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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume IV (1876-1877)

Davies, J. E.
Report on recent progress in theoretical physics,   pp. 241-264 PDF (6.7 MB)


Page 253


Recent Progress inr Theoretical Physics.
rotation of 900, we know that the difference of phase is then one-
half an undulation. If A denote the length of the longer undula-
tion, and 2', that of the shorter, then--
        6=m2       (m + )!'; or 2A     m M    _ 27n+1
                                     2'  n    -   2m
   As - =m, and A may be determined by experiments in ref rac-
tion, the value of m is known when 0 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., XVII). 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 d±. So that the equations become:
                            (1Z3
                         = b2 d 2+ Cd3~
                      dt2      de2     dz
                      d     b2 dz       dze
                      d.t2=    d*     cd
   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 Verdet says: "La methode de
MJac~Zullagh est tres remarquable: c'est un bel exemple de ce qu' on
peutfaire quand on est re'duit a de simples conjectures."
   The matter has since been treated by M. Briot in an " Essai
sur la theorie mathernatique de la lnmiere." 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 differential equations of vibratory move
rn ent, differential coefficients of odd orders, the presence of which
indicates the rotatory power.
   Airy has suggested similar equations for the rotation produced
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