same position as the station-line with respect to the surveyor, who keeps his face directed towards the distant station. The crossings of the fences, roads, streams, &c., and the corners of fields, and other remarkable turns in the boundaries to which offsets are taken, are to be shown by joining lines in a manner somewhat similar to the form which they assume on the ground.

It is a too common error with the inexperienced surveyor to neglect this approximation to the real forms of the

objects, as also to make his entries faintly, and with a careless hand. It cannot be too strongly impressed on the surveyor that the work which he is called upon to perform depends for its accuracy in a very great measure on the order, system, and neatness bestowed on all the steps, whether of delineation or of measurement. Proper attention in keeping the field-book saves much time in plotting, and guards against the errors unavoidably arising from reference to a confused field-book. Moreover, care bestowed in the first essays will amply reward the surveyor, by giving accuracy of freedom, and steadiness of hand, qualities indispensable to his success.

Field-Work.

eye,

On commencing the measurement of a station-line, the letter corresponding to the starting point in the rough diagram, or handsketch, is entered first at the

bottom of the middle column, and on each side are written the letters marking the extremities of the line, thus: from A to B, A being the starting point. In the same manner, on ariving at the end of the line corresponding to the point B, the letter B is written in the middle column above the closing distance, and above the letter a line is drawn across the middle column to denote that the line terminates in that point. In the form of field-book given in the preceding page are entered the observations for the line A B on the diagram in page 15. The numbers placed within a vinculum on the right hand side of the page, indicate the changes of the ten arrows. If the line be a short one, and a staff at either extremity be seen from every part of it, it may be ranged by the eye. If the line be so long, or on such uneven ground that the staff, fixed at its extremity, is occasionally lost sight of, the line must be ranged either by the eye or with a telescope, from a commanding position; pickets or ranging rods being placed at convenient distances to mark the right line. Advancing along it with the chain, the distance of the crossing of every fence or natural boundary, as also of all points from which offsets are taken, is noted in the field-book, together with the lengths of these offsets measured to the right or left. At every station, that is, any of the points determined by the intersection of the sides of the triangles or of tie-lines with those sides, a picket is driven, so that the precise spot may be readily found again in subsequent parts of the operation. The number of links written in the field-book as corresponding to the distance of such station, is encircled by a line to distinguish it from other points, and by the side of the circle the letter corresponding to the point in the diagram is written. This process is continued until the measurement has extended to the extremity of the line, of which the entire length is written down in larger characters than the rest; and, as an additional distinction,

C

written in a line parallel with the vertical sides of the fieldbook; for example, "2664" in the form of field-book, given in page 16. When it is not convenient to measure exactly from any of the marks left for the tie-lines, the place measured from may be described as being so many links from one station towards another; and where a station-mark is not measured to precisely, the exact place at which the measurement stops is shown by writing "turn to the right (or left)" so many feet towards such a station, it being always understood that these auxiliary distances are measured along the station-line.

In this manner, the sides of all the triangles are measured in succession, and their dimensions, with the additional assistance of offsets, give the means of ascertaining all boundaries, external and internal, positions of houses, &c., and of finding the area of the whole and of every part by direct computation from the field-book. But to obtain the contents of each inclosure by computation, would be a process very laborious and generally unnecessary: the contents of the whole should be ascertained by computation from the sides of the large circumscribing triangles; the areas of the inclosures may be afterwards obtained by measurement from the plan, their accuracy being tested by a comparison of the sum of the areas of the inclosures with the area comprised within the exterior boundary, as obtained from direct computation.

Reduction of Lines to a Horizontal Base.

I now come, in connexion with this question of areas or superficial contents, to the consideration of an important principle, namely, the reduction of the lines measured over steep slopes to the horizontal plane.

Having to lay down on a plan or flat surface boundaries and lines at different inclinations, in order to avoid distortion in the outline, and to bring all the details duly

within the triangular framework, it is absolutely necessary that we refer to, or project all lines and points upon a plane. The plane adopted to receive this common projection is the horizontal plane. It is not, therefore, the actual surface that we have to protract, but the diminished quantity that would result, had the whole been reduced to a horizontal base.

This distinction, which is indispensable for the purpose of laying down a plan of the surface, is supported, when the question is viewed under its social aspect, by the obvious principle that since plants shoot up vertically, the vegetable produce (with the exception of grasses, and a few other objects of culture), on a rounded eminence, does not in general exceed in quantity what would have grown upon its base.

A diagram makes this proposition evident: for let the vertical lines a, b, c, &c., represent the position of plants growing as closely as

possible, or as is judged advantageous, from the horizontal surface a, g: it is manifest that if a curved line be drawn resting on the base a, g, and representing

g

the inclined surface of the soil, the same number of plants only can grow in the vertical direction which plants tend to assume. The arrangement, therefore, as a matter of graphic necessity, is not inconsistent with the order followed by nature in respect of many varieties of produce.

Reduction of Lines to a Horizontal Base may be effected by Calculation.

All sloping or hypotenusal distances are, consequently, reduced to their horizontal lengths. When the lines are long, and the slopes much varied and considerably inclined,