in the Undvlatory Tlieory. 171 



the sums just mentioned vanish, then it is seen that those 

 quantities are altogether arbitrary, and the movements will be 

 the same as those expressed by the author's formulas in his 

 other paper * ; or such a medium will propagate elliptic or 

 rectilinear vibrations indifFerentlyf. 



(9.) Mr. Whewell % had observed the difficulty of conceiving 

 any mechanical conditions for the production of elliptic polari- 

 zation, and that not even a plausible hypothesis had been 

 proposed so as to give a physical interpretation to the lan- 

 guao^e of analysis, especially as conveyed in the equations ob- 

 tained by Prof. Maccullagh. 



From what has just been stated, this difficulty appears now 

 to be, at least in a general way, overcome by the conclusion 

 of Mr. Tovey. 



It is easy to conceive the physical possibility of a portion 

 of the Eether possessing an unsymmetrical arrangement of its 

 molecules. For example, at the bounding surface of a me- 

 dium and of vacuum, or generally of two media of different 

 densities, we can hardly suppose the change of density in the 

 aether to take place abruptly ; but must from all analogy ima- 

 gine a thin stratum on either side, within which there is a 

 gradual alteration in the arrangement of the molecules; and 

 this more considerable as the difference of the refractive 

 powers is greater. It is conceivable that this variation may 

 in some instances be of sufficiently great amount to give the 

 requisite conditions of unsymmetrical distribution within this 

 stratum, though on either side of it the symmetrical arrange- 

 ment may subsist. 



(10.) With regard to the value of n, experiment shows 

 that the state of the same ray as to polarization produces no 

 difference in the magnitude of its refractive index. Hence it 

 follows that in all the preceding different cases in which the 

 value of 11 has been expressed (whether on the hypothesis of 

 unsymmetrical or of symmetrical distribution) the terms in- 

 volved must vary in magnitude, so that the whole expression 

 shall remain constant, or the values (26. 40. 41. 45. 59.) all 

 equal. Thus, in general, writing h for the sum of the ar- 

 bitrary terms a and /3, we express the value of ii by the for- 

 mula »^ = -^S [ap 2sin2^]. (61.) 



* L. & E. Phil. Mag. and Journal of Science, vol. viii. p. 426 and 

 p. 502. 



t See also the same author's paper on the nature of the vibrations in 

 quartz, vol. xiv. 183i), pp. 169 and 323, 



X Hist, of Ind. Science, vol. ii. p. 448: 1837. 



