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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, DE, is then kept steady, while the protractor is gently pushed along until the edge of the arm agrees with the station-point, C. It is to be remarked, however, that these two last methods do not enable us to use the divided radius of the improved protractor for laying off distances; as we cannot adjust zero to the station-point, unless we have the means of pushing the instrument forward, as well as laterally.

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 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 XIII., the line, H K, of the section, which is the hypothenuse of the right-angled triangle, HKN, is represented on the ground plan below by the line, Η Κ, 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 XIII. 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; FG, 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.

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