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rectangular bar F, are all straight, it follows that if a, b, c, d on VP be joined by straight lines, an orthographic projection of the face A, B, C, D, of the bar will have been obtained, which will, on measurement, be found to be an exact counterpart of it. But this projection only gives the length and depth of the bar; and as it is necessary to know its other dimension, or width, a view showing that dimension must be obtained. Now it is evident that a view of the bar, looking at it from above and in the direction of the arrow, will Fig. 13 supply the information required. If, then, visual rays, or projectors, proceed as before from the four corners of the face of the bar seen from above, to the plane HP below, they w r ill penetrate that plane at the points a, b', e,f, and these points being joined as before as the same conditions obtain there is produced on HP an orthographic projection of the top face of the bar which determines its width. With these two projections, or views of the original, it will be seen that a workman could produce any number of such bars without the assistance of a model or other guide. To distinguish the two pro- jections of the same object, the one obtained on VP is known as an " elevation " or vertical projection, and that obtained on HP is called a " plan " or horizontal projection. CHAPTER III PRACTICAL GEOMETRY AND MECHANICAL DRAWING As it has been necessary, in explaining the difference between a .mechanical and a freehand or perspective drawing, to make use of terms which pre-suppose a knowledge of geometry by the student which he may not possess, and as it is advisable to take nothing for granted