Recent Progress in Theoretical Physics. 253 



rotation of 90°, we know that the difference of phase is then one- 

 half an undulation. If X denote the length of the longer undula- 

 tion, and /, that of the shorter, then — 



a = VI A — (m + -i-) / ; or _ = = 1 — 



A VI 2m 



a 



As — = m, and A may be determined by experiments in refrac- 

 tion, the value of ??^ is known when is measured. By pursuing 

 this method, Mr, Babinet found the value of — = 1.00003 : a 



value which, small as it is, is the largest known for [non-magnetic] 

 rotatory polarization." 



The first mathematical explanation of rotatory polarization as it 

 occurs in quartz, appears to have been given by MacCullagh, in 

 1836 (Trans. R. Irish Acad,, XYII), He succeeded perfectly in 

 explaining the phenomena as they occur in uniaxial crystals, by 

 introducing into the ordinary equations of vibratory motion in 



fluids, terms of the form c —L. So that the equations become: 



d?q 72 d^^ d^T) 



de d?} ^ dz^ 



^ _ 52 ^ c ^ 

 dC ~ 'dz" ~ dr} 



Cauchy also appears to have furnished similar equations to M. 

 Jamin, at the request of the latter, who compared them carefully 

 with experiments, and found a perfect agreement so far as uniaxial 

 crystals are concerned (Verdet-Lecons D'Optique Physique, Vol. 

 II, p. 323). For biaxial crystals Yerdet says: "Za methode de 

 MacCidlagh est ires remarquable : cest tin bel exemple de ce qu'' on 

 peutfaire quand on est reduit a de simples conjectures.^'' 



The matter has since been treated by M. Briot in an "iissai 

 sur la theorie viathematique dela lumiere.''^ He supposes a forced 

 distribution of the ether in rotatory crystals, so that the lines of 

 ethereal molecules are arranged in elliptic helices. This supposi- 

 tion introduces into the diS'erential equations of vibratory move 

 ment, differential coefficients of odd orders, the presence of which 

 indicates the rotatory power. 



Airy has suggested similar equations for the rotation produced 



