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and found to be a most reliable apparatus. Since 1907, Professor Hoxton, 

 at whose request I have made this report to the Society, has adopted it, 

 with certain excellent improvements — as to mass of the bob, fixity of sus- 

 pension point, and screening of the ball from accidental currents of air, 

 which I hope he will sometime describe to us. 



Allow me a word to acknowledge our debt_to the mathematics in this 

 problem. 



When Foucault made his modest appearance before the French Acad- 

 emj^ in 1851 his experiment produced a great stir among the mathemati- 

 cians. Binet immediately followed Foucault with a long and interesting 

 dynamical discussion of it. Poinsot next arose and declared that the 

 Foucault result was not a matter of Djmamics but purely one of Geometry. 

 One after another of the leaders pushed in and for a number of sessions 

 the poor physicist was hidden by the cloud of brilhant theorists. Although 



FiQ. 4 



these debates may have resulted in small help to the experiments, one 

 should not forget that Airy, Bessel, Binet and their followers have in a 

 problem of the greatest mathematical difficulty reached conclusions of 

 signal value to him. Throughout their work they have, as we easily see 

 on review, emphasized the importance of small oscillations. Mr. Airy 

 showed us nearly a centurj^ ago that with exceedingly small amphtudes 

 of vibration, friction and atmospheric resistance, so far as it depends on 

 the speed, have no effect on the vibration-time, while Bessel points out the 

 remarkable effect of vibrations not small in causing sympathetic oscil- 

 lation in the air so that the vibrating mass is virtually increased — a re- 

 markable fore-shadow of electrical inertia in great speeds. Again Binet 

 and Hansen, as reported by Price, have shown that with exceedingly small 

 vibration, the spherical pendulum, to a first approximation, describes 

 an ellipse in same direction as the earth's rotation, and that the major 



