AL CAPACITY OF A U>NO NARROW CYLINDER, &C. 



Substituting the value of Un M y from (11), the integral in (12) becomes 



The corresponding quantity for the action of the upper disk on itself is 

 got by putting A^A, and 6 = 0, and is 



In the actual case, A, = A t -\E t when E is the whole charge; and the 

 lower limit of the capacity is therefore 



but since we have assumed that b is very small compared with a, we may 

 express our result with sufficient accuracy in the form 



or, the capacity of two equal disks is equal to that of a single disk whose 

 circumference exceeds that of either disk by b log y . 



If the space between the disks is filled up, so as to form a single disk 

 uf sensible thickness, there will be a certain charge on the cylindric surface; 

 but, at the same time, the charge on the inner sides of the disks will vanish, 

 and that on the outer sides of the disks will be diminished, so that the capacity 

 of a disk of sensible thickness is very little greater than that given by (16). 



