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blending of colours, the angles subtended at different distances by objects of known dimensions, such as the height of a door, or a man, and the well-known rate at which sound has been ascertained to travel*, will all materially assist him. According to the “Aide Mémoire,” the windows of a large house can generally be counted at the distance of 3 miles; men and horses can just be perceived as points at about 2200 yards; a horse is clearly distinguishable at 1300 yards; the movements of a man at 850 yards; a man's head clearly visible at 400 yards; and partially so between that distance and 700 yards.

These directions, however, cannot be considered as infallible, as the power of vision differs so materially; but nothing can be more easy than for an officer to make a scale of this kind for himself.

Another easy mode of judging distances is by marking on a scale or pencil held at some fixed distance from the eye, the apparent diameter or height, at different measured distances, of any objects the dimensions of which may be considered nearly constant; the average height of a man, a house of one or two stories, the diameter of a windmill, &c., will furnish suitable standards; and a short piece of string, with a knot to hold between the teeth, will serve to keep the pencil always at the proper distance. Suppose these scales to have been carefully marked for four or five of these objects, at the distance of 150, 200, 300, &c., yards, they will evidently afford the means of obtaining an approximate distance; but even without this scale, if the pencil b be held up to the eye at any distance a, and the height or diameter of any object h of


* About 1100 feet in one second. A light breeze will increase or diminish this quantity 15 or 20 feet in a second, according as its direction is to or from the observer. In a gale a considerable difference will arise from the effects of the wind. A common watch generally beats five times in one second. See "Philosophical Transactions," 1823. The number of pulsations of a man in health is about 75 per minute. Either of these expedients will serve as a sort of substitute for a seconds watch. The velocity of sound is affected by the state of the atmosphere, indicated by the thermometer, hygrometer, and barometer; according to Mr. Goldingham, of an inch rise in the barometer diminishes the velocity about 9 feet per second. Mr. Baily rates the velocity of sound, at 32° Fahr., at 1090 feet per second, and directs the addition of 1 foot for every degree of increase of temperature above the freezing point.


known dimensions be observed, then the distance from this object

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In reconnoitring the outline of a work which cannot be approached closely, for the purpose of tracing parallels and determining the positions of batteries, the best plan is to mark, if possible, the intersections of the prolongations of the faces and flanks with the line on which the distances are being paced or measured, instead of merely obtaining intersections of the salient and re-entering angles with a sextant. Soon after sunrise, or a little before sunset, are the best times for these observations, as lights and shades are then most strongly marked; in the middle of the day it is often impossible to distinguish anything of the outline of a work of low profile, even at the distance of 200 or 300 yards.

If the perpendicular distance from the angle, or any other point of the face of a work, is required to be ascertained in the field; and the line marked on the ground for the purpose of laying out a battery, it can be readily done by the following method:

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Suppose, in each of the figures above, A to be the point from which the distance is required on a line perpendicular to AB; measure any distance CD, in a direction nearly parallel to AB, and take the angles at C and D, formed by the line CD, and each of the points A and B; B being some marked object, situated anywhere on

the line of the work, probably a salient or re-entering angle. From these data ascertain the values of AB, and the angle ABD, either by calculation or by any of the practical methods already described; BE is then the secant of the angle ABD to radius A B, and the difference D E between this quantity (to be found by means of a table of secants), and the calculated distance BD being laid off either on the line D B from D towards B (as in fig. 1), or on the prolongation of this line (as in fig. 2), the distance AE becomes the tangent of the same angle also to the radius AB; and the distance required for the battery can therefore be laid off on the ground by increasing or diminishing the length of this line AE.

The direction of the capital of a work, and the distance from its salient, can be thus determined in the field.

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PRT equal to that observed at O; T being in the prolongation of SP. The triangles OSP and RTP are therefore similar, and the angle T being bisected by the line TV, it results that RP: PV:: PO: PX; which distance, laid down on the line PO, gives the point X required in the prolongation of the capital. The sides of the small triangle TPR and TV being all capable of measurements, OS, SP, and SX can, if required, be all found by a similar simple proportion*.

It is, however, generally practicable to obtain a plan of any attacked work and of its environs, more or less correct; and on this

* With a pocket or prismatic compass this operation may be more easily performed; by taking up a position on the prolongation of each face, and observing their inclination to the magnetic meridian, that of the line bisecting the salient, or the capital of the work, is at once known; for the mean between the two readings will be the bearing of the salient when the observer is upon the capital; and by measuring a base in a convenient situation, the distance may be readily found.

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any perceptible errors discovered during the reconnaissance are marked. On approaching a place by day, the officer should be alone, so as to attract little attention; but supported at a distance by troops, hid from observation by any cover that can be taken advantage of. By night he should be accompanied by a strong party; and by advancing as near as possible towards daybreak, and retiring gradually, he would be enabled to make more correct observations as to the outline and state of repair of the works than at any other time.

The numerous conventional signs recommended in most continental military works are extremely puzzling, difficult to remember, and are mostly unintelligible. In a little work, the " Aide Mémoire Portatif," published in 1834, there are no less than ten pages devoted to these signs. Beyond the few that are absolutely necessary, and generally understood, it is far better to trust to references written on the face of the sketch, and the explanatory report, than by endeavouring to convey so much information by these conventional symbols and attempts at mathematical representations of the ground, to render a drawing so confused and difficult to comprehend that it really becomes of less value than an indifferent sketch with copious and clear remarks.

Below are given a few conventional signs, applicable only to military sketches :

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On the following page are those of most general use in topographical plan-drawing: the boundary lines are those employed in the Ordnance Survey; a similar arrangement could of course be adopted to mark the divisions of any other country, however they may be designated.


-Smithies. A small horse-shoe with the open side turned towards the



Turnpike roads. The side from the light shaded.

Cross roads. Narrower, and both sides alike.

Railroads. Both sides dark, very narrow, and perfectly parallel.

Canals. Distinguished from roads by the parallelism of the sides, the locks, and bridges, and by having the side next the light shaded like rivers. Canals and navigable rivers to be coloured blue.

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