trained the eye to accuracy. It is well adapted for reconnoissances of a country, and it is much used by military engineers. The civil engineeer would, however, frequently find the same advantage in using it in his preliminary examinations of countries for the purpose of selecting general lines of communication.

In the field, when the eye alone is depended upon, the horizontal lines are traced in pencil, by close parallel hatchings; and when the whole drawing is finished the normal contours are traced at the required vertical distances apart, by following the general direction of the pencil lines, and checking their truth by means of the trigonometrical elevations or other heights marked on the map. The contours, when a complete circuit is made, must return to the point of departure, and if it were attempted by the eye alone to trace normal contours which are isolated from each other, no degree of previous experience would suffice for the attainment of the object.

"Vertical" Style of Hill Drawing.

The practice has long prevailed of transferring to the fair drawing or to the copper plate for engraving, not the horizontal lines as sketched in the field, but vertical lines at right angles to them, which represent the course that would be followed by water in its descent down the slope. This style of hill-drawing is called the "vertical style," in contradistinction to the first described, which is called the "horizontal style." The vertical style is rarely used for the field-work; but whatever style may be adopted in the field, the maps when engraved have hitherto been etched in the vertical style.

It seems difficult on first consideration to account for this substitution of vertical lines for the horizontal lines, as originally drawn in the field, especially when it is con

sidered that any change must diminish in the copy the value due to the original document. Also, for engineering purposes, the change is inconvenient, as the horizontal lines must again be restored by tracing them at right angles to the vertical ones; and such a change cannot be made without introducing errors. The chief cause of the alteration seems to be that the vertical lines can be etched by the draughtsman, and more especially by the engraver, with greater facility and rapidity than the horizontal lines: it is believed, however, that, to a certain extent, the greater facility of engraving in the vertical style is due to the artists having exclusively practised in that style.

For a small scale, such as that of 1 or 2 inches to a mile, when it is intended to introduce into the plan all the details that the scale admits of, etching with the crowquill for the fair plan is to be preferred. But for plans aiming at less exactness of detail, or prepared on a larger scale (from 3 inches to a mile and upwards), washing in the tints with Indian ink is much preferable, as it admits of greater rapidity of execution. The field-work is, nevertheless, finished as before described in pencil, and normal contours are, if possible, traced and drawn with the pen; the tints of Indian ink are then laid on according to the rule of the depth of tint being proportional to the height of the hills and the steepness of the slopes. To soften the tints, when it is required to represent a rounded form, two hair pencils are used, one as the colour brush, the other as the water brush. The shades are laid on with the colour brush, and softened by passing the water brush rapidly along their edges. The water brush should not have much water, as it would in that case lighten the shadow to a greater extent than is intended, and leave a ragged harsh edge. Tints may be rounded without softening the edges with the water brush, by using very light colour, and applying one tint over another, with the boundary of the

upper tint not reaching to the extreme limit of the tint below it; a beautiful effect of clearness and transparency is by this means given to the drawing. Also, when depth of shade is required, it is best produced by the application of several light tints in succession; for when the full depth is given by a single wash, its effect is rough and opaque. No tint is to be laid over another until the first is dry; and a little indigo mixed with the Indian ink improves its colour, and adds to the richness of effect.

The roads must be left either untinted or lighter than the adjacent shade, in order that they may be easily seen on the map. When woods have to be represented, the shading used for the trees, instead of interfering with the shadows due to the slopes, may be made to harmonize with them, and to contribute to the general effect by presenting greater or less depth, according to the position of the woods on the sides or summit of the hills.

"German" System of Hill Drawing.

The extended adoption, in some parts of the Continent, of the style of hill drawing, known as the German System, renders it necessary that some reference should be made to it. The fundamental principle of the system (which may be applied equally to the horizontal or vertical style) is, that the depth of shade shall be mathematically proportionate to the angle of inclination. This system differs from that which we have described in two particulars ;first, the omission of height as an element in the estimate of the intensity of shade; secondly, the attempt to make the depth of shade vary with mathematical accuracy according to the rate of inclination. By omitting to consider elevation as an element influencing the management of light and shadow, the effects of harmony and keeping are lost, and the physical relief or representation is less per

The

fect: the plan presents an appearance of spottiness, in which the subordinate features often appear as prominent as the great and more important mountain masses. object of making the depth of shade mathematically proportionate to the rate of inclination may be important, but it is extremely difficult of attainment in practice; and the use of the "anglometer" or "clinometer," for determining the angle of inclination, as proposed by some advocates of the system, would be found inadequate to the purpose, unless the inclinations were first set out with long rods on the ground to which the instrument could be applied. The tracing of vertically-equidistant contours would be the most rapid and accurate way to obtain the inclination required. Supposing it to be practicable on the plan to make the intensity of the shades strictly proportionate to the rate of inclination, the work thus completed could not be applied in practice with a degree of exactness proportionate to the truth of execution, because the relation of different degrees of intensity of shade cannot be estimated with precision, and does not admit of exact admeasurement; whereas the adoption of normal vertically-equidistant contours solves the problem more correctly, owing to the exactness with which the horizontal distances and the heights can be measured. This system has been advocated and applied in different countries under various modifications, details of which will be found in SIR J. C. SMYTH'S Topographical Memoir, and LIEUT. SIBORN'S Instructions in Topographical Plan Drawing.

Topographical Modelling.

The object of a plan is to portray nature as corretly as possible: a model approaches more nearly to the truth by affording a substantial representation of the forms.

This must not, however, be understood as implying that a model is, in all cases, preferable to a plan. For example, in applying it to projects in which lines of levels are required, a plan giving the levels from direct measurement in the field, by horizontal contours or otherwise, is more serviceable than a model, correctly constructed by scale from the same data, but which data are not written upon the model. For when the heights are to be referred to for purposes of calculation, they must be remeasured from the model with chances of error greater than those presented by the plan. The plan in such a case gives the recorded heights as obtained from direct measurement in the field; whereas the model gives them only when deduced by a secondary process from measurements on the diminished scale; and in proportion as the scale of the model is diminished, so are the chances of error increased. This objection would not, of course, apply, were the heights, as obtained from the measurements in the field, written upon the model.

Under such a condition, and independently of it also, models are of great value, for the purpose of giving a correct general knowledge of the country, especially to those who have not made hill drawing a study; but their value, as applicable to practical purposes, is greatly enhanced when they are made in parts, capable of being separated, so as to exhibit vertical sections of the geological stratification. Mr. Sopwith, who has directed much attention to this subject, has shown, "by a series of small models constructed of differently coloured plates of wood, the advantage of expressing in a solid form those fractured conditions of the strata, a right understanding of which is of the greatest importance, both to the working of coal mines and of metallic veins. Many of the complicated phenomena of curvatures and complex intersections

of plane surfaces cannot be adequately represented by any