OF ELECTRO-DYNAMIC FORCES. 511 



the positive electricity in both elements moves, form with each 

 other the angle e, and with the connecting right line the angles 

 © and ©', the magnitude of the force with which the elements of 

 the current reciprocally act upon each other is determined by 

 the expression 



a a' 



rr 



■ (cos s — I cos cos ©'), 



and repulsion or attraction occurs according as this expression 

 has a positive or negative value. The expressions of the i-ota- 

 tory momentum exerted by one coil of the dynamometer upon 

 the other, developed at p. 502 and 503, are all deduced from this 

 fundamental principle. 



The former of the two fundamental principles mentioned re- 

 fers to two electric masses and their antagonism, the latter to 

 two elements of a current and their antagonism. A more inti- 

 mate connexion between the two can only be attained by recurring, 

 likewise in the case of the elements of the current, to the con- 

 sideration of the electric magnitudes existing in the elements of 

 the current, and their antagonism. 



Thus the next question is, what electric magnitudes are con- 

 tained in the two elements of a current, and upon what mutual 

 relations of these masses their reciprocal actions may depend. 



If the mass of positive electricity in a portion of the conduct- 

 ing wire equal to a unit of length be represented by e, and con- 

 sequently the mass of the positive electricity contained in the 

 elements of the current, the length of which is = a, by a e, and if 

 u indicates the velocity with which the mass moves, the product 

 e u expresses that mass of positive electricity which in a unit of 

 time passes through each section of the conducting wire, to 

 which the intensity of the current i must be considered as pro- 

 portional ; hence, when a expresses a constant factor, 

 aeu = i. 



If now a e represent the mass of positive electricity in the ele- 

 ment of the current a, and u its velocity, —ote represents the 

 mass of negative electricity in the same element of the current, 

 and — u its velocity. 



We have also, when 



a^ u' = i', 



a! e' as the mass of positive electricity in the second element of 

 the current «', and u' its velocity, and lastly, — «' e' as the mass 



