1900.] 



on Recent Studies in Gravitation. 



291 



period of the hanging sphere — i. e. if the larger sphere revolved in 240 

 seconds. But in the conditions of the experiment the vibrations of 

 the small sphere were very much damped, and the forced oscillations 

 did not mount up as they would in a freer swing. The disturbances, 

 which were mostly of an impulsive kind, continually set the hanging 

 sphere into large vibration, and these might easily be taken as due 

 to the revolving sphere. In fact, looking for the couple with 

 exactly coincident periods would be something like trying to find if 



Pknod, 1 25 



Fig. 10. — Upper curve a regular vibration, 

 disturbance dying away. 



Lower curve a 



a fork set the air in a resonating jar vibrating when a brass band was 

 playing all round it. It was necessary to make the couple period, 

 then, a little different from the natural 120 second period, and, 

 accordingly, we revolved the large ephere once in 230 seconds, when 

 the supposed quadrantal couple would have a period of 115 seconds. 

 Figs. 10 and 11 may help to show how this enabled us to 

 eliminate the disturbances. Let the ordinates of the curves in 

 Pig. 10 represent vibrations set out to a horizontal time scale. The 

 upper curve is a regular vibration of range + 3, the lower a dis- 

 turbance beginning with range + 10. The first has period 1, the 

 second period 1*25. Now cutting the curves into lengths equal to 

 the period of the shorter time of vibration, and arranging the lengths 

 one under the other as in Fig. 11, it will be seen that the maxima 

 and the minima of the regular vibration always fall at the same 

 points, so that, taking 7 periods and adding up the ordinates, we 

 get 7 times the range, viz. ±21. But in the disturbance the 

 maxima and minima fall at different points, and even with 7 periods 

 only, the range is from + 16 to — 13, or less than the range due to 

 the addition of the much smaller regular vibration. 



