162 Professor Powell on certain points 



been regarded as evanescent by M. Cauchy and others: and 

 this as a consequence derived from the hypothesis of a uni- 

 form distribution of the aetherial molecules in space. Mr. 

 Tovey's object in the paper referred to is to show that when 

 this is not the case, elliptic polarization is the result. 



Highly valuing this investigation, but conceiving that the 

 remarkable conclusion was not so fully explained as its im- 

 portance seemed to render desirable, in a paper inserted in 

 the Phil. Trans, for 1838, part ii.*, I endeavoured to establish 

 and further elucidate the conclusion by what seemed to me a 

 more direct and perspicuous method. 



The intimate connexion between these theoretical views 

 and the important points discussed in the brief but masterly 

 papers of Sir J. Lubbock, was soon rendered evident. The 

 direct object of these papers was chiefly the illustration of 

 Fresnel's views respecting the axes of elasticity and the wave 

 surface; and there appeared at first sight some degree of con- 

 tradiction between these deductions and the views just re- 

 ferred to. I endeavoured to drav/ attention to the difficulty in 

 a short communication to the British Association at Birming- 

 ham, 1839t. 



In consequence of some correspondence and further dis- 

 cussion, I drew up a supplement to my last-named paper, 

 which was inserted in the Phil. Trans. 184-0, part i., in which 

 I pointed out the modifications which the former conclusions 

 would receive in connexion with the principles thus elucidated. 



This supplement, however, was very brief: other points 

 also appeared to call for further notice, and the whole inves- 

 tigation seemed to require re-casting. My present object is 

 therefore to offer in the first instance a general review of the 

 main investigation in such a form as I trust may meet all the 

 difficulties which have been urged ; and further, to point out its 

 bearing on the several topics with which it stands connected. 



(3.) To expi'ess undulations we shall suppose the common 

 formulas adopted for the vibration of a single molecule of 

 aether, the assemblage of which expressed by the summation 

 2, represents a ray of light: and as in all the investigations 

 on this subject, if ? >) ? be the displacement of a molecule in 

 the direction of the three rectangular axes of x y z^ and 

 further if we take the ray as coinciding with the axis .x-, then 

 on the principle of transverse vibrations, we have 

 ? =0 



») = S [a sin {nt—kx)^ ,, \ 



? = 2 [psm{nt-kxy\ ^^'' 



[• Of which an abstract appeared in L. & E. Phil. Mag. vol. xiii. p. 222. 

 — Edit.] 

 t See Sectional Proceedings, p. 3. 



