Mr. Earnshaw on the Motion of Luminous Waves. 47 



mission of waves of light through a luminiferous medium. It 

 is necessary also to observe that the quantities k x & 2 k 3 are all 

 possible, and finite ; for were one of them otherwise, vibra- 

 tions parallel to the corresponding axis of symmetry could in 

 no case be transmitted ; but as no media having this property 

 have been yet found, we are permitted to assume that the law 

 of molecular force and the mode of arrangement of the parti- 

 cles are such as to make k x & 2 k 3 possible in all cases. We 

 are now at liberty, without affecting the generality of our in- 

 vestigations, to suppose that the axes of symmetry were the 

 coordinate axes employed in my former paper ; in which case 

 D = E ==• F m 0, and the equations of motion are 



^=-2S(A r sin^).£, 

 ^=-2£(B r sin^).,,, 



^r=-2s(C r sin^^).?; 



wherefore if w t/ o" be the velocities of transmission of vibra- 

 tions which are parallel to the axes of symmetry, and if A be 

 the length of the wave, then 



«"(t)'-*( B ^). 



«-e)'-*(*"2)- 



The right-hand members of these equations involve A im- 

 plicitly} in a manner which depends upon the arrangement of 

 the molecules of the aether and the law of molecular force ; 

 and thus a relation is established between the length of a wave 

 and the velocity of its transmission ; but unhappily the ex- 

 pressions are of such a nature as to imply that there is di- 

 spersion in vacuo. The case therefore stands thus : dispersion 

 in a refracting medium cannot be accounted for on the finite-in- 

 terval theory unless there be also dispersion in vacuo. Now 

 as there is no dispersion in vacuo, I infer generally, that the 

 finite-interval theory cannot account for dispersion. 



Again, by referring to my former communication, it will 

 be seen that the equations of motion do not depend upon 

 the position of the front of the waves traversing the me- 



