ST8 McnucAL OAPAcmr or A LONG NARROW CYLINDER, 



When b Tiy great, the distribution of electricity is expressed by the 



X-/ 



which hew that, as the ratio of the length to the diameter increases, the 

 deMtty become* more nearly uniform, and the deviation from uniformity becomes 

 more confined to the parts near the ends of the cylinder. 



To indicate the character of the approximation, I have calculated ? and 

 the three terms of the denominator of A' 4 for different values of the ratio of 



/.. When this ratio is less than 100, the third term is unavailable. 



9 lit term. 2nd term. 3rd term. 



10 3-68888 . 2-68888-0-43151 



20 4-38203.3-38203-0-13680 



30 478749 . 378749 - 0'09775 



50 5-29832 . 4'29832-0'07191 



100 5-99146. 4-99146-0-05291-0-13566 



1000 8-29405 . 7'29405-0-02818-0'00892. 



Examples of the application of the method to the calculation of the 

 capacities of a cylinder in presence of a plane conducting surface, and in 

 presence of another equal cylinder, will be given in the notes to the forth- 

 coming edition of Cavendish's Electrical Researclies, as illustrations of measure- 

 ments made by Cavendish in 1771. 



Electric Capacity of a Disk of sensible Thickness. 



We may apply the same method to determine the capacity of a disk of 

 radius a and thickness b, b being very small compared with a. 



We may begin by supposing that the density on the flat surfaces is the 

 name as when the disk is infinitely thin. 



Let a and ft be the elliptic co-ordinates of a given point with respect to 

 the lower disk, or in other words let the greatest and least distances of the 

 point from the edge of the disk be a (a +) and a(a-yS). 



