﻿276 Mr. R. D. Kleeman on the Recombination 



of the induction-coil. After a few seconds, the connexions 

 of d with e and the earth were broken simultaneously : this 

 allowed the leak in the adjustable chamber to run into the 

 electrometer and that in the standard chamber to get stored 

 up. At the end of about twenty seconds, the current through 

 the primary circuit of the induction-coil was broken, and the 

 first two swings of the electrometer-needle were read. 



After having discharged the electrometer, the connexion 

 between c and d was broken, and d connected with e, thus 

 allowing the charge in the standard chamber to be shared by 

 the electrometer. The third and fourth swing of the needle 

 were taken in this case, since the first and second were difficult 

 to read accurately on account of the rapid motion of the 

 needle. 



When a quantity of electricity is suddenly discharged 

 into an electrometer, the swings of the needle may be large ; 

 and if the mean of two large swings is taken as the ultimate 

 position of rest of needle, a considerable error is introduced 

 on account of the damping of the needle. 



It became necessary, therefore, to devise a formula for 

 obtaining the correct position of rest of needle from two of 

 its swings. 



Let V denote the potential-difference of the quadrants of 

 the electrometer, and a* the corresponding reading on the 

 scale. Then the forces of restitution acting on the needle 

 oscillating about x 0j are VK 2 — %K 1 , ocK x — VK 2 , where K l5 

 K 2 are constants. Since x K 1 = YK 2 , each of these forces is 

 equal to K x («r — x), and therefore the needle executes an 

 harmonic vibration about .r , whose period is independent of 

 the value of x Q . 



But since there is a damping effect on the vibrations of 

 the needle, the amplitudes of the vibrations will decrease, 

 but any two successive amplitudes should bear a constant 

 ratio to one another. This was found to be the case : for 

 example, the ratios of a number of pairs of consecutive ampli- 

 tudes were found to be *54, "54, '55, *55. 



Let t? denote the ratio of two successive amplitudes of 



the swinging needle, and let ,r 1? x 2 denote two successive 

 extreme deflexions, of which x x is the further away from 

 zero. Then 



where n= cc ; therefore a? = %i — [x\ — x 2 ) -] p . 



