of the Axes of Elasticity, in Biaxal Crystals. 225 



ture to communicate it to the Academy until the date of my 

 second memoir (May, 1841) ; and even then I had not studied 

 it with the attention which I now conceive it merits. It was 

 only very lately, in fact, in some conversations which I had 

 with M. Babinet during a short visit to Paris, that my attention 

 was strongly drawn to the subject of dispersion in crystals, par- 

 ticularly the dispersion of the axes of elasticity. My thoughts 

 then naturally reverted to the hypothesis which I have men- 

 tioned, and since my return I have found that it affords a com- 

 plete explanation of all the phenomena.* 



I have also found that it gives the general law, extended to 

 biaxal crystals, of that elliptic and circular polarization which 

 has hitherto been detected only in quartz and in certain fluids ; 

 while for the case of rectilinear polarization it gives a law (very 

 possibly a true one) more general than that of Fresnel, but 

 quite as elegant, and differing very slightly from it. The hy- 

 pothesis, therefore, is still too general for our present purpose. 

 To make it include only those crystals to which the law of 

 Fresnel is rigorously applicable, the alternate derivatives Xi, 

 Pi, Zi, X 3 , Y 3 , Z 3) &c., must be supposed to vanish in the func- 

 tion which represents the potential. Then, the axes of co- 

 ordinates having any fixed directions within the crystal, the 

 axes of elasticity will be the principal axes of an ellipsoid re- 

 presented by an equation of the form 



Atf + By 1 + <7s 2 + 2Ztys + 2Exz + 2Fxy = 1, 



in which each of the six coefficients the first, for example ex- 

 presses a series of the form 



A Kr 



^ + * ' 



where A denotes the wave-length, and all the other quantities 



* I am indebted, for my information on the subject, to a short article, drawn 

 up by MM. Quetelet and Babinet, in the Bulletin of the Eoyal Academy of 

 Brussels, VOL. n. p. 150 ; as also to Poggendorff's Annals, VOL. xxvi. p. 309 ; 

 VOL. xxxv. p. 81. 



Q 



