86 PROPERTIES OF CIRCULAR CURRENTS. 



values of c, which increase in arithmetical progression ; the dotted 

 parts of the curves correspond to the central space arranged for 

 the magnet. 



734. The parameter c will in general be determined by the 

 resistance, and the dimensions which we give to the coil. 



For a uniform winding with the wires in contact, we have for the 

 relation between resistance and volume, 



R- 



which determines y. 



The expression for the volume U' comprised within the surface 

 produced by the revolution of the curve of the parameter <r, is 



U' = 27r sin OdO I u*du --{" sin BdO = - -KC* (sin * Odd. 

 Jo Jo 3 Jo 3 Jo 



TT A 



The integral ar I sin OdO is a number ; if we represent it by N, 

 we shall have J 



3 



The cavity inside the coil comprising the core is usually cylin- 

 drical, and the proportion which it deducts from the preceding 

 volume may be expressed by - N# 3 , a representing the parameter of 

 the curve which would bound a volume equal to that of the cavity. 

 The volume U of the channel is accordingly 



an equation which would give c as a function of U. 



Considering u as the radius vector of the curve which would 

 correspond to the element dl of the current, and the parameter c as a 

 variable, the expression for the action of the coil at the centre for unit 

 current is 



V/ 



G = \-.sm0 



(dl 

 = . 

 )c* 



