414 Note 23: charge of middle plate of three 



Hence the charges of the inner and outer surfaces of the disk are 



w and (a o>) 

 a a v 



respectively, where the value of the elliptic co-ordinate cu is that corresponding 

 to the edge of the other disk. 



If a is the radius of either disk, and c the distance between them, 



_ 



If we now place another equal disk on the same axis at a distance c from 

 one of them, the potential being the same for all three, the new disk will 

 greatly diminish the charge of the surface of the disk which is next to it, but 

 it will not have much effect on the charges of the other surfaces. 



The result will therefore be that the charges of the two outer disks will 

 together be greater, but not much greater, than that of a single disk at the 

 same potential, but the charge of each of the surfaces of the middle disk will 

 be the same as that of one of the inner surfaces of a pair of disks at distance c. 

 Hence the charge of the middle disk will be to that of the two outer disks together 

 as o> to a. 



If we substitute for the square plates of twelve inches in the side disks of 

 13-8 inches diameter which would have nearly the same capacity, then if the 

 distance between the outer disks is 1-15 inches, c = -575 and co = 1-936 and 

 a = 3-5 w, or the charge of the middle disk would be 3-5 times greater if the 

 outer disks had been removed. 



If the distance between the outer disks is 1-65 inches, c = -875 and o> = 2-293, 

 whence = 2-2 co, or the charge of the middle disk would have been 2-2 times 

 greater if the outer disks had been removed. 



It is evident, however, that in the assumed distribution the potential is less 

 at the edges of the outer disks than at their centres. The electricity will therefore 

 flow more towards the edges of the outer disks, and, as this will raise the potential 

 near the edge of the middle disk, the charge of the middle disk will be less than 

 on our assumption. I have not attempted to estimate the distribution more 

 approximately. 



Cavendish found the charge of the middle disk \ and J of what it would 

 have been without the outer disks. This is much less than the first approxi- 

 mation here given, but much greater than Cavendish's own estimate, founded 

 on the assumption that the distribution of electricity follows the same law in 

 the three plates. 



