248 ON THE REFLEXION AND REFRACTION OF LIGHT. 



given in the Mfaamque Analytique became abundantly suffi- 

 cient for the solution of the problem. 



In conclusion, it may be observed, that the radius of the 

 sphere of sensible action of the molecular forces has been re- 

 garded as insensible with respect to the length X of a wave 

 of light, and thus, for the sake of simplicity, certain terms have 

 been disregarded on which the different refrangibility of dif- 

 ferently coloured rays might be supposed to depend. These 

 terms, which are necessary to be considered when we are 

 treating of the dispersion, serve only to render our formulae 

 uselessly complex in other investigations respecting the pheno- 

 mena of light. 



Let us conceive a mass composed of an immense number of 

 molecules acting on each other by any kind of molecular forces, 

 but which are sensible only at insensible distances, and let 

 moreover the whole system be quite free from all extraneous 

 action of every kind. Then a?, y and z being the co-ordinates 

 of any particle of the medium under consideration when in 

 equilibrium, and 



the co-ordinates of the same particle in a state of motion (where 

 w, v, and w are very small functions of the original co-ordi- 

 nates (a;, y, ), of any particle and of the time ($)), we get, 

 by combining D'Alembert's principle with that of virtual ve- 

 locities, 



d*u 5. d*v ~ d*w 5, } 



Su + + ~ 



Dm and Dv being exceedingly small corresponding elements 

 of the mass and volume of the medium, but which neverthe- 

 less contain a very great number of molecules, and S<p the 

 exact differential of some function and entirely due to the in- 

 ternal actions of the particles of the medium on each other. 

 Indeed, if &<f> were not an exact differential, a perpetual *motion 

 would be possible, and we have every reason to think, that 



