Note 24: Cavendish's formula for disturbed capacity 415 



NOTE 24, ARTS. 338, 652. 



On the Capacity of a Conductor placed at a finite distance from 

 other Conductors. 



Cavendish has not given any demonstration of the very remarkable formula 

 given in Art. 338 for the capacity of a conductor at a finite distance from other 

 conductors. We may obtain it, however, in the following manner. 



If the distance of all other conductors is. considerable compared with the 

 dimensions of the positively charged conductor, C, whose capacity is to be 

 tried, the negative charge induced on any one of the other conductors will- 

 depend only on the charge of the conductor C and not on its shape. This induced 

 charge will produce a negative potential in all parts of the field; let us suppose 







that the potential thus produced at the centre of the conductor C is - , 

 where E is the charge of C and # is a quantity of the dimensions of a line. 

 If L is the capacity of C when no other conductor is in the field, then the 







potential due to the charge will be j , and the potential, which arises from 



ft 



E 



the negative charge induced on other conductors, will be - , so that the 



x 



actual potential will be E ( j - -) . 



Dividing the charge by the potential we obtain for the actual capacity 



" x-L' 

 or the capacity is increased in the ratio of x to x - L. 



The idea of applying this result to determining the value of x by comparing 

 the charges of bodies, the ratio of whose capacities is known, is entirely peculiar 

 to Cavendish, and no one up to the present time seems to have attempted 

 anything of the kind. 



The height of the centre of the circles above the floor seems to have been 

 about 45 inches. If we neglect the undercharge of other conductors and consider 

 only the floor, x would be about 90 inches in modern measure, but as a capacity 

 x is reckoned by Cavendish as zx "inches of electricity," the value of x in 

 "inches of electricity" would be 180. 



If we could take into account the undercharged surfaces of the other con- 

 ductors, such as the walls and ceiling, the "machine," etc., the value of x would 

 be diminished, and it is probable that the value obtained from his experiments 

 by Cavendish, i66J, is not far from the truth. 



