136 J. A. POLLOCK AND S. H. BARRACLOUGH. 



and ft = (2 ^pp/v)*, p/2-r being the frequency of the current 

 alternations, /* the magnetic permeability and a- the specific 

 resistance of the material of the conductor. 



The maximum current flowing along a cylindrical shell 

 of the conductor of radius r and of thickness dr is : — 



Ioe -Ha-r) 



- v a 2 Jar 



dr 



The maximum value of the sum of the mechanical forces 

 on unit length of such a shell is given by the product of 

 the above expressions. For unit length of a cylindrical 

 tube, of inner radius b and outer radius a, the product 

 becomes : — 



2/3 ,, -2pa( 28r 7 I; ~ 2/3a ( 1 2 ^ , 



— — He \ e dr + - e - e dr 



a J air 



The value of the first term is : — 



Ilfl_ e ~2/%-b) 



a \ 



and that of the second lies between 



a o a b 



For copper /» = 1 and o- may be taken as 1,600. If we 

 assume that the frequency of alternation in the discharge 

 is 10 6 per sec. then ft or (2irfip/<r)% = 50vr. With these values 

 and as in the case of the tube under consideration a/b differs 

 little from unity, no term in the expression for the product 

 except the first is of importance, and the maximum value 

 of the sum of the forces acting radially inwards on unit 

 length of the cylindrical tube may be written 



n 



a 



or the force per unit area 



2 7TCr 



