ruler (Fig. 9) consists of a bevelled edge piece of timber (more generally of ebony) or brass, to the centre of which is fitted a pair of small wheels joined by a long axle bar. These wheels are capable of revolving, and a slight lateral pressure with the hand will cause the ruler to move. This form of parallel ruler also affords an efficient and handy method of drawing one line at right angles to another. Thus, assume that a line is required at right angles to AB (Fig. 10). Place the ruler with its edge along AB, and with a pencil or a pricker mark any point C in the line AB, and also mark the ruler at this point. Now parallel the ruler up to about D, and make a mark on the paper just at the point where the mark is shown on the ruler. Let this point be D. A line joining DC will then be perpendicular to AB.

The Straight Edge.-The term " straight edge" literally includes all kinds of straight line rulers, but the name is generally applied to very long flat rulers. These rulers are made of peartree, mahogany, ebony, or preferably of steel, and range from 3 to 6 feet in length, one edge of the ruler being bevelled. It is of the utmost importance that the ruler for long lines be perfectly straight, or considerable discrepancy will arise in plotting. The ruler, therefore, should be tested often, and should be hung in a vertical position when not in use.

FIG. 9.

The Compasses. -This instrument consists of two arms of brass or electrum, which are connected in a joint at the top, thus allowing the extremities to be set at varying distances apart. When the arms terminate in

two points (Fig. 11) the compasses are termed dividers, and

versa.

are used for transferring distances from a plan to a scale, or vice In the other form of compasses, one arm terminates in a fine point and the other in a bow pen (Fig. 12) or pencil holder (Fig. 13).

They are used for describing circles or arcs.

FIG. 11.

FIG. 12.

FIG. 13.

FIG. 14.

As usually supplied by instrument-makers the lower half of one arm of the compasses is detachable (Fig. 14), and the compasses may be used with the pen or pencil, or as dividers, as required. A lengthening bar is also provided so as to give the compasses a greater span when necessary.

respect t mpasses (Fig. 15) are sometimes used when the radius parallel lines arc required is too large for the ordinary com

passes to be employed. The arms of this instrument are provided with boxes or clamps at the upper end, by which they are attached to a lath at any required distance apart.

Copying Plans.-The simplest and most generally adopted method of copying plans is by tracing on transparent cloth or paper. The cloth or paper is stretched tightly over the plan to be copied, and is retained in position by drawing pins or weights, the details of the plan showing through sufficiently to allow of an exact copy being traced in ink or pencil. When a copy is required

on ordinary drawing paper, the plan to be copied may be placed over the new paper and the angular points of the drawing pricked through. Lines are then drawn from point to point as in the original. A much easier method, however, is to make a tracing of the plan and transfer the details from the tracing to the new paper with transfer paper. Transfer paper is made by rubbing one side of some thin paper with black lead. By placing this paper with the blackleaded side down between the proposed plan and the tracing, and going over all the lines of the drawing on the tracing with a blunt-pointed instrument, such as one blade of a drawing pen, a copy will be made in black lead, and can afterwards be inked in.

FIG. 15.

The dull side of tracing cloth is the better to ink on, but colour should be applied to the back or glazed side as it is much more easily accomplished, and shows up distinctly. The greasy nature of cloth often renders it difficult to make the ink run freely; this is remedied by rubbing the cloth with pounce or powdered chalk before inking in. A little soap put in the colour also answers the same purpose.

CHAPTER III

GEOMETRY

Ir is essential that an elementary knowledge of geometry be acquired before commencing the actual study of surveying. The extent to which the former subject is treated in this work represents only the parts that are absolutely necessary, and every detail should be thoroughly known before proceeding farther.

Geometry may be divided into three sections, namely, Definitions, Theorems, and Problems. A theorem is an assertion or statement which is to be proved, and a problem is something required to be done.

Euclid has demonstrated a large number of theorems and shown the constructions of numerous problems, but the writer has deemed it sufficient to accept Euclid's proofs for the propositions given in this work. If it is desired to refer to the proofs, almost all will be found in Euclid's First Book of Geometry.

Definitions

A point is that which denotes position or beginning of magnitude, but which has no magnitude, i.e. has neither length, breadth, nor thickness.

A line is length without breadth. The extremities of a line are points.

A straight line is that which lies evenly between its extreme points, and is the shortest distance between any two points, as AB (Fig. 16).

A plane rectilineal angle is the inclination of two straight lines to one another, which meet in a point, but are not in the

same straight line, as A (Fig. 17). When several angles are at one point, as A (Fig. 18), any one of them is expressed by three letters, of which the letter at the vertex or point where the

A

B

A

FIG. 16.

FIG. 17.

lines meet is placed in the centre; thus the angle contained by the two lines BA, AC is expressed as the angle BAC or CAB, and that which is contained by the lines AC, AD is expressed as the angle CAD or DAC.

One angle is said to be less than another when the lines which form that angle are nearer to each other than those which form the other, at the same distance from the vertex. The magnitude of the angle does not depend upon the length of the lines by which it is formed.

There are three kinds of angles, namely, right, obtuse, and acute.

A right angle is made by a straight line standing upon another straight line in such a position as to make the adjacent

angles equal to one another. Thus in Fig. 19 the line AB stands upon the line CD, and makes the angle CBA equal to the angle ABD.

An obtuse angle is greater than a right angle, as Fig. 20. An acute angle is less than a right angle, as Fig. 21.

A plane triangle is the space enclosed by three straight lines.