perfect work done by the theodolite. In making surveys of estates and parishes, while on half-pay, I suffered much for want of a better system of plotting than any I could find, after making every inquiry, and searching books on the subject. Such methods as these do not meet the exigences of practical men, and hence it is usual to employ the chain alone. The theodolite is very little used among private surveyors; they reject the system altogether; and, indeed, many use the chain so skilfully that, under ordinary circumstances, it leaves nothing better to be desired. The theodolite is, however, an invaluable instrument; and if the proper use of it, together with a more satisfactory method of plotting, were more generally known among private surveyors, much of this prejudice would certainly give way.

"Anxious to discharge the duty confided to me in the most beneficial manner, I have given much study to this as well as to other branches of my duty, and have the honour to submit, at least for trial and discussion, the following very cheap and simple means; which are, in all respects, the nearest approach to perfection that I can contrive:

"The pattern semicircular protractor, at the price of no more than £2 17s., was contrived and made from my drawing and instructions, some few years ago, and must be too well known in the department to need description.

"As, when away from home, it seldom happens that the surveyor can obtain a good drawing-board, or even a table, with a good straight edge, I fix a flat ruler, A, to the table, B B B (plate XI. fig. 1), by means of a pair of clamps, CD, and against this ruler I work the pattern square, E, one side of which has the stock flush with the blade; or, if a straight-edged board be at hand, then the square may be turned over, and used against that edge

instead of the ruler, A. Here, then, is the most perfect kind of parallel ruler that art can produce, capable of carrying the protractor over the whole of a sheet of plotting paper of any size, and may be used upon a table of any form. It is convenient to suppose the north on the left hand, and the upper edge of the blade to represent the meridian of the station.

"This protractor is held in the hand while the vernier is set, which is an immense comfort to the sight; and it will be seen that, as both sides of the arm are parallel with the zero and centre, the angle may be drawn on the paper against either side, as the light or other circumstances may render desirable.

"From this description, and a mere glance at the plate, it is clear that angles taken with the theodolite can be transferred to the plot as accurately as the protractor can be set, namely, to a single minute; and that, too, in a rapid and pleasant manner.

"By means of the notch at the end of the arm, this instrument may be used in the manner of a circular protractor, should a square not be at hand.

"This protractor is specially for plotting a survey, and therefore is figured from left to right: but should it be required for other purposes, to set off an angle from right to left, then mark off the supplement of that angle."

The experience of practical men is always highly valuable, and we are indebted to Mr. Howlett for the above useful remarks. His method of carrying the protractor forward is excellent, and the instrument itself is a very good one; as I can vouch for, from long experience.

Notwithstanding the superiority of moving the protractor forward by means of a T ruler, I think military men will often be disposed to use the large three-bar parallel ruler on account of its portability. One bar is

fixed, either by means of leaden weights or small screws, while the others advance over the paper, pushing forward the protractor.

There is another method, which ought to find a place here, being still more suited to our wish, for portability, as it requires no ruler to work the instrument with. A number of parallel lines are ruled upon the paper at about an inch or so apart, to represent meridians, which are marked north and south. The semicircular protractor is then set to the required angle: a point is next marked on the paper for the first station, and the protractor is then adjusted to any convenient meridian so that the ruler part or base of the instrument may coincide with one of the meridian lines, while the bevilled or fiducial edge of the arm cuts the station-point: a line has then to be drawn along the edge of the arm through the station-point, and the bearing is laid down. A common flat ruler is, however, useful in this method of protracting. Lay the ruler along any convenient meridian; and, having set the protractor to the required angle, place its base, A B, along the edge of the ruler, DE (see fig. 2, plate XI.), so that the arm, G, may not touch the station, C: the ruler, D E, is then kept steady, while the protractor is gently pushed along until the edge of the arm agrees with the station-point, C.

SECTION XI.

ON PLAN-DRAWING METHODS OF SHADING HILLS, ETC.

We have seen, in the foregoing sections, the manner of proceeding in the field, in order to obtain the necessary measurements of a survey. It has also been shown how those measurements are laid down on paper, or plotted, so as to furnish a rough skeleton plan of the work. I shall now speak of plan-drawing, in its more limited sense, or the method of expressing upon paper, according to certain conventional rules, the various objects which the face of a country presents, and that are required to be delineated by the topographical draftsman: but of these, the drawing of hills alone demands serious attention, for all the rest give us no difficulty whatever.

Objects having elevation can only be expressed upon a flat surface, such as paper, by means of shade, or by being thrown, as it is called, into relief; and consequently we can only give this appearance of relief, or being raised above the surface of our paper, in a ground plan, to bodies whose forms present either slopes or curves; unless we depart from the principles that govern a ground plan, and give an elevation to such bodies, in the manner seen on very old maps and plans: a practice which has universally been discontinued, since the introduction of the present system of plan-drawing.

A hill, therefore, presenting slopes, can, according to our conventional system of shade, be faithfully expressed on a ground plan, so as to convey an idea of elevation to all

who are acquainted with the principles of plan-drawing; but we are unable to give the appearance of elevation to a building, because its walls are perpendicular. In reality, this is a matter of no consequence whatever, for the mind at once connects the idea of height with castles, churches, houses, &c., and our method of shading hills enables us, at the utmost, only to form a loose judgment of their height as compared to each other, for we cannot determine by it the actual elevation of any single hill. But for ordinary military purposes, an approximation to their comparative height is generally sufficient; and when, for any particular object, it becomes necessary to determine the actual elevation of any point above the sea, a river, &c., we can ascertain it either by levelling, or by a problem in the application of trigonometry to the measurement of heights; and likewise, but with less accuracy, by means of the mountain barometer.

The theory most generally adopted, supposes the light to fall vertically upon the hills, in parallel rays; according to which steep slopes, receiving those rays at a more oblique angle than more gentle ones do, are therefore illuminated in a less degree, than the latter, and must be shown in a plan by a darker shade; while such portions of the ground as are horizontal, and receive, consequently, the rays of light perpendicularly to their planes, being thus illuminated in the greatest degree, are left without shade in a plan; but, as it is scarcely possible to fix a criterion for the depths of tint in shading to express ground, it is idle to suppose that, practically, the shading can ever be so exact as to enable us to measure by it the positive height of a hill.

I fear it is almost impossible, by means of plans and descriptions, to convey at once to the mind of a student a clear perception of our conventional system of expressing