THEORY OF THE DISPERSION OF LIGHT. 263 



have any position whatever in respect to particular lines of direction which may sub- 

 sist among the molecules of the etherial medium. 



Now, supposing the arrangement of the molecules to be perfectly uniform, since the 

 direction of the ray (x) must pass through m, it follows that the sums of the distances 

 of all those on each side of the line x, whether in the plane of 3/ or of z, will be equal, 

 or the hypothesis (36.) (37.)> o^ (48.) (50.) exactly fulfilled, /or all positions of x in the 

 medium. 



If the arrangement be not uniform, the same hypothesis in general may be approxi- 

 mately fulfilled in proportion as we suppose a greater number of such molecules taken 

 into account, or the summation extended to a greater number of terms, that is, a 

 greater number of molecules within the sphere of the influence of the propagation of 

 motion from the molecule first agitated. But if we suppose any portion of the ether 

 be so circumstanced that the sphere of influence is more limited, then the conditions 

 (36.) (37.) will not be fulfilled even approximately, or the hypothesis (38.) (39.) will 

 obtain ; though they would approach more or less towards fulfilment in difl^erent 

 positions of the ray. The diminution of the sphere of influence may arise either from 

 a decrease in the force, or an increase in the distances of the molecules. 



(19.) Here also we may remark, in connexion with what was observed before (§. 1 1 .), 

 that at the bounding surface of vacuum and a medium, or generally of two media of 

 different densities, we can hardly suppose the change of density in the ether to take 

 place abruptly ; but must, from all analogy, imagine a thin stratum on either side, 

 within which there is a gradual alteration in the arrangement of the molecules, and 

 this more considerable in proportion to the difference of refractive powers of the 

 media. 



Thus, even supposing the molecules uniformly distributed in the two media or por- 

 tions of space, it is evident that within this stratum they will not be uniformly ar- 

 ranged. And hence, though on either side the conditions (36.) (37.) should be ful- 

 filled, within the stratum the conditions (38.) (39.) would take efflect. 



Conclusion. 



(20.) The general conclusions which I conceive have been obtained are as follows : 



When light is elliptically or circularly polarized, that is, when one of the two com- 

 ponent vibrations is retarded behind the other, then, in the differential equations of 

 motion, the opposite terms do not destroy each other in the summation ; that is, the 

 arrangement of the molecules is not uniform. 



When light is plane-polarized, or unpolarized, that is, when there is no retardation, 

 or the phases of the component vibrations are simultaneous, then the opposite sums 

 destroy each other ; that is, either the arrangement is uniform, or the sphere of the 

 influence of the force so great, that the conditions are fulfilled very nearly. 



Since both kinds of light can be propagated indifferently through ordinary media, 

 it follows that the sphere of influence of the force, or number of molecules taken into 



