Undulatori) Theory of Light. 4.25 



cipal optical phacnomena presented bv what are called uniaxal 

 '^P.T ^ , Professor, following, as I suppose, the method 



otM l^resnel, has deduced results similar to these, except 

 tnat, by his reasonnig, the direction of vibration in the sphe- 

 rical waves IS ihe same as we have found it to be in the sphe- 

 roidal and the converse. But I apprehend that the 104th 

 and llJth articles of his valuable tract on this subject are in- 

 consistent with each other; and that the latter, on which the 

 question depends, is erroneous. 



I perceive, from the British Association's Report on Physical 

 Optics, that the investigations of M. Cauchy give, for the di- 

 rec ion of vibration, the same result as mine; but it appears 

 that Jus investigations are not founded so immediately as 

 mine upon the physical constitution of the medium. 



(13.) The deductions of the last two articles rest upon the 



tTonr(2!r ^'''' ""'^ ''''' '"' ^ '" '" " '"' ^'"' ^^ '''' ''^"''" 



'"-vv/O-f.i?.-)' 



, /"=n/(-f-!7'--)^ 



hence these deductions require a corresponding modification. 

 But this IS easily effected; for we may suppose the variations 

 of the sums 5% sf , s,f , ,'\ s/^ s'„\ &c. depending upon the 

 directions of the coordinates, to be in general small fractions 

 of the sums themselves. Hence, in the last equations, we 

 may regard -if, llL. as constant, and (paper at p. 270 of 



vol. viii.,) equal one to the other; and thus, if we nut ^ 



^'TT^ = A, we have, instead of the values of v^ and t^, found in 

 articles 9 and 6, 



^^' = ^•70-77 + ^^-) 



(6.) 

 ^n= \/(Vcos^S + c/sin'5) • ^ (l - ^ f &c.V 



It appears by these equations that the values of v. and v , 

 and the ratio of one of them to the other, depend, in some 

 measure, upon x^, x^^, the lengths of the waves. This is con- 

 firmed by experience. See Airy's Tracts, p. 354-. 



{\i.) h is well known that light moves through glass, in 

 its ordinary state, with the same velocity in all directions; 



Third Scrirs. Vol, 9. No. 56. Dec. IS.'^G. 3 E 



