LAW OF BIOT AND SAVART. 



443 



The force is moreover applied to the element, and is per- 

 pendicular to the plane Pds. Its direction is on the right of the 

 current that is, on the right of an observer placed in the element, 

 and looking at the pole, for the action of the element on the pole is 

 in the opposite direction. 



VII. Law of Biot and Savart. The experiments of Biot and 

 Savart (444) demonstrate that the magnetic action of a rectilinear 

 current on a pole, is inversely as the distance of the current from 

 the pole. 



According to a remark of Laplace, this law is satisfied if we 

 assume that the action of a pole on an element of current is inversely 



as the square of the distance that is to say, if we have /(?) = 



We may conversely prove that the law of the square is the only one 

 which satisfies Biot and Savart's experiments. 



Fig. 107. 



Consider, in fact, two parallel rectilinear currents, unlimited and 

 of the same strength AS and A'S', at distances a and a' from the 

 pole P (Fig. 107). For two elements ds and ds\ comprised between 

 the same two radius vectors drawn through the point P, and the 

 distances of which from this point are r and r', we have 



ds _ r a 



ds' r a ' 



and therefore 



rds' = r'ds 



