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 zM of the evolute in Fig. 23.  The process of finding one upon the other branch xN 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.

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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.

M. Clerc, the well known inventor of the sun lamp, has tried to overcome troubles of this sort, and has attained a simple, elegant, and at the same time cheap solution.  The cut shows the arrangement.  The apparatus is connected at the points, BB’, with the lighting circuit.  The current entering by the terminal, B’, passes through the coils of a bobbin, S, before reaching the points of attachment, a and b, of the lamp, L, the normally working one.  Thence the circuit runs to B. Within the coil, S, is a small hollow cylinder, T, of thin sheet iron, which is raised parallel with the axis of the bobbin during the passage of the current through the latter.  At its base the cylinder is prolonged into two little rods, h and h’, which plunge into two mercury cups, G and G’.  The cut shows that one of the cups, G’, is connected to the terminal,