METHODS BASED ON THE PROPERTIES OF THE SPARK. 193 



of equilibrium of the needle an electrified sphere A is placed. If 

 suitable precautions are taken that the action be confined to that of 

 the two spheres, and that the distribution on the sphere A is not 

 appreciably modified by the electricity induced on the sphere a, 

 then, if M and - m are their electrical charges, R and r their radii, 

 and D the distance of the centres, the values of the potentials are 

 very approximately 



v=M * 



R D' 

 -m M 



The electrical action is then 



Mm V 2 RV 



D 2 



On the other hand, if n be the number of oscillations of the 

 needle in unit time, when there is no electrification ; N, the num- 

 ber when the sphere A is raised to potential V ; K, the moment 

 of inertia of the needle ; /, the distance from the axis to the centre 

 of the small sphere ; we have 



Determining the moment of inertia K by the ordinary methods 

 (700), this equation will give the potential as a function of the 

 dimensions of the apparatus. The approximation should be carried 

 further if this method were to be used in more accurate experiments. 



821. METHODS BASED ON THE PROPERTIES OF THE SPARK. 

 The ordinary experiments in statical electricity bring into play 

 charges and differences of potential far greater than can be mea- 

 sured by the preceding methods. In this case the methods which 

 can be used, and which moreover are very old, are based on the 

 properties of the electrical spark. 



When conductors at different potentials are brought near each 

 other, equilibrium is effected before contact by a sudden discharge 

 of electricity across the dielectric. This passage, which is known 

 as the disruptive discharge, is a very complicated phenomenon, the 

 mechanism of which is unknown, and which depends on the nature, 

 the shape, and difference of potentials of the conductors ; it also 

 VOL. n. o 



