In order to find the radius of curvature at any point on the generated curve, it is necessary to find not only the location of the instantaneous axis, but its motion. This is done as shown in Fig. 25. P being the given point, CD is the corresponding position of the connecting rod, OC that of the crank. Draw through D a perpendicular to OD, produce OC to cut it in E, the instantaneous axis. Assume C A perpendicular to OC, as the motion of the crank. Then the point E in OC produced will have the motion EF perpendicular to OE, of a magnitude determined by producing OA to cut this perpendicular in F. But since the _intersection_ E of the crank produced is to be with a vertical line through the other end of the rod, the instantaneous axis has a motion which, so far as it depends upon the movement of C only, is in the direction DE. Therefore EF is a component, whose resultant EG is found by drawing FG perpendicular to EF. Now D is moving to the left with a velocity which may be determined either by drawing through A a perpendicular to CD, and through C a horizontal line to cut this perpendicular in H, or by making the angle DEI equal to the angle CEA, giving on DO the distance DI, equal to CH. Make EK = DI or CH, complete the rectangle KEGL, and its diagonal ES is, finally, the motion of the instantaneous axis. EP is the normal, and the actual motion of P is PM, perpendicular to EP, the angle PEM being made equal to CEA. Find now the component EN of the motion ES, which is perpendicular to EP. Draw NM and produce it to cut EP produced in R the center of curvature at P. This point evidently lies upon the branch _z_M of the evolute in Fig. 23. The process of finding one upon the other branch _x_N is shown in the lower part of the diagram, Fig. 25. The operations being exactly like those above described, will be readily traced by the reader without further explanation. * * * * * AUTOMATIC COMMUTATOR FOR INCANDESCENT LAMPS. Incandescent electric lighting, already pushed to such a degree of perfection in the details of construction and installation, continually finds new exigencies that have to be satisfied. As it is more and more firmly established, it has to provide for all the comforts of existence by simple solutions of problems of the smaller class. Take for example this case: Suppose a room, such as an office, lighted by a single lamp. The filament breaks; the room becomes dark. The bell push is not always within reach of the arm, and it is by haphazard that one has to wander around in the dark. This is certainly an unpleasant situation. The comfort we seek for in our houses is far from being provided.