298 Messrs. Ayrton and Perry on the Determination 



In this way we have obtained the n differential equations 

 connecting l7 <j) 2 , . . . <j> n , and their first and second differential 

 coefficients with respect to t. As, however, these equations 

 can only be regarded as true when n is infinite, and as the 

 labour of solution is very great when n is great, it seems use- 

 less proceeding further with the solution. 



If we regard the motion of the ball as a harmonic motion 

 of period P, determined by assuming the connexions as rigid, 

 combined with motions of much shorter periods P 1? P 2 , P 3 , . . . 

 &c, there will be some little difficulty in finding the motion 

 of shortest period P 1? namely the kick above mentioned ; but 

 we know that when the wire is, as in our experiments, very 

 thin, the kick cannot be much less than the time of a complete 

 vibration of the ball when freely suspended by a point on its 

 surface, or 



where a is the radius of the ball. But this periodic time is 

 0'528 seconds, or about one twelfth of that of the pendulum 

 moving as a whole, which is about 6 seconds. 



Since the tendency of the ball to add this quick vibration to 

 its motion is due to its rotational energy, it may be diminished 

 by lessening the moment of inertia of the ball (that is, by 

 making the ball small), or by diminishing the angular velocity 

 of the pendulum (that is, by making the pendulum as long 

 and its swing as small as possible). We may regard, then, the 

 motion of the ball as compounded of a pure harmonic motion 

 with an amplitude of about 30 centimetres and a periodic time 

 of 6 seconds, with another motion having a very small ampli- 

 tude and with a period of about half a second. But we have 

 proved in the paper on our seismograph*, that in such a case 

 the compound motion would differ very slightly from that of 

 a pure harmonic motion, even if there were no internal fric- 

 tion in the substance of the wire (supposing the pendulum 

 started without shock); but as internal friction, of course, 

 exists in the wire, this error becomes exceedingly small. 



2. Next, with regard to the stretching of the wire arising 

 from variations in the centrifugal force of the ball while 

 swinging. Since the time of a complete vibration of our pen- 

 dulum was nearly 6 seconds and the arc about 30 centimetres, 



* "On a Neglected Principle that may be employed in Earthquake 

 Measurements," Trans. Asiatic Soc. of Japan, vol. v. part 1 ? p. 181 ; re- 

 printed in Phil. Mag. July 1879. 



