hills upon a plan; yet, if he will only have the patience to labour a little for himself, I think he may contrive to make it out. In the first place, he has to bear in mind that all distances shown upon a plan are horizontal ones; for instance, referring to plate XII., the line, H K, of the section, which is the hypothenuse of the right-angled triangle, H K N, is represented on the ground plan below by the line, H K, which is equal to H N in the section; and in the same way, M B, a precipitous fall in the section, only occupies the space from M to B on the ground plan. Thus it is seen that the height of mountains or the depression of valleys exercises no influence upon the situations of objects in a plan. I may mention here that the level of the sea is, in great surveying operations, considered as the horizontal plane, to which all measurements must be reduced.

But as regards the expression of hills on a plan; suppose we are standing on one of a perfectly conical form, it is obvious that rain falling on its summit will trickle down towards the base in minute, diverging streams; our vertical style of shading hills has been likened to these. The immediate purpose, however, of plate XII. is to show the principle upon which slopes are expressed by means of shade: this is made light or dark according as they are gentle or steep. The section given represents ground of varied character; A is on a level with the sea; from that point the hill has a steep rise to C, from whence it is somewhat more gentle as far as D; at E a descent begins, and continues to F, from whence there is a steep slope to G, and so on. I have endeavoured to make the shading of the ground plan to agree with the section: for instance, that from C to A is darker than between D and C. From D to E the ground is level, and therefore no shade appears. The slope from E to F, being greater that from D to C, is

shaded darker; F G, being steeper, is made darker still, and the deep shade from M to B is equal to the shading of both of the slopes L K and K H.

I shall not fatigue my reader with any further description: he must now try and make out the corresponding parts of the ground-plan and section for himself. But perhaps he may stumble at the threshold, not knowing what a section is; the term profile would have been better, for that means a vertical section. It may serve to convey an idea of a profile of a hill, if the reader will call to mind the appearance it would present in hazy weather, when nothing but the outline is visible; or, referring to the ground plan in plate XII., let him conceive the ground there represented to be cut away from the dotted line A B, so as to leave the face of the remaining part of the ground perpendicular: this face would then present the exact appearance of the profile given in the plate.

By a little attention to what has been said above, I think the student will be able to comprehend the nature of a ground plan of hill features, with its corresponding section, as here shown.

METHODS OF SHADING HILLS, ETC.

The shading of hills may be performed by using a blacklead pencil, with a pen, by washes of Indian ink or neutral tint, &c.

There are two modes of expressing inclinations of ground with the pen or lead pencil, distinguished as the vertical and horizontal manners. In this country, opinion is divided as to which method is the best for general purposes. The vertical mode, as already stated, assumes the pen strokes to represent such minute rills as water forms when trickling down the slope of a hill. The horizontal manner marks the contours of hills by waving lines, each line

continuing on the same level while following every undulation of the ground; as, in some hilly parts of this country, sheep paths may be observed, often covering the entire faces of steep declivities, at a few feet apart, and horizontally pursuing their windings. Plate XIII. shows the same hill, drawn in both the horizontal and vertical styles.

Mr. Burr, the Professor of Military Surveying at Sandhurst, showed me some years since what I think a very ingenious and striking way of conveying a just idea of this style, by means of a model in plaster of Paris, representing some hilly ground. He had enclosed his model in a wooden box, which was then filled with water. A scale, divided into quarters of an inch, having been placed upright in the box, the water was allowed to run off through a hole near the bottom, by a quarter of an inch at a time, as indicated by his scale. At every successive fall of the water, he traced lines on the model, indicating the curves shown upon its surface by the successive lowering of the water. When the operation was completed, the surface of his model exhibited a number of lines, all of course perfectly horizontal; closing upon each other where the hills were steep, and diverging again where the slopes became more gentle. A model so prepared is easily represented on paper, and with great accuracy; and I cannot do better than recommend those who are desirous to obtain a thorough knowledge of ground, to consider the horizontal method with attention, as it reduces the delineation of hills to something of a fixed principle. In practice, either or both of the styles may be used at the pleasure of the draftsman, or as may be best suited to the nature of the ground he wishes to pourtray. The sketch in plate V. is a specimen of the horizontal manner of shading.

The vertical style of sketching hills used to be generally practised in the British service; so much so, that I do not