94] 



COMPARISON OF THEORY AND EXPERIMENT. 



295 



comparison.) In order to compare theory with experiment, let us 

 calculate how many revolutions in one circle 

 go to one of the other. Let us call this 

 ratio m. We have then from 141) 



150) 



m = 



V 



Fig. 1031. 



It is noticeable that this ratio depends only 

 on the constants of the system and the 

 velocity of spinning, hut not on the circum- 

 stances of projection. This is shown in the 

 figures. In each group m is made an integer, 

 by properly adjusting the height of the disc, and the rate of spinning, 

 which is main- 

 tained constant by 

 stroboscopic ob- 

 servation. If the 

 apex is merely 

 drawn aside, and 

 let go, the curves 

 have cusps. If 

 pushed to one 

 side, the curves 

 have loops, and 

 if to the other, 

 there are no loops, 

 but the curve is 

 a sort of curvi- 

 linear polygon, 

 and if the spinning 

 is rapid enough, 

 there are in- 

 flexions. The ratio 

 m is the same for 

 the three types of 

 curve. The slight 

 perturbations no- 

 ticeable in the 

 figures arise from 

 the slight loose- 

 ness in the tracing 



point, and permit p . g 1Q4 



of counting the 

 number of revolution of the top about its axis (thus determining r), 



