SECTION IX.

METHOD OF CONDUCTING A MILITARY SURVEY.

IT may now be of service, if I proceed to furnish an example of the most simple manner in which the survey of a tract of country may be commenced and carried forward. I shall suppose the survey such as might be wanted for military purposes, and that a small theodolite and common measuring chain are to be used. (Plate X.)

The selection of a base line is the first consideration ; and on examination, the direction of AB, along a piece of level ground, is found the most eligible. The next object is to choose commanding points for stations, so situated with respect to each other that good triangles may be formed; that is, sufficiently wide apart, and forming angles not too acute. These important matters being arranged, the base, AB, must be carefully measured three times over, and the mean taken, which is 3574 feet.

Marks, such as small flags, having been placed at C, E, and F, the most favourable points on the ridge running parallel to the river; also at H and G: the theodolite is set up at A, and the following angles taken, namely, CAE, CAF, CAB, BAG, and BAH. These may be entered in the field-book thus :

The instrument is then taken to the other end of the

base, and angles are observed at B.

It should be observed, that when time permits, it is usual to take all such angles three times over, each time turning the circle of the theodolite, for greater correctness, and as a check against error. In this case, an entry would. be made thus :—

With respect to the circle of the instrument, you may begin to work from any part of it; by which, should the dividing not be very perfect, the errors compensate each other, and to save time in the field, enter the readings as

*

*It is not consistent with the plan of this work to enter into the niceties of trigonometrical surveying; yet it may be useful for me here to mention that the accurate division of the circumference of a circle, turned in metal, into 360 parts, and these again into smaller subdivisions, is a work of the greatest difficulty. By means of his large dividing machine, constructed at great labour and cost, Mr. Simms, of Fleetstreet, has brought the division of the circle, perhaps, as near to perfection as is possible; but still this must only be considered an approximation to geometrical accuracy. "The attainment of perfect accuracy in this work," observes Sir J. Herschell, "has hitherto baffled the utmost stretch of human skill and industry; nor, if executed, could it endure. The ever-varying fluctuations of heat and cold have a tendency to produce, not merely temporary and transient, but permanent, uncompensated changes of form in all considerable masses of those metals

you obtain them from the circle, and work out the quantity for each angle at home. Suppose you commence taking angles, with the index showing 50° 10′, the entries at B would be thus, to agree with the preceding example :—

The requisite angles having been observed from each end' of the base, the instrument is moved to E, and angles taken, namely:

which alone are applicable to such uses; and their own weight, however symmetrically formed, must always be unequally sustained, since it is impossible to apply the sustaining power to every part separately: even could this be done, at all events force must be used to move and fix them, which can never be done without producing temporary, and risking permanent, change of form."

Besides the errors to which all instruments are subject, there are others which arise from defective vision, atmospheric indistinctness, &c. &c.

The effect of these sources of error may be in a great measure obviated: First, by taking the readings of both the verniers of a theodolite, and using the mean of the two readings. Secondly, by what is called repeating; in which process the angle is not taken again, by separating the upper plate and bringing the vernier back to zero, and then taking it a second time; but, without detaching the two plates after the last observation, turning the whole instrument bodily round to the first station, and then unclamping the vernier plate, and turning it round to the second station; the difference between this and the first reading, before starting, will be double the mean angle. Keep the two plates still together, and turn the whole round, repeating the process as before, and the difference between this third reading and the reading at starting will be three times the angle required.

After which, angles are observed from other stations. Previous to plotting, I recommend a diagram or figure to be drawn, representing the base line, and the several triangles; of these, it is a good plan to make a list,

* Two angles of any triangle being known, the third angle is their supplement to 180°

To lay down the triangles:- First draw a line on the paper, and take from the scale you intend to use, 3574, for the number of feet in the base; lay off this distance along the line, and one end of the length so marked on the line will be A, the other B.

The next consideration is whether the triangles shall be protracted by the sides or the angles; if by the sides, their lengths are worked out by means of plane trigonometry, and then laid down; for example: In the triangle, ABE, one side, namely the base, A B, is given, and the three angles; by means of which we are enabled to find the other two sides, A E and E B, by an application of the first case of trigonometry. The distances so found have then only to be taken from the same scale as the base, and the triangle, AEB, is easily constructed. Again, in the triangle, BEF, we have the side, EB (as just found), and the angles, to find EF and B F. Also in the triangle, ACE, the side, A E, has been found, which, with the angles, give AC and CE. The other triangles are obtained in the same way. Thus, every side whose length is found becomes a base line for a succeeding triangle; and in this way a succession of triangles may be carried over the face of a country.

But in a survey of small extent, and especially when time, as during warfare, becomes an object of importance, the triangles may be protracted by the angles. Indeed, when the sides of the triangles do not exceed two or three miles, and the scale not more than four inches to a mile, a good protractor of five or six inches radius enables us to lay down the triangles with sufficient accuracy and great despatch.

To commence then protracting by the angles: We find that, having the theodolite placed at A, our first set of