their heads, which are nearly level with the top of the ballasting; and when this cannot be effected, they are drawn and redriven. They do not stand in the middle of each line of rails, as will be seen by referring to the above measures and the plate, but are nearer each outside rail of the two lines.

To these piles double and single transverse ties, or sleepers, sometimes called transoms, are attached as follows: A square shoulder is cut, 1½ inches into the pile, on one side for the single ties, and on both sides for the double ones; the single ties are 6 inches broad, and 9 inches deep; the double ties are 6 inches broad, and 7 inches deep. They are made of American pine, and when let into the shoulders of the piles, they are securely bolted to them; the double ties are 13 inches, and the single ones 9 inches below the line of rails. On these are laid longitudinal timbers, 15 inches broad, and Railways. 7 inches thick; these are also of American pine, and are bolted to the cross ties with screw bolts and washers, the heads of which are countersunk into the longitudinal timbers.

The entire transverse section is horizontal where the railway is straight, and inclined according to the radius in curves; and when the whole is bolted together, it forms what is in fact a road at fifteen-feet bearings. The line is then ballasted, and the longitudinal bearings are packed in the usual manner with fine sand or gravel, till they are raised in the middle from a half to one-third of an inch; they are then planed to a uniform surface, and a plank of elm, oak, or ash, 13 inches thick, and 8 inches broad, is laid on them, with a copious intervening bed of tar, and nailed down; the heads of the nails being punched in, to allow the plank to be planed; the upper surface of the plank slopes inwards 1 in 20.

The rails are screwed down to the plank and longitudinal bearer, after the former has been planed; with felt underneath them. The whole of the timber is kyanized, and the joints, butts, bolts, washers, keys, spacers, and nails, also the whole of the longitudinal bearers, are tarred. In fixing the rails, square-headed screws are used outside the rails, and countersunk ones inside, to be clear of the flange of the wheels; the outside screw is first completely tightened and then the inner one; a roller weighing about 10 tons being previously drawn several times along the rail, and followed up closely by the screwing.

The principle on which the railway is intended to be constructed chiefly consists in the piles being a constant retaining power, holding the road down against the packing, which would otherwise force it up; so that this latter can be driven much harder in than by the ordinary mode. Mr. Brunel is said to calculate that he throws an upward pressure against the base of each longitudinal timber, equal to one ton per foot forward, or about one ton per square foot. He thus obtains 3 tons for every 3 feet length of rail, while a stone block containing 4 cubic feet, only weighs about a quarter of a ton, which is therefore the pressure with each 3 feet of rail laid in the usual way; neglecting the impact with which the stone block is forced into its seat by the caddy and lever, a very uncertain quantity, but which perhaps never amounts to, on the whole, less than as 3 : 2 in favour of the longitudinal bearings. The timber used in a mile of this railway, is about 420 loads of pine, and 40 loads of hard-wood; these require 6 tons of iron bolts, and 30,000 wood screws. The rails are about 44 lbs. per yard, and the cost of the first portion, laid from London to Maidenhead, including laying, ballasting, sidings, draining, and all other work, is stated at £9200 per mile.

Such is the mode of construction on this railroad, which has so much agitated the minds, not only of the shareholders, but of the whole railway public. This, however, ought not to have been the case, for the matter lies in a very small compass, and a short experiment should have determined it; it is merely a question of expense. The first outlay must, of course, be great, and it is only necessary to know whether the future saving will be commensurate with it. A desire for a greater width of gauge seems now gradually gaining ground among those best entitled to judge on the subject, and the public will not long rest satisfied with a velocity of twenty miles an hour. Whether Mr. Brunel has taken the right measures to compass these desirable objects, will require much more room to discuss than we have here; but this we know, that the Great Western, for the twenty-three miles now open to the public, is by far the smoothest and easiest line we have ever travelled on.

Velocity of the wheels. The relative ratio between the motion of the wheels and that of the piston will be much more advantageous at a given velocity as the wheels are large, within certain limits; the greater degree of stability acquired, from the increased width of gauge is also desirable, if not carried too far; but we must confess we should ourselves be afraid of jumping from 4 feet 8½ inches, to 7 feet, without more experience. Another Railway company jumped from 2 feet 9 inches to 5 feet in their length of bearing, and the result was sufficiently inauspicious.

The effect of the diameter of the wheels on the velocity of the piston, may be thus computed:

Let \( v \) = the velocity of the wheels, \( p \) = the velocity of the piston, \( l \) = twice the length of the stroke, \( m \) = the number of miles per hour the engine travels.

We then have

\[ v = \frac{3 \cdot 14159 \cdot d \cdot l}{m} \]

or,

\[ p = \frac{3 \cdot 14159 \cdot d \cdot l}{m} \]

and \( e = 88m \) feet per minute;

also \( p = \frac{88 \cdot m \cdot l}{d \cdot 3 \cdot 14159} \)

\[ = \frac{28 \cdot 01127 \cdot l \cdot m}{d} \]

This for all ordinary purposes may be taken at

\[ p = \frac{28 \cdot 01127 \cdot l \cdot m}{d} \]

with a stroke of 18 inches, or \( l = 3 \) feet, if we take \( d = 9 \) feet, and compute for the different values of \( m \), the values of \( p \), we may derive from them any other values of \( p \), for all diameters of wheels by simple proportion. For the quantity \( p \) when \( d = 9 \), our formula becomes

\[ p = \frac{9 \cdot 33709}{m} \]

and the table will stand as follows:

| \( m \) | \( p \) | \( 9p \) | |-------|--------|---------| | 10 | 933709 | 8403381 | | 15 | 1405563| 12605057 | | 20 | 1867418| 16806762 | | 25 | 2334272| 21008448 | | 30 | 2801127| 25210143 | | 35 | 3267981| 29411829 | | 40 | 3734836| 33613524 | | 50 | 4668545| 42016905 | | 60 | 5602254| 50420286 | | 70 | 6535963| 58823667 | | 80 | 7469672| 67227048 | | 90 | 8403381| 75630429 | | 100 | 9337050| 84033810 |

By means of the column \( 9p \) we have the value of \( p \) for any other diameter of wheel, by simply dividing the number in that column for the required value of \( m \) by the given diameter of the wheel; thus, for instance, with a 5-feet wheel,

\[ \frac{16806762}{5} = 3361352 \text{ feet per minute, for the velocity of the piston.} \]

At 60 miles an hour, with the same wheel, we have

\[ \frac{50420286}{5} = 10084 \text{ feet per minute.} \]

In the same way, if we have any other length of double stroke than 3 feet, we have only to take the value of \( p \) from the table for the given number of miles per hour, multiply it by 3, and divide it by the length of double stroke in feet, or calling \( l' \) the new double length of stroke, and \( p' \) the required velocity of the piston in feet per minute,

\[ p' = \frac{3p}{l'} \]

Coming now to look at the Great Western Railway in its Reports at more general bearings, we may examine the late reports on the Great Western, its construction, which, published as they are by the directors, have the sanction at least of authority to give them We are sorry, however, to say, that they possess none; they have left the main question as undecided as ever, and present little else but irrelevant matter, or that which contradicts itself. Our inquiry will naturally embrace, first, the reports themselves, and, secondly, the experiments on which they rest.

The first is Mr. Hawkshaw's, and this is so completely set at rest in the reply of Mr. Brunel, that no one would require any discussion respecting it. Mr. Hawkshaw states that at the risk of being tedious, he has endeavoured to develop the process by which he has arrived at his "opinions," because he thinks it better that his report should "partake more of the nature of demonstration than of mere assertion;" and he then informs us that the Great Western Railway "has been applauded to the skies as wonderful; it has been derided and run down as little less than nonsensical. Now it is neither one nor the other of these." He has not furnished any "demonstration" of this fact, and is much less fortunate in another assertion, namely, that on coming first on the Great Western line of railway, that which immediately strikes the attention is the "enlarged capacity of all things." We have travelled on that line now four times, but are not aware, from our own observation, that all the things which were on it possessed a larger "capacity" than those which we have met on other railways.

Coming next to the report of Mr. Wood, we find it stated that nearly all the experiments upon which it rests for its foundation, were made both by and under the superintendence of other persons, and the mere dressing them up, a purely arithmetical operation, has alone been performed by Mr. Wood. To those who are at all acquainted with that gentleman's knowledge of formulae and figures, this would be quite a sufficient intimation of what might be expected; but, in addition to this, hardly any of the experiments are given in the report, and no formulae; and thus the only essential things, from which a right conclusion can be drawn, have been withheld from the shareholders. In the meantime the farce has been played out, and the curtain has fallen.

We shall not stop to notice such mistakes as, that one ton and a half is to one ton and a quarter as four to three; but proceed to the tabular matter in the report, selected from all the records which have been taken of the various experiments, we presume, as that which was most worthy of being laid before the directors and the public, as a fair statement of the capabilities of the Great Western Railway as compared with others; and it should be remembered that Mr. Wood sets out by laying down a rule that, unless his inquiries were conducted in such a way, as to "elicit by incontrovertible and practical experiments, the relative capabilities of the two systems of forming and constructing railways," it would "not only be a waste of time, but would be attended with perhaps still worse consequences."

The advantages which have been aimed at in the extension of the gauge, from 4 feet 8 inches, to 7 feet, and in Mr. Brunel's other alterations, are principally as follows. A greater speed; a decrease of friction, by enlarging the diameter of the wheels; greater stability, by keeping down the centre of gravity, through the body of the carriages being inside the wheels, and not over them, as in other railways. The main objections made to his system, are the increased cost of forming the railway; the greater weight and size of the engines and carriages; the additional friction on curves; the extra cost of construction both in carriages and engines, and the impossibility of a junction with other railways. It is to strike a balance between these that Mr. Wood has produced what he states as "correct and indisputable results."

On the question of speed, Mr. Wood decides that the less powerful engines on the ordinary railways go within three miles an hour of the most powerful ones on the Great Western, and he presumes from this, that the more powerful ones would exceed the best of the Great Western engines; the effective power yielded by the former being apparently much greater than that which is obtained from the latter. This very extraordinary statement is attributed to the resistance of the air, which Mr. Wood seems to think a new discovery in railway matters, although Newton, Robins, Smeeaton, Hutton, Dalton, Pambour, and others, have given it in print from nearly two hundred years ago up to the present day, and practical men have all along considered its effects on railways, whilst theorists alone have stated it to be of no consequence. It is twelve months since anemometers were planned, and estimates obtained for their erection at the stations along the London and Birmingham railway, by the writer of this article, at the desire of Mr. Bury, who has contracted for the locomotive power on that line. With respect to the speed of the Great Western engines, in consequence of those improvements to be expected in all mere mechanical contrivances, and which the usual engines have been ten years benefitting by, whilst those on the Great Western line are yet insufficiently tried, Mr. Brunel states, that since Mr. Wood's experiments, he has so improved the very engine with which the highest velocity was then attained on those trials, that, all other things being the same, her performance was, and is as follows:

| Load | Average speed | Coke per ton | |------|---------------|--------------| | Mr. Wood, Sept. 1838 | 15-9 | 38½ | 2-76 | | Mr. Brunel, Dec. 1838 | 40-0 | 40 | 0-90 |

The decrease of friction in large wheels is admitted as well as other conveniences, although it is stated, these can be arrived at with a less guage than 7 feet, and 6 inches is given as the maximum increase on the old width requisite for improving the engines. The weight per passenger appears to be the same with the Great Western and the ordinary railway carriages, although Mr. Wood states they have 1½ tons on each wheel, while the ordinary ones have only 1¼. That there is a greater stability and steadiness of motion in the carriages, Mr. Wood denies.

We have now to examine the tables given in this report, containing the incontrovertible experiments which are presented as affording a foundation for the opinions delivered, and it will be quite sufficient for every purpose of testing their value, if we take those on the deflection of the rails and supports on the Great Western and other railways. These experiments, it appears, were made almost exclusively on the short space of about two miles in the clay cuttings near Paddington, undoubtedly the worst part of the road.

Mr. Wood states that stone blocks afford decidedly the firmest and most unyielding base, and that between longitudinal bearings, the usual sleepers, and the Great Western plan, not much difference of deflection exists. The weight of the engines not being given, we must chiefly confine our observations to the quantity of deflection produced by the coaches, the weight of which, on one wheel, is as 6 to 5 on the Great Western, compared with other railways.

| Engines | Coaches | |---------|---------| | Great Western in a perfect state. | -13113 -02453 -10517 -02473 | | Do. with the piles cut. | -0979 -01047 -06923 -00843 | | Do. with the transoms cut. | -07743 -00513 -0768 -00353 |

The above are means of three deflections taken at a single transom, a double one, and mid-way between them. Comparing now the effect of coaches on this and other railways, we have as follows:

| Vertical deflection | |---------------------| | London and Birmingham, 60 lb. parallel rail, 3-75 feet bearings on blocks | -0261 | | Do. do. 50 lb. fish belly, at 3 feet bearings on blocks | -03277 | Liverpool and Manchester 62 lbs., parallel, 3 feet on blocks ........................................... -03853 Manchester and Bolton, on longitudinal bearings ......................................................... -05703 Grand Junction 65 lbs., parallels, on blocks, 4 feet bearings ........................................... -0301 " the chair under the rail .......................................................................................... -0149 " the block under the chair ....................................................................................... -0714 " 65 lbs. parallels on sleepers ..................................................................................... -10293 " the chair under the rail ......................................................................................... -0717 " the sleeper under the chair .................................................................................... -0511

Grand Junction, lateral deflection on blocks, rail ......................................................... -01615 Do. do. do. chair ...................................................................................................... -0200 Do. do. block .............................................................................................................. -0053 Do. on sleepers .......................................................................................................... -0188 Do. do. chair .............................................................................................................. -0112 Do. do. sleeper ........................................................................................................... -0125 Do. on longitudinal timbers, rails ............................................................................... -02985 Do. do. chair .............................................................................................................. -0387

Engine. Coaches.

From the tables in the report whence we have formed the above means, we find that a 60 lbs. parallel rail at 45 inches bearing, deflects only -0261, while a 62 lbs. parallel at 36 inches bearings, deflects -03853, and a fish-belly at 36 inches bearing, and 50 lbs. in weight, only deflects -03277.

In the 50 lbs. rail upon blocks, at the joint chair, there is more deflection than in the middle of the rail, and about three times as much as at a single chair with the weight of a coach; whereas, in the 60 lbs. rail, the deflection is more at the single chair than at the joint, but, in this case also, it is least in the middle of the rail with a coach. In the 62 lbs. rail it is also greater at the single than the joint chair, and less in the middle of the rail than at the single chair.

In the Manchester and Bolton experiments, the rail deflects more than the timbers at the transoms and joints, but in the middle, the timber deflects more than the rail. With the 65 lbs. rails, either on sleepers or blocks, the deflection is considerably more, either with an engine or a coach, at the chairs than mid-way between them; and whilst the rail only deflects -0301, and the chair which supports it less than half this, namely, -0149; the block which supports the chair deflects five times as much as the chair itself, namely, -0714. These are called incontrovertible experiments.

In addition to this, Mr. Babbage, no mean authority, who has seen the original records of the experiments, which the report made to the directors does not contain, states in his speech at the meeting of Great Western proprietors, held on the 9th January 1839, that with respect to the increased power required through the resistance of the air, that instead of 15 per cent. being necessary to gain an increase of speed of 3 per cent., it turned out that from the use of the same formula, and the same experiment whence Mr. Wood had deduced the above results, that the increased power required was only as 2 to 1, instead of 5 to 1, as stated by Mr. Wood.

It is astonishing to see what mistaken ideas many persons have entertained amongst the proprietors of this railway. One stated that although the resistance of the air might have been known, yet, it was never taken into consideration at such speed as had now been attained in railway traveling. What, then, becomes of the experiments of Robins and Hutton, which upset the ancient parabolic theory of projectiles, and established the present practical system of gunnery; the deduction of these writers were carried up to velocities considerably greater than that in which air can rush into a vacuum, that circumstance forming one great guide in establishing their results.

Another person wished to know, when such a very great advance had been made by Mr. Brunel in so short a time, Railways, by which, with fully one-third less fuel the load drawn by the North Star engine, was increased from 16 tons to 40, at an increase in velocity also; why the same could not be done with all other engines upon narrower railways, and thus an equal effect produced with a much less costly mode of construction. The simple answer to which is, that on the railways with the original gauge, the engines have been made gradually more and more perfect up to their present state; whereas on the Great Western, this has yet to be done. Mr. Brunel, in the above improvement on the North Star, has not made any new discovery in the organization of a locomotive; he has has only brought its mode of operation nearer to that which is in action on other lines of railway.

Other persons have said, that granting Mr. Brunel does obtain the speed and power he has anticipated, his engines will then do too much, that passengers will never be found to assemble in sufficient numbers to fill such heavy trains, and that consequently all the extra cost of the new system will in the end be thrown away. This argument is no more tenable than the others, and throughout the whole inquiry there appears a lamentable want of nearly every requisite for coming to a right conclusion; even the instruments used in the experiments are inadequate for that which they were intended to show; of those used to ascertain the motion of the carriages, Mr. Babbage states, that having tried three similar ones of different lengths merely, he could make each of them tell different stories, and whichever he pleased give the greatest result; also that when he tried the very same instrument used in the experiments of Mr. Wood, instead of finding anything like corresponding measures of the oscillations, his so grossly exceeded those which formed the basis of the report, that they were beyond all magnitude; and after travelling 120 miles in those trials, he came to the conviction that everything in the shape of an experiment connected with that instrument, must be thrown overboard.

No inquiry, in fact, could have ended more unsatisfactorily than have these experiments on the Great Western railway; for result and their records, which should, above all things, together of the experiments with any formula used, have accompanied the report, were not published with it. This is the most unfortunate error of the Great Western; for as they were chiefly made by other persons, and not by Mr. Wood, they require to be examined, first, as to their correctness as experiments, and secondly, as to how they have been dressed up to produce to the proprietors. In the first case, there might be some little difficulty, but in the second, every proprietor could have judged for himself, and be ought to have had the means put in his hands to do so. Strange to say, too, Mr. Wood has quarrelled with his own report, and declares he made the North Star engine do just the same as Mr. Brunel has done. Why then did he not publish this himself, instead of giving a very different experiment, after placing which in his own report, he blames the directors for sending it forth to the public?

The whole of the proceedings in this discussion serve to show, as we have before stated, that it is high time some government measure was brought forward to regulate, at least, the general principles of railways; many persons are afraid of this interference with what is justly considered private rights, but to these we would say, that on several of the leading lines in England, a far worse oligarchy now exists than can be called into operation by any measure of government, thoroughly sifted as it would be in parliament by the numerous members of both houses who are interested so many ways in the right management of these important concerns.

The result of the Great Western discussion is as follows: Summary. The unanimous abandonment of the piles; the substitution with retention of the wide gauge and continuous bearings. As far as the railway public are concerned, they will be but little affected by this. The rails are much too light and want depth, and their shape should be the subject of properly conducted experiments. The gauge being retained, all the necessary information relative to its efficiency and economy, will, no doubt, in time be made known. The question of longitudinal or transverse bearings is of much less import than is generally imagined. The part of the line on piles between London and Maidenhead, twenty-three miles, if it be retained and kept in good order, will soon set at rest the question of expense in maintaining the way. Thus, then, so far as the public are concerned, all is well; but the effect of this decision on the interests of the proprietors has received no light whatever; there is nothing even to show that in adopting a heavier rail, there is the slightest necessity also to adopt a greater scantling of timber; and it is extraordinary that a point so easily submitted to experiment and calculation, should have been entirely passed by in the final report to the proprietors.

We have hitherto looked principally to the construction of a railway; there is, however, an equally important point to be considered, and that is, the working of it after it has been constructed. On this will mainly hinge the degree of profit which may be expected; for, let all our previous instructions be duly considered, and properly followed out, with such deviations only as may be rendered necessary by local circumstances; or let a railway be constructed in the best and most advantageous manner, yet it will soon be discovered that, if it is not worked on a sound and effective system, it will turn out a vastly different speculation to what it would be under proper management.

For this purpose every thing should centre in one committee of directors; these may with advantage subdivide themselves into smaller bodies, for particular purposes; all business transacted by these subdivisions being merely preparatory, and nothing being finally concluded till brought before the general body. There should be no boards of direction at each end of a line, but that terminus which is best situated to effectually overlook the whole of the various business, should be made choice of for the seat of government. There should be ample inspection into every department, but it should be inspection only; all orders should come from one committee, and through one general head. It may often happen, and always with advantage, that both ends of a railway may be opened before the middle is finished; still every thing should centre at the governing end of the line, at one point; and the mode by which this government should be carried on, must now be considered a little more at large.

The first question which arises is, by what system can a joint stock company be so managed as to obtain the same amount of alacrity, vigilance, and industry in its service, as characterises the conduct of individuals when acting for themselves, and to combine with these qualities an honest and economical administration. The system of management by boards of directors has stood the test of considerable experience, and, where the proper men are found for directors, this system is admirably adapted to answer the primary object of a board, viz. to deliberate and decide on principles. More information and greater variety of view is brought to bear upon a subject when it is discussed by several men, than almost any individual intellect could furnish; and, as joint-stock companies consist of persons in almost all classes of society, a board composed, as it should be, of individuals holding a large amount of stock, and giving their services gratuitously, for that reason, as well as from a sense of public duty, by embodying various interests, claims and secures the confidence of all.

It is well known, however, that a body consisting of many individuals is utterly unfitting for executive functions. It is admitted as a principle, that executive administration is best and most efficiently exercised by one and one only, and, accordingly, every board, whether of government commissioners, or of joint-stock companies, or of charitable institutions, has some one to whom is entrusted the executive superintendence, and control of that, whatever it be, on which the board exercises its legislative and judicial functions. Connected with this executive are other officers, many or few, exercising a separate jurisdiction over their several departments, and in all details independent, yet held together, for the purposes of combination, by the executive officer.

In the management of railways, such an officer is more especially required where the heads of departments are necessarily numerous, in consequence of the several branches of business into which the working of a railway is divided; where each department employs a considerable number of men, two alone, those of the police and porters, amounting almost to a regiment, and where all are to be brought to act with the precision and regularity of a steam engine. It would be impossible to produce unity of action amidst such conflicting elements, without a close, active, and unremitting personal superintendence, such as may be accomplished by an individual, but can never be effected by a board.

Several attempts at a different system of management have been made by railway companies, but they have not been found to answer. A favourite project has been much talked of lately, viz. that a committee of three should be chosen from the body of the directors, in which triumvirate should reside all administrative and executive functions, and so much of the deliberative and judicial as relates to the ordinary affairs of the company, and that each triumvir should receive a salary sufficient to command his whole time for the company's service, the chairman receiving a higher remuneration than his colleagues. The advocates of this plan contend, that it would first secure unity of action in the principles of management, with prompt execution in the details, a ready redress of grievances, and remedy, or rather prevention of abuses. Secondly, that it would give the personal responsibility of a few to the proprietors, in place of the collective responsibility of many; and, thirdly, that it would keep in check the undue power and influence which, under a different system, the executive officers would be likely to acquire.

This view appears more plausible than sound, more specious than solid. In the first place, the triumvirate would monopolize the whole power of the company, and the board would go to sleep. The board of which the triumvirate form a part, would meet too seldom, and know too little, to be a match for three men, who would act together every day and know every thing, and who, above all, would enter into debate with the larger body, and vote as directors upon questions affecting their own conduct. It has always proved a thoroughly vicious system to have an executive officer a member (as in many boards he is) of that body, whose orders he is to execute, and to whom he ought to be responsible; and this applies to the triumvirate.

In the second place, the responsibility of each triumvir would merge in the collective responsibility of the whole board, and men would be exercising a power for which, practically, they could not be called to an account; for, when the board had confirmed an act of the triumvirate, what chance would the proprietors have to make them accountable? The results of irresponsible authority, it is well known, are jobbing and every sort of peculation.

In the third place, it is not likely that three men chosen out of a body of directors, would be the men best fitted for the situations contemplated. Not only is the number out of which they would be chosen too few to present sufficient of the peculiar ability required, but the selection of the individuals would be rather determined by personal predilections than by their fitness. It would be an appointment to

Railways be canvassed for, and the men who would take the most pains to get it, would be just those least suitable for it.

It will be readily seen, also, that under such a triumvirate no really good officer could act. The perpetual meddling with matters they know little about, the jealousy of their authority, and the necessity to be busy in order to give a colour to the notion that they do work, which would inevitably belong to such a body, would disgust an officer who knew his duty and wished to do it, and they would be left to perform the business with none but subordinates. So far, then, from attaining the advantage contended for, a triumvirate committee of management constituted on the above plan, would tend to greater evils than those sought to be remedied by it. The old Navy board, abolished by Sir James Graham, is a case in point: this board was an executive one, and yet subordinate to the admiralty, and the natural consequence followed; they were continually working against the orders they received from the superior board, in order to carry out their own plans, not openly, but covertly; there was, in fact, a constant undercurrent of opposition, from which the business of the country notoriously suffered.

If, indeed, the proprietors of any railway would agree to invest the whole power of management in three commissioners, chosen from the country at large, as the fittest men to be found, making them responsible to the proprietors assembled in general meeting, and assimilating this triumvirate as nearly as possible to a government board, more favourable results might be anticipated than from any other plan; but how should any company get three paid commissioners, who are not proprietors, to look sufficiently closely to the economy, out of which a good dividend should arise?

The conclusion, then, is, that the present system of direction is, on the whole, the most suitable for managing a concern, whose nature is commercial, and the end of which is the realising of a profit to the proprietors, upon a money investment. A very important principle, however, is too much lost sight of in the composition of boards of directors. The practice is, for the same persons to be selected year after year, till all sense of responsibility to the constituent body is lost, and the board becomes an oligarchy, of a spirit akin to the old self-elected municipal corporations, the members losing year by year their interest and sympathy in the views and feelings of their constituents, and yet prone to consider them as identical with their own.

For this the appropriate remedy is, periodically a new infusion into the direction from the body of the proprietors, and for which parliament has in most cases provided, by requiring a certain portion of directors to retire every year. If the proprietors give common attention at their general meetings, and are careful to select for directors the fittest men, not allowing the re-election of retiring directors to take place, as a matter of course, they will find their interests as well secured under the system recommended, as they are likely to be under any other, namely, one general board and an efficient executive officer. We should always recommend one thing, which is, that the half-yearly reports should be printed and sent to the proprietors, at least a fortnight before the general meeting.

If we look back at the rapid progress which we have made in the science of locomotion during the last half-dozen years, and at the degree of comfort and accommodation which, in conjunction with rapidity of transport, have been afforded to the public, at in most cases so very moderate a cost, the strides by which we have attained our present advanced position, are certainly sufficiently gigantic; but if we look forward, it requires but little of the gift of divination to perceive, that in a very few years more, a still greater change will take place, more particularly in the essential article of comfort. In conducting a mode of transit so essentially new, and in which all our previous Railways machines and appliances had to be completely reorganised, and numerous inventions of almost every kind were to be produced at a moment's call, to meet the various difficulties and wants which were continually arising out of such a novel mode of conducting the business of travelling in what may be called the wholesale way, it has been singularly fortunate, that in almost every instance, the various railway companies have kept on the safe side, that is to say, they have not done too much. They have erred on the best side they could commit an error on; they have been too cautious. It seems as if it required a certain time merely to travel at twenty miles an hour, and let the mind sober down a little before much else could be attempted. This feeling may now be rapidly expected to give way, and we shall find that as confidence is acquired, all the requisite arrangements will become consolidated in much more perfect and improved forms.

There is nothing now which ought to be more attended to by railway companies, than keeping their fares down; and this has in most instances been very much neglected. When parties possess such a complete monopoly as a railway, they should be particularly careful not to show it. The expenses in many instances are certainly very great, and the companies have much to suffer in their progress through Parliament, and the rough grinding they have generally received from the rapaciousness of landowners. Accidents, too, must happen, estimates will be exceeded, and these sources of expenditure must be met by a corresponding rate of price; but when the railways are made, the feeling seems to be too general amongst some of these proprietors, that this is the moment for making reprisals upon the public for all losses, vexations, mishaps and mistakes.

In some cases railways have charged more for the carriage of passengers than the stages or mails did, trusting to beat them on the question of time only. In part the receipts are great; a certain sum must be set aside for a good dividend, and the rest is to be spent somehow or other. The same thing is observable in the statistics of the road trusts, many of them largely in debt, yet spending their money on fancied improvements, instead of getting out of debt, and then lowering the tolls.

The effect of this on travelling is fully shewn in the report of the Irish Railway Commission. For instance, the travellers from Brussels to Antwerp by railway in the year 1836 were 872,893, whereas those on the Liverpool and Manchester Railway for the same year were only 522,991, being the largest number for any year since the opening. Now, the population of Brussels, Antwerp, and Mechlin was 209,200, whilst that of Liverpool, Manchester, and Warrington was 486,812, considerably more than double, or the ratio of population was as 2:327 to 1, whilst that of the travelling was only as :599 to 1. We must seek for the solution of this problem in the respective fares of the two companies. In the Liverpool and Manchester Railway, Mr. Pambour states, that there are 13 first-class trains to 16 second-class; and as the last class hold most passengers, suppose we omit the mails, and say

\[ \frac{13 \times 5.5s. + 16 \times 4s.}{29} = \frac{135s.}{29} = 4.6724 \text{ shillings, the average fare.} \]

We have no means of ascertaining the numbers on the Brussels railway, but if we take the dearest and cheapest, and compare them in the same ratio as we did the others, we shall have

\[ \frac{350 \times 13 + 120 \times 16}{29} = \frac{6470}{29} = 2 \text{ francs 23 cents per passenger on the average,} \]

or about 1.784 shillings, or 4s. 8d. in the one case, and 1s. 9½d. in the other, or, allowing for the value of money in the two countries, about double the price; and this double Railways price is accompanied with only one-fourth of the travelling; the ratio of population to that of travelling being very nearly 4 to 1. A still stronger case is that of the Paisley canal, where the fly-boat fare is 1d. per mile. Here, with a population of 262,725, the passengers in 1835 were 373,290, whilst in the same year, with a population of 486,812, the Liverpool and Manchester railway had only 473,849 passengers. The railway company from Paris to St. Germain's has tried the experiment of low prices with complete success; their greatest reduction of fares was at the station of Nanterre, where they were lowered from 7½d. to 5½d., and the result was, that twelve days, ending the 4th December 1838, at the low fares, compared with twelve days ending November 22, at the high ones, showed an increase of 839 passengers; and although the diminution in price was 34 per cent., the increase in the amount received was 16½ per cent.

We therefore strongly recommend that fares should be moderate, or it will form the best plea in the world for the establishment of competing lines; and it should be remembered that railways will to a certain extent drive vans and waggons off the road, which were the ordinary vehicles for the travelling poor, and they ought to have a substitute, if it were merely an open box without seats. Soldiers are generally conveyed at 1d. each per mile, and their baggage at 3½d. per ton per mile; this is less than half what is charged on some railways in second-class carriages.

The general system of working a line, which we have here laid down, is that which is adapted for a first-rate railway. On secondary lines it will perhaps be necessary to place several of the departments under one person's superintendence, instead of having a head to each; but as this would be merely on the score of lessening expenditure, it should not be resorted to without there be a rigid necessity for it. On short lines this necessity will exist. When this is the case, one person might take the coaching department, goods' department, and the police, porters, and guards; the disbursement clerk might be dispensed with; one engineer might take the locomotive department, the construction and repairing department, and also the maintenance of the way, having good foremen in each case. But it is so much better to have a responsible head in every department, that we should always recommend that course to be adopted whenever it is practicable, that is to say, whenever the income of the company will allow it. It may, however, well deserve consideration, in every railway establishment, whether, at each of the stations of every kind, it would not save a considerable expense to have the parties, or a part of them, sworn in as police, so that they might on occasion act in either capacity. Attention to the number of entrance and exit gates, in planning out the stations, will also conduce to economy, as each of these will in general require an attendant policeman. There are numerous other means by which, in the middling and smaller class of railways, a moderate expenditure as well as a good arrangement, may be combined; but so much depends on the localities, together with the nature and extent of the traffic, that nothing definitive can be pointed out, except from a careful consideration of these; and the best step which the directors of all railways can take previous to forming any system whatever, is to consult a properly qualified and experienced person, both as to general principles and as to details.

EXPLANATION OF THE PLATES.

Plate CCCCXX. fig. 1, is a plan of a sliding rail and eccentric for a crossing or siding place. The eccentric being attached by rods to the sliding rails (which move on a joint at the opposite end) draws them to either line, as required.

Fig. 2 is a longitudinal, and fig. 3 a transverse section of the same.

Fig. 4 shows a plan and section of a fixed point.

Fig. 5 shows the general arrangement of the whole of the preceding figures, to form a complete crossing.

Fig. 6 is a plan, fig. 7 a longitudinal, and fig. 8 a transverse section of the mode of laying the blocks, sleepers, and rails in an excavation, together with the ballasting, and an approved method of drainage. The blocks are shown as laid diagonally in the manner they have been on the London and Birmingham Railway. The drains are of brick.

Plate CCCCXXXI. fig. 1, is a mail carriage, as at present used, with its springs.

Fig. 2 a side, and fig. 3 an end view of a first-class carriage.

Plate CCCCXXXII. fig. 1, shows a close second-class carriage, with brakes which are worked by the handle at the top of the right hand end.

Fig. 2 is a plan of the buffer and draining apparatus for the first and second-class carriages, and the mails.

Fig. 3 is a third-class carriage, and fig. 4 a plan of the drawing apparatus. In these carriages there are no buffer springs, but merely blocks at each end of the body. On some railways, the second-class carriages shown here are not used, but the third class, with the addition of a roof, is called the second-class. When this is the case, the ends are generally closed, but the sides are left open.

Fig. 5 shows a different form of buffering apparatus used on the Dublin and Kingston Railway; the buffer rod goes the whole length of the carriage, with a similar head and spring at the other end.

Plate CCCCXXXIII. figs. 1 and 2, are an end and side view of an approved earth waggon; and fig. 3 a plan of the same, which has been very generally adopted. The brakes are shown in both.

Plate CCCCXXXIV. fig. 1, is a ground plan of the London and Birmingham Railway engine-house at Birmingham, showing also the mode of laying on the water; a, b, c are the main water pipes; d, e, f air vessels placed over the main pipes, to prevent the ram of the water when the cleansing and forcing cocks are shut suddenly, which, with a considerable head of water, would endanger the breaking the pipes; c, e, f cleansing and forcing cocks; these have strong hoses attached to them, by means of which an engine standing over the cleansing pits d, d, may be worked, and the boiler cleansed, and also filled when the steam is up, the usual force of water on the jet being 78 lbs. 10 oz. to the square inch; c, e, f lines of rails from the central turntable to each engine pit.

VOL. XIX. Railways.

Plate CCCXXXVI. fig. 1, elevation and section of a water apparatus for washing the carriages as constructed on the London and Birmingham Railway; d air vessels to prevent the rain when the cocks are shut suddenly; a saddle cocks fitted with hollow plugs, one of which is shown detached at g; c hollow space to be filled with charcoal, as a security against the water being frozen; b the connection with the feed pipe by means of a union joint; e the feed pipe; f holding down pins.

Fig. 2, elevation of the west end of the great Blisworth cutting on the London and Birmingham Railway, showing the method of undercutting the rock.

Fig. 3 is a section of the side walls at the same place; the left-hand side shows a section of the wall in the recesses, and the right-hand side shows the same through a buttress, together with the inverted drainage.

Fig. 4 is an elevation of fig. 3.

Fig. 5 shows the method of drawing bridges to answer both for cuttings and embankments. The left-hand side is for a cutting and a bridge over the railway; the right-hand side is for an embankment and a bridge under the railway.

Fig. 6 is a plan of the fixed engine-house at Camden Town, on the London and Birmingham Railway, where the trains are drawn up from Euston Square. There are four lines of rails for a double railway, between these and the stairs leading down to the engine-room, on each side of which are the boiler rooms, with receptacles for fuel, &c. The working wheels for the endless rope are in the engine-room, and the well and tightening sheave behind it. The mode of working these is shown on a larger scale in Plate CCCCXXIV.

Plate CCCCXXVII. fig. 1, plan of a station; a road to the booking offices; b building containing booking offices, waiting rooms, and the offices requisite for the general railway business; on the opposite side of this building, on the road a, is the departure platform, and line of rails which go to the left; c, the first-class carriage house; f, the second-class carriage house; g, the stables for the goods' station; h, the goods' waggon house; c, the gullet for embarking horses and private carriages; i, the engine house; p, coke store, with tank over it; m, store-house for the engine department; k, repairing house and engine manufactory; n, latrine room; r, road next the arrival stage to the town for the passengers inwards; b, offices for goods and general store department; q, goods' arrival and departure sheds, with roads, t and s, to and from the town; a, the point from which the engine turns in the goods' arrival trains with a rope; r, workshops, lodging houses, &c.

Fig. 4, another plan of a principal station in which turntables are required; the same letters refer to the same things.

Fig. 5 is an elevation and fig. 6 a plan of the fittings to a booking office; a, the counter; b, the clerks for booking second-class passengers; c, the clerks for booking first-class passengers. The first-class passengers enter by the right-hand door c', having received their tickets, pass through c' to the door c", which leads to the first-class working-room and the platform. The second-class passengers enter by the left-hand door b', and in like manner pass through b" and b", which leads to the second-class waiting-room and platform.

Plate CCCCXXVIII. Turntables in plan and section, with details.

Fig. 1, the plan; fig. 2, the section; fig. 3, elevation of the frame; fig. 4, catches; these should have long handles to lift them by; fig. 5, elevation of roller and turntable on it; fig. 6, the roller; fig. 7, section of the roller; fig. 8, provision to lock the plate when required, by inserting a bolt through the plate and frame.

Plate CCCCXXIX. a, the steam whistle which is made use of to warn workmen on the road, and persons on the stations, when the engine is approaching; b, an elevated dome, up which the steam pipe rises to nearly the top to prevent the explosion of the engine throwing water out of the boiler. This dome, when closed off, forms the manhole; c, working safety valve, the lever of which acts as a spring weighing-machine; d, lock-up safety valve, which is screwed down to the required pressure by a series of springs; e, chimney; this generally has a wire gauge at the top to prevent the escape of sparks, and sometimes a damper to regulate the force of the blast-pipe; f, smoke box, in which are the cylinders, the end of one of which is seen at g, with the cock h, which is to let out condensed water or priming from the cylinder. There is a large door in the front of the engine, opening into the smoke-box, to allow of repairs being made to the cylinders, tubes, &c., inside; i, i, three guage cocks, to ascertain the height of the water in the boiler; A, water guage, shewing in a glass tube the height of the water in the boiler. This guage communicates by a cock at the top with the steam, and by one at the bottom with the water. It also has a second cock at the bottom, for the purpose of emptying it when necessary; l, steam regulator, by turning which the steam is shut off, or let into the cylinders; m, railing round the place where the engine-man and fireman stand; n, fire box, containing the furnace, round which a thickness of about three inches of water circulates from the boiler; the top is also full of water to the height of that in the boiler; o, supply pipe connected with the tender, from which water is pumped in at pleasure by means of the pumps p, which are worked by arms fixed on the piston rods, and running in guides; q, the handle which turns the pet cock; this is used by the engine-man to ascertain when his pumps are in proper order, in which case it throws out water, but when they are damaged it gives out steam; there is one on each side of the engine; r, cock by which the boiler is emptied, and the engine blown off. Plates also blow off at the bottom of the boiler, and open into the chimney, which is also used to cool the engine internally; s, strengthening rods to the frame-work of the engine; t, t, stays from the framing to the boiler; u, draw-box to which the tender is attached; v, door to the furnace; there is a similar one to the lower part of the fire-box, which is formed into the ash pit, and is open to the front for the purpose of increasing the draft; w, the frame-work of the engine. Some makers place this with its breadth horizontal instead of vertical, and Mr. Barry of Liverpool has his bearings inside the wheels instead of outside; x, x, the axle guides which play up and down in grooves in the sides of the axle-boxes; y, hook for attaching carriages to the foremost end of the engine; there is a similar one on the other side; z, the buffer.

The lower part of the boiler has a number of brass tubes running through its whole length, through which the flame and hot air rush in their passage to the chimney, up which the steam, after it has performed its offices in the cylinders, is thrown through an iron pipe called the blast pipe. This is one of the most essential of all the improvements of the locomotive. The boiler is cases with wood, to preserve the heat as much as possible; its tubes last about two years, and cost about £1 each.

The steam pipe, by which the steam is conveyed to the cylinders, is divided into two after it enters the smoke-box, and one goes to each cylinder; these are all made of copper, and the entrance and exit of the steam into the cylinder is regulated by slide valves worked by eccentrics on the cranked axle, which move levers fixed to the weight bars. The pistons are formed of metal rings in several divisions, so placed as to break joint. The piston rod is fixed with a joint to the connecting rod; and this last gives motion to the cranked axle, having its end next the piston rod fixed to the cross heads, each end of which work in guide-blocks, thus causing a parallel motion in the piston rod.

The cranks are placed at right angles to each other, to enable the engine to get over her casters; one piston thus works at the greatest advantage, when the other is at the least. By the eccentrics on the crank axle, and a series of levers, the slide valves are continually worked backwards and forwards with the engine, and this motion can be reversed instantly, so as to cause the engine to go in the opposite direction when required; this is done by means of the hand wheel near the fire-box, which moves against a pin having three notches in it, and the handle is placed in the upper or lower notch, the engine goes either forward or backward, and when in the middle, the slide valves no longer work. There are many modes by which this is arrived at by different makers, and there is generally two starting handles, by pulling which the slides can be worked by hand; these are constantly in motion while the engine is going.

Proper cups containing oil are placed over each of the working parts, so as to ensure a steady and constant supply of oil to every moving portion of the engine. These cups have a tube inside them, which leads through to the part which is intended to be supplied with oil, and a cotton wick is put through the tube, one end of which hangs over the top into the oil cup, and thus acts as a syphon. The axle boxes are filled with grease, and have a cover on the top to ensure a proper lubrication of the axles.

Inside bearings are often used to strengthen the engine, and ensure its correct action; they also steady the cranked axle against the horizontal force of the piston rods. The whistle is formed by a pipe through which the steam is allowed to pass; likewise, by means of a cock, it then rushes against the thin edge of the upper, domed part, which is convex like a bell, and gives out a clear sound when the cock is properly turned, which may be heard at a very great distance.

The buffers consist of leather cushions stuffed with horse hair, and their use is to break the shock arising from any concussion which the engine may receive. Each of the wheels has a cover, called a splasher, placed over them, to prevent their throwing the dirt from the rails into the machinery. Sometimes two pair of wheels are coupled together; this gives more adhesion, and is generally done to goods' engines only, which also have usually their wheels of less diameter than those used for passenger trains, velocity being not so much an object as power of draught. Mr. Stephenson does not now make his engines with any flanges on the middle pair of wheels.

(a.m.)