1877.] B. S. Bvowgh— On a Case of Li(/Iitni?i^. 59 



The usual rod-protectors appear to be only suitable to such structures 

 as themselves determine lines of maximum induction, e. g. church spires, 

 factory chimnies, jBiagstaffs, &c. 



The case of lightning referred to at the beginning of this paper is of 

 peculiar interest because we know precisely the mechanical effect produced 

 by the flash, and from this we can work back and estimate roughly the 

 potential and quantity of the electrical discharge. 



In the first place we can calculate the force .I'equired to burst the cylin- 

 di'ical portion of the porcelain insulator into which the iron stalk is cement- 

 ed. 



Let r = radius of the inside of the cylinder 

 E = „ „ outside „ 



and F = the resistance to bursting 



where/" = GQ x 10* grammes on the square centimetre. 



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

 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 shewn 

 that the surface density ( cr ) on the inner side of the binding wire is ap- 

 proximately 



Q 



O" = - — Pv 



4i7r^ U ^ d — a (^^ d -i- a — ^^ </ — 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 bind- 

 ing wire. 



But 2 TT 0-2 = F 



V 2 TT 



Whence 



Q = J-^ • 4 TT^ R ^"T^a Wd + a- ^ d - a) 

 which is the expression for the quantity of the charge on one insulator. As 

 there were M insulators broken, this result must be multiplied by 14 in 

 order to obtain the total quantity of the discharge. 



Again the electrostatic capacity of the binding wii'e is 



2 7rR(7 



S = 



where c = 1"9 about. 



d + ^ d'_. 

 log,- 



\/ d^ — a^ 



