602 GENERAL THEORIES. 



a function not only of the distance r, but also of their relative 

 motion, and the problem thus stated appears indeterminate. One 

 hypothesis is to assume that this action, while directed along the 

 right line joining them, and proportional to the product of the 

 masses, and inversely as the square of the distance, comprises a 

 term proportional to a power of the relative velocity u of the two 

 masses, and another term proportional to a power of their relative 



velocity parallel to their distance. These powers must be even, 



if the action is not to be modified when both the directions of the 

 two motions and of the currents themselves are changed, and 

 the problem is satisfied by taking them equal to 2, which gives 

 the elementary law 





Weber examined first the simple cases of two elements in the 

 prolongation of each other, or perpendicular to the same right line. 

 In the former case, it must be assumed that the action of the two 

 masses contains a term which depends on their relative velocity, 

 and he supposed that this term was proportional to the square of 

 the velocity. The second case led Weber to bring in the acceleration 

 along the same right line, and the simplest hypothesis was to assume 

 that this fresh term was proportional to the acceleration. From 

 this follows another elementary law 



It remains to determine the coefficients a, ft, a! and /?', which 

 enter into these two expressions (i) and (2). 



620. Consider, in the first place, two bodies moving respectively 

 on two fixed curves s and /, with the constant velocities v and v'. 

 When the two moving bodies traverse the elements ds and dsf, which 

 are at the distance r t and make with each other an angle e, we 

 have 



ds ds' 



v = and v= - 



