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as already explained; but a more correct method is to fix the two ends of the chain in the holes at C and C', and the arms being separated as far as this will allow them to be opened, the centre lines give the directions of the sides containing the right angle.

This brings us to the other and most important use to which the instrument can be applied, that of determining, by inspection from the scale marked in red on the inner faces of the arms, the distance from any object which cannot be approached.

The only conditions for the performance of this operation are, that it shall be possible to measure a base (either to the right or left) at right angles to the line directed on the object; and that this base shall not exceed the distance sought, or be less than one-tenth part of its length.

The method of proceeding is obvious. One arm is laid in the direction of the object AD, and the other opened out to an angle of 90°. A mark is then put up, as at E, and any convenient distance measured, which can be done with the tape used with the scale of chords, or with the

Telegoniometre it

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self, opened out to a straight line when it forms a measuring-rod of double the length of each arm.

The distance can, of course, be always kept within the limits prescribed; and at its extremity, B, the instrument is again laid down, one of its arms being in the direction of the measured base, and the other again pointed on the object D. The chain is then applied in a similar manner as in measuring angles by the scale of cosines, but, instead of reading off the angle on this scale, the distance from A is read off on the scale of distances, giving the tangential length A C to any radius, A E, upon which this scale may have been graduated.

Suppose this to have been 100 feet, and the base measured 300; the number of feet obtained by inspection has simply to be multiplied by 3, for the distance sought from A to the object D.

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 two or three hundred 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

K

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 AB, and the difference, DE, 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 DB 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 any

* 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.

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 day-break, 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 inmost continental military works are extremely puzzling, difficult to remember, and are mostly unintelligible. In a little work, the "Aide Memoire 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 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 references.

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 of Ireland; a similar arrangement could of course be adopted to mark the divisions of any other country, however they may be designated.

n

A

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

Limekiln.

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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