■4 Me GREEN, ON THE REFLEXION 



may be satisfied, and the principles given in the Mecanique Analytique 

 became abundantly sufficient 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 regarded as unsensible 

 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 differently 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 formulas uselessly 

 complex in other investigations respecting the phenomena 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 x y and % 

 being the co-ordinates of any particle of the medium under consideration 

 when in equilibrium, and 



x + u, y + v, z + iv, 



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

 and w are very small functions of the original co-ordinates (x, y, %) of 

 any particle and of the time (/)), we get, by combining D'Alembert's 

 principle with that of virtual velocities, 



5; ' D »•{S'*'' + £ J '' + ^H =SZ,, '• ^ * (1); 



Dm and Dv being exceedingly small corresponding elements of the mass 

 and volume of the medium, but which nevertheless contain a very great 

 number of molecules, and $<j> the exact differential of some function 

 and entirely due to the internal actions of the particles of the medium 

 on each other. Indeed, if ^0 were not an exact differential, a perpetual 

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

 forces in nature are so disposed as to render this a natural impossibility. 



