principal question here is not whether the solution be easy or difficult to comprehend, but whether it be a real and complete solution of the problem. We shall have occasion to point out, further on, the way in which very intricate cases may often be made very simple and easy to realise.
PIG. 21.
Example 2. A very simple illustration of finding centroids by general investigation occurs in common spur-gearing, or generally in any two bodies which turn about parallel axes at a fixed distance apart with a uniform velocity-ratio. If a and b (Fig. 23) be two con-plane sections of such bodies, and c and d the two centres about which they revolve, then if we consider a as fixed, the point d must move in a circle round c, the dis- tance d c being unalterable, and at the same time b must be turning about the as yet unknown -pela But the normal to the path of d must always coincide with the line of centres d c; the instantaneous centre must there-
