_Drawings for Lithographers and Engravers._--The drawings required by the lithographic draughtsman are simply outline drawings or tracings, with the shaded drawing for reference when such is required. The shaded drawing should be traced when in outline only with a fine-pointed pencil, not too hard. The engraver prefers such a tracing to the drawing itself, unless he can have the latter before it is shaded. He will, however, require the shaded drawing as a guide in copying in the shadows. As the drawing always gets soiled under such circumstances, unless protected, it is prudent to place it upon a board of the exact size, with a glass over it to fit, the glass being kept in its place by a strip of paper pasted round the edge. The drawing will not be required at all if only an outline engraving is to be made. In that case, the lines that are to be shade lines must be indicated on the pencil tracing; a dot in red ink on each of such lines will be sufficient.
A scale should always be put upon lithographs and engravings, instead of merely stating that it is drawn to some particular scale, because the paper just before receiving the impression is damped, and consequently expands. For this reason, no engraving is of the same size as the original drawing; and as the degree of moisture varies, no two engravings from the same plate ever are exactly equal in size. Hence the necessity for drawing the scale is obvious.
The Plate relating to this Section is No. 26.
_To compute the Sides of Triangles._--Let A B C be the angles of a plane triangle, and _a_ _b_ _c_ the sides opposite. Then, for right-angled triangles, we have
_b_ = _a_ sin. B _b_ = _c_ tan. B or _b_ = _c_ cot. C _c_ = _a_ cos. B _c_ = _b_ cot. B _c_ = _b_ tan. C
_To compute the Areas of Triangles._--When two sides and the included angle are known, _a_ and _b_ representing the two sides and θ the included angle,
To find by logarithms the area in acres and decimals of an acre,
Log. A = log. _a_ + log. _b_ + log. sin. θ - 15·30103.
When two angles and the included side are known, β and θ being the angles and _a_ the included side,
_a_² sin. β sin. θ A = ------------------. 2 sin. (β + θ)
To find by logarithms the area in acres and decimals of an acre,