STEEL-yard, is one of the most ancient presents which science has made to society; and though long in defuncte in this country, is in most nations of the world the only instrument for ascertaining the weight of bodies. What is translated balance in the Pentateuch, is in fact steelyard, being the word used by the Arabs to this day for their instrument, which is a steelyard. It is in common use in all the Asiatic nations. It was the flatera of the Greeks and Romans, and seems to have been more confided in by them than the balance; for which reason it was used by the goldsmiths, while the balance was the instrument of the people.—Non aurifices flatera sed populari truitina examinare. Cic. de Orat. 238.

The steelyard is a lever of unequal arms, and, in its most perfect form, is constructed much like a common balance. It hangs in theers E (fig. 1.) resting on the nail C, and the scale L for holding the goods hangs by a nail D on the short arm BC. The counter weight P hangs by a ring of tempered steel, made sharp in the inside, that it may bear by an edge on the long arm CA of the steelyard. The under edge of the centre nail C, and the upper edge of the nail D, are in the straight line formed by the upper edge of the long arm. Thus the three points of suspension are in one straight line. The needle or index of the steelyard is perpendicular to the line of the arms, and plays between the sheers. The short arm may be made so massive, that together with the scale, it will balance the long arm unloaded. When no goods are in the scale, and the counter weight with its hook are removed, the steelyard acquires a horizontal position, in consequence of its centre of gravity being below the axis of suspension. The rules for its accurate construction are the same as for a common balance.

The instrument indicates different weights in the following manner: The distance CD of the two nails is considered as an unit, and the long arm is divided into a number of parts equal to it; and these are subdivided as low as is thought proper; or in general, the long arm is made a scale of equal parts, commencing at the edge of the nail C; and the short arm contains some determined number of those equal parts. Suppose, then, that a weight A of 10 pounds is put into the scale L. The counterpoise P must be of such a weight, that, when hanging at the division 10, it shall balance this weight A. Now let any unknown weight W be put into the scale. Slide the hook of the counterpoise along the long arm till it balances this weight. Suppose it then hanging at the division 38. We conclude that there is 38 pounds in the scale. This we do on the authority of the fundamental property of the lever, that forces acting on it, and balancing each other, are in the inverse proportion of the distances from the fulcrum to their lines of direction. Whatever weight the counterpoise is, it is to A as CD to 10, and it is to the weight W as CD to 38; therefore A is to the weight W as 10 to 38, and W is 38 pounds: and thus the weight in the scale will always be indicated by the division at which it is balanced by the counterpoise.

Our well-informed readers know that this fundamental property of the lever was discovered by the renowned Archimedes, or at least first demonstrated by him; and that his demonstration, besides the defect of being applicable only to commensurable lengths of the arms, has been thought by metaphysicians of the first note to proceed on a postulate which seems equally to need a demonstration. It has accordingly employed the utmost refinement of the first mathematicians of Europe to furnish a demonstration free from objection. Mr D'Alembert has given two, remarkable for their ingenuity and subtlety; Foncenex has done the same; and Professor Hamilton of Trinity college, Dublin, has given one which is thought the least exceptionable. But critics have even objected to this, as depending on a postulate which should have been demonstrated.

The following demonstration by Mr Vince, we think unexceptionable, and of such simplicity that it is astonishing that it has not occurred to any person who thinks on the subject.

Let AE (fig. 2.) be a mathematical lever, or inflexible straight line, resting on the prop A, and supported at D by a force acting upwards. Let two equal weights b and d be hung on at B and D, equidistant from A and E. Pressures are now exerted at A and E; and because every circumstance of weight and distance is the same, the pressure at E, arising from the action of the weight b on the point B, must be the same with the pressure at A, arising from the action of the weight d on the point D; and the pressure at E, occasioned by the weight d, must be the same with the pressure at A, occasioned by the weight b. This must be the case wherever the weights are hung, provided that the distance AB and DE are equal. Moreover, the sum of the pressures at A and E is unquestionably equal to the sum of the weights, because the weights are supported solely at A and E. Let the two weights be hung on at C the middle point; the pressure at E is still the same. Therefore, in general, the pressure excited at the point E, by two equal weights hanging at any points B and D, is the same as if they were hung on at the middle point between them; but the pressure excited at E is a just measure of the effort or energy of the weights b and d to urge the lever round the point A. It is, at least, a measure of the opposite force which must be applied at E to sustain or balance this pressure. A very fastidious metaphysician may still say, that the demonstration is limited to a point E, whose distance from A is twice AC, or = AB + AD. But it extends to any other point, on the authority of a postulate which cannot be refuted, viz. that in whatever proportion the pressure at E is augmented or diminished, the pressure at this other point must augment or diminish in the same proportion. This being proved, the general theorem may be demon- Steel-yard. ted in all proportions of distance, in the manner of Archimedes, at once the most simple, perspicuous, and elegant of all.

We cannot help observing, that all this difficulty (and it is a real one to the philosopher who aims at rendering mechanics a demonstrative science) has arisen from an improper search after simplicity. Had Archimedes taken a lever as it really exists in nature, and considered it as material, consisting of atoms united by cohesion; and had he traced the intermediate pressures by whose means the two external weights are put in opposition to each other, or rather to the support given to the fulcrum; all difficulty would have vanished. (See what is said on this subject in the article STRENGTH of Timber, &c.).

The quantity of goods which may be weighed by this instrument depends on the weight of the counterpoise, and on the distance CD from the fulcrum at which the goods are suspended. A double counterpoise hanging at the same division will balance or indicate a double quantity of goods hanging at D; and any counterpoise will balance and indicate a double quantity of goods, if the distance CD be reduced to one half. And it sometimes occurs that steelyards are so constructed that they have two or more points of suspension D, to which the scale may occasionally be attached. It is evident, that in this case the value or indication of the divisions of the long arm will be different, according to the point from which the scale is suspended. The same division which would indicate 20 pounds when CD is three inches, will indicate 30 pounds when it is two inches. As it would expose to chance of mistakes, and be otherwise troublesome to make this reduction, it is usual to make as many divided scales on the long arm as there are points of suspension D on the short arm: and each scale having its own numbers, all trouble and all chance of mistake is avoided.

But the range of this instrument is not altogether at the pleasure of the maker. Besides the inability of a slender beam to carry a great load, the divisions of the scale answering to pounds or half-pounds become very minute when the distance CD is very short; and the balance becomes less delicate, that is, less sensibly affected by small differences of weight. This is because in such cases the thickness which it is necessary to give the edges of the nails does then bear a sensible proportion to the distance CD between them; so that when the balance inclines to one side, that arm is sensibly shortened, and therefore the energy of the preponderating weight is lessened.

We have hitherto supposed the steelyard to be in equilibrium when not loaded. But this is not necessary, nor is it usual in those which are commonly made. The long arm commonly preponderates considerably. This makes no difference, except in the beginning of the scale. The preponderancy of the long arm is equivalent to some goods already in the scale, suppose four pounds. Therefore when there are really 10 pounds in the scale, the counterpoise will balance it when hanging at the division 6. This division is therefore reckoned 10, and the rest of the divisions are numbered accordingly.

A scientific examination of the steelyard will convince us that it is inferior to the balance of equal arms in point of sensibility: But it is extremely compendious and convenient; and when accurately made and attentively used, it is abundantly exact for most commercial purposes. We have seen one at Leipzig which has been in use since the year 1718, which is very sensible to a difference of one pound, when loaded with nearly three tons on the short arm; and we saw a wagon loaded with more than two tons weighed by it in about fix minutes.

The steelyard in common use in the different countries of Europe is of a construction still simpler than what we have described. It consists of a batten of hard wood, having a heavy lump A (fig. 3.) at one end, and Fig. 4. a swivel-hook B at the other. The goods to be weighed are suspended on the hook, and the whole is carried in a loop of whip-cord C, in which it is slid backward and forward, till the goods are balanced by the weight of the other end. The weight of the goods is estimated by the place of the loop on a scale of divisions in harmonic progression. They are marked (we presume) by trial with known weights.

The chief use that is now made of the steelyard in these kingdoms is for the weighing of loaded waggons and carts. For this it is extremely convenient, and more than sufficiently exact for the purpose in view. We shall describe one or two of the most remarkable; and we shall begin with that at Leipzig already mentioned.

This steelyard is represented in fig. 4. as run out, Fig. 4. and just about to be hooked for lifting up the load. The steelyard itself is OPQ, and is about 12 feet long. The short arm PQ has two points of suspension c and b; and the stirrup which carries the chains for holding the load is made with a double hook, instead of a double eye, that it may be easily removed from the one pin to the other. For this purpose the two hooks are connected above an halp or staple, which goes over the arm of the steelyard like an arch. This is represented in the little figure above the steelyard. The suspension is shifted when the steelyard is run in under cover, by hooking to this flape the running block of a small tackle which hangs in the door through which the steelyard is run out and in. This operation is easy, but necessary, because the stirrup, chains, and the flage on which the load is placed, weigh some hundreds.

The outer pin b is 14 inches, and the inner one c is seven inches, distant from the great nail which rests in the sheers. The other arm is about 10\frac{1}{2} feet long, formed with an obtuse edge above. On the inclined plane on each side of the ridge is drawn the scale of weights adapted to the inner pin c. The scales corresponding to the outer pin b are drawn on the upright sides. The counterpoise slides along this arm, hanging from a saddle-piece made of brafs, that it may not contract rust. The motion is made easy by means of rollers. This is necessary, because the counterpoise is greatly above a hundred weight. This saddle-piece has like two laps on each side, on which are engraved vernier scales, which divide their respective scales on the arm to quarters of a pound. Above the saddle is an arch, from the summit of which hangs a little plummet, which shows the equilibrium of the steelyard to the weigher, because the sheers are four feet out of the house, and he cannot see their coincidence with the needle of the steelyard. Lastly, near the end of the long arm are