Mr. R. S. Brough on a Case of Liahfninfj. 109 



then T-, .W—r'^ 



where f= 66 x 10* grammes on the square centimetre. 



Now the line-wire was bound to the insulator by a thinner 

 wire passing round it. The surface-density could not have 

 been uniform round the binding wire, but must have been 

 greatest on the side touching the insulator. 



By the method of electrical images in two dimensions it 

 may be shown that the surface-density (o-) on the inner side 

 of the binding wire is approximately 



Q 



^ —•- — - — • 



4z7r'^R\/d — a{\/d + a — \/d — a) 



where Q is the total charge on the binding wire, d the distance 

 of the binding wire from the stalk of the insulator, and a the 

 radius of the binding wire. But 



■■■"s/l 



whence 



Q=\/. 



^AnT''n\/d-a{\/d-¥a-s/d-a), 

 27r 



which is the expression for the quantity of the charge on one 

 insulator. As there were fourteen insulators broken, this 

 result must be multiplied by fourteen in order to obtain the 

 total quantity of the discharge. 



Again, the electrostatic capacity of the binding wire is 



^ 27rRc 



^ d-s/d^-d' 



where c=l*9 about. 

 But VS=Q; 



/ 



log. 



c 



a{s/ 



X 



d- s/r^- 



-a' 



s/d-a) 



Avhich is the expression for the potential of the discharge. 

 Now, in the particular case under consideration, 



