THEORY OF ELECTRODYNAMICAL ACTION. 99 



To extract from experiment an answer to this 

 inquiry was far from easy, for the elementary forces 

 were mathematically connected with the observed 

 facts, by a double mathematical integration ; a / 

 long, and, while the constant coefficients remained 

 undefined, hardly a possible operation. Ampere 

 made some trials in this way, but his happier 

 genius suggested to him a better path. It occurred 

 to him, that if his integrals, without being specially 

 found, could be shown to vanish upon the whole, 

 under certain conditions of the problem, this cir- 

 cumstance would correspond to arrangements of 

 his apparatus in which a state of equilibrium was 

 preserved, however the form of some of the parts 

 might be changed. He found two such cases, which 

 were of great importance to the theory. The first 

 of these cases proved that the force exerted by any 

 element of the voltaic wire might be resolved into 

 other forces by a theorem resembling the well- 

 known proposition of the parallelogram of forces* 

 This was proved by showing that the action of a 

 straight wire is the same with that of another wire 

 which joins the same extremities, but is bent and 

 contorted in any way whatever. But it still remain- 

 ed necessary to determine two fundamental quan- 

 tities ; one of which expressed the power of the 

 distance according to which the force varied; the 

 other, the degree in which the force is affected by 

 the obliquity of the elements. One of the general 

 causes of equilibrium, of which we have spoken, 



H2 



