214 Astronomical and Nautical Collections. 



dence and refraction, for each kind of undulations, must 

 always be the same with the relation of the velocities of pro- 

 pagation in the two mediums ; so that if the different rays 

 passed through thera with the same velocities, they would 

 be equally refracted, and there would be no dispersion. We 

 must therefore suppose that, in refractive mediums, the undu- 

 lations of different lengths are not propagated with the same 

 velocity, or, in other terms, are not shortened in the same 

 proportion. This consequence appears, at first sight, to be 

 contradictory to the results of the elaborate calculations of 

 Mr. PoissoN on the propagation of sonorous undulations in 

 elastic fluids of different densities : but it must be observed 

 that, in this theory, the general equations are founded on the 

 supposition, that each infinitely thin stratum of the fluid is 

 repelled by the stratum in contact with it only, and thus that 

 the accelerative force extends to infinitely small distances 

 only, in comparison with the length of an undulation. This 

 supposition is, without doubt, perfectly admissible for the 

 undulations of sound, the shortest of which are some tenths 

 of an inch in length : but it may possibly be inaccurate for 

 the undulations of light, the longest of which are several 

 thousand times shorter. It is very possible that the sphere 

 of activity of the accelerative force, which determines the 

 velocity of propagation of light in a refractive medium, or 

 the mutual dependence of the particles of which it is com- 

 posed, may extend to distances which are not infinitely 

 small in comparison with the fifty thousandth of an inch : for 

 such a supposition is not contradicted by anything that we 

 Jcnow of their limited spheres of activity. Now it is easy to 

 infer, from mechanical considerations, that if the sphere of 

 activity of the accelerative forces extends actually to sen- 

 sible distances, in comparison with the length of the luminous 

 undulations, those which are the longest must be less retarded 

 in their progress by the density of the medium, or less short- 

 ened, in proportion, than the shorter undulations, and must, 

 consequently, be less refracted : a conclusion which agrees 

 with the only general rule, that has hitherto been experimen- 

 tally discovered, for the phenomenon of dispersion. 

 . However this maybe, the facts sufficiently show that lumi- 



