Electrostatic Capacity of a Conductor. 119 



measured in the direction of the force, and ^S perpendicular 

 to it, we have (see Fig. 5) 



drcosa = dp drcosa-dp' 



^Scosa = Ipdu) dScosa = /p'dio' if / is length of cylinders. 

 . dr do do' 



• dr _ \ /dp dp\ 



" dS~Idd\t~ p) 

 Integrating along a line of force, being therefore con- 

 stant: and denoting limits of p and o corresponding to the 

 two cylinders by the suffixes i and 2 



fdr I / 02 - p2\ 



I - Oo p\ 



= T^7.l0g 



f>'2 Pi 



IdQ ""-' 



But if Ri and R2 are the radii of the two cylinders, and 

 Di and D2 the distances of h! from their centres 



£2^ _ R2 p]_ _ Ri 



p'2 D2 p'l Di 

 by the properties of conjugate points 

 and . fd^ _J_-, R2 Di 



"J ds'W^^'D^ ' r; 



The coefficient of being thus independent of d, it is 

 easy to perform the second integration. 



I f /dd 2-rtl 



V 





since limits of are and 27r 



..by formula -j^ = -^ 



