Excerpt from Contributions From the Physical Laboratory of the University of Michigan, Vol. 2

This result can also be explained as follows. The projections of the velocities of P1, P2, P3 along the tangents to the circular sections of the cone at P1, P2, P3 are in the same ratio as the distances of P1, P2, P3 from the vertex of the cone. As the reaction of the cone is not normal to its axis, it follows that the ratios of these distances opi: 0132: 0133 will change. But the projections of the velocities cf pi, P2, P3 along the tangents to the circular sections at the given points cannot change as both the reaction of the cone and the stress in the rod are at right angles to this direction. This is where the difficulty comes; our geometrical conditions require an acceleration at right angles to the direction in which the forces act.

Simple illustrations of problems of the same nature as the preceding.

In Fig. 2 two particles of mass m and MI are connected by a weightless rod of length a and also constrained to move along the parallel curves 0 and 01 which are at the distance a. The curves are com posed of straight lines with arcs of circles at one extremity. If the curves are smooth, the stress in the rod is immaterial; if no external forces act on the system, the particles may be started at A and A, with any common velocity but when they reach E and E1 a difficulty is encountered, as the moment the particles move along the circular arcs their velocities are no longer equal but must be in the ratio a The reactions of the curves and the stress in the rod are at right angles to the direction of motion and there fore cannot produce the required change in the velocities. We could also start the particles at D and D1 with velocities in the ratio a bzb and when they come to E and E1 there would be the same difficulty.

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