Fig. 208.
These half-circles are divided into any convenient number of equal divisions: thus in Figure 208, each has eight divisions, as a, b, c, etc., for the outer, and i, j, k, etc., for the inner one. The pitch of the thread is then divided off by vertical lines into as many equal divisions as the half-circles are divided into, as by the lines a, b, c, etc., to o. Of these, the seven from a, to h, correspond to the seven from a' to g', and are for the top of the thread, and the seven from i to o correspond to the seven on the inner half-circle, as i, j, k, etc. Horizontal lines are then drawn from the points of the division to meet the vertical lines of division; thus the horizontal dotted line from a' meets the vertical line a, and where they meet, as at A, a dot is made. Where the dotted line from b' meets vertical line b, another dot is made, as at B, and so on until the point G is found. A curve drawn to pass from the top of the thread on one side of the bolt to the top of the other side, and passing through these points, as from A to G, will be the curve for the top of the thread, and from this curve a template may be made to mark all the other thread-tops from, because manifestly all the tops of the thread on the bolt will be alike.
For the bottoms of the thread, lines are similarly drawn, as from i' to meet i, where dot I is marked. J is got from j' and j, while K is got from the intersection of k' with k, and so on, the dots from I to O being those through which a curve is drawn for the bottom of the thread, and from this curve a template also may be made to mark all the thread bottoms. We have in our example used eight points of division in each half-circle, but either more or less points maybe used, the only requisite being that the pitch of the thread must be divided into as many divisions as the two half-circles are. But it is not absolutely necessary that both half-circles be divided into the same number of equal divisions. Thus, suppose the large half-circle were divided into ten divisions, then instead of the first half of the pitch being divided into eight (as from a to h) it would require to have ten lines. But the inner half-circle may have eight only, as in our example. It is more convenient, however, to use the same number of divisions for both circles, so that they may both be divided together by lines radiating from the centre. The more the points of division, the greater number of points to draw the curves through; hence it is desirable to have as many as possible, which is governed by the pitch of the thread, it being obvious that the finer the pitch the less the number of distinct and clear divisions it is practicable to divide it into. In our example the angles of the thread are spread out to cause these lines to be thrown further apart than they would be in a bolt of that diameter; hence it will be seen that in threads of but two or three inches in diameter the lines would fall very close together, and would require to be drawn finely and with care to keep them distinct.
Fig. 208 a.
Fig. 209.