It will be, perhaps, observed by the reader that it would be more expeditious, and perhaps cause less variation, were we to set the compasses to the radius of the circle and mark off the point k, as shown in [Fig. 153], commencing at the point a, and marking off on the one side the lines b, c, and d, and on the other side e, f, and g, the junction or centre, between g and d, at the circle being the true position of the point k. For circles struck upon flat surfaces, this plan may be advantageous; and in cases where there are not at hand compasses large enough, a pair of trammels may be used for the purpose; but our instructions are intended to apply also to marking off equidistant points on such circumferences as the faces of pulleys or on the outsides of small rings or cylinders, in which cases the use of compasses is impracticable. The experienced hand may, it is true, adjust the compasses as instructed, and mark off three or four of the marks b, c, &c., in [Fig. 152], and then open out the compasses to the distance between the two extreme marks, and proceed as before to find the centre k, but as a rule, the time saved will scarcely repay the trouble; and all that can be done to save time in such cases is, if the holes come reasonably close together, to mark off, after the compasses are adjusted, three or four spaces, as shown in [Fig. 154]. Commencing at the point a, and marking off the points b, c, and d, we then set another pair of compasses to the distance between a and d, and then mark, from d on one side and from a on the other, the marks from f to l and from m to t, thus obtaining the point k. This method, however expeditious and correct for certain work, is not applicable to circumferential work of small diameter and in which the distance between two of the adjacent points is, at the most, 1⁄20 of the circumference of the circle; because the angle of the surface of the metal to the compass point causes the latter to spring wider open in consequence of the pressure necessary to cause the compass point to mark the metal. This will be readily perceived on reference to [Fig. 155] in which a represents the stationary, and b the scribing or marking point of the compasses.
Fig. 155.
The error in the set of the compasses as shown by the distance apart of the two marks e and i on the circle in [Fig. 152] is too fine to render it practicable to remedy it by moving the compass legs, hence we effect the adjustment by oilstoning the points on the outside, throwing them closer together as the figure shows is necessary.
Fig. 156.
