a straight line with a transit instrument or a theodolite*. Such has been the practice in North America, where the proposed direction is determined by means of the compass. Also, the lines are there set out without a telescope, simply by the aid of sights raised on the instrument, and instead of being ranged by staves or rods, they are ranged by the bearing of large trees which stand in the line of sight.

It is obvious that great want of precision must result in ranging a line, when the only object to determine its direction is a tree of considerable diameter. Yet the errors due to this cause are not so considerable as those consequent on variations of the compass, which have been known to exceed half a degree in the course of a day†.

* Surveyors in South Australia ranging sections, have found that all the squares on one side of a range of hills came in with great exactness, while those on the other side, although worked with the same care, could not be made to check. Circumferentors having been used in the operations, the irregularity here noticed was supposed to be due to differences in the local attractions.

+ I am indebted for the information embodied in the following chapter to the able report On Surveying as applicable to the Colonies, made by Captain Dawson, R.E., to the Secretary of State for the Colonies, 1840. It is important to notice, that since the date of the report, this system of survey has been followed in Australia, New Zealand, and other British colonies, and that it has in all cases proved admirably adapted to the purposes in view.

The anticipations as to cost and rapidity of execution, as well as accuracy, have been fully realised.

CHAPTER VIII.

HILL DRAWING AND "CONTOURS."

ALL objects marked in position on an outline map, are protracted according to the laws of the orthographic projection; in other words, their respective distances are reduced to a common horizontal plane. But as surveying aims at making a faithful image of the surface of the country, the map remains incomplete if the rise and fall of the hills, the undulations of the surface, and its whole relief be left unrepresented. It would evidently be an imperfection, that on the same plan or map, the highest mountain ground and the lowest land, should all appear as if on the same level. There are several methods adopted for the purpose of conveying the necessary knowledge on this point. The first and the most general is that called Hill Drawing or Hill Sketching.

REPRESENTATION OF HILLS BY LIGHT AND SHADE.

In the same manner that a certain disposition of light and shadow can convey to the mind an idea of the familiar objects around us, so can a physical representation of a hilly surface, by means of light and shade, portray the form and height of the hills, the depth and direction of the valleys, and the massive external characteristics of the natural stratification of the country. The only difficulty arises from this circumstance, that the representation of the natural features must be made as if seen from above, a point of sight to which the eye is not accustomed; for in the limited view which it can embrace of objects around,

the effects of perspective always present the apparent different from the real forms. Nevertheless, by attending to the principles and effects of light and shade, plans may be so shaded and finished that an inspection of them would make the observer acquainted with the relief of the ground, as it would appear if a reduced model of it were placed under his eye*.

Steepness of the Slope, an element to regulate the Shade.

The side or slope of a hill, being inclined to the horizon, receives in proportion to its surface a smaller quantity of vertical light than the summit, or than a horizontal plane at its base. A horizontal surface receives an equal portion of light with the inclined surface resting upon it,

Vertical Rays of Light.

and as the inclined surface is of greater extent, it will be darker than the horizontal, in proportion to the degrees of inclination and consequent increase of the extent of surface. A sheet of white paper, bent into the form of a

* The Ordnance Map of England, (which is published on a scale of 1 inch to the mile,) with a representation of the natural inequalities of the ground by means of light and shade, has proved of incalculable value to the engineers and surveyors employed to design and lay out improved lines of communication throughout the country. By a simple inspection of the map, a knowledge is obtained of the prominent ridges and of the most practicable passes through them, and the engineer can at once direct the surveyor to proceed to the minute examinations of those lines which are likely to prove available for the proposed work. Without access to such maps numerous trials, surveys, and sections would have to be made at considerable expense of time and labour in order to combine as much topographical information as is conveyed on the Ordnance Maps.

ridge, and placed under a vertical light, affords a simple illustration of this effect, the shade becoming darker, as the inclination is increased*. From this is derived directly the principle that in the representation of the varied forms of ground, the shade applied to the side of hills should be proportionate to the steepness of the slope. The draughtsman thus gives a physical representation of the hills, generally intelligible to all, and enabling the engineer or professional man to estimate the relative steepness of the hills from a comparison of the relative intensity of the shades.

Height also to be an element to regulate the Shade.

Height, as well as steepness, is a characteristic to be attended to in the representation of hills. On looking at a reduced model of ground, the highest point attracts the eye in the first instance; in the same manner it should retain its prominence in its representation on the plan, and all differences of altitude should have their relative importance in the drawing. This is effected by combining height with steepness as the two elements to regulate the depth of shade. This combination produces a correct physical representation, by imitating the effects of aërial perspective. The higher points of the country, being nearest the eye, are supposed to present a greater intensity of light and shadow, both of which diminish in degree as the surface becomes of less altitude, because of the supposed intervention, between the surface and the eye, of a greater body of the atmosphere. Through this cause the valleys are slightly shaded or tinted; thereby they cannot be confounded with the tops of the highest mountains, which alone are to be left quite white. Were

* MITCHELL's Outlines of a System of Surveying, page 69.

this principle unattended to, the flat parts of valleys, and the level summits of mountains, being both left unshaded, could not be distinguished from one another, and the true appearance of relief would be lost.

Relative importance of features to be preserved.

In the representation of ground, all features, whether of primary or subordinate importance, whether high mountains or small ridges, should be represented as fully as the scale will admit; but each feature, as in nature itself, or in a model, should be in proper keeping, the smaller features being kept subordinate to those of greater magnitude. The importance of preserving each feature or object in its proper "keeping" is well understood in drawing or painting when cultivated as a branch of the fine arts, and it is one of the elements most conducive to beauty and truth of representation. When unattended to, the drawing presents a harsh effect of spottiness. Until of late years it was altogether neglected in topographical drawing; high mountains, howsoever extensive their base might be, or however varied their ramifications into other subordinate forms, were represented much in the same manner, and with the same tone, as the inferior hills of the low country.

Mr. Dawson, (for more than half a century connected with the Topographical Department of the Ordnance Survey of England and Wales,) was the first to correct this defect, by establishing the following general principles.

1. That a plan is to be considered as a full-face portrait of a country.

2. That mountains, hills, and hollows, are to be considered as features varying the general face of the ground.

3. That every feature must be conceived and ex