A SYSTEM OF PARTICLES. 243 



/ P' TV/ ' 

 hence the action on a particle of A is C[ — + — ] but this is 



retained at rest by a corresponding quantity of A at distances £,' ; 



Similarly, the action on a particle of B at the confines of the 

 medium gives us 



a' 



, 3IP- M- P'Q- MP" 



hence -^ + ^^ = ^v + -^> 



or ]yp = P^Q^ 

 M = PQ; 



and, by substitution in the above approximative equations, 



the integrals being evidently equal 



= »" 



or the velocity with which the motion of a particle of JS is trans- 

 mitted, is equal to the same quantity for a particle of A. 



8. Thus far we have neglected the influence, which the particles 

 of matter with which the media are united, (such are the elements 

 of solid bodies) exert directly on the motion. Such influence will be 

 calculated by I'esuniing our equations, and supposing, in addition to the 

 forces exerted by the particles which have motion, other forces pro- 

 duced by particles at rest. 



IjCt A.v, Ai/, As be the co-ordinates of a material particle, mea- 

 sured from the place of rest of the particle under consideration ; 

 Vol.. VI. Pakt II. 1 1 



