In this example we have supposed the number of divisions to be an even one, hence the point K, Fig. 152, falls diametrically opposite to A, whereas in an odd number of points of division this would not be the case, and we must proceed by either of the two following methods:--
In Fig. 158 is shown a circle requiring to be divided by 17 equidistant points. Starting from point 1 we mark on the outside of the circumference points 2, 3, 4, &c., up to point 9. Starting again from point 1 we mark points 10, 11, &c., up to 17. If, then, we try the compasses to 17 and 9 we shall find they come too close together, hence we take another pair of compasses (so as not to disturb the set of our first pair) and find the centre between 9 and 17 as shown by the point A. We then correct the set of our first pair of compasses, as near as the judgment dictates, and from point A, we mark with the second compasses (set to one half the new space of the first compasses) the points B, C. With the first pair of compasses, starting from B, we mark D, E, &c., to G; and from I, we mark divisions H, I, &c., to K, and if the compasses were set true, K and G would meet at the circle. We may, however, mark a point midway between K and G, as at 5. Starting again from points C and I, we mark the other side of the circle in a similar manner, producing the lines P and Q, midway between which (the compasses not being set quite correct as yet) is the true point for another division. After again correcting the compasses, we start from B and 5 respectively, and mark point 7, again correcting the compasses. Then from C and the point between P and Q, we may mark an intermediate point, and so on until all the points of division are made. This method is correct enough for most practical purposes, but the method shown in Fig. 159 is more correct for an odd number of points of division. Suppose that we have commenced at the point marked I, we mark off half the required number of holes on one side and arrive at the point 2; and then, commencing at the point I again, we mark off the other half of the required number of holes, arriving at the point 3. We then apply our compasses to the distance between the points 2 and 3; and if that distance is not exactly the same to which the compasses are set, we make the necessary adjustment, and try again and again until correct adjustment is secured.