one of the largest rivers in Scotland. It is first formed of several small streams rising on the north of Ben Lomond, or flowing from Loch Katrine and the other lakes in the adjacent country. It proceeds easterly in a direct course for above 100 miles, receiving in its progress the tributary waters of the Goodie, the Teith, and the Allan above Stirling, and below it the Devon, the Carron, the Avon, the Almond, the Leith, the Esk, the Leven, the Tyne, and others; and it discharges itself into the German Ocean in about 56° 10' of north latitude. The windings of the Forth, both above and below Stirling, are extremely beautiful. From its junction with the Teith above Stirling to the earse ground below Gartmore the windings extend about 28 miles, although the distance in a direct line is only about 20. From Stirling harbour to Alloa the length of the river is 10½ miles, although in a straight line it is not more than 5, and here it is comparatively narrow, shallow, and winding. From Alloa to Grangemouth the distance is 5 miles; and here the Forth widens, with a variable depth of from 4 to 15 feet at low water. From Grangemouth to the Long Craig Beacon at North Queensferry, a distance of 10 nautical miles, proceeding downwards the depth increases in the first mile from 10 to 15 feet, and in the second mile to 25 feet at low water, and at the third mile to 53 feet, while the remaining part of the distance—7 miles, including the great anchorage of St Margaret's Hope—has a depth generally of about 60 feet at low water. At Queensferry the river is 2 miles wide; at Kinghorn nearly 6; between Dysart and Aberdty about 12; and between St Abb's Head and Fifeness, where the Forth joins the German Ocean, it is from 35 to 40 miles. Near Queensferry, between Inchgarvey and the north shore, it deepens to 37 fathoms. Between Elie and the south shore its depth is sometimes 30 fathoms; and it never exceeds this depth to the westward of its junction with the north sea, except as above stated.

The Forth, like other streams connected with the ocean, ebbs and flows twice in 24 hours, but the flood and ebb run about two hours longer in the middle than at the shore. The tide flows 4½ miles above Stirling shore. At this harbour spring tides rise 7 feet 9 inches, and at Alloa 19½ feet.

It was high water, according to Captain Thomas's observations in 1815, at

| Location | Spring Tides | Neap Tides | |-------------------|--------------|------------| | Elie Harbour | 21.11 p.m. | 14 feet | | Leith and Burntisland | 2.15 | 16 feet | | Hopetoun House | 3.30 | 17 feet |

The tides at Leith and Kinghorn rise sometimes as high as 19 feet above low-water mark, the average being 17½ feet.

There are in the Forth, as elsewhere in similar rivers and arms of the sea, particular currents. Among the most remarkable are those known by the name of Leeks above the Queensferry, which are particularly observed from Culross to Alloa. "These consist in an intermission of the tide at certain places during the flood, and before high water the sea ebbs. On the contrary, while the sea ebbs, and before low water, the ebb intermits, and a flow commencing, continues some time; after which the ebbing is resumed until low water. This is seen during two hours, and the irregularity occupies more or less of the river according as it is spring or neap tide."

Certain winds, acting upon the great mass of the Atlantic Ocean, affect the times at which it is high or low water in the Forth, while their effect upon the extent of the rise or fall of its waters is frequently very considerable.

The prevailing winds of the Forth will be seen by the following table, constructed from observations taken every day, at ten o'clock forenoon, on the island of Inchkeith, for the ten successive years ending on 31st December 1826.

| Direction of the Winds | Description of the Winds | |------------------------|--------------------------| | | Light Airs | Breezes | Gales | Storms | Total | | South | 96 | 165 | 29 | 2 | 392 | | South-West | 42 | 181 | 111 | 5 | 339 | | West | 275 | 807 | 267 | 22 | 1371 | | North-West | 44 | 157 | 13 | 3 | 217 | | North | 26 | 145 | 20 | 1 | 152 | | North-East | 68 | 90 | 23 | 24 | 205 | | East | 334 | 345 | 34 | 29 | 739 | | South-East | 104 | 169 | 6 | 5 | 224 | | Changeable | 101 | 12 | | | 113 | | | 1090 | 1971 | 503 | 88 | 3652 | The prevailing winds and their relative force, as indicated at the Calton Hill Observatory, may also be seen from the following table constructed from the observations taken there every day under the superintendence of the astronomical observer for the same ten years, ending on 31st December 1826. The entry in the register for each day is applicable to the winds of its whole 24 hours.

| Direction of the Winds | Moderate and Calm | Fresh | Sharp | High | Very High | Extremely High | Total | |------------------------|------------------|-------|-------|------|-----------|---------------|-------| | South | 85 | 2 | | 17 | 3 | 4 | 111 | | South-West | 310 | 43 | 1 | 178 | 68 | 30 | 630 | | West | 444 | 54 | 3 | 235 | 54 | 8 | 798 | | North-West | 207 | 33 | 4 | 143 | 48 | 9 | 444 | | North | 61 | 6 | 4 | 17 | 5 | 3 | 99 | | North-East | 122 | 11 | 2 | 45 | 41 | 2 | 168 | | East | 361 | 37 | 4 | 45 | 4 | 4 | 471 | | South-East | 131 | 8 | 3 | 14 | 2 | 1 | 158 | | Changeable | 688 | 44 | 4 | 119 | 29 | 29 | 789 |

From these tables it will be observed that the prevailing winds in the Forth, the gales and the storms at Inchkeith, and the "very high" and "extremely high" winds at the Calton Hill Observatory, chiefly proceed from westerly directions.

The waters of the Forth and its tributary streams are all fresh until they mingle with that of the ocean. Long before the river becomes two miles wide they acquire a saltiness which differs little, if at all, from that of the sea. The water in the neighbourhood of the coal-works on the Forth has been often evaporated for the sake of the salt, which was here at one time an extensive article of manufacture.

The constituent parts of 10,000 parts of the waters of the Forth were found by Mr Murray, in the course of three different analyses made in different ways, to contain:

- Muriate of soda: 242:51 - Sulphate of magnesia: 7:86 - Sulphate of soda: 9:99 - Muriate of magnesia: 34:49 - Muriate of lime: 9:45 - Sulphate of lime: 304:30

Mr Murray placed most confidence in the results obtained from the last of these analyses.

The minerals of which the banks of the Forth are composed will be found described under the counties of East Lothian, Mid-Lothian, West Lothian, Stirling, Clackmannan, Perth, and Fife, by all of which the Forth is bounded. Coal, besides being wrought in these counties, was once worked near Culross and Torryburn under the bed of the river, and partly by pits within high-water mark. At the mouths of these pits there were piers, at which vessels were loaded with coals. But the mines above referred to have for many years been filled with water. At West Wemyss, however, there are still extensive coal mines worked under the sea.

The bed of the Forth consists to a great extent of mud, and in many places the sandstone bottom is covered with it to the depth of 20 feet. Its banks above Alloa, and a great way below that place, are formed of this material, which is brought down by the waters from the higher levels; and the cases of Stirling and Falkirk, &c., which have been formed from its accumulation, are secured at their lowest levels by sea dykes against inundations occasioned by the rise of the tides. The recent alluvial cover to the westward of Alloa has been found by Mr Bald in some places to be no less than 90 feet deep, and to contain trunks and branches of large trees, and beds of sand and sea shells, particularly of the oyster, cockle, mussel, donax, &c.; and similar beds of shells not only abound at and below Alloa, but are found several miles to the westward of Stirling similarly situated. Many of the oyster-shells are of uncommon thickness, and larger than any specimens that can now be found. What makes the westerly position in which these uncommonly large shells are found very remarkable is that there are no specimens of the oyster now found farther up the Forth than Queensferry.

There is also a bed of marine shells on the banks of the Forth near Borrowtounness about three miles in length and several feet in thickness, and which is situated many feet above the present level of the waters of the Forth. This circumstance would favour the opinion that the sea in this quarter had at one time occupied a higher elevation in relation to the land than at present; an opinion which is further supported by the fact of the skeleton of a large whale having been found some time ago in the lands of Airthrey, near Stirling. The surface of the ground where the remains of this huge marine animal were deposited was ascertained by Mr Stevenson to be 24 feet 9 inches above the present level of the high water of the Forth at spring tides. The skeleton of another whale, with a bone harpoon sticking in it, was also found seven miles farther inland, on what is now the Blair Drummond moss.

But if the land has been gaining on the waters in the upper part of the Forth, ground has been lost farther down the estuary. The sea has made considerable encroachments at North Berwick; at Newhaven an arsenal and dock; built in the reign of James IV, in the fifteenth century, has been swept away. On the coast of Fife, in 1803, the last remains of the Priory of Crail and the ground on which it stood met with a similar fate; and no traces can now be found of the lands which extended into the sea, and formed, in 1225, the estuary, the fisheries of which were then a subject of an important dispute between the monks of Dryburgh and those of the Isle of May; all that now remains of this estuary is a small streamlet called the Drill burn, which flows through a portion of the sands in West Anstruther harbour.

At Largo Bay the sea seems now to be covering ground which was formerly dry land. Here a submarine forest has been discovered, the roots of the trees penetrating into a brown clay, over which is irregularly distributed a covering of sand and fine gravel. The peat upon it is composed of land and fresh-water plants, amongst which are hazel nuts, and the remains of birch, hazel, and alder trees. The root of one tree, apparently an alder, was here traced by Dr Fleming to an extent of more than 6 feet from the trunk.

On almost all the shores of the Forth there is an abundant supply of sea-weed, which has often been burned at various places to form kelp, but this trade is now given up. The produce of the rocks and what is cast ashore in storms is now therefore only used as manure.

Numerous porpoises are often seen tumbling and disporting in the firth, and seals lying on the rocks or swimming fishes along the coasts. Sharks of several species have occasionally made their appearance, and have been brought ashore by the fishermen in their nets about Anstruther and elsewhere. Numerous cetacea from 20 to 30 feet long have often been stranded in the Forth. From twenty-five to thirty of these animals were at one time on shore between Cambus-kenneth and Alloa. A male Beluga or white whale, apparently of full growth, appeared in its waters in 1815. It was killed by the salmon fishers near the same place, and sent to Edinburgh, where it was dissected by the late Dr Barclay.

The salmon is abundant in the Forth, and salmon fisheries have been established for many years at Stirling, Abercorn, near Queensferry, and many other places on both sides of the firth, as far down as Largo Bay. The whole of these fisheries belong to thirty proprietors, and such of them as were let in 1854 produced a gross rental of £1,316. The rent of the town of Stirling's fishing then amounted to £354, of another proprietor to £240, of another to £126, of two others to £70 each, and others were let under that Forth.

sum, a few at a rent of L5, and thirteen of them brought no rent at all, as they appear to have been considered of little value.

Herrings, &c.

Herrings are also plentiful in the Forth, and at various fishing stations the fishery is prosecuted successfully. To give some idea of its extent, in the Anstruther district in Fife, which includes all the sea-ports from St Andrews to Buckhaven inclusive, the total number of barrels or casks of herrings taken (1854) amounted to 17,906½, whereof 11,468 were sold fresh, 3699½ were sold and exported to Continental markets, and 2739 cured and sent to Ireland.

The number of full-sized cod and ling caught and cured was 84,855, of which 1089 casks were dried, and 1865½ barrels were pickled. In addition to these, 9858 casks of full-sized cod and ling were caught and sold in a green state and sent to and consumed in Leeds, Preston, Birmingham, Edinburgh, Glasgow, Cupar, Stirling, Perth, Dundee, &c. The value of the annual average of haddock's fresh has lately been estimated at L4,000, of smoked L12,000, of turbot, halibut, lobsters, crabs, &c., L458, and of periwinkles, L136.

There were engaged in this district, in 1854, 500 boats, 2099 fishermen, 97 coopers, 1444 gutters and packers, and 1063 labourers, all in the employment of 68 fish-curers. The value of the boats and their appurtenances was reported to the fishery commissioners to be L61,991.

In the Leith district, which includes all the portion of the firth above North Berwick on the south, and East Wemyss on the north shore, the total number of casks or barrels of herrings taken (in 1854) were 16,045½, whereof 6695½ were cured, and 9350 were sold fresh; 13,714½ were sold to Continental markets, and 496½ sold and sent to Ireland. The number of ling and cod caught by the fishermen of this district were all sold fresh, and have been estimated to the commissioners at 5900. All the other fish caught here were also sold and consumed in a fresh state. There were employed in this trade, in 1854, 354 boats, 1166 fishermen, 100 coopers, 489 gutters and packers, and 224 labourers, all in the employment of 25 curers. The value of the boats and their appurtenances was reported to be L21,771.

Besides the fisheries in the Forth above stated, there were 35 boats, 134 fishermen, 25 coopers, 205 gutters and packers, and 40 labourers employed in the same trade by 2 curers at Carty Bay, and 30 at Dunbar, and the fish taken by them are generally sold fresh.

In addition to the Scotch fishermen, it may be mentioned that all parts of the firth are occasionally fished by English vessels, and a dozen at a time of English fishing smacks, and as many as 20 French boats, have been occasionally seen by the Anstruther fishermen to be so employed; 40 sail of foreign vessels were at one time known to have been fishing cod near St Abb's Head.

Lobsters and crabs are caught at all the fishing-stations in the Forth, as well as in the Anstruther district. Mussels, cockles, limpets, and whelks are also collected and sold in great quantities at the places where they abound, and oysters are extensively fished at the oyster beds, which are met with near Inchkeith and farther up the Forth.

Wild-fowl.

There is nothing remarkable about the wild fowl resorting to the firth in winter. The solan geese of the Bass have been already described under the head Bass, to which the reader is referred.

Besides the Bass, in the entrance to the Forth, there is another island, the May; and the larger islands farther up the Forth are Inchkeith, Inchcolm, and Inchgarveigh, which will be found described in separate articles. The smaller islands are Fidra, the Lamb, and Craigleith, near the Bass, and Mickry and Cramond islands, near Inchcolm.

The principal obstructions to the navigation of the Forth between Alloa and Stirling have hitherto arisen in a great measure from the two fords of the river, the one called the Town ford and the other the Abbey ford, and from the channel being rendered shallow partly by large boulders and partly by accumulations of peat. The peat accumulations have arisen chiefly from the proprietors above Stirling clearing several thousand acres of their lands for cultivation, by removing the peat which covers them, and moving it into the river in order to be carried away by the current to the sea. This practice has been followed since 1732. The moss covering the soil varies in depth from 14 to 4 or 5 feet, but the greater proportion is 10 feet. Mr Drummond of Blair-Dummond, from 1783 to 1839, floated away upwards of 1600 acres of this substance.

The principal sandbanks which obstruct the navigation farther down the firth are the Drum-sands, near Cramond, banks, and the Sand-end on the east of Burntisland harbour.

The principal rocks which require to be avoided by the dangerous mariner are the South Carr Reef, lying N.N.W. from Dun-rocks bar, the North Carr, about a mile and a quarter east of Fifeness, the Blae to the west of Kinghorn Ness, the Commons to the west of Burntisland, Craig Waugh S.E.½ E. of Inchkeith, and the Gunnet Rock, Pallas Rock, Long Craig, Briggs, and Harwit in its neighbourhood; and several miles farther west and nearer Inchcolm, the Oxcare, Careraig, and Mickry Stone. Many of these rocks are seen at the lowest ebbs; their position, together with the different land-marks, which are necessary to point them out to the mariner, are delineated on the Admiralty Charts, and the sailing directions for the Firth of Forth, contained in the Coaster's Assistant, which is published in Leith. To show their position still better, floating buoys have been placed upon Craig Waugh, the Gunnet, the Harwit, and the Pallas Rocks; and beacons have been erected on the Oxcare, the North Carr, and on the Long Craig, and on most of the other dangerous rocks, and on several shoals and sand-banks.

Besides these provisions for aiding the navigation, there are two lighthouses on the Isle of May, one on the Island of Inchkeith, and various other lighthouses are now erected on all the harbours and landing places of importance in the firth.

The anchorage of the Firth of Forth is excellent. Mr Anchor-Osborne, in a report to the Lords of the Admiralty on 2d May 1853, says of it, "Between the Humber and the Frith of Cromarty there is no other harbour or anchorage into which large ships of war can safely run for shelter or rendezvous other than the Frith of Forth, and more particularly in the reach above the Queensferry, where the shelter is complete. But as the Frith of Cromarty is away from all important interests, the Frith of Forth must be considered the only war port north of the Humber, and therefore a most fitting place for a naval arsenal." But besides the great and important anchorage at St Margaret's Hope, in the reach above the Queensferry, which is more particularly referred to in this Admiralty Report, Leith Roads to the west of Inchkeith is another which is capable of holding a large fleet of ships of war of any size. The minor anchorages in the firth, which are also very good, are at Aberlady Bay, the western part of Largo Bay, Burntisland, St Davids, Limekilns, &c.

The landing-places in the Forth are, on the south side the Harbours, harbours of Dunbar, North Berwick, Port Seton, Morrison's Haven, Fisherrow, Leith, Newhaven, Trinity, Granton, South Queensferry, Borrowstounness, Grangemouth, and Stirling shore, and on the north side Crail, Anstruther, Elie, Pittenweem, Leven, Methil, West Wemyss, Dysart, Kirkcaldy, Kinghorn, Pettycur, Burntisland, Starleyburn, Aberdour, St Davids, Inverkeithing, North Queensferry, Charleton, Crombie Point, Culross, Kincardine, and Alloa. Great improvements and new erections have been lately made at most of these harbours which are of any note; and in particular, the Duke of Buccleuch's magnificent harbour in progress of formation at Granton, and the extension of Leith Pier into deep water may be referred to. Of less magnitude is the deepening of the channel of the Forth between Alloa and Stirling by commissioners acting under the Act of Parliament 6th and 7th Victoria, cap. 47. Since the passing of this act in 1843, a channel of about 500 yards in length has been formed through the Abbey ford, giving about 3 feet 6 inches greater depth of water than formerly. A channel about 1000 yards in length has also been formed through the Town ford, which is not yet fully completed as regards its depth of water. In these operations many thousands of large boulder stones and the peat accumulations which formed obstructions to the navigation have been removed, and no doubt is entertained by the inspectors, who have reported to Government on the subject, but a depth of 16 or 17 feet at spring-tides will be obtained up to Stirling when the works in progress are completed. Upwards of L9000 (including the expense of the act and of erecting a quay at Stirling) have already been expended by the Harbour Commissioners on these operations, and L7000 more is about to be expended upon them. This sum is to be paid to the commissioners by the town-council of Glasgow for damage likely to arise to the improvements in progress on the Forth, from the liberty obtained by the City of Glasgow to draw a large quantity of water from Loch Katerine. In addition to these sums the revenue of the Forth Commissioners, which is considerable, will enable them still further to extend their works.

Further, the low-water ferry landing-place at Burntisland, belonging to the Edinburgh, Perth, and Dundee Railway Company, is a great improvement at that port; and at Kirkcaldy, Buckhaven, and other harbours, extensive works are in progress under Harbour Commissioners.

The coasting and foreign trade of the Forth is carried on in vessels varying in size from 18 to 500 tons. The principal port to which they belong is Leith; but there are several whalers and large vessels engaged in the Australian, American, Mediterranean, and Baltic trades, which belong to other ports in the Forth.

The traffic in goods and passengers between the ports in the Forth and London, Greenock, Glasgow, Liverpool, Hull, Newcastle, Dundee, Perth, Aberdeen, Inverness, Peterhead, and almost every considerable seaport in Scotland, is conducted chiefly by vessels of joint-stock companies, which vessels sail periodically. Joint-stock companies are also engaged in the Leith trade with Hamburg and Rotterdam. The Glasgow, Greenock, and Liverpool trade is chiefly conducted through the Forth and Clyde Canal, as to which see Navigation, Inland, and Grangemouth.

The number and tonnage of the vessels belonging to the ports in the Forth in 1855 are as follow:

- At Alloa, including the creeks of Kinocardine and Stirling, 74 vessels, with a tonnage of 12,402 - At Borrowstounness, including the creeks of Charleston and Limekilns, 47 vessels, with a tonnage of 3,781 - At Grangemouth, 54 vessels, with a tonnage of 9,233 - At Inverkeithing, 23 vessels, with a tonnage of 2,361 - At Kirkcaldy, including the creeks of Largo, Leven, Wemyss, Dysart, Kinghorn, Burntisland, and Aberdour, 60 vessels, with a tonnage of 7,987 - At Leith, including the creeks of Granton, Fisherrow, Cockenzie, and Dunbar, 176 vessels, with a tonnage of 25,404

Total 434 vessels, with a total tonnage of 60,868

To facilitate the communication between the northern Bridges and southern parts of Scotland by a passage across the Forth, wooden bridges were erected at an early period, and the old stone bridge of Stirling was erected before 1571; the new stone bridge and the railway bridge near it were erected only a few years ago. There was once a project of erecting a suspension bridge at the Queensferry, and another project of making a tunnel there; but both the schemes were abandoned.

The passage of the river and firth by ferries has been an object of legislative enactment since 1467. Before the introduction of steam navigation, the traffic at these ferries was chiefly conducted by open boats, pinnaces, and yawls of various sizes, and from the want of low water piers they seldom departed from either side except at high water. Most of these ferries are still private property. The private rights of the Queensferry passage were purchased by Parliamentary Trustees in 1809, and large sums have been expended on its improvement. The ferries of Kinghorn and Burntisland were also under Parliamentary Trustees for many years; but they have now ceased to be so, and the Fife and Mid-Lothian ferries and their landing-places at Kinghorn, Pettycur, and Burntisland, are now the property of the Edinburgh, Perth, and Dundee Railway Company, who afford the ferry accommodation as a portion of the railway business. For the extent and particulars of this trade, reference is made to the article Fife. FORTIFICATION

Is the art of securing a portion of ground, whether occupied by a town, or including within it a dock-yard, port, or harbour, or serving, in military language, as the position of an army, from the attack of an enemy, by surrounding or covering it with works of defence; and as such works are so many obstacles placed in the way of the advance of their assailants, whilst they are at the same time the means of sheltering the defenders, it is the art of enabling a small number of men to defend themselves against the attack of a much larger. Various modifying terms have been adopted in connection with the general one of fortification, but none of them are of much use in considering this subject; and some may lead to error, by inducing an engineer to restrict himself under some circumstances to a very limited view of his subject. Thus, fortification natural and fortification artificial, imply a very useless distinction, as every engineer must avail himself both of the natural advantages or obstacles of the ground, as well as of the obstacles his science and genius enable him to add to them; and thus in every fortification nature and art must act together. Again, fortification regular and fortification irregular, are terms equally defective, as no fortification can be possibly regular unless it should so happen that the ground it occupies, as well as the ground surrounding it, is on all sides perfectly identical in its levels and general character. Fortification permanent and fortification field or temporary, refer again only to the immediate object of the works, or to the application of the science, and in no way affect its principles, which remain the same whether the work is a simple earthen intrenchment, or a great fortress surrounded by masonry walls. Fortification offensive and fortification defensive, are of all the most objectionable terms, since, strange as it may appear, they imply a contradiction to fact, as the perfection of defence depends as much on its active or offensive operations as on the protection its covering works afford, whilst the perfection of attack is equally dependent on the skill with which its covering works are constructed and pushed forward towards the fortress attacked, as on its offensive operations, or on the fire of its batteries.

The principles of defence then should be studied unshackled by any of these limiting distinctions, and the engineer should apply his means to his end, using without restriction the works best suited to his purpose; and it is in this way that the study of the subject will be here treated.

ELEMENTARY FORTIFICATION.

It is often desirable to examine the exact meaning of technical words, as a ready mode of acquiring a distinct notion of the ideas they were intended to convey; and of obtaining a glimpse of the historical progress of the science in which they are used. Fortify, Fortification, Fortress, Fort, are all words depending on the Latin words fortis, forte, strong, and fortifico or forte facio, to make strong; hence the idea they suggest is that, by some artificial or other arrangement, additional strength is bestowed upon one combatant over another, or upon one party of combatants over another party. A shield, the trunk of a tree, or bank of earth, or any other similar contrivance which shelters the body of one soldier from the missiles of his opponent whilst it leaves him free to discharge his own, may be considered a simple element of fortification.

A bank of earth, when reduced to the requisite thickness, and moulded into a proper form, with such slopes as the particular tenacity of the earth may require to insure stability, or which the intended direction of the fire over its summit may render necessary, becomes a parapet, so called from the Italian words paros, a defence or guard, and petto, the breast, or, in English, a breastwork. If the breastwork or parapet were only made sufficiently high to permit the soldier to fire over it, he would be greatly exposed after firing, and be forced to crouch down in order to obtain cover. The parapet is therefore made sufficiently high to cover the soldier when standing up, so as to enable him with ease and security to reload, as well as to move from one place to another. This increased height has rendered it necessary to introduce a banquette or step (accessible by an easy slope) from which the soldier can fire and then retire by the interior slope to the lower ground behind it; the name banquette being derived from banchetta, a little bench or step. As parapets are usually formed artificially, the earth for their construction is derived from a ditch, which being dug immediately in front of and parallel to the parapet, forms by its depth an additional obstruction to an advancing enemy. Ordinary intrenchments are formed of the simple parapet and ditch, but in forts and fortresses the height is still further augmented by elevating the parapet on another mound of earth called the rampart (riparo, in Italian), and as this additional mass requires a greater quantity of earth, the ditch is also made both wider and deeper. In this manner the difficulties of attack are increased, additional cover is given to the magazines or other buildings within the fortress, and the command over the country is increased and improved in efficiency, by elevating the soldier so that he can see over the many minor obstacles likely to restrict his field of view. A natural and simple mode of distinction may be therefore derived from the presence or absence of a rampart, and the two leading sections of the subject stated thus: parapet, or field fortification, and rampart, or town fortification.

In order to study efficiently the results of combining together these simple elements, and forming from them extensive works of defence, it is necessary that we should know the manner in which such works are represented on paper. As in architecture, of which in earlier times fortification was only a military branch, this is effected by the plan, the section, and the elevation, of which the two first are the most important. The plan of a work is the orthographic projection of the lines of intersection of the planes of its slopes on the plane of construction. The elevation is a similar projection on a vertical plane. The section or profile is taken on a plane perpendicular to the lines of intersection of the planes or slopes, and therefore represents the traces of these planes on the sectional plane. Fig. 1 represents a small portion of a simple parapet in plan and profile, and leads to the following explanation of terms:

In the plan, ee represents the crest of the parapet or highest ridge line of the work. In delineating the mere outline form of a work, it is this line which is always drawn, and is called the trace. Between ee and ee is the superior slope; between ee and a line parallel to it, through s of the profile, is the exterior slope, prolonged in this case to the bottom of the ditch dd, being continuous with the scarp sd; gg, crest of the glacis, or ridge of a slightly elevated mound of earth raised on the exterior edge of the ditch, or of the counterscarp, and sloping gently outward, so as to bring the assailants directly in the prolongation of the superior slope of the parapet, and therefore into the line of fire from its crest, and by its elevation to increase the amount of descent into the ditch. Within the crest of the parapet is seen the interior slope of the parapet, bounded by bb', the banquette, between bb' and bb, and the interior slope of the banquette, bounded by aa.

Relief.—This term is adopted to show either the height of any point of the work above the plane of construction, which is sometimes equivalent to the plane of sight, and Fortification may then be called constructive relief; or the height above the bottom of the ditch, when it may be called absolute relief. The relief taken in the latter sense is a very important datum, as it expresses the total amount of the obstruction offered by the parapet and ditch to the ascent of the assailant, and also as it is necessary in regulating the length of lines, which mutually defend each other, as will be seen hereafter. Relief of a work refers to the relief of the crest of its parapet. Command of a work means the height of the crest of its parapet, either above the plane of sight if horizontal, or above any point of that plane specially referred to, or above the crest of the parapet of any other work in front of it; the difference of height, therefore, between the crest of the parapet in fig. 1 over the crest of the glacis is the command of the parapet over the glacis; in the one case it is absolute, in the other relative command. An examination of the profile figure brings also under consideration, in respect to the row of palisades, another simple principle, namely, that an enemy should be stopped as he advances to the parapet by every obstacle which can be thrown in his way, and thus kept exposed as long as possible to the fire either of the work in front of him, or of some other work taking him in flank; if simply opposed by a front fire from the parapet, palisades, arranged as these are, would only check for a very short time the progress of an enemy, and are more useful for gaining time on the part of the defenders than for ultimate defence.

Many other obstacles may, however, be so arranged as to assist materially in rendering even the simple direct fire more effective.

Abattis.—These are formed of trees cut down, and arranged side by side with the branches interlaced together outwards, and the stems inwards; the branches should be freed from foliage, and their ends cut sharp. They may be arranged either in one or more rows, and when placed so that the fire from the parapet should sweep along their summits, they would, their stems being firmly fastened down by pickets to the ground and partly buried in it, occasion great loss to the enemy whilst attempting to remove them under fire.

Fig. 2 exhibits an arrangement of this kind; and it will be observed that on this profile the exterior slope of the parapet and the scarp have been formed into one gentle slope, whilst the counterscarp retains its ordinary slope. By this modification the difficulty of descending into the ditch remains as before, and the sloping pickets in front of the abattis prevents the assailants from immediately endeavouring to clear it away. In simple inclosed works, such as redoubts, as well as in lines, the defence frequently depends on direct fire alone; and in these cases an arrangement of the profile, as here figured with obstacles, would be far more effective in checking an enemy than an ordinary profile though in itself more difficult of ascent, without such obstacles, and in consequence would render it impossible that an ordinarily watchful garrison should be surprised; and this is a very important consideration, as a vigorous and bold enemy could scarcely be stopped if he had succeeded in arriving at the foot of the scarp unchecked.

Fig. 3 is another adaptation of an abattis formed only of large branches securely picketed down to the ground. In this case the form of the ground is taken advantage of, and even the profile of the defensive line is modified, a trench being cut out behind it, and the banquette being formed on the surface of the ground itself. The engineer will often, by simple arrangements of this kind, be able to carry his defensive lines over a large extent of ground in a short period of time, and to obtain a much more effective defence from the natural facilities afforded by the ground than he would have done by superadding to them, at the expense of great labour and much time, elevated works, not so well fitted to scour the face of the ground, and to act immediately upon the obstacles then checking the progress of the assailants.

Chevaux-de-frise.—The cheval-de-frise is an artificial substitute for an abattis. It consists of a strong horizontal beam, about 12 feet long and 9 inches square, through which are passed strong lance-like rods of either wood or iron, sharp at both ends, and about 6 inches apart. Several of these Fortification may be joined together by means of a ring at one end and the hook at the other end of the beam. The difficulty of making chevaux-de-frise, as their construction requires a number of carpenters and much wood, renders them unfit for sudden emergencies, and they are also, under ordinary circumstances, easily removed or destroyed; but with these, as with all military implements, there may be opportunities of using them with effect. If planted at the bottom of a hollow, exposed to a well-directed fire, and so placed that they must either be pushed uphill forward or pulled uphill backward, and then secured to the ground, either by chains, or by being fastened to upright posts, they would often prove a formidable obstacle. They are more generally used as a barrier to close an open work.

Fraises.—The fraise is distinguished from the palisade by being fixed in a horizontal, or nearly a horizontal position.

They are made about 10 feet long and 5 inches thick, being bound together by two ties, one nailed above and the other below them; without which precaution they would be much more easily torn away. They are sometimes fixed on the counterscarp as well as on the scarp.

Fig. 5 represents, in section, a row of fraises on the scarp. In this profile the ordinary banquette for musketry is represented by dotted lines below a wider terreplein formed for artillery to fire over the parapet, or a barbette, as it is usually called; but this will be more fully explained in a future paragraph.

Chausse-trapes.—These are made of four points of iron so arranged that one should always project upward in whatever manner they may be thrown on the ground. The points are either 2 or 4 inches long, and they are thrown over a space about 12 feet broad. Without doubt, troops coming suddenly, and in the dark, on such obstacles as these, would be much annoyed by them; and, in consequence, they were formerly much used, more so than they are now.

Trous-de-loup, or wolf-traps, are holes made in the ground in the form of a truncated cone, the sides of which are as little sloped as is consistent with the stability of the soil. They are made from 5 to 6 feet deep, and 6 or 8 feet in diameter. At the bottom a sharp picket is fixed, from 3 to 4 feet long, or, in place of it, the branch of a tree cut into sharp points, or a number of smaller sharp pickets, or a quantity of chausse-trapes. The figure shows the arrangement of trous-de-loup proposed by Wenzel, in plan and in section. If along the defensive line of a position, either on the glacis or on the scarp, when gradually sloped as in fig. 2, small trees or shrubs are planted, and on an emergency cut down, and the points of their stumps sharpened, they become very annoying to an assailant. Harrows have also been used, and, in short, every expedient which ingenuity can suggest should be adopted by an engineer to check the progress of an advancing enemy, and to keep him as long as possible under fire.

Stockades.—Before proceeding to an investigation of the principles which should regulate the relief and thickness of ordinary parapets, viewed in reference to simple defensive lines and to direct fire, it is right to notice the stockade as a substitute, and in some circumstances an advantageous one, for a parapet. The stockade is formed of either one row of stout palisades, or two rows, one behind the other; and the following is one of the simplest modes of constructing it:

A row of very strong palisades, pointed at the top, from 8 to 12 inches square, is formed, with intervals of 3 inches between every two palisades, and behind this row is formed another corresponding to the open intervals in the first. These second palisades are only from 5 to 7 inches thick, and are cut square at the top, every second one being cut short, or to the length of 4½ inches, so as to fire over it as through a loophole. This stockade is shown in plan, elevation, and section; it has a banquette of earth, which may be replaced when desirable by a wooden step. By cutting out the triangular portion shown in the section, and throwing the earth up against the front of the palisades, an exterior slope and scarp are formed which keeps an enemy constantly in view. Such a stockade as this brought up close to the edge of a steep bank, requiring defence, has a great advantage over a parapet, as the men behind it have a much more effective command of the ground before them when firing through the loopholes than they could possibly have when firing over a parapet. It is here supposed that artillery fire cannot be brought to act in front against the stockade, but it may possibly be brought to act against it in a longitudinal, or, as it is called, enfilade direction; and in this case the line of stockades should be interrupted by traverses, which are usually banks of earth placed transversely to the line they are intended to protect from enfilade fire.

Fig. 9 shows the adaptation of a stockade of this description to the defence of precipitous ground. When stockades Fortification.

are formed into inclosed works, they constitute what are called "tambours."

It may in a similar manner be desirable to throw an ordinary parapet forward to the edge of a bank, the slope of which supplies the function of a scarp, and hence to dig the ditch behind instead of before it, as in fig. 10, where it will be also observed that the slope of the banquette is broken into two steps, the tenacity of the earth when first excavated allowing it to stand firm; and the principle of this excavated form of structure is also adopted in sunken batteries.

Sometimes the object of the parapet is merely cover and not active defence, in which case the banquette is omitted as in fig. 11; and the work is called an epaulement. In this profile it will be observed that a space is left between the face of the epaulement and the internal ditch, which is called a berm. Such a space should always be left, whether the ditch is within or without, when the work is to be formed of any considerable elevation, as it forms a stage upon which the builders can stand, and lessens the height to which the diggers have to throw the earth from the ditch; and it is very important to keep the berm clear by throwing forward or back the earth as quickly as it is raised. The distinguishing characteristic of an able engineer is to be found in the power of varying his appliances at will—thus the abattis may become the fraise, or may displace the palisade, as in fig. 12. Were this principle not kept in view, more evil than good would sometimes result from systematic instruction; as the person who had acquired a knowledge of some one contrivance might be found crippled by his constant efforts rather to conform to it than to look about him for some other better fitted for the existing circumstances. In this Fortification profile a berm is represented, as it would be difficult to arrange the abattis, and to build the parapets without it.

The arrangement of the trous-de-loup, combined with stakes driven into the ground, is shown in fig. 13, an advanced glacis having been formed of the earth thrown out of the excavations. The ditch is in this case triangular; and it is scarcely necessary to add, that the choice of any particular form must be determined by the engineer from a knowledge of the nature of the ground itself, only remembering that the contents of the ditch, or ditches, must supply material for forming the parapet; and further, that as its depth adds to the difficulty of assault, it should not be diminished except from necessity. After these elementary remarks, the student may be considered prepared to enter on the consideration generally of parapet or field fortification.

RULES FOR DETERMINING THE DIMENSIONS OF PARAPETS.

Determination of the Relief of a Parapet.—First, in respect to the protection of troops in a normal position, where the ground is considered horizontal. Now, the minimum for a simple parapet may be here stated at 6' 6" as a musket ball would penetrate the parapet for about 6' below its crest, and the maximum at 8 feet, a height which gives the defenders perfect security under almost every circumstance of fire, including even that of mounted soldiers.

Deflade.—Secondly, where the ground is uneven, and it is necessary to deflade the work from the point or points which command it. Now, figure 14, No. 1, explains the first case in which the points A, B, C, are on the same level, the distance AB being the space intended to be protected by the parapet at C. The line CF represents the supposed height at which it is presumed the assailants may fire, or in this case 8 ft.; BE will be the same; and AD cut by the line drawn from F to E will also be 8 ft. In fig. 14, No. 2, A, B are still considered to be in one horizontal plane, but C is considerably elevated; and hence, adopting the same data as to height, and drawing the line FE and the line CB parallel to it, AD, or the height of the parapet, equal to AI + ID; ID being equal to BE, or CF, or N, the normal height. Calling also AB, or the distance to be covered, d; AH, or the distance from the commanding point, D; HC, or the height of C above A and B, H; we have

\[ \frac{AI}{CH} = \frac{AB}{BH} \]

or \( AI : H :: d : d + D \); and hence

\[ AI = \frac{d}{d + D} \cdot H, \text{ and } AD = N + \frac{d}{d + D} \cdot H \quad (1). \]

So that the necessary height of the parapet increases as the height of the commanding point increases, or as the distance AB to be deflated increases; and diminishes as the distance from the commanding point increases. Taking

\[ D = 600 \text{ ft., } d = 30 \text{ ft., } H = 60 \text{ ft., } AI = \frac{60}{21}, \text{ or } 2 \text{ ft. } 10 \text{ in., and } AD, \text{ or the height of the crest of the parapet, } \]

equal to 8 ft. + 2 ft. 10 in. = 10 ft. 10 in.; or taking D = 1200 ft., or 400 yards, AD = 9' 6".

Fig. 14, No. 3, represents A lower than B by a quantity = AO = GH = h; hence AD = AO + OI + ID, and

\[ OI = \frac{OB \cdot CG}{BG} = \frac{d}{D + d} (H - h), \text{ or } AD = N + h + \frac{d}{D + d} (H - h) \quad (2); \]

an equation which shows that the deeper A is sunk below B and C, the more elevated must be the parapet, and hence that this is a very unfavourable condition of parapet. For example, let A be 2 ft. below B, and all other data the same,

\[ \frac{d}{D + d} \cdot (H - h) = 2 \text{ ft. } 9 \text{ in., and } AD = 8 \text{ ft. } + 2 \text{ ft. } 9 \text{ in. } + 2 \text{ ft. } = 12 \text{ ft. } 9 \text{ in.; or when } D = 1200 \text{ ft., } \] Again (fig. 14, No. 4) in this figure A is higher than B, or than C, which is the lowest of all; and if H still represents the difference of level of A and C, and the difference of level of A and B, \( AD = N - h - \frac{d}{D + d} \cdot (H - h) \) . . . (3);

and, of course, so far as concerns the height alone of the parapet, this is the most favourable condition of all.

Any other case is easily resolvable by one or other of the formulae; thus, when A and C are on the same level, and B higher than A, H becomes O, and No. 2 becomes

\[ AD = N + h - \frac{d}{D + d} \cdot h. \]

And in No. 3, if B be higher than A, it becomes positive, and \( AD = N + h - \frac{d}{D + d} \cdot (H + h) \) . . . (4);

or if h be 0, A and B being on the same level, \( AD = N - \frac{d}{D + d} \cdot H. \)

In equation (4), if the station C, though below A and B, falls between the horizontal line drawn through A, and the line BR or BA be prolonged till it cuts the surface of the ground, sloping from B towards D, then \( \frac{d}{D + d} \cdot (H + h) \) is less than h, and AD is greater than N; but should C be below the line BR, then \( \frac{d}{D + d} \cdot (H + h) \) is greater than h, and AD is less than N; or, in other words, if the line of defilade passing through BA meets the ground at R within the prescribed limits of defilade, or the effective ranges of musketry and artillery, which may be now assumed as 500 yards for the first and 1000 yards for the second, if the point C be above that line the parapet at A must be made higher than the normal height, and if below it may be made lower.

A comparison between the numerical results attached to equation (2) will exhibit the great disadvantage, to the defenders of simple lines, of having any ground near to their own moderately elevated, and care should be therefore taken either to occupy the ground or to throw back the lines opposite such eminences as far as possible, and should it have the character of a ridge, to bring some portion of the fire of the line to act in the direction of its length. The space AB to be defiladed must depend upon circumstances, but the minimum to allow for a safe communication for the troops behind and actually defending the parapet ought not to be taken below 30 feet, and where troops are required to be drawn up behind the parapet at 90; but in cases of double lines or of inclosed works the distance must of course vary, as the object will then be to protect not only the troops nearest to the enemy from a direct fire, but the troops arming the more distant parapet from a reverse fire.

In assuming the normal height as 8 feet, on the supposition that the fire might proceed from mounted soldiers, a condition is adopted which is not generally likely to occur in the attack of intrenchments: if, however, the normal height were assumed at 7 feet, the space behind the parapet must be very imperfectly defiladed, as the trajectory of the ball, being in its descending curve, will come to the ground at a much nearer point than in the original supposition of a straight line of trajectory; and hence it is desirable to adhere to the normal height of 8 feet. In equation (3), and in one case of (4), as explained, the height of the parapet becomes less than N, but should the diminution extend so far as to reduce the height of the parapet below 7 feet, the absolute relief should be restored to its proper amount, or to 7 feet, by excavating the ground behind the parapet, or, in other words, forming a terreplein below the level of the plane of site. In a similar manner, in respect to equation (2), and in one case of (4), where the parapet becomes greater than N, it would be very inconvenient to augment the height above 12 feet, and it is preferable therefore to excavate behind the parapet, whenever the defilade requires so great an increase of height.

In the preceding observations the parapet has been considered as forming a simple continuous line, deriving its reciprocal defence solely from its own direct fire; but such a condition would most frequently be found inapplicable, even as regards form, in consequence of the natural inequalities of the ground, and, with few exceptions, unsatisfactory, as regards defence, in consequence of the imperfect operation of direct fire from the top of a parapet, which can only be brought to bear upon some external line, and must therefore leave the foot of its scarp unseen and unprotected, after an advancing enemy has come within the limiting line of defence. A fire, therefore, so directed as to take the enemy in flank has been adopted, and a line or work is therefore said to be flanked when some portion either of its own parapet, or of the parapet of another work, has been so arranged that the fire from it shall take an enemy advancing towards the other portion in flank. In lines of intrenchments this arrangement leads to a bent line, having angles projecting towards the country called salient angles, and angles retired from the country called re-entering angles; and it is evident that in this arrangement (fig. 15) the lines AB and AC, which are flanked by BD, CD, do in their turn flank BD and CD, and that flanking defence may therefore be called reciprocal defence, a term which more accurately defines its object and value.

Referring back, then, to the subject of defilade, it is evident that a bent line of this kind affords more facility for defilading than a straight one, as it is often possible so to arrange the position of the angles that the salients shall occupy high points of ground, while the re-entering angles though placed on lower shall be compensated for this defect by being further removed from the commanding ground of the enemy.

Whilst a simple straight line has the disadvantage of defilade pending for its defence solely on direct fire, it has the advantage of not being exposed to a fire from the enemy so directed as to sweep along its whole length from one end to the other, a fire which is called *enfilade* fire, and is necessarily very destructive, as it produces the same effect in attack as a flanking fire in defence, by taking the defenders of the line in flank. To guard against this evil, should it be indispensable to take up a position in front of ground of a superior command, the long lines AB, AC should at least be so directed that their prolongations should fall in low ground at EF, and not as they would do in the case of AB, AC, on the high ground at EF; and of course, if possible, and where the high ground is not continuous, that the prolongations of both short and long lines should fall on the low ground between the commanding eminences, an arrangement which will be more especially beneficial should the low ground be marshy or otherwise difficult of occupation by an enemy. Such observations as these can only be suggestive, since no fixed rules can be laid down for an engineer in such cases, as he should look at his ground and adjust his works so as to make the most of the natural advantages it presents, and to neutralize, as far as possible, the ill effects of any disadvantages it may possess. To determine the height of the parapet by defilading in the manner stated, it is necessary to have a correct plan of the ground, and to know the exact levels of the points A, B, C, in every case; but the defilading may be effected by levelling poles or boning rods where there is no such plan. In this case the inner boundary of the ground within the parapet required to be defiladed being staked out, a boning rod of 7 or 8 feet high, according to the intended normal height of the parapet, should be placed at BC, on the staked-out line, and another of equal height on the commanding point or ground, fig. 16, supposed to be either at or within the range of the projectiles against the fire of which the work is to be secured. A rod about 12 feet high is then fixed at A, and a cross-piece or marker, as in levelling staves, is raised up or down until it meets the point where the visual line from the top of B to the top of A intersects the pole at A; so that this operation is simply the mechanical determination of the height obtained in the other method by calculation. If it be required to defilade the whole space between two parallel lines, or that included between the two lines forming the salient angle in fig. 15, it is evident that the work must be defiladed from both sides, and further, that the soldiers standing on the banquette of one line should be secured from the fire of the ground in front of the other, or from the fire called "reverse fire," as taking them in rear. This is effected by placing a mound of earth or traverse between them, and determining its height as well as the height of the parapets in the following manner:—On the commanding point C is placed the boning rod CD of the normal height, and another BE, at B, or at the position of the traverse of the same height; then the height of the crest of the parapet of A is determined by the intersection of the visual line from D to E with the pole fixed at A, at the point a, which is here high, as C is so much higher than A. See preceding rules and equations. In like manner a pole of the proper height being fixed at the extent of range on the opposite side at C', the visual line from D' to E determines the height of the parapet of A' at a', which is much lower than the parapet of A, as A' and b' are nearly on the same level. Now, to defilade the banquettes, and to determine the height of the traverse necessary for that purpose, set up on the banquette of A a pole bb' of the same height as CD, CD', BE, and the visual line from D' to b' determines the height of the traverse at f, which is necessary to secure the banquette of A from the reverse fire of C', whilst the visual line drawn from D to b' determines the height of the traverse sufficient to protect the banquette of A' from the reverse fire of C'. The application of these principles is shown in reference to a work formed of two lines (or faces as they are called), terminating in a salient angle, by fig. 17; whether that work is connected with a line of intrenchment as in a redan, or is detached as in a ravelin and other outworks, or forms part of a peculiar system or arrangement of works as in the tenaille system of Monta- lembert, called by its author the angular system; terms and works which will be hereafter more fully explained. Here the commanding point is supposed to be at M, and to secure the defenders of the face AB from a reverse fire, it is necessary to interpose the traverse cd, called from its object a *parados*. The length of the traverse cd is determined by the line MB, beyond which it should project sufficiently to give ample security to a space about 50 feet wide behind the parapet. At the other end, the traverse is not carried up to the salient angle, as it would interfere with the communication, but is completed by ba, perpendicular to the other face, by which arrangement the space within the salient and the banquette are left free. The two lines MdB, and Mcf, will be directed to points raised above the banquette by the normal height assumed, whether 7 or 8 feet, and thus determine the height of the traverse. It may, however, happen that the commands are so situated as to produce an enfilade fire along both the faces AB, AB'; fig. 18. In this case a small work is formed DAD' in connection with the parapet, by drawing lines parallel to the crest of CB and CB' at a distance from it equal to the breadth of the banquette, and then determining, in the manner explained, the height of A necessary to defilade a certain length of the banquette of CB and CB' sweeping Fortification.

Bonnet.

it, and assuming the greatest of the two as the height of the parapet at A. This work is called a bonnet; and when the height necessary to defilade the whole of one or both faces is found to exceed 12 feet, the height of A should be restrained to that limit, and traverses, T, T', T'' be placed at such distances as shall cause a complete defilade without exceeding the height of 12 feet.

The internal space may frequently be sufficiently defiladed by raising the salient portion of the parapet without disturbing the line of direction of the crest; but in that case the banquette of the two faces would not be covered from the enfilade fire, and hence the necessity of a bonnet. The increased height of the parapet of the bonnet renders it necessary to adopt two banquettes b, b', one below the other, and each provided with steps to facilitate ascent, fig. 19.

The operation of defilading may be also effected by planes of defilade; as, for example, if the line which marks out or limits the space to be defiladed be first drawn, and a plane be supposed to pass through a line either 6 ft. 6 in. or 8 ft. (or whatever height between these may be assumed as the normal height N) above the limiting line, and through a point the same height above the commanding point, this plane will determine the height of the parapet, the crest of which will necessarily be in it. Practically it may be done thus:

On the boning rods marking the ends of such portion of the limiting line as can be included in one operation, mark the normal height N considered necessary, and then remembering that a vertical plane through the boning rods would necessarily intersect the defilading plane in a straight line, place one edge of an equilateral-triangular frame of wood in the intersecting line by directing it to the marks on the boning rods, and then attach the frame in that position to an intervening rod. The base of the triangle will now be in the defilading plane, and by moving the triangle on the base as a hinge until the mark on the boning rod at the point of command is just seen along the surface of the frame, it is evident that the triangle itself will then be in that plane also. Fixing the frame in this position, it is only necessary to look along its surface in any direction in order to mark on the boning rods set up on the line of the crest of the parapet the necessary height at each point.

Where the parapet is continued not only on the flanks but also in the rear, so as to form an inclosed work, it may often be necessary to defilade it in various directions as in fig. 20. Where two traverses or paradoss cross each other, they must, of course, be so placed that they shall not only complete the defilade of the whole interior space of the work, but secure from reverse fire the banquette on each side, the normal N being therefore, at least, 6 ft. 6 in. above the banquette. Where traverses of this kind become necessary, the engineer must take into account the space they will occupy, and plan his work accordingly; and should he be able to render the difficulty of attacking one side of his works very great, he may so construct one or more of the traverses that they may be used as retrenchments, and thus increase the means of defence; for example, S being the salient of greatest strength, bed might be first defended, and then bed.

This subject has been enlarged upon because it is one of the most important in engineering, as the safety of a long line of works may be endangered by defective defilading. Though exhibited here in a practical form, it depends essentially on geometrical principles, and instruction therefore in descriptive geometry is now considered essential in all schools of military engineering.

Having determined the relief of the crest of the parapet in reference to the plane of site, all the other vertical dimensions depend upon it, as shown in several of the preceding figures; whilst the horizontal are regulated either with regard to the slopes required to ensure stability, or the thickness necessary to resist the enemy's missiles. For example, it has been determined that the penetration at a mean range in common earth, after having been dug up and well-rammed, and the thickness for security, are as stated below:

| Weapon | Penetration | Required thickness for security | |-----------------|-------------|--------------------------------| | Musket | 1 ft. 6 in. | 3 ft. | | 6-pounder | 3 ft. 6 in. | 4 ft. 6 in. | | 9 " | 6 ft. 6 in. | 7 ft. 6 in. | | 12 " | 8 ft. 6 in. | 10 ft. | | 18 and 24 pounder | 11 ft. 6 in.| 13 ft. |

But as neither the 18-pounder nor 24-pounder is now often brought into the field, the thickness of parapet has been usually assumed to be 14 ft. In the Austrian service, in which, as in the Russian, the 18-pounder is a recognised field-gun, it is usual to allow the following thicknesses:

For defence against Musket balls: 4 ft. " 3-pound shot: 4 ft. " 4 and 6 pound: 8 ft. " 8 and 12, and 7 and 10 pound howitzers: 13 ft. " 18-pounder shot: 16 ft.

With light, sandy, or gravelly soil, or, when tamping can only be imperfectly performed, a greater thickness ought to be allowed; and, as the presence of a wide and deep ditch must always materially strengthen the work before which it is placed, there can be no other reason than want of time, want of men, or difficulty of ground, for reducing the thickness of the parapet below 14, or at the utmost 12 feet. If wood be used, the same authority gives us the necessary thickness for resisting musket balls at from $5\frac{1}{2}$ to $6\frac{1}{2}$ inch; against 3, 4, or 6 lb. shot, $3'3''$ to $4'11''$; against 8 and 12 lb. shot, or 7 and 10 lb. shells, $4'9''$ to $5'4''$; and against 18 lb. shot, $6'6''$. Brick walls from $2'8''$ to $3'3''$ thick; and rubble walls from $3'3''$ to $3'10''$ will resist field-guns. For forming the parapet under peculiar circumstances of difficulty the engineer will avail himself of every fitting substance which may be at hand; such as bags of wool, mattresses, fire-wood, manure heaps, as well as fascines, either by themselves or packed in gabions. Of these latter substances the resistance is not great; the penetration in wool being double that in rammed earth, and the strength of fascine works being rapidly diminished by the speedy fracture of the branches when exposed to a sharp fire.

With these data it will be easy to regulate all the dimensions of the parapet, the height of its crest, or the relief of the work, having been first established. Thus the plane of the banquette or step on which the men stand, when firing over the parapet, should for convenience be $2'3''$ below the crest, and on no account should exceed $4'6''$. The breadth or tread for a single rank should be $3'$; for a double rank $4'6''$; the surface should slope backwards $2$ or $3$ inches in the $3'-3$ or $4$ inches in the $4'6''$, so as to discharge water freely and keep the banquette dry; the base of the interior slope of the banquette up which the men mount should be twice its height; if the height of the parapet exceed the normal height, it will be desirable to form two treads or steps to the banquette, the lower about seven feet below the crest, so that one rank of men may stand there whilst reloading the muskets of those in advance of them; or, to adopt steps with a rise to each of $1'$, and a tread of $1'$ or $1\frac{1}{2}'$, sloping slightly to the rear, by which arrangement the necessary excavation of the ditch will be diminished, and less of the interior space occupied. The interior slope of the parapet should be $1'$; or a base of $1'$ to $4'$ of the height, and should never exceed a slope of $1$ to $3$—the superior slope or plongée, of the parapet, by which the fire is directed towards the point on which it is to act, should not be less than $\frac{1}{2}$, nor more than $\frac{1}{2}$ of its thickness, and in service is generally made $\frac{1}{2}$; but as the increase of the slope facilitates the destruction of the crest, it should be kept as small as possible; and it is usual on the continent to retain the angle of the crest as a constant quantity, at $100^\circ$, and hence to increase the base of the interior slope as the plunge increases, and vice versa; but this is not satisfactory, since the height of the soldier's shoulder remaining constant,

whilst the direction of the prolongation of the line of plunge varies, the fire will not be always in the true direction; and it seems therefore preferable to keep the base of the interior slope as small as possible, and to make the top of the parapet at the crest horizontal for one or two feet, commencing the plunge at that point, and bringing it inwards in proportion to the increase of plunge. This flat space will facilitate the use of sand bags (bags filled with earth), which are sometimes so arranged on the crest of the parapet as to form loopholes for the musketry, whilst they add to the cover of the men; the base of the exterior slope of the parapet is equal to its height, in earth of a medium tenacity, so as to form an angle of $45^\circ$; and in some particular cases where the materials would naturally stand at a steeper slope, it may be made $\frac{3}{4}$. The bases of the slopes of the scarp and counterscarp of the ditch, as being cut in undisturbed ground, need not exceed $\frac{1}{2}$ of the depth as a general rule, though occasionally in very loose ground the slopes will require to be as gradual as in the exterior slope, or slope of made ground, in order to insure stability. Where steeper slopes are deemed indispensable, the earth must be supported in place by a retaining coating (or wall) called a revetment, which may be formed of fascines (long cylindrical bundles of faggots), hurdles, sods, planks, clay puddling, and, in interior works, of sand bags. The base of the interior slope of the glacis should be equal to its height, and the exterior slope have a plunge of $1$ foot in $12$. The command of the crest of the parapet over that of the glacis should be such that an assailant, having arrived on the crest, should not be able to fire into the interior of the work; a condition which requires a command over the glacis of $5\frac{1}{2}$ feet, so that with a parapet of $7$ feet high the maximum height of glacis would be $1\frac{1}{2}$ feet. The minimum height of the glacis is determined by another condition, viz., that the fire from the parapet should be in a plane not more than $2$ feet above the surface of the glacis; and in no case should the plunge or slope of the glacis be greater than that of the parapet. An advanced glacis is sometimes adopted either for rendering the cover more effectual, or to occupy a favourable line for first opposing the progress of the enemy. Fig. 21 shows this arrangement, $g', g''$ being the first or ordinary glacis, and $g^{'}, g^{''}$ the second or advanced glacis. The slope of neither glacis should be such as to withdraw the assailants from the grazing fire of the parapet, and if it be not possible to extend the slope of $g^{'}, g^{''}$ so far as to keep it in the prolongation of the line $C-g'$, it should be at least so arranged that no point of the slope should be more than $2$ feet below that line or the plane corresponding to it, namely, the plane passing through the crest of the parapet and the crest of the advanced glacis.

To form the advanced glacis, the slope at $g$ is prolonged below the surface of the earth to $g'$; the excavation supplying material for the raised glacis. When it is intended that the defence of this advanced glacis shall be derived solely from the parapet, either an abattis or rows of stakes may be placed immediately behind it, so as to stop the advance of the enemy when at the point of maximum exposure, but such glacis may often assume the character of successive intrenchments, and be defended with vigour and success.

This figure will be again referred to when treating on defence by mines. The height or relief of construction of the parapet having been determined by the amount of cover required, and the thickness by the nature of projectile expected to be brought against it, the whole profile or section has necessarily been completed on the principles pointed out, and the bulk, therefore, of earth contained in any portion of the parapet will be equal to the area of the mean or average profile multiplied by the length of that portion. Now, this earth must be obtained from the ditch, and hence the dimensions of the latter depend on those of the former, Fortification.

whilst at the same time the volume of any portion of the excavated ditch will also be equal to its mean section multiplied by the length of that portion. If then, P represent the area of the mean section of this portion of the parapet, D the area of the mean section of the corresponding portion of the ditch, and L the length of this portion, LP should be \(= LD\), providing the earth of the excavation were of the same bulk as after it; but such is not the case, and after having been broken up from its previously closely packed condition, it is found that the "remblai" or earth built up exceeds the "debais," or earth excavated by a coefficient varying with the nature of the soil, being in sandy soil nearly 0. Thus if \(\frac{1}{m}\) represent the coefficient, it is in sand 0; in earth of medium tenacity \(\frac{1}{2}\); and in very strong and naturally compressed earth \(\frac{1}{3}\); so that to render the earth of the ditch just equal to that of the parapet, the above equation should be \(LP = L(D + \frac{1}{m}D)\) and \(P = D + \frac{1}{m}D\), or \(D = \frac{m}{m+1}P\). As, however, the earth resulting from this excess, even allowing for the greater length of the ditch in polygonal works, will be required for forming the glacis, or for making up the banks in the salient called "barbette," and intended for raising guns sufficiently high to fire over the parapet, the dimensions of the ditch may be safely estimated without reference to the excess, as follows:

Let \(x\) be the breadth of the bottom of the ditch, and \(y\) its depth; and let the sum of the bases of the slopes of the scarp and counterscarp be represented as a function of the depth by the fraction \(\frac{r}{s}y\); then \(x + \frac{r}{s}y\) will be equal to the breadth of the ditch at top, and \(D = \frac{y}{2}(x + x + \frac{r}{s}y)\)

whence \(x = \frac{D}{y} - \frac{r}{2s}y\), and \(y = \frac{s}{r}(-x + \sqrt{x^2 + \frac{2}{s}D})\).

Now as the defensive object of the ditch requires that it should be both deep and wide enough to form a decided obstruction in the way of an enemy, the width ought not to be less than 18 feet, whilst the depth should have no other limit than that arising from the difficulty of raising the earth which makes 12 feet about the maximum. Taking then \(y = 12\), \(\frac{r}{s} = \frac{3}{2}\), and \(D = 108\) superficial, \(x = 9 - 9 = 0\),

and the width of the ditch therefore \(\frac{2}{3}\) of 12 = 18; the ditch being triangular.

Assuming a profile area of 70, corresponding to a parapet 7 feet high and only 6 feet thick, and making \(x = 0\) for a triangular ditch, \(y = \sqrt{\frac{2}{r}D} = 9.7\), and the width of the ditch = 14\(\frac{1}{2}\) feet; with a profile area of 116 feet corresponding to a parapet 7\(\frac{1}{2}\) feet in height and 12 feet thick, the depth of the ditch, if triangular, is 12\(\frac{1}{2}\) feet and its width 18\(\frac{1}{2}\); so that this profile appears about the maximum for a triangular ditch with a profile area of 163 feet, corresponding to a parapet 8 feet high and 18 feet thick. With a banquette 4\(\frac{1}{2}\) feet wide a triangular ditch would give \(y = 14\frac{1}{2}\) feet, so that such a form would be inconvenient; but taking \(x = 4\) as the width of the bottom of the ditch, \(y\) or the depth becomes 12' 4", and the width of the top of the ditch 22\(\frac{1}{2}\) feet—a very well-proportioned ditch.

In the preceding cases the base of slope of the scarp has been assumed as equal to its height, and that of the counterscarp slope as half the height. Should the nature of the soil be such as to require the base to be equal to the height in both scarp and counterscarp, \(\frac{r}{s}y = 2y\); and where the soil is sufficiently firm to admit of a base of one-half in both, \(\frac{r}{s}y = y\). In the first of these cases even the large profile area last named may be made triangular with a depth of 12\(\frac{1}{2}\) feet, and breadth of 25; and in the second a triangular ditch is inadmissible even with an area of 116 feet, as it would require a depth of more than 15 feet; and it could only be used with profile areas up to 85 superficial feet, for which a depth of 13 feet would be required. Before leaving this subject, a few words may be said respecting the "berm." The most effectual scarp in respect to defense is that which forms one continuous plane with the exterior slope, or at least which commences immediately where the other ends, as the absolute relief of the parapet is therefore made a maximum, and there is no berm; but in many cases it would be imprudent to carry the parapet up to the edge of the scarp, as the latter might be easily injured and occasion a fall of part of the parapet, and further, the difficulty of construction would be greatly increased by having no intermediate stage between the bottom of the ditch and the top of the parapet. The "berm" or step between the top of the scarp and bottom of the parapet is made from 2 to 4 feet according to the nature of the ground, and it then becomes possible in most cases to increase the slope of the scarp to a base of \(\frac{1}{2}\) or \(\frac{3}{4}\), at least to such a slope as shall bring the prolongation of the exterior slope of the parapet to the base of the scarp.

The berm is encumbered with such obstacles as shall prevent an enemy from making it a halting place (see fig. 12). The slope of the counterscarp is usually \(\frac{1}{2}\), \(\frac{1}{3}\), or \(\frac{2}{3}\), when that of the scarp is \(\frac{1}{2}\), \(\frac{2}{3}\), or 1; and it should be added that the bottom of the ditch ought always to slope on each side towards the centre, so as to carry off the water, and that it should be so arranged as to prevent the enemy from collecting together, and reforming his men in the ditch which in all cases of simple lines, without flanking defences, he would do were the bottom left free from obstructions.

APPLICATION OF THE PARAPET IN COMBINED OR RECIPROCAL DEFENCE, CONSTITUTING PARAPET OR FIELD FORTIFICATION.

The parapet has been hitherto considered principally in its character as the simplest element of defensive works, affording at once protective cover to the soldiers behind it and an obstruction to the advance of their enemies; but it is now time to consider the manner in which this parapet may be so arranged as to constitute a series of defensive and mutually defending works. Were the antiquity of an invention to be estimated in reference to an epoch in the social history of any race of mankind rather than to a point in absolute time, there can be little doubt that earth-works would, as might be naturally expected, claim the priority over all other modes of defence. In North America vestiges of circular intrenchments, as well as of works of a more complicated outline, have been discovered, the antiquity of which is unknown; and even now, when a small party of the aboriginal inhabitants have been suddenly encountered by a much greater number of a hostile tribe, they have been known to excavate a hollow space in the ground, and, throwing out the earth, to form around them a circular intrenchment, in which they have defended themselves to the last. In Ireland its ancient inhabitants have left similar relics of their earthen defences, as in Great Britain the Romans have left of theirs, but the further consideration of the value of earthen works, when adopted in the defence of extensive fortresses, will be resumed in a future passage, and they will be considered here only in connection with the arrangements adopted by an army in the field for its own immediate security. The art of constructing all kinds of temporary works in the field for this purpose is usually called field fortification, a name here replaced by that of parapet fortification. An army intrenched, or fortified, in the field, produces, in many respects, the same effect as a fortress; for it covers a country, supplies the want of numbers, stops the advance of a superior enemy, or, if he chooses to risk a battle, obliges him to engage at a disadvantage. "In a war of march and manoeuvre," says Napoleon, "if you would avoid a battle with a superior army, it is necessary to intrench every night, and to occupy a good defensive position. Those natural positions which are ordinarily met with are not sufficient to protect an army against superior numbers without recourse to art. Those who proscribe lines of circumvallation, and all the assistance which the science of the engineer can afford; deprive themselves gratuitously of an auxiliary which is never injurious, almost always useful, and often indispensable. It must be admitted at the same time that the principles of field fortification require improvement. This important branch of the art of war has made no progress since the times of the ancients. It is even inferior to what it was two thousand years ago. Engineer officers should be encouraged in bringing this art to perfection, and in placing it on a level with the rest."

Whenever Napoleon had time and occasion for strengthening his position by field-works, he acted upon the principles recommended in the above extract, as almost all his predecessors had done. In the wars which followed the revolution of 1688, in those of Queen Anne's reign, and during the Seven Years' War, we find the commanders of each period, William III., the Duke of Marlborough, Marshal Villars, Marshal Saxe, Frederick II., and Marshal Daun, practically exemplifying their conviction of the great utility of field-works. A few redoubts saved Peter the Great at Pultowa, and enabled him to gain a decisive victory over his formidable antagonist; and at Bomino, some slight open field-works, thrown up by the Russians, caused the French great loss, and rendered too costly to be of almost any avail the victory which, by incredible efforts of gallantry, they gained. It has been argued by some, against intrenchments and field-works, that they have oftener been carried than successfully defended, and that hence incommensurate importance has been attached to them. But it should be remembered, on the other hand, that victory in such circumstances has generally been purchased at an expense which rendered it in effect equivalent to defeat; and that a practice which the greatest commanders of ancient and modern times have approved and followed cannot be one of doubtful utility. At Austerlitz, where the contending armies were nearly equal, Napoleon was preparing to superintend the construction of intrenchments when he found himself called upon to receive battle; and in Portugal, the Duke of Wellington showed to what importance the art of the engineer might be turned for influencing, not merely the fortune of a campaign, but the fate of a cause. The lines of Torres Vedras, which formed the ne plus ultra of the powerful French army under Massena, and from which the tide of war was rolled back broken into Spain, were perhaps the most remarkable works of the kind ever constructed.

"Lisbon," says Sir John Jones, "being situated at the extremity of a peninsula formed by the sea and the Tagus, it is plain that if an army be so posted as to extend across the peninsula, no enemy can penetrate into the city without a direct attack on the army so formed. It was on this principle that the lines covering Lisbon were planned by Lord Wellington. Nature drew the rude outline of a strong defensive position, and art rendered it perfect. A tract of country thirty miles, extending from the mouth of the Zizandra on the ocean, to Allandra on the Tagus, was modelled into a field of battle; mountains were scarped perpendicularly, rivers dammed, and inundations formed; all roads favourable to the enemy were destroyed, and others made to facilitate the communications of the defenders; formidable works were erected to strengthen and support the weak parts, whilst numerous cannon, placed on inaccessible points, commanded the different approaches to them, and gave an equality of defence to the whole position." These lines were not continuous and connected works; they consisted of independent forts, redouts, flèches, redans, batteries, &c., so placed as to command and enflade every approach, and to support each other by a cross or a flanking fire. The first line occupied a front of twenty-nine miles between the sea and the Tagus; and by means of telegraphs intelligence could be conveyed from one extremity to the other in a few minutes; whilst the troops were disposed in masses in the rear of the works ready to move upon any point that might be attacked, by interior communications shorter than any by which the enemy could advance. "The aim and scope of these works," says Colonel Napier, "was to bar the passes, and to strengthen the fighting positions between them, without impeding the movements of the army. These objects were attained; and it is certain that the loss of the first line would not have been injurious, save in reputation, because the retreat was secure upon the second and stronger line, and the guns of the first were all of inferior calibre, mounted on common truck carriages, and consequently immovable and useless to the enemy." Both lines occupied a front of fifty miles, on which there were erected one hundred and fifty forts, mounting in all about six hundred pieces of artillery.

Before this formidable position, defended by a double line of works, and by an army massed and ready to move upon any point by interior communications, the French remained five months, wasting their numbers and resources; until at length, finding it utterly impracticable to force any part of even the exterior line, they were obliged to retire from Portugal, closely followed and harassed by the army which they had previously driven out of Spain. Yet though the lines of Torres Vedras were thus perfect in themselves, and though one of the ablest of the French generals and a veteran French army were foiled before them, it is not meant to refer to this system of separate field-works as a model to be followed on all occasions; for whilst the old method of covering a considerable front by a continued line of regular bastions and curtains has been universally condemned by modern engineers, it is nevertheless certain that there are situations where a partial application of continued lines may be most judiciously made. In fact, it is not by any fixed rule, but from the nature of the ground and of the position to be defended, that the species of works calculated to be most useful should, in every case, be determined.

At this point it is necessary to remember, that in any protracted defence, or, indeed, in any efficient defence, artillery must be combined with musketry; and hence that in the arrangement of lines provision must be made for the

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1 Military Maxims of Napoleon. 2 War in Spain, p. 124. The French army which invaded Portugal under Massena consisted of three corps, under Marshals Ney and Junot and General Regnier, amounting in all to 66,000 infantry and 6000 cavalry, besides a strong body of the imperial guard, which crossed the Pyrenees after the invading force had commenced its march from the neighbourhood of Salamanca. The force collected to oppose this threatened invasion did not exceed 48,000 infantry and 3000 cavalry, of which about a half was composed of Portuguese levies, yet untried in any general action, and of which a very unfavourable opinion still continued to be entertained. In point of numbers, and still more in the composition of their army, therefore, the French had a decided superiority; but all their advantages were neutralized by the defensive position of Torres Vedras. 3 History of the War in the Peninsula, vol. iii. Fortification.

When it is possible so to place guns that they may bear on definite lines or points, such as a natural ravine, an artificial road or other communication, a line of abattis or other obstacle, the ditch, the scarp, the glacis of some portion of the works which must be passed in advancing to the attack, or the point in front of a salient, it is desirable that they should be preserved in that position, ready to act at the right moment; and hence it is that they should not fire over but through the parapet, and the opening made in the parapet for this purpose is called an "embrasure." It is more usual to make these embrasures in field-works shortly before they are required to be used, so that the parapet may be made quite solid and firm in the first instance, and without the trouble which attention to the preservation of the opening would necessarily occasion in construction. In order to obtain command over a glacis constructed in reference to the exterior slope of the parapet, and yet to insure cover, the parapet must be raised so as to cover the men serving the gun placed on the usual barbette terreplein—(see fig. 22)—which would otherwise fire over the ordinary parapet, and not, as here represented, through an embrasure. The section shows by dotted lines the difference of level between the terreplein of the gun and the plane of the banquette of the ordinary parapet. The dimensions of the embrasure are determined on simple principles—the interior opening or neck is made only 20 inches wide to avoid unnecessary exposure of the men, and the exterior opening is made half the thickness of the parapet, measured along the ridge line of the exterior slope;(see fig. 23). When the guns are intended to flank the ditches, or to fire along a ravine, or the crest of a natural scarp, which fulfils the function, as an obstacle, of the ditch, the embrasures are cut in the ordinary parapet, and the guns stand on the natural terreplein of the work, as stated above.

The portion of parapet left below the embrasure is called genouillère, from genou, the knee; and for field-guns should be 3½ feet high; the portion between two embrasures is called merlin, from the Italian merlone, a battlement; the bottom of the embrasure is called its sole; and in the same manner as has been suggested in respect to the superior slope of the parapet, it should be horizontal for the first four feet from the neck or interior opening, and then slope downwards as much as may be necessary to attain the amount of depression required in firing. The direction of the embrasure depends on the intended direction of the line of fire, and is either perpendicular to the crest as at a/b, or oblique as at m/n (fig. 23). In the latter case, should the obliquity be very great, or exceeding 70°, the crest of the parapet must be made re-entering, as at o/i, so as to strengthen it near the neck, and to enable the gun carriage to be brought up square to the parapet; o P should be at least 8 feet; the sides of the embrasure are called cheeks, and should be rivetted either with planks, with sods, with fascines, or with gabions (hollow cylinders made of wicker work; and filled with earth). In fig. 24, on the left, at B, a direct embrasure is seen cut straight through the parapet; and on the right at A, an oblique one, both being intended to enfilade the ditches opposite them; and it will be observed that, from the obliquity of the right-hand embrasures, the interior of the work becomes so much exposed, that a traverse, T, behind the embrasure, becomes necessary. Barbettes are also shown in this figure—one at the salient at D for four guns, and another at C, perpendicular to the face or branch, for two. The terreplein of the barbette should be from 3 to 3½ feet below the crest of the parapet; its height from front to rear from 18 to 20; and its breadth, for a single gun, from 15 to 18, according as it may be necessary to fire more or less obliquely; and a breadth of 12 to 15 feet should be added for every additional gun. To add to the lateral sweep or range of the gun, without diminishing the banquette, or, in other words, the musketry fire, the barbette may be made wider in the rear than in front. In proportion to its magnitude should be the number of "rampes," or slopes of approach; as, for example, at C only one, at D three. The ramps should be from 8 to 9 feet wide, and their slope should have a base equal to 4 times the height of the barbette. The lateral slopes of the barbette and of its ramps should be revêted whenever it is possible to obtain sods, fascines, or hurdles, in order to economize space in the work, as the base of the slope may be then reduced to ¼ or ⅓ the height; more generally they are left unreved, with slopes of ¼. The terreplein of the barbette may require, as at C, to be covered in flank by a traverse. The mode of constructing a barbette in a salient is exhibited in fig. 25 a.

At any point g of the face AB raise a perpendicular gh, either 18 or 20 feet in length, to include the amount of re- coil; at the point $h$ thus determined raise a perpendicular to $gh$ and prolong it to its intersection with the other face $AC$ at $E$, then setting off $AF$ on the other face equal to $AE$. On the capital $AD$, set off a double perpendicular at any point $i$, prolonging it both ways, and making $ik$ and $il$ each at least equal to $\frac{1}{2}$ feet to represent the half breadth of the platform on which the gun-carriage is intended to stand and move; through the points $k$ and $l$ draw parallels to the capital, cutting the faces on the points $m$ and $n$; join $m$, $n$, and parallel to the line $mn$ draw the line $OP$ at 18 or 20 feet distant from it, when $m$ $n$ P O, form the platform. Join FO and EP, and AEPOE will represent the contour or trace of the barbette. The manner in which the crest of the parapet is formed above the salient A, and the mode in which the firing may be effected in directions perpendicular to the faces, as well as in the direction of the capital, is shown in fig. 25 b.

In the case of a partly sunken parapet, in which the portion above the banquette is raised above the plane of site, and the portion below the banquette excavated as in fig. 26, the barbette constructed in the hollow portion will enable the gun to fire over the parapet; and it should be protected by forming a bonneted embrasure, which may be sometimes made large enough, as here represented, to hold two guns. It need scarcely be added that an engineer ought to be ready in adapting any of the expedients here briefly noticed to the circumstances of any particular case, and that a mind stored with resources against any possible casualty is one of the highest endowments of a really good officer. It must be obvious indeed that even a limited knowledge of the art of war opens a wide field for the exercise of the talents and resources of engineers in field fortification; but the possession of a military coup-d'oeil, or of that intuitive judgment which comprehends at a glance the true bearing or character of objects as well as events, is necessary to enable them to convert theoretical stores of information to the best practical uses. In passing through a country, it requires an experienced eye to seize quickly on whatever it presents calculated to prove advantageous or disadvantageous to an army destined to attack or defend it; to appreciate the value of villages, stone-inclosures, and broken ground; to know where to dam up rivers, to scarp heights, to form abattis, trous-de-looup, and other obstacles; to select the best situations for field-forts and redoubts, and the best sites for batteries; and to arrange all the defensive means employed, with reference to the number of troops destined to act upon the different parts of the line, so that the movements of the defenders may not be obstructed or retarded, and the communications throughout may be short and easy. The variety of ground, however, upon which military operations are for the most part carried on, precludes the possibility of laying down fixed rules in regard to this subject; the accidents of ground, and the peculiar circumstances of each individual case, must, as already observed, determine the extent and description of the works to be constructed, as well as the obstacles most proper to be formed for retarding, if not obstructing, the advance of an enemy.

At the same time, though the observance of fixed rules be impracticable, general principles are of universal application; and certain maxims founded upon them hold equally good in regard to the construction of field-works as in that of the more complicated works of a fortress. These are, first, that the works to be flanked must never be beyond the range of the projectiles used in the works flanking them, or in other words the length of the lines of defence never exceed the effective range of musketry; secondly, that the angles of defence should be about right angles; thirdly, that the salient angles of all works should be as obtuse as possible; fourthly, that the ditches should be as efficiently flanked as is possible; fifthly, that the relief of the flanking works must be determined by the length of the lines of defence; and, sixthly, that in the construction of field-works, reference should not only be had to the direct and immediate obstacles which the work itself is calculated to present to the enemy, and the positive effect of its fire on the approaches to it, but the relative value of the work should likewise be considered with respect to the support it can receive from or give to other works. These principles or maxims are of invariable application.

Field-works are either open at the gorge as in fig. 1, 2, 3, 4, Pl. CCLIX, or inclosed all round as in fig. 5, 6, 7; namely—

Redans, or simple heads...........................................fig. 1. Double redans, or queues d'hircande............................fig. 2. Tennalled heads.....................................................fig. 3. Bastioned heads....................................................fig. 4. Redoubts..............................................................fig. 5. Star-forts...............................................................fig. 6. Bastioned forts.......................................................fig. 7. Lines à crémaillères..................................................fig. 8. Lines of redans.......................................................fig. 9. Lines of tenailles.....................................................fig. 10. Lines of bastions.....................................................fig. 11. Lines of demi-bastions..............................................fig. 12. Lines broken or with intervals....................................fig. 14.

The first class are of the simplest kind of field-works, and serve as a mere cover in front of avenues, bridges, (see fig. 13), causeways, and the like; but being quite open at the gorge, they are only suited for defence when their extremities rest on rivers, or obstacles which prevent their being turned, or when within the full sweeping fire of works.

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1 Shaw's Course of Field Fortification, p. 9, et seq. Much assistance has been derived from this useful work in the compilation of this article, as well as from the admirable Treatise on Field Fortification by Flachmeister, translated by Rieffel into French, the figures of which have been freely used. in their rear. To increase the strength of a redan, its faces are sometimes broken into a kind of flank, as in fig. 1, Pl. CCLIX. In the double redan, or queue d'honrde, fig. 2, the re-entering faces defend each other; the tennelled heads are used in situations which require a greater extent of front; and the bastioned heads are also employed in similar circumstances. See fig. 3 and 4.

Redoubts are works closed on all sides; they are constructed of a square or polygonal figure, but most commonly square, as, when of this form, each front can furnish a strong perpendicular fire. Provision should be made for defending the ground before the angles, which, however, are sometimes rounded or cut en crémaillère, so that a fire may be delivered from them. See fig. 5.

Star-forts were proposed in order to remedy the defects of redoubts having the ground before them undefended by a flanking fire, so that a cross fire might be delivered from the adjacent sides. But according to Jomini, "star-forts are the very worst description of fortification; they cannot have flanks, and the re-entering angles take so much from the interior space that it is impossible to place troops and artillery in them sufficient for their defence;" an opinion confirmed by the practice of Sir Richard Fletcher and Sir John Jones in the construction of the lines of Torres Vedras, where the trace of the redoubts was made subservient to the conformation of the ground, to the object in view, and to the protecting them as much as possible from the fire of the enemy's position.

In bastioned forts, fig. 7, the flanking defence obtained for the ditch is nearly perfect. As bastioned forts are only constructed in cases of great importance, no labour or expense should be spared in the formation of such works.

Forts with demi-bastions, fig. 12, are objectionable, as the ditches are only defended by an oblique fire of their faces. The parapets of all these works should be of sufficient thickness to resist the fire of the heaviest guns that can be brought against them. In some cases, however, the parapets need only be strong enough to resist the fire of light field-guns, whilst in others it will be sufficient if they serve as a cover to the men within them against musketry. The latter kind is generally that which is thrown up in an evening after taking up a position, and which, if the army does not move next day, it may be considered as necessary to strengthen in some parts, according to circumstances.

Continued lines, or connected works, are resorted to in order to inclose the front, or to connect important works or forts. The most simple tracing is that of redans joined together by curtains (fig. 9); but as the ditches of these curtains can only be defended by an oblique fire from the faces of the redans, this defect may be remedied by breaking the curtains so as to form nearly right angles with the faces of the redans, in which case they are called lines of tenailles.

Lines en crémaillère have long faces, with flanks perpendicular to these, in order to defend their ditches. When the faces can be directed towards ground upon which it is impracticable to establish enfilading batteries, the construction is considered as good.

Bastioned lines form the strongest trace which can be given to continued lines, when the ground will admit of its adoption. A perfectly regular trace is only suited for level ground. The ditches in field-works are often sloped en rampe towards the adjoining flanks, in order that the déboulé, or quantity of earth excavated, may not exceed the remblai, or quantity contained in the mass of the rampart or parapet, a circumstance which often occurs in field-works, where there is seldom any rampart, and only cover sufficient for the defenders.

Lines with intervals. Fig. 14 shows the general trace of lines of this kind. The salient works should never be beyond the range of musketry from the re-entering works, and the angles of defence between the two lines should be as near as possible to right angles.

Têtes-de-pont, or bridge-heads, are works generally open at the gorge, and whose flanks rest upon a river, in order to cover one or more bridges. The best situation for these works is the re-entering sinuosity of a river. As têtes-de-pont, fig. 13, are usually constructed for the purpose of enabling a retiring army to cross a river in order, and to check an enemy pressing upon it, the tracing and profile should be such as to secure a double advantage to the greatest extent possible. In Sir Howard Douglas's able work on the Construction of Military Bridges will be found much valuable scientific information upon this important subject.

The obstacles which are usually added to field-works, in order to render the approaches more difficult to the enemy, such as palissades, barricades, abattis, trous-de-loup, chevaux-de-frise, barrows, and crown-feet, have been already noticed.

For the defence of open towns and villages, the following methods, recommended by the French minister of war in 1814, are considered as the best that have yet been suggested: "To admit of a town being advantageously intrenched, it is necessary that it should not be commanded within any short distance, that the houses should not be of a construction easily set on fire, and that its extent should not be out of proportion to the means and time at the disposal of the defenders. The first thing to be done is to clear the approaches to the town, by levelling houses, hedges, shrubberies, and whatever may favour the assailants. Wood ought to be cut two feet from the ground, that it may serve to impede the advance of the enemy without masking the fire of the defenders. The next object is to form or complete the inclosure round the town. For this purpose advantage is taken of buildings, walls, and fences applicable to the defence. The openings which remain must be closed by palisades, stockades, or ditches strengthened by abattis. All streets leading out of town must be barricaded. The barricades must be sufficient to resist field artillery, and high enough not to be easily got over; and they ought to be flanked by loopholing the neighbouring houses. When pressed for time, carts filled with dung and the wheels taken off, sand-bags, bales of wool or cotton, and furniture taken from the neighbouring houses, all form good barricades. If there should be any old castle, church, or large substantial building, it should be converted into a keep, by blocking up useless entrances, loopholing walls, and surrounding them by a ditch or abattis. If a town is situated near a stream or river, by which part of it may be covered by inundations, this should never be neglected."

Villages are intrenched on similar principles, and being generally surrounded by gardens with live hedges, the latter may be made use of in forming the lines of defence. If there should only be sufficient troops to defend part of a village or town, a part only should be intrenched and separated from the rest by means of carts and barricades. If there are very few houses, it may be necessary to confine the defence to the church or churchyard, which may in all cases serve as a sort of keep.

The destruction of bridges. Nothing is of greater consequence to a retiring army than to be able to destroy the bridges in its rear, in order to retard the advance of the enemy. Its safety, nay even its existence, may depend upon the success with which this operation is performed. In order to destroy a stone-bridge, a trench in the form of a cross is made in the crown of the arch, the branches of which are about ten feet in length, and sunk to the top of the arch-stones. One hundred and sixty pounds of powder are placed in each cut or trench for an arch three feet thick, strong planks are then laid over the powder, and the whole being well covered with rubbish, the fire is communicated by means of a sancisson or long powder-hose. Stone bridges are also destroyed by simply cutting a trench about eight... Fortification.

teen inches deep across the crown of the arch, and placing in it 345 pounds of powder covered in the manner just described. This quantity has been found sufficient to destroy semicircular arches of twenty-five feet in span, and three feet in thickness at the key. Wooden bridges may be destroyed in different ways; they may be pulled to pieces, burned, or blown up. When there is time to take them to pieces, they are unspiked, and the timbers so separated that they may be speedily removed. The best method of burning such bridges is to tar them, and to cover and surround them with fascines or tarred brushwood. When it is necessary to blow up wooden bridges, this may be effected by means of 220 pounds of powder suspended under the superstructure, and fired in the manner above described.

A ford is rendered impassable by throwing in large stones, by sinking boards with spikes standing upright in them, by scattering in it crows' feet, or by placing harrows taken from the neighbouring farms. A low rubble wall may be formed across, so as not to be perceptible above the water; strong stakes may be driven into the bottom, and trees fastened to them; waggons loaded with stones, and the wheels taken off, may in like manner be employed; not to mention a number of other things which may be easily found, and which will answer the purpose equally well. The rendering a ford impassable by such means is only second in importance to the destruction of a bridge, when the enemy whose progress it is desired to retard has either no pontoon-train at all, or has outstripped it by the rapidity of his advance. In this way, much valuable time may be gained on the one hand and lost on the other.

In order to bring a retiring army into the position when the business of intrenching itself would naturally begin, some portions of the subject of defence have been in part anticipated in the preceding passages, and the main line of argument will be now resumed.

The essential characteristic of all works formed of earth is, that the musketry fire, on which the defence must mainly depend, being discharged over the crest of the parapet, the line of fire will be nearly in the plane of the superior slope of the parapet, and perpendicular to the line of its crest; and hence opposite a salient angle, as in the redan, fig. 27, there


will be a large space of ground at A, in this case extending over $180^\circ - 60^\circ = 120^\circ$, not defended by the fire of the work itself, and which is called a dead angle. Opposite re-entering angles, on the other hand, the defect is of a different kind, as the plane of the superior slope or plane of fire passing so high above the foot of the scarp, necessarily leaves it unseen and unprotected, notwithstanding that the two lines theoretically flank each other. The object, therefore, in arranging all field works for mutual defence should be so to regulate their reliefs that the line of defence should terminate at such a distance from the ground as to give an effective defence to the part of the work intended to be flanked. The redan may be considered the most simple form of defensive work, though a portion of straight parapet terminating by short returns at each flank, either in the form of épaulements or of regular parapets, may occasionally be combined with defensive works, and is an ordinary form of offensive work in batteries. The redan is open in the rear, and the line BDC is called the gorge—in this case a straight line—Fortification.

The lunette is a redan to which flanks or lateral wings have been added; and in form, therefore, it resembles a bastion. In Plate CCLIX., fig. 14, lunettes are shown so arranged that the faces of those in rear may flank the faces of those in front; but with respect to the distribution and arrangement of the works destined to form lines of intrenchment more will be said hereafter.

The tenaille is a work the reverse of a redan, as it consists of two lines forming a re-entering angle facing the exterior. It can, from its form, only be used in direct or approximate connection with other works which shall close up or cover the ends of its lines. Either alone or combined with redans it is very commonly used in continued lines of intrenchments. Plate CCLIX., fig. 9, represents a line of redans joined by straight lines, and fig. 10 a line of irregular tenailles, whilst the annexed cut, fig. 28, represents a normal arrangement of tenailles, with irregular sides, by which a redan, as DEF, is interposed between every pair of tenailles. The line en crémaillère, Plate CCLIX., fig. 8, is also derived from a combination of irregular tenailles, and is in many circumstances a very satisfactory arrangement. In selecting between these and other arrangements, including the bastion trace, Plate CCLIX., fig. 11, the engineer must be guided by his judgment on the nature of the ground and the special objects to be attained, and cannot therefore be bound by any rigid rules. A slight consideration, however, is sufficient to show that the combination of regular tenailles, in cut 28, is only applicable to ground in itself regular, an observation which applies to every strictly systematic arrangement in fortification. In almost every case the ground will be more or less irregular, and the works to defend it must be so also. When it is necessary to approach closely to a bank of a river or a ravine, the crémaillère line, Pl. CCLIX., fig. 13, is the simplest and best, the short or flanking sides being so placed as to face the probable direction of approach, and next to that the combined redan and tenaille. Of open works, lunettes admit of the most scientific arrangement, as they can be so placed in lines with intervals as reciprocally to flank each other, and thus to form a line of defence very similar to a regular bastioned line. The employment, however, of works open at the gorge must be restricted to positions where the enemy can only approach in front, his advance in other directions having been rendered impossible either by other works, or by obstacles so arranged as to close that particular line of approach to an enemy. In every case it is desirable to take advantage of any peculiarities in the features of the country, and so to modify them as to produce such insurmountable obstacles as may relieve the minds of the defenders from apprehension of danger in that direction, and leave them at liberty to direct their attention more exclusively to the weaker points of their position; but in no case should even the apparently inaccessible points be left unguarded, or rather unwatched, as an enterprising and skilful adversary will sometimes surmount difficulties which had appeared to others insurmountable. As such naturally defended points in a position can only be looked upon as exceptional advantages, it is evident that works left entirely open at their gorges would be liable to easy and frequent surprise, and therefore prove but imperfect instruments of defence. On this account it has been usual to prescribe as a rule that such works should only be left unclosed when within range of musketry fire from the defences behind them; but it is better to lay down as a fixed principle that in every case they should be secured at the gorge, as the power of driving an enemy out of the interior of such a work when taken is in reality of no value, as his object would not be to remain in its interior, but to turn its parapet to his own uses. The manner in which this is generally done is shown in fig. 30, which is a lunette se-


cured at its gorge by a loop-holed stockade, which is an obstacle effective against an enemy, and, at the same time, easy of destruction, should he succeed in temporarily obtaining possession of the works. Any of the obstacles previously described, such as abattis, &c., may be used for the same purpose, but they have the disadvantage of not covering the defenders of the work from the enemy's fire. An engineer in deciding between open works, such as those described, and close works, which will now be described, ought to take into consideration not only the circumstances of ground as regards the security of the work itself, but also the ease or difficulty with which support can at any moment be afforded to its garrison. Open works are not fitted for any position where they are likely to be left to their own resources, even for a moderately short time, as small bodies of men cannot be expected to stand firm against a vigorous attack from an overwhelming force, unless satisfied that support is at hand. Closed works, therefore, in which the parapet is continuous on all sides, can alone be relied upon under such circumstances; and even then the nature of the obstructions adopted in their construction should be such as to afford the garrison a reasonable confidence, that by a vigorous defence they may be able to hold the enemy at bay; for no general should expect to find in soldiers, as a body, that heroism which leads to self-sacrifice without hope. The easy capture of the redoubts at Balaklava, garrisoned by the Turks, is an illustration of this principle; for though it is possible that they might have been longer maintained by French or British soldiers, it would have been unreasonable to expect that their defenders should remain firm until overpowered and cut down by their assailants, which must have been the result had not a supporting force been at hand to relieve them. As general rules, therefore, it may be laid down, that in all detached works the mode and time of relief should be palpable to the garrison; the nature of the constructions such as to inspire confidence in the garrison as to its power of resistance for a reasonable time; and,


the work will be held for a considerable time, and in consequence that a more secure and comfortable lodging will be desirable for the garrison. Magazines for ammunition may be also constructed either against or in such traverses; and fig. 32 (see next page) represents, in plan and section, one which, formed behind a gabion traverse, is isolated from the parapet in front of it. This magazine is sunk partly in the ground, the sides being formed of planks and the roof of strong scantling, forming a ridge in the centre covered first with fascines and then with a coating of two or three feet of earth. Its dimensions are—length 8 feet, breadth 5, height 6.

Having thus generally sketched, as it were, this section of our subject, it is necessary to determine the least size which can be given to redoubts, so as to ensure a sufficient A general formula may be easily obtained for determining the least regular polygonal trace in the following manner:—Let \( x \) be the side in feet of any regular polygon, \( n \) the number of sides, \( A \) the interior surface reckoned from the foot of the banquette, \( y \) the number of men forming the garrison, \( f \) the number of linear feet allotted to each soldier, \( F \) the number of square feet occupied by each man in the interior,—then

\[ f = nx, \quad \text{and} \quad Fy = A, \quad \text{or} \quad y = \frac{nx}{F} = \frac{A}{F}; \quad \text{whence} \quad \frac{nFx}{F} = A. \]

Again, let the perpendicular \( Cd \), from the centre of the polygon (fig. 33) to its side \( AB \), be \( p \); the distance \( db \) from the side \( AB \) to the boundary line of the available interior space \( mn \) be \( d \); then \( Cb = p - d \); and as \( Cd : AB :: Cb : mn \),

\[ p : x :: p - d : mn, \]

or

\[ mn = \frac{px - dx}{p} = x - \frac{dx}{p}. \]

Now, the value of \( p \) expressed as a function of \( x \) and of the angle of the centre \( \phi \), which is \( x \cdot \frac{1}{2} \cot \frac{1}{2} \phi \), varies with the nature of the polygon; and replacing, therefore, the variable coefficient \( \frac{1}{2} \cot \frac{1}{2} \phi \) by \( \beta \), \( p = \beta x \), and \( mn \),

the side of the interior space \( mnpo = x - \frac{dx}{p} = x - \frac{dx}{\beta x} = x - \frac{d}{\beta} \), and \( Cb = mn \times \frac{1}{2} \cot \frac{1}{2} \phi = \beta \left( x - \frac{d}{\beta} \right) \).

The surface of the interior triangle \( Cmn = \frac{1}{2} mn \times Cb \) is therefore \( = \frac{1}{2} \beta \left( x - \frac{d}{\beta} \right)^2 \), and \( A = \frac{n\beta}{2} \left( x - \frac{d}{\beta} \right)^2 \); whence

\[ \frac{nFx}{F} = \frac{n\beta}{2} \left( x - \frac{d}{\beta} \right)^2, \quad \text{and by reduction} \quad x = \frac{1}{\beta} \left( d + \frac{F}{f} + \sqrt{\frac{F}{f} \left( 2d + \frac{F}{f} \right)} \right). \]

The variable \( \beta = \frac{1}{2} \cot \frac{1}{2} \phi \) is as follows:

- In the triangle, 0·288 - Square, 0·500 - Pentagon, 0·688 - Hexagon, 0·866

and taking the square under the following conditions:—\( d = 12 \) feet, \( f = 3 \), \( F = 6 \times 3 = 18 \), \( x = 62·81 \) feet (21 yards), which may therefore be taken as the side of the smallest square redoubt to be defended by one rank only of soldiers, the garrison being 84 men with a single rank; and a reserve equal to \( \frac{1}{2} \) of the garrison; \( f = 2 \), and \( x = 76·66 \) feet, or nearly 26 yards, the garrison being 150 men. If there are to be two ranks, \( f = \frac{3}{2} \) and \( x = 89·6 = 30 \) yards nearly, the garrison being 240 men; and if two ranks, with a reserve equal to \( \frac{1}{2} \) the whole garrison, \( f = 1 \) and \( x = 115 \) feet, or about 38 yards, the garrison being 456 men.

Triangular redoubts are rarely used, from their small interior space as compared with the length of their parapet; thus the smallest triangular redoubt intended to be defended by a garrison of two ranks should have a side \( (x) 54 \) yards in length, and a garrison of 324, the total length of parapet required to be constructed for this force being 162 yards; whereas a square redoubt of 38 yards' side will accommodate a garrison of 456 men, admitting of a two-rank defence, and of a reserve of \( \frac{1}{2} \) the whole garrison, with a total length of parapet of only 152 yards; and this objection of limited space is further strengthened by the great amount of dead-angle space before the salients. Keeping these numbers, as regards square redoubts, in recollection, the engineer will be able at once to determine his arrangement of the proposed garrison, and yet to limit himself to the least amount of work in parapet. If, however, he has to provide for guns, for traverses, or for other constructions, he must increase the side of his square, remembering that in the case of the square of 38 yards' side the augmentation of 1 yard per side will require only the addition of 12 men to the garrison, making it 468, and the additional interior space for their accommodation of 216 square feet; whereas there will be a gain of space of 549 square feet, leaving an excess towards the objects stated of 333 square feet; and if the side were increased to 45 yards, and the garrison to 540 men, there would be a surplus interior space of 2709 square feet, being sufficient for barbettes for three guns and for one howitzer, and for a traverse; and this size may therefore be assumed as the best for a normal redoubt. It is generally stated that, passing this limit, some of the forms of forts should be adopted, as diminishing to a certain degree the defects of redoubts, by introducing more or less perfect flanking defence; but in practice it will be often preferable to use a larger redoubt, as the flanking defence obtained on very short lines must be extremely imperfect, and therefore more liable to deceive by false security than to benefit. In Pl. CCLIX., fig. 5, one of the angles is shown with an indented parapet as a means of correcting the defect of a dead salient; but this is difficult of construction, and it will generally be preferable either to cut it simply off as in another angle of the figure, or to round it as in a third, or to occupy it by a gun en barbette, as in the fourth. Of forts, fig. 6 exhibits a star fort of eight points formed upon a square, which is far preferable to one of six points formed upon a triangle, as giving comparatively more available space. The defect, however, in this trace is, that though the intermediate angle \( F \) is sufficiently open—as it exceeds 60°,—the angles \( A \) and \( B \) are less than 60°. Down to the lowest limit of such forts, in which \( AB \) of fig. 6 is taken at 60 yards, and the sides \( AE, EF, EB \) at 20 yards, there is still sufficient space to accommodate the necessary garrison, which should be in that case about 900 men. It is useless to describe those forms of star forts, which would not accommodate the required garrisons; but that represented in fig. 34 (next page) is well fitted for a large garrison. A simple construction on a pentagon is:—Bisect \( AB \) in \( C \); make the perpendicular \( CP = \frac{1}{2} AB \); join \( AP \) and \( BP \); make \( BD \) and \( AD \) each \( \frac{1}{2} \) of \( AB \), and joins \( de, dc \). In this case the angles at \( A \) and \( B \) will be 64°, and the short sides (with an exterior side of 120 yards) each 23 yards. From what has been already said in a preceding page, half-bastion forts, CCLIX., fig. 12, will rarely be adopted; but when the extent of the proposed garrison is such as to require a large amount of accommodation, and there is time to undertake such works, the bastioned trace should be adopted, as it introduces a principle not observed in the preceding traces, namely, that of defending the whole by a part, the opposite flanks EG, FG of the two bastions GEA, GFBFG, defending the intervening curtain GG between them, as well as the faces AE, BF of the bastions—whilst the fire of one flank necessarily sees the scarp of the opposite one and defends it. The bastions are indeed, like their analogous lunettes, works in themselves; the curtain being only a connecting line, forming several bastions into one connected whole. Pl. CCLIX., fig. 7, is a square bastioned fort, but the pentagon is a better form, and should be adopted when practicable. It may be said that the bastioned form of field forts has been derived from the more massive structures adopted in the permanent defences of fortresses, whilst the other traces have naturally sprung out of the earliest and rudest works even of savage tribes, for they too had their redoubts, and have only been reduced to more definite rules by the progress of military science. The history, therefore, of the bastion trace, so interesting in itself, will be postponed to a future page. Little more then requires to be said on this section of the subject, further than to point out the great importance of field-works, in securing a base of operations for an advancing army. Pl. CCLIX., fig. 13, exhibits, for example, a bridge head consisting of a bastioned front, with either simple straight branches or branches provided with a short flank as shown in the figure (see also fig. 35 below). This is, as stated before, technically called a horn work; and if there had been two such fronts so placed as to throw a bastion in the centre, and connected as before with the river by straight branches, the work would have been called a crown work. Lunettes also may be used, and even redans constructed, as fig. 1 of the plate (left side), for a similar purpose, where the object is simply first to secure the bridge from the enemy's attack and fire, and secondly to allow the defending army to manoeuvre on the opposite side when desirable: but just in proportion to the numbers passed over the bridge, and to the extent of advance contemplated, will it be necessary to increase the importance of the works forming the bridge head, as it will be often necessary to form more than one bridge in connection with it. Nothing can be more fatal to a retreating army than to find itself driven back to a river, and to have no sufficient line of intrenchment to enable it to maintain its ground whilst its arrangements for passing the river are in progress. Fig. 35 exhibits one such arrangement in which the horn work front has been much enlarged, and a lunette as a keep introduced within it. The mode in which the troops can move out at the sides, under protection of covering and flanking parapets, is shown, as well as the barbettes for guns, which become necessary in works having so important an object. Fig. 36 represents a line of tenaille intrenchments in front of the lunette, and a line of intrenchment is also shown on the near side of the river, from part of which the last terminal branches of the tenailles are flanked. In this figure T, T represent traverses, and F, F either chains or lines of pickets placed across the stream; the object of the first being to secure the bridge from the ricochet fire of the enemy, and of the second to secure it from destruction by burning or explosive bodies launched by the enemy in the stream, and allowed to float down. More extended intrenchments might be formed of lines of lunettes with intervening intrenchments; but it is unnecessary to pursue the subject in this suggestive manner further, as the engineer must necessarily adapt his works to the nature of the ground, and to the extent of the army for which he is required to prepare in this manner a defensive position, from which it may either advance or retire, without risk or confusion, as the necessities of war may require.

RAMPART OR TOWN FORTIFICATION.

If, as has been stated, the simple lines or works of parapet fortification appear to have been adopted even by the rudest tribes of wandering savages, for their temporary defence or security, the more massive and artistic works of rampart defence would seem to imply a certain amount of civilization. As an art, indeed, fortification is very nearly as ancient as the existence of society. When men first assembled together for the purpose of mutual protection, and placed their habitations on the same spot, the law of necessity, springing in this case out of the principle of self-defence, rendered it indispensable for them to adopt some means for securing their families and their property against the sudden inroads of enemies. Hence, when Cain, the son of Adam, built a city, he surrounded it with a wall; and, in like manner, the Babylonians, when they built cities soon after the Deluge, encompassed them with similar defences. In the early ages, men considered themselves as sufficiently protected by a single wall, from behind which they could with safety discharge their darts, arrows, and other missiles, against an assailant. But when, in the progress of improvement, new and more powerful means of attack were discovered, it became necessary to increase, in a corresponding degree, the inert force of resistance; and accordingly the feeble defensive structures of the primitive ages were in time succeeded by solid ramparts, flanked and commanded by elevated towers. In short, as the power of attacking fortresses or places of strength was augmented by successive devices and inventions, the means of resistance were proportionally increased, until the art of fortification arrived at a state of comparative perfection, in which it remained for many ages nearly stationary.

The various improvements which were from time to time made in strengthening the walls, and adding to the defences of ancient cities, are recorded in history, and need not be detailed in this place. The first walls which we read of consisted of brick, the material employed by Cain for the protection of the city which he founded, and called by the name of his son Enoch. Amongst the ancient Greeks, brick and rubble stones intermixed were used for the same purpose, as we find from the description of the wall which connected Mount Hymettus with the city of Athens; but, in addition to such structures, should be noticed the works, surrounding several cities, of Cyclopean structure, built of huge stones, placed with their longer axis transversely to the line of wall, and arranged with great care and skill, though without mortar. The walls of Babylon and Nineveh indicate a prodigious advancement in the art of fortification, and are justly accounted amongst the wonders of the ancient world. Those of the former city, ascribed by some to Belus, and by others to Semiramis, were thirty-two feet in thickness, and one hundred feet in height, surmounted by towers at an average ten feet higher, and cemented by means of bitumen or asphaltum; they encompassed a vast area, and presented a solid defence, which no means of attack known in ancient times were sufficient to overcome or beat down. The walls of Jerusalem, though of smaller dimensions, appear to have been little inferior in strength and solidity to those of Babylon; for, in the siege of that capital by Vespasian, all the Roman battering-rams and other engines, though used with the utmost vigour, required a whole night to disengage four stones in the masonry of the tower of Antonia. But when fortification had arrived at the state in which we find it in the works of these and other cities, it remained stationary for ages, and perhaps even retrograded somewhat, until the discovery of gunpowder, the invention of artillery, and the application of both to military purposes, effected an entire revolution in the principles of attack and defence. Then the round and square towers, which had formed secure flanking defences against assailants armed only with arrows and with darts, afforded no protection against the projectiles discharged by cannon; and even those battlements which had defied the catapult and the battering-ram speedily yielded to the force with which they were now assailed, whilst their defenders were at the same time destroyed, or buried in their ruins.

It being thus found that the ancient system of fortification was of little or no avail against the new method of attack which had been discovered, and which came into general use towards the close of the fifteenth century, it became indispensably necessary to adopt another method of defence. The plan of fortifying with bastions is believed to have commenced with the Italians early in the fifteenth century; though Papacino D'Antoni, professor of artillery and engineering of Turin, states, in his Architettura Militare (1759), that several small bastions had been constructed in the preceding century, and that the ruin of a large bastion which had formed part of the fortifications of Turin, built for Duke Louis of Savoy, still existed in the royal gardens at that time. The bastions on the enceinte of Verona, built by the Italian engineer Michelini, in the year 1523, are generally supposed to be the oldest extant; and the next, probably, are those still to be seen in the citadel of Antwerp, and which were constructed for the Emperor Charles V. in the year 1545, by the Italian Fortification-engineer Paciotto D'Urbino. These bastions are small, with narrow gorges and short flanks and faces; and they are placed at a great distance from one another, it being the invariable practice, at the time when they were built, and for a considerable time afterwards, to attack the curtains, and not the faces, of the bastions.

Errard of Bois-le-Duc, one of the principal officers of the engineer corps first organized by Sully, prime minister of Henri IV., and from which has sprung the French Corps du Genie, was the first in France who laid down rules respecting the best method of fortifying a place, so as to cover its flank. At the command of the minister, he wrote a book on the subject, which was published in 1594, and in which the details of his method are explained. As a writer on fortification, he was preceded in France by Beril de la Treille, who published his work on fortifying towns and castles in 1557. Errard fortified inwards; and in the square, pentagon, hexagon, heptagon, and octagon, he made the flank perpendicular to the face of the bastion; but in the enneagon, and in all polygons of a greater number of sides, he made it perpendicular to the curtain. In endeavouring to accomplish his object, however, he made the gorges too small, the embrasures too oblique, and left the ditch almost defenceless. This engineer constructed part of the enceinte of the citadel of Doutens, as well as the citadel of Amiens, and also some works at Montreuil and Calais.

The Chevalier Antoine de Ville, who succeeded Errard, published a treatise, dated 1629, in which he completed much that his predecessor had only sketched, and rectified various defects in the method of the latter. The Chevalier was employed under Louis XIII., and constructed new enceintes for Montreuil and Calais. His plan of fortifying has been denominated by some the French method, and by others the Compound System (Système à trait composé), because it united the Italian and Spanish methods, from the latter of which it differs only in having no second flanks and flanchant lines of defence, and in not confining the flanked or salient angle of the bastion to ninety degrees. The leading maxims of the Chevalier de Ville were, to place the flanks perpendicularly to the curtain, to make them equal to the demi-gorges, or each equal to a sixth part of the side of the interior polygon, and, in the hexagon and all higher polygons, to confine the flanked angle to ninety degrees. But this plan is liable to nearly the same objections as that of Errard; for here, also, the embrasures are too oblique, especially in the polygons, and the ditch is necessarily but ill defended.

Sixteen years after the publication of De Ville's treatise appeared the work of the Comte de Pagan, which issued from the press in 1645, and contained the development of a system which, in a short time, entirely superseded those of his predecessors. In fact, it was the Comte de Pagan who first disengaged the science of fortification from a number of suppositions which custom had in some measure consecrated, and which, resting more on abstract mathematical reasoning than on practical observation and experience, had hitherto retarded the progress of the art. This engineer acquired great reputation during several sieges which he assisted in conducting under Louis XIII.; but having become blind at the age of thirty-eight, he was obliged to retire from the service, in which he had already obtained the rank of maréchal-de-camp, and he died six years after completing the treatise above-mentioned, in which he embodied a full exposition of his system. The Comte de Pagan made the flank perpendicular to the line of defence, in order as much as possible to cover the face of the opposite bastion; and he also pointed out a method of building casemates in a manner peculiar to himself. Vauban borrowed from the Comte de Pagan the length of his perpendicular, and Allain Manesson Mallet, whose construction... still remains in favour with many, also proceeded upon the principles laid down by this scientific soldier.

The Maréchal de Vauban was born in 1633; and in 1655, at the time of the Comte de Pagan's death, he had already acquired reputation at several sieges. Vauban followed up the principles suggested by Pagan, and employed them extensively in practice, with consummate skill and judgment. He constructed thirty-three new fortresses, repaired and improved one hundred; and having conducted about fifty sieges, he left his extensive works, and a treatise De l'Attaque et de la Défense des Places, published in 1737, to speak for themselves. From the different constructions observable in these works have been compiled the systems which, in the military schools, are denominated Vauban's first, second, and third systems of fortification, and which the reader will find developed in the sequel. Had the genius of Vauban been applied to the discovery of a method for securing a permanent superiority to the defence of fortified places, posterity would have been greatly indebted to him, and even humanity would have had cause to rejoice in such a triumph of military art. But, being engaged in the service of the most ambitious monarch of modern times, Louis XIV., he applied his great talents to forward his master's views, and soon perfected that irresistible system of attack, which has ever since been so successfully followed. Before his time the general superiority was on the side of the defence; but ever since, the case has been so completely reversed, that the success of an attack made with adequate means, and scientifically conducted, is a matter of ultimate certainty.

Nor should the protracted siege of Sebastopol be considered an exception to this rule, as the principal cause of its hitherto successful defence must be sought in its freedom from investment and the consequent incessant renewal of its garrison, thus withdrawing the siege operations from the influence of the sound maxims of Vauban.

Considering that at this time, when the public mind is generally impressed with a desire to have a more practical bearing given to general education, there still may be a tendency on the part of public authorities to retrograde as regards military education, and to substitute for the mathematical sciences the classical languages, it is well to notice briefly the characters of Errard, of Pagan, and of Vauban. Errard was one of the most distinguished members of a corps formed out of the best instructed and most experienced military men he could find, by the great Sully, who was grand-master or master-general of the artillery in the reign of Henri IV. of France. This corps, called by Sully "Engineers ordinary to the King," has now become the Corps du Genie, and has to this day maintained its high character as a body of scientific men. Compte Pagan had from his earliest years devoted himself to the study of mathematics and fortification. At the age of thirty-eight he was afflicted by blindness, but before that time he had served with distinction at twenty-five sieges, and acquired the rank (then second only to that of marshal of France) of field marshal. Besides his celebrated work on fortification, he published several others on Astronomy. Vauban was no ordinary man in any sense. As the inventor of parallels in sieges, and of the ricochet fire, he stands on the first rank of military engineers for invention, and when it is considered that he conducted fifty-three sieges and shared in 140 battles and skirmishes, he must be considered an equally experienced one. At fifty-five years of age he attained the highest honour of the French army, being created marshal of France; yet amidst this stirring and successful military life he never failed to turn to account the geometrical knowledge for which he was distinguished when a youth, and which had obtained for him the early notice of the Prince de Condé. His mind was, therefore, never idle, but constantly directed to projects of public utility, whether military or civil, and he left behind him records of such labours in twelve folio manuscript volumes, entitled Mes Ouvrages, at once a monument of his own ability and industry, and a beacon to guide subsequent engineers to that course of useful as well as intellectual activity which it ought to be their pride to follow.

M. Minno Baron de Coehorn, first a general of artillery, then a lieutenant-general of infantry, and ultimately director-general of all the fortified places belonging to the United Provinces of Holland, was the contemporary and rival of Vauban. This able engineer, convinced that, however expensively the rampart of a town may be constructed, it cannot long resist the shock of heavy ordnance, invented three different systems for throwing such obstacles in the way of a besieging force, that, although the place be not thereby rendered impregnable, it can only be approached with great difficulty and hazard. But these methods, without much modification, are only applicable to low and swampy situations, such as are to be found in Holland, and are therefore not available where the localities are of a different or opposite description. At the same time, Bergen-op-Zoom, Mannheim, and other places fortified by this engineer, particularly the two former, have very great merit, insomuch as it is impossible for a besieger to penetrate into any of the works, without being exposed, on all sides, to the fire of the besieged, who are under cover; and from artillery and musketry it is scarcely possible for an assailant to shelter himself. In fact, Coehorn was a great master, and combined, as will be observed hereafter, many of the means of defence springing from another source with the bastioned trace. He published his first work on fortification before he had acquired much practical experience; and in fortifying Bergen-op-Zoom, which is allowed to be his masterpiece, did not reproduce, except as fragments, any of his published systems.

Since Vauban's time several improvements have been suggested, particularly by Cormontaigne, who entered the corps of French engineers in 1716, nine years after Vauban's death, and died a maréchal-de-camp in 1750. Some account of the systems of Cormontaigne will be found in a subsequent part of this article. The three methods delivered by Belidor are all applicable to an octagon of two hundred toises. Scheiter distinguished his systems into great, mean, and little, in imitation of Pagan, requiring the exterior sides of the polygon to be, respectively, two hundred, a hundred and eighty, and a hundred and sixty toises; he adopted from Castriotto detached bastions, and made use of a continuous fausse-braye. Fritsch, a Pole, proposed two methods, which he exemplified on different polygons. Doggen, a Dutchman, published a large volume on fortification, in which, after enumerating various modes employed by different writers for determining the salient angle, he selected three as the most approved, and proposed as many methods of construction, one of which is borrowed from Fritsch, the Pole. Pietro Sardi, an Italian, suggested a peculiar method of construction on a hexagon. The Sieur de Fontaine found the flanked or salient angle of the bastion by adding fifteen degrees to half the angle of the figure, from the square up to the dodecagon, in which last it becomes ninety degrees, and at this he continued it in all the higher polygons. He also constructed outwards, and, in every regular figure, made the curtain equal to seventy-two

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1 Mallet constructs outwards, making in every figure or polygon the demigorge equal to a fifth part of the side of the interior polygon or figure, the capital of the bastion equal to a third part of the same side, the curtain equal to three-fifths or thrice the demigorge, and the angle of the flank equal to 98°. The faces of the bastions and the flanks are determined by the lines of defence, which are razant. From these data all the other lines and angles are easily found.

2 See his work De l'Attaque et de la Défense des Places, passim. Fortification.

Fortifications, the face of the bastion to forty-eight, and the flank, which he placed perpendicularly to the curtain, to eighteen toises, or a fourth part of the curtain. Ozanam and Muller delivered each four methods of construction, the particulars of which will be found in their respective works. In 1751, Charles Bisset, who, as an engineer-extraordinary, served with the Duke of Cumberland in the Netherlands, and was present during the siege of Bergen-op-Zoom by the Maréchal Lowendahl, published a treatise on the theory and construction of fortification, in which there are many sensible and judicious remarks; and the same general description may be applied to an Essai sur la Fortification, ou Examen des Causes de la grand supériorité de l'Attaque sur la Défense, published anonymously in 1755. In a work entitled Science de la Guerre, which appeared at Turin eight years before the date last mentioned, a new method of construction is proposed, in which the principal objects to be attended to are, that there be mines under all the works, and that a regular communication be kept up with the chambers by means of subterraneous galleries, to be resorted to in proportion as the enemy approaches the body of the place. The third volume of the Œuvres Militaires contains some useful observations and maxims relative to irregular fortification; and in the Supplement to the Rèveries of Maréchal Saxe, by Baron d'Espagnac, the subject of fortification generally is amply discussed, and an accurate description given of the different means of attack and defence. Besides the writers above enumerated, may be mentioned the Chevalier St Julien, an able engineer, who published a method by which, he asserts, works may be constructed at a less expense, yet in such a manner as to render the defence or attack more formidable; Francesco Marchi, of Bologna, who, in 1599, furnished no less than a hundred and thirty-nine different methods of constructing fortifications, many of which are very valuable, and afforded useful hints to subsequent engineers, who have indeed greatly profited from his work; Bombelle, who established three kinds of fortification, called the grand royal (grand royal), the mean royal (moyen royal), and the little royal (petit royal); Blondel, who published a system divided into two principal heads, the great and the little, whose exterior sides are respectively two hundred and a hundred and seventy toises; Donato Rosetti, a canon of Livorno, who wrote on the method of constructing works in what he calls fortification à rebours, or fortification in reverse, so denominated because the re-entering angle of the countescarp being opposite to the flanked angle, it will, according to him, be necessary to attack it from the reverse side of the other works; and Antonio de Herbart, major of artillery in the Duke of Wurtemburg's service, who published a treatise on fortifications with what he calls angular polygons. The treatise entitled Nouvelle Manière de fortifier les Places, tirée des méthodes du Chevalier de Ville, du Comte de Pagan, et de M. Vauban, avec des Remarques sur l'ordre renforcé, sur les dessins du Capitaine Marchi, et sur ceux de M. Blondel, which appeared in 1689, is full of strong reasoning, whence the author deduced a new system; but it contains little that is really original, though it gives numerous references to what had previously appeared, and dispenses the different parts in a judicious manner. M. de Montalembert's system of casemated and reverse fire has been in part adopted in the splendid fortress of Alessandria in Italy, constructed under the directions of Napoleon.

Of the more recent treatises on fortification, by far the most elaborate and complete is that of M. de Bousnard, entitled Essai Général de Fortification, d'Attaque et de Défense des Places, dans lequel ces deux Sciences sont expliquées et visées l'une par l'autre à la portée de tout le monde; a work which enjoys a deservedly high reputation. It is remarkable for great accuracy and research, and may be considered as embodying in itself every thing that is valuable in connection with the subject of which it treats. M. de Bousnard's work, therefore, though intended to serve as an elementary treatise on fortification, is too expensive for the pecuniary means of a great number of inferior officers, whose instruction the author professes to have had chiefly in view: but to teachers of fortification it is altogether indispensable; and as long as the science and practice shall continue on their present footing, it will be deservedly considered as the most comprehensive and valuable work on the attack and defence, as well as the construction, of all kinds of fortification.

With regard to Carnot's Traité de la Défense des Places Fortes, it was written to serve a temporary purpose; and the exaggerated celebrity which it acquired on its first appearance has been succeeded by an equally unfounded neglect. The more prominent innovations recommended in this treatise were, first, an alteration, which, however, was not original, in the trace or outline of the polygon; secondly, the suppression of the exterior revêtement of the covered-way, known as the counterscarp; thirdly, the detachment of the scarp-wall from the rampart, and the construction of the latter without revêtement; fourthly, destructive personal conflict with the besiegers by means of frequent sorties; and, lastly, making vertical fire the basis rather than an accessory of the defence. With regard to the first of these proposals, all of which the reader will find very ably discussed in Jones's Journals of Sieges in Spain and Portugal; we have only to remark, that by means of an increased expenditure for retrenchments and casemates, as recommended by Carnot, the strength of particular portions of the polygon may be increased; and that, if he has failed in tracing a perfect front, founded on the basis of Montalembert's system of casemated and reverse fire, he has at least rescued a valuable suggestion from unmerited neglect, and rendered an important service to science by directing the attention of military men to the means most likely to create a barrier against the growing powers of the attack.

The Traité de Fortification Souterraine, suivi de quatre Mémoires sur les Mines, by M. Mouzé, lieutenant colonel of engineers in the French service, was published at Paris in 1804, and is justly considered as the most complete work on the subject it treats of which has yet been given to the public. Subterranean fortification is a branch of the art which, until a very recent period, was wholly neglected in this country, and in which our engineers were far behind their brethren of the continent. We learn from Colonel Jones's work on the Peninsular Sieges, that the Duke of Wellington's army in Spain was unattended by a single regularly-trained sapper or miner until late in the year 1813; and many valuable lives were sacrificed, from the want of these valuable, or rather indispensable auxiliaries. In this respect things are now changed, and the engineer has the assistance of a body of men well instructed in the duties of the trench, the sap, and the mine; but it cannot yet be said that the corps of sappers and miners has been sufficiently augmented, whilst it may be feared that the growing idea that the ordinary navvies might with advantage replace them, may check the desire of increasing the body. In war, it must be remembered that discipline is as important as skill, and that the labourer who would have worked with the greatest effort under ordinary circumstances might be found very ineffective when forced to work on his knees in a sap, and when exposed to an enemy's fire obliged to remove calmly the man before him when killed, and then, with equal composure, to step into his place.

The preceding hasty and imperfect summary of the pro- Fortification

The progress and literature of fortification has been given principally in connection with the bastioned trace, as the one more generally used both in the French and English schools in teaching the principles of the science; and justly so, as, theoretically speaking, it exhibits the most perfect arrangement of flanking or reciprocal defence. It is, however, desirable, before going further, to recur back to the earlier epochs, and to investigate the manner in which the ancient arrangement of a wall, with its round or square towers, passed into the present systems of defence. The accompanying figure (No. 37), will explain the natural and probable manner in which the old tower or rather tower-fort (baluardo) was changed into a pentagonal bastion. If, for example, lines of defence be drawn from the extremes of two adjacent curtains to the angles \(a\) and \(c\) of the square tower-fort A, a space would be left, \(c a b\), unseen from the adjacent forts B and C, and therefore undefended, except by downward or vertical fire from machicolations, or projections from the walls supported by corbels made for that express purpose. Such a space would be turned to account by the besiegers in fixing their scaling ladders; and the change of the straight line \(ac\) into the two faces \(cb, ab\) seems but the result of a self-evident necessity. As the work became enlarged, the portions of the fort within the connecting walls \(m m\) were omitted, and the flanks \(de, fa\) alone remained of the old work, forming with the faces the bastion \(faded\), which only required to be improved in proportions to become the bastion of modern times. It is, however, said that the towers were sometimes placed with an angle salient as in B, and if so, omitting the portions \(n n\), the resulting bastion has a strong analogy to those of Errard before mentioned. By using the old wall merely as a retaining wall, and as an obstacle against escalade, and adding to it a rampart and a parapet of earth, the Italians completed the system of bastioned defence, which, notwithstanding all the modifications of the French, ought to be called the Italian system. In this system, whilst imitating the construction of the old towers by using casemated or masonry-vaulted chambers for artillery, in addition to the guns mounted on the rampart, the Italians placed the musketeers on the banquette of the parapet, and made them fire over it. Now this arrangement of the musketry fire is an essential characteristic of the Italian system, and the reliefs of the several works are hence restricted within certain limits, as it is necessary so to determine the levels of the opposite flanks that the fire along their superior slopes shall defend the whole of the intervening curtain: but there are other modes of using musketry as well as artillery fire in the defence of the ditches, and on these were founded other systems of fortification.

The first Italian writer on fortification was Tartaglia, whose work was published in 1546; but the really first writer on the science was Albrecht Dürer, at once a great painter, a sculptor, an engraver, and a civil and military architect, whose work is dated 1527, being published one year before his death. This remarkable man founded his system on the old circular tower-forts C, fig. 37, in which the dead space is much less than in the square, and enlarging them to an enormous extent, he adopted the word, "Bastei," or in the plural "Basteien," for his new work. As the attention of military men was at this early period more directed to cannon than to the rude musket as an instrument of defence, it was natural that the latter should be less considered in these arrangements than the former. Dürer based his systems on the principle that the defences of basteien or other works which depend only on the cannon placed on their terreplein, may be effective whilst the enemy is at a distance, but cannot be so when the enemy, under cover of his epaulements, has advanced to the ditch; and leaving therefore to the cannon on the terreplein the task of firing upon the enemy's troops and batteries at a distance, he placed his cannon, and it may be said also his musketry, either in vaulted galleries running along the base of the scarp, or in caponnières, also vaulted or casemated works, built across or transverse to the ditch. The great circular bastei of his third and most improved system was no less than 130 yards in diameter, with a scarp 120 feet high, a ditch in front 100 feet wide, and a massive envelope, about 80 feet thick and 100 feet high, formed of earth with thick masonry revêtements both in front and in rear, as a mask between the main work and the counterscarp. Such gigantic proportions as these have led many to consider Dürer as little more than a speculative writer, but this would be an unjust estimate of his real merits. Reducing his works to more reasonable dimensions, they would, with proper modifications, have become practicable, and have afforded many useful hints to the scientific engineer. The defects of the circular form were compensated by the grazing fire of the caponnières in his system, and the main work was retained in an effective state by the cover afforded to it by the envelope. We shall have occasion to refer again to Dürer, but in the meantime it may be said that whilst the Italians are properly considered the originators of bastioned systems with an earthen parapet over which the musketry fire is directed, Dürer has an undoubted claim to be considered the author of the other branch of fortification in which casemated defence in the main works, as also in caponnières, becomes the essential characteristic—a branch which has proved as fertile in results in modern times as the bastioned system.

Systems of Permanent Fortification

1. Vauban's First System

Before commencing to draw a plan of fortification, it is usual to determine upon some polygon on which to describe it. In this figure, accordingly (see Plate CCLX. fig. 1), we have taken the angle of an octagon, and called the length of the side 360 yards. In constructing a fortification, a figure is determined on, as near that of a regular polygon as possible, within which the enceinte or chain of main works is to be contained. The enceinte or body of the place consists of as many bastions, connected with curtains, as there are sides to the figure, and each of these is made as near 360 yards as possible, so that every part may be within range of such arms as are to be employed in its defence.

The principal or outline denotes the contour or line by which the first figure of the work is defined. This line is supposed to pass along the superior part of the cordon, and is that from which all the other parts of the work are set off.

The exterior side, or side of the polygon above mentioned as equal to 360 yards, is that upon which the front of the fortification is described, and it extends from the flanked angle of one bastion to the corresponding angle of the next, as AB. These lines are bisected, and a perpendicular, DC... is drawn from the point of bisection towards the place, its length being proportional to the extent of the exterior side and adjacent angle of the polygon; that is, one-sixth for the hexagon and all figures of a greater number of sides, one-seventh for the pentagon, and one-eighth for the square.

The lines of defence AEG, BEH, are drawn from the extremities of the exterior sides through these points, and produced to an indefinite length; and upon the lines so drawn are set off two-sevenths of the exterior sides, equal to 102½ yards, which marks out the point for the shoulder of the bastion E and F. The distance between these points is then laid along the continuation of each line of defence, and a line is drawn connecting them the curtain GH, from the extremities of which lines are drawn to the point marked off for the shoulder of the bastion, and thus form the flanks. And in this manner is drawn a front of fortification, which being repeated round the sides of the polygon, completes the works of the enceinte or body of the place.

Vauban divided his first system into three parts; namely, the little, the mean or intermediate, and the great. The first he used for small forts of four or five sides, citadels, horn-works, and crown-works, making the exterior sides from 120 to 240 yards, the perpendicular in the square equal to one-eighth, and in the pentagon one-seventh, and the faces of the bastions in each equal to two-sevenths of the exterior side. In the mean or intermediate, which is adapted for all sizes of towns, the exterior side varies from 250 to 360 yards, the perpendicular is one-sixth, and the faces are two-sevenths. In the great the exterior side varies from 360 to 520 yards. This kind was never adopted for all the sides of a place, but only when one of these happened to be near a river or a marsh; in which case the distances of the bastions should be so regulated that they may not be out of musketry range from one another. When the curtain becomes unavoidably too long, this defect is in part remedied by erecting on it a flat bastion, which is not so high as the rest of the works.

Ground which will admit of being regularly fortified throughout is seldom or never to be met with, but, nevertheless, the rules of regular fortification must be observed as nearly as possible; that is, the flanked angles should not be less than 60°, the lines of defence should not exceed musket range, and the sides should be lengthened or shortened so as to obtain a well-proportioned front upon each. After an irregular place has been reduced to as regular a form as possible, lines are drawn parallel at the distance of about 30 yards from the houses, in order to give sufficient space for the rampart; and these lines form the interior polygon, which may be fortified inwards, by setting off the demigorges of the bastions, and raising their flanks at an angle of 100° with the curtain: Or, the exterior side may be formed and fortified inwards by drawing a line parallel to each of the interior sides; and when the angle is that of a polygon of more than five sides, the distance from the exterior to the interior sides should not be less than 100 yards. If a side extend from 360 to 520 yards, the perpendicular should be diminished to about 50 yards, and the faces of the bastions be made from 100 to 120 yards. When a side is very long, it may be divided into several parts of from 340 to 360 yards each, which may be fortified with flat bastions, as was occasionally done by the Italians, an example of which may be seen in the bastion Anastasius at Corfu. All these dimensions may, however, be now much increased, and placed more in relation to the range of the modern musket.

The ditch or fosse is an excavation of from 12 to 24 feet in depth, and from 30 to 50 yards in breadth, surrounding the rampart on the exterior side, and the earth dug out of which serves to raise the rampart and parapet. The side of the ditch next the place forms part of the escarpe, the side next the country is called the countescarp, and it is made circular opposite the salient angles of the works. In fig. 1 arcs are described with a radius of 30 yards, opposite the salient angles of the bastions, tangents to which are drawn upon the shoulders of the neighbouring bastions, and thus form the ditch. The general dimensions of a ditch should be such that its excavation, or deblai, would produce sufficient earth, or remblai, for the formation of the works. The breadth varies from 30 to 50 yards, in order that, in passing across it to the assault, the enemy may, for a considerable time, be exposed to the fire of the works; and its depth must also be such as to render difficult the escalade of the parapet, as well as to prevent the besiegers at the crest of the glacis from being able to see to breach the lower part of the revêtement of the escarpe. The line of the countescarp is drawn from the rounding at the salient angles of the bastions upon the shoulders of the bastions next adjoining, in order that the whole of the ditch may be defended by the fire of the flanks of the collateral bastions. Ditches are of three kinds; wet, dry, and such as may occasionally be rendered either wet or dry. The wet ditch is calculated to prevent sudden surprises or assaults, excepting during hard frost, as in the attempt made to surprise Bergen-op-Zoom in the year 1814; but, independently of this exception, the number of bridges of communication, which require continual repair, and the difficulty of making sorties, which a wet ditch creates, renders it extremely inconvenient. A dry ditch, which is capable of containing works for its own defence, and by means of which communications round the works may more easily be maintained, is therefore preferable to a wet one; but the third kind, which unites the advantages of the other two, should, when practicable, be preferred to either. It is only in particular situations, however, that the advantage of such a ditch can be obtained.

The tenaille, in the form given to it by Vauban, does not appear in the works of earlier engineers, but it seems to be naturally derived from the trace of Rimpler (1673), in which the middle flank is analogous in function to the tenaille, and occupies its position; it is a work placed in front of the curtain, and is formed by the continuation of the lines of defence, at the distance of ten yards from the angle of the shoulder; the ends are then drawn parallel to the flanks of the bastions; it is made sixteen feet broad; the angle formed by the meeting of the two lines which determine its rear is then cut off; at the distance of ten yards, parallel to the curtain; and another line is drawn at the distance of sixteen yards, parallel to this, and forming a small curtain upon the line of defence or front of the tenaille. The relief or height of the tenaille is determined by that of the neighbouring flanks, and it has a parapet of seven or seven and a half feet in height, and from twelve to fifteen feet in thickness. The use of the tenaille is to cover the postern gate, which is often made in the curtain or flank, when the ditch is dry, to protect the troops who may be formed behind the work for the defence of the ditch; and when the ditch is a wet one, to cover the boats which may be collected for the same purpose. It also serves to augment the defence, as its fire, from being more horizontal, and nearer to the plane of the bottom of the ditch than that from the flanks, is of course proportionally more effectual.

The ravelin or demi-lune was a work originally designed to cover the entrance gate and ridge of a fortress, but it soon assumed the dimensions and performed the office of a most important work of defence, appearing as such in some early Italian traces. Speckle, the great German engineer, who fortified Schlottstedt, Hagenau, Ulm, Colmar, Bâle, and Strasbourg, was, however, the first who recognized fully its importance, and laid down as a rule that "great ravelins materially augment the defensive power of..." Acting upon this principle, the ravelins of Speckle were even larger than those of Cormontaigne's system, and covered nearly the whole of the faces of the bastions, the faces of the ravelin being directed on the salients of the bastions and their capitals, extending about 150 yards in advance of the exterior side of the polygon. Speckle was another man of science, having studied mathematics and military engineering in his youth, and then perfected his knowledge by personally visiting and studying the most remarkable Italian fortifications existing in his time. The Ravelin is a work constructed opposite the curtain, and composed of two faces meeting in an outward or salient angle, with two demi-gorges formed by the counterscarp. Its use is to cover the curtain, the gates, and the flanks of the bastion. The ravelin is constructed as follows: eleven yards are set off along the faces of the bastion from the shoulder; an arc is described from the angle of the flank upon the perpendicular produced, with a radius of 160 yards; from this intersection lines are drawn bearing upon the points set off at eleven yards from the shoulders of the bastion, but not further than the lines of the counterscarp; and at the intersection of the lines of the counterscarp or re-entering angle six yards are set off on the capital or line bisecting its angle, whence lines are drawn parallel to the lines of defence till they meet those of the counterscarp. Stairs, called pas-de-souris, are constructed here in order to facilitate the entrance of the ravelin from the ditch. The ditch in the ravelin, which is twenty-four yards in breadth, is made circular at the salient angle, and drawn parallel to the faces till it joins the main ditch.

The covered-way was first described by Tartaglia in 1554, so that it must have been used at a very early epoch of Italian fortification. Some of the first bastioned fortresses were, however, without this highly important work; and it is recorded that at the siege of Vienna by the Turks, the garrison having made a sortie, some companies were pursued by the Turks up to the counterscarp, and forced over it into the ditch. The necessity of being able to assemble the troops intended for a sortie under cover from the enemy's fire, and to afford them when repulsed a place for reforming and checking the enemy's progress, and thus insuring an orderly retreat into the body of the place, soon became apparent, and a covered-way was supplied to works originally constructed without one. It is a space of ten yards in breadth, extending all round the counterscarp of the ditch, and covered by a parapet of from seven to nine feet in height, with a banquette. The superior part of this parapet forms a gentle slope towards the country, which terminates at the distance of from forty to seventy yards; and this slope is called the glacis. The covered-way serves for drawing up troops in order to make sorties, and costs less than any other part of the works in proportion to the difficulty of taking it. In the salient and re-entering angles of the covered-way spaces are contrived which have been denominated places of arms.

The salient places of arms are formed by the circular parts of the counterscarp, and the prolongation of the branches of the covered-way till they intersect. The re-entering places of arms are constructed with two faces, forming a salient angle of 100° with the covered-way. The demi-gorges of the re-entering places of arms are generally from twenty-four to thirty yards; but when they are intended to contain a redoubt or intrenchment, they are from forty to forty-eight yards. The re-entering places of arms are meant to flank the branches of the covered-way, and to contain the troops for its defence. The salient places of arms also serve for assembling the troops destined to defend the covered-way.

Traverses are constructed across the covered-way, upon the prolongation of the sides of the ravelins and bastions, perpendicular to the line of the counterscarp; they are from eighteen to twenty feet thick, and serve to cover the troops from the enfilading fire of the enemy. Other traverses should be constructed between these, so that the distance from the one to the other should not exceed thirty-six or forty yards. Openings are cut into the parapet of the covered-way about ten or twelve feet wide, in order to keep up the communication from one part to another round the ends of the traverses, which, however, may be shut by a gate when required. In the more improved systems of Cormontaigne and others, these passages are constructed in such a manner that each can be defended by the fire from the traverse in rear of it.

The glacis, as already stated, forms a gentle slope or declivity from the parapet of the covered-way towards the country, and varies from forty to sixty yards. Its parapet cannot be ruined by the fire of the enemy; it covers the revêtement of the body of the place; and being an inclined plane, it can be easily seen and defended from any part of the works.

The rampart is an elevation of earth, being the part of the works situated next to the town. It must be thick enough to receive a mound of earth, called the parapet, and also leave sufficient space behind it for working the guns, as well as room for the defenders to pass round freely. The ditch is immediately in front of the rampart, the faces of which are revêted or built up with stone walls, backed interiorly, at every fifteen or twenty feet, by buttresses or counterforts of masonry, to strengthen it. The rampart is divided into the interior slope, the terreplein, the banquette, the parapet, and the exterior slope or escarp. See fig. 4, profile.

The revêtement or face of masonry around the work on both sides of the ditch is intended to prevent the earth forming the rampart from falling into the ditch. To ascertain the proper thickness of masonry for this purpose has always been a work of considerable trouble and difficulty. General Sir Charles Pasley of the royal engineers has given the following rules: 1st, For full-scraped revêtements without berms, and for demi-revêtements having berms equal to one-fourth the height of the masonry, the thickness of the wall should be seventeen-sixtieths, and the length of the counterforts or buttresses one-fifth of their height. 2dly, For demi-revêtements without berms, the mean thickness of the wall should be three-tenths, and the length of the counterfort one-fifth of the height. 3dly, For counterscarp revêtements, having only to retain simple terrepleins, the mean thickness should be one-fourth, and the counterfort one-sixth of the height. In all these cases Colonel Pasley supposes the revêtement to be countertopped, that is, to have the exterior slope in a vertical plane, and the interior face inclined, so that the base of the wall may be broader than its upper surface by one-fifth of its height; and he also supposes the counterforts to be rectangular, and the intervals between their centres to be equal to four times their width. 4thly, He recommends that the foundations be made deeper in rear than in front, and that the courses of masonry form an angle with the horizon of about 10° excepting at the exterior points, where it should be made horizontal, to prevent the rain from penetrating, and that the interior face of the wall should be of an irregular form. In order to diminish the lateral pressure of the earth against the revêtements, several tiers of arches may be built between the counterforts in the form of segments of a circle.

The cordon is a round projection of stone, about a foot in diameter, which goes quite round the revêtement wall, near the top, and serves to throw the drip of rain off the face of the masonry. It is also a considerable obstacle to besiegers, in placing their ladders for escalade against the escarp.

The profile or section of Vauban's first system is given in Plate CCLX., fig. 4, in order to illustrate the relative relief or height of the respective works, and also to show the command which each has over the others. When the height of the rampart, including that of its parapet, is 20 feet, and that of the parapet of the covered-way is 9 feet above the plane of the site, then the rampart will have a command of 20 feet over the country, and 11 feet over the crest of the covered-way; and the latter, again, will have a command of 9 feet over the field. There are three sorts of command, namely, in front, in rear, and in enfilade. That in front is when any eminence directly faces the work which it commands; that in rear is when the eminence is behind the work; and that in enfilade is when the eminence is situated laterally on the prolongation of any line or work.

The last, which is the most dangerous kind of command, is best remedied by raising the salient of works exposed to it (see woodcut 18, p. 775), or by erecting traverses. In drawing this figure, a line, called the line of site, and supposed to be the surface of the ground on which the fortification stands, is drawn, and perpendiculars are erected on it equal to the respective heights of the different parts of the works corresponding to the lines in the figure. Thus shows the terreplein of the rampart, b the banquette or step to enable the soldiers to fire over the parapet, c the parapet, d the revêtement, e the escarpe, f the counterscarp, and so on.

2. Vauban's Second and Third Systems.

Having thus endeavoured to explain, with as much minuteness as possible, the principles of Vauban's first system, we trust, from what has been said, that no great difficulty will be experienced in understanding the methods of other engineers who have constructed works varying but little in the main from those prescribed by this system, whilst even these varieties have arisen from difference of situation and local peculiarities, more than from any other cause. The same general observation, indeed, applies to the other methods of construction followed by Vauban himself, who, in his second and third systems (Plate CCLX. fig. 2), merely modified, according to circumstances, the principles upon which the first is based. When this celebrated military engineer was called upon to repair or improve the fortresses of Landau, Brisach, and others, and found these places already surrounded with strong walls surmounted by small towers at the angles, he did not, as some might have supposed, proceed to destroy these defences, but, with his accustomed judgment and ability, he immediately took advantage of them, and constructed, nearly in the same proportions as in his first system, large counterguards or bastions in front of the towers which crowned the angles of the wall, just as the Italian Castriotto had done in 1684. And by this method an important object was attained; for, as in front of each tower, or rather tower-bastion, there ran a ditch which cut off all communication between it and the counterguard, so the enemy, even if they should have succeeded in establishing themselves in the counterguard, would still have another ditch to cross, and another wall to breach, before they could attempt to give the assault.

There is so little difference between the second and third systems of Vauban, that a description of the former will be sufficient to enable the reader to distinguish and appreciate the peculiarities of the latter. In the second system, the interior side of the polygon, from the centre of one tower-bastion to that of the next, is supposed to be equal to 240 yards, and from its extremities, at the distance of 24 yards, perpendiculars are erected equal to 36 yards, for the flanks of the tower-bastions. A line is then drawn parallel to the interior side AB, till it meets the oblique radius of the polygon, or line drawn from the centre of the polygon bisecting its angle, and this being done on both sides of the angle forms the tower-bastion. The oblique radius is then produced 78 yards, and lines of defence are drawn to the angle where the tower-bastion joins the curtain or line AB. On these lines of defence, the faces of the counter-guard, or exterior bastion, are set off equal to 128 yards, and from the point forming the shoulder, flanks are directed to a point set off on the line AB, at the distance of 70 yards from its extremities. From the salient angles of the tower-bastions arcs are described with a radius of 14 yards for the breadth of the ditch, and tangents to these arcs are drawn parallel to the faces of the tower-bastion, but stopped where they would meet a line drawn from the salient angle of the tower-bastions, at the distance of 20 yards from the flanks.

The tenaille is the same as in the first system, excepting that, at its ends, it is carried down till it meets the line drawn between the flanked or salient angles of the tower-bastions. The ditch in front of the counterguards, or, in other words, the main ditch, is constructed in the same manner as in the first system. The ravelin is formed by setting off 90 yards from the re-entering angle of the counterscarp, and directing its faces to points set off on the counterguards, at the distance of 20 yards from the shoulders. A flank is formed by cutting off the corners of the ravelin at the distance of 14 yards on its demi gorge, and 20 on its face; and this flank serves for the placing of guns in such a manner that their fire may be directed into the counterguard, or into the ditch before them, as occasion may require. Again, at the distance of 48 yards from the re-entering angle of the counterscarp, lines are drawn parallel to the faces of the ravelin for the redoubt; a ditch is formed in front of this, and parallel thereto, about 18 feet in breadth; and the redoubt thus constructed has a command of 4 feet over the parapet of the rampart, as the tower-bastions have over the counterguards. The covered-way and glacis are formed as in the first system. It sometimes happens that redoubts are constructed in the re-entering places of arms; in which case their demi gorges are made from 15 to 40 yards, and their faces set off at an angle of 100 degrees, as before.

3. Cormontaigne's System.

The difference between the systems of Vauban and Cormontaigne may easily be discovered by an examination of Plate CCLX., fig. 3. Vauban makes the faces of his bastions two-sevenths of the exterior side, and Cormontaigne one-third. Vauban, in his first system, produces the faces of his ravelin to the distance of 11 yards upon the face of the bastion from the shoulder, and in his second and third systems, to the distance of 20 yards; but Cormontaigne makes the capital of his ravelins about 120 yards, and produces the faces to the distance of 30 yards from the shoulder; by which means the flanks are better covered, and the bastions and ravelins are enlarged. And this is an advantage; for he is thus enabled to construct a larger redoubt in his ravelin, the curtain and flank are also better covered, and, as the former is shorter, communications are more easily kept up between the bastions. Cormontaigne gives the same breadth to his covered-way as Vauban, but he arranges in a different manner the communication round the extremities of the traverses, as may be seen by inspecting the plate. By this zigzag line of communication, which resembles the crémaillère trace adopted by Speckle in his covered-way, the passage round the extremity of one traverse may be defended by the fire of the other in its rear, or nearer to the body of the place, and the advance of assailants along the covered-way completely checked. As Speckle planned in 1589, or long before the invention of ricochet fire by Vauban had rendered traverses an essential element in fortification, his object was not the same as that of Cormontaigne, but simply to ensure a more perfect flanking defence of the branches of the covered-way than that afforded by the places of arms of his systems. The ditches are, as shown in fig. 3 of this Plate, on different levels—the main ditch being about 23 feet deep, the ditch of the re- Fortification.

doubt of the ravelin only 7 feet, so that from this latter ditch there is a fall of 16 feet to the main ditch, rendering it impossible to attack the ravelin by its gorge without the aid of ladders. An examination of the several figures which represent Vauban's and Cormontaigne's systems, as also the outworks of fig. 3, Plate CCLXI, will at once render evident the vital defect of the ordinary arrangements of outworks—that they expose by their ditches the scarp of either the body of the place, or of the work on which their faces or branches are directed, to be breached. In the system of Cormontaigne, as well as in the modern system next to be considered, the increased projection of the ravelins, by throwing the intervening bastion into a deeply re-entering position, secures it from attack by approaches until the salients of the ravelins have been taken; but this great advantage is diminished by the power of breaching the bastion from the glacis through the opening afforded by the ravelin. For the purpose of covering the communication to the re-entering place of arms, a demi-caponnière, or work composed of a parapet and glacis, was thrown across the ditch of the ravelin, as shown in the figure of the modern system, Plate CCLXI, fig. 2. This work afforded cover also to troops assembling preparatory to a sortie upon the enemy when making the passage of the ditch, but, from the depth of the ravelin ditch, it was insufficient to mask the revêtement of the bastion behind it. It will presently be shown how this object was afterwards effected; and it may be fairly said that without any material change as to system, the general result of Cormontaigne's variations from Vauban's trace is an unquestionable improvement.

4. The Modern System.

The modern system, which is shown in Plate CCLXI, fig. 2, varies but little from Cormontaigne's. Its perpendicular is one-sixth of the exterior side, and the faces of the bastions are one-third. The flanks are at right angles with the lines of defence, whereas in Vauban's system they form an angle of about eighty-two degrees; which is not so good, because, in the modern system, the guns placed in the flanks can fire straight along the ditch without being moved or turned on their platforms. The ravelin is formed by setting off thirty-four yards from the shoulder angle of each bastion along the face, which line forms one side of an equilateral triangle, the vertex of which, opposite the centre of the curtain, forms the salient angle of the ravelin. The redoubt of the ravelin is formed by drawing its faces parallel to those of the ravelin from the shoulder angle of the parapet of the bastion; and it has flanks with a ditch about twenty yards in breadth. The cavalier in the bastion is drawn parallel to the faces of the bastion, at the distance of forty-eight yards. The ditch on the faces is ten yards in width, but there is no ditch on the flanks. The coups connected with the cavalier retrenchment is drawn perpendicular to the faces of the bastions, at thirty-four yards for the counterscarps of the coups, whilst the scarps are at ten yards, and parallel to these. This system originated in the School of Military Engineering instituted at Mézières in 1750, and was for some time called the System of the School of Mézières. It has, however, been successively much improved; and the system which is now recognised as the modern system is that of General Noizet. Referring, however, to fig. 2 of the Plate, it will be seen that coups have been introduced on the faces of the ravelin; and as the ditch of the ravelin in this system has by many engineers been sunk less by 7 or 8 feet than the main ditch, there is a sufficient fall between the two to check the enemy in his passage to the latter, whilst the demi-caponnière is raised so much higher, and therefore begins to mask more effectually the revêtement of the bastion. In General Noizet's system this demi-caponnière is formed into an elevated mask, which effectually secures the revêtement from the breaching effect of the fire from the enemy's battery on the crest of the ravelin glacis. This is shown in the annexed woodcut; and the system modified from the former modern system in this respect, as well as in other arrangements, is now the normal bastioned