No useful purpose is served, and much valuable time is wasted, in attempts to accomplish freehand, forms that may be perfectly achieved by proper implements. Familiarity with the use of these will be found of great assistance in all design in which geometric construction, apparent or not, plays so large a part. Of this the average beginner has little conception, and though Geometry has been a subject of their early training, they seldom have any clear idea as to its employment in design. Except in few instances, they are unpractised in the use of geometrical instruments, and at times oblivious that these serve any practical purpose. _Mathematical Equipment_ In design, where accuracy is of paramount importance, a reasonable equipment is imperative. Drawing boards vary in size, but for most ordinary work the antiquarian will suffice; the best type being that commonly used in engineering and architectural offices, with battens for adjustment and invariably a steel guide for the T square. Large T squares are more reliable on account of the wider head, the better sort being in mahogany with bevelled ebony edge. When accuracy is essential, the T square should only be employed for horizontal lines, those in a vertical direction being attained by the use of the set square, when the right angle can be assured by contact of the base of the latter on the edge of the T square. Set squares indispensable for ordinary work are those of the angles of 45 degrees and 60 degrees. They should be large, about twelve inch, and in celluloid, which, being translucent, tends to greater accuracy. Bevelled set squares, usually in mahogany with ebony edge, are desirable when the ruling pen is used, and should be placed with the bevelled side to the surface of drawing as a precaution against blotting through the ink running off the edge from the pen. For the same reason the edge of the T square should be slightly tilted, so as not to be in contact with the drawing when ruling lines with the pen. The mathematical instruments in common request are dividers, indispensable in scale drawing. For delicate work spring dividers with needle points ensure greater accuracy. The bow or pencil compass, large with extending bar, and small; with spring bows, for minute work. For very large circles the beam compass is employed, consisting of a wood bar with two sliding clamps fitted respectively with point, and either pencil or pen which can be adjusted to the required radius. For ink drawings the bow or pen compass is employed for circular curves; spring bows for extremely small details, medium for general purposes. The large compass in the ordinary set is provided with both pen and pencil joints, which can be adjusted as required. _Use of the Ruling Pen_