investigation into the nature qf the curves to which they corre-
spond. We shall examine briefly both methods of determination.

Let the relative motion of any two con-plane figures P Q and A B be known. In order to find the corresponding centroids we must first convert this given relative motion into an absolute one (in the limited sense in which we use the word), by sup- posing the system as a whole to receive such a motion that one of the figures, e.g. A B. (Fig. 19), comes to rest in reference to ourselves. We can then find the paths or curves in which

Fig. 19.

two points P and Q move, and draw normals to those paths at P and at Q; their intersection gives a point in the centroid belonging to A B. Another pair of normals, drawn from P l and Q 1 give another point 1 of the same centroid, and so on. The

second centroid, M^ can be found in a similar way by

bringing P Q to rest and making A B the moving figure, but it may be determined more easily as follows. The N pole- 1 is a point in both curves when the moving figure is in the position P t Q v its distance from the point P in that figure is 1 P 1 and from Q> 0i 61; it therefore is necessary only to describe arcs of circles about P and Q with the radii = O l P 1 and O l Q l in order to find