236 REPORT—1885. 
pets 
order to explain experimental results.’ Introducing the term CO’, as F 
defined above, the equations become— 
daily da 
m5 CF tae ev *u 
: (67) 
pe RG Sa Re 
vi Cora + de = (0 + Lorry ) | 
These equations will not lead to satisfactory results. 
Circular ' and elliptic polarisation are also treated of by Ketteler, and 
are explained on the supposition that terms of the form — ( fV + i 
come into the equation for U, and.terms + (#0 + oT) into that for V. 
d 
N?-1] : 
— N being 
the refractive index, while the value of N in a crystal like quartz may 
be found from the formula— 
N’?—1= (N,?—1) (1 + cos?0) + (Ny? —1) sin? @+ [(N,? —N,?) sin‘ 0 
+ 4°? cos? 0(N,? — 1)(N,? cos? 0+ N,? sin?9—1)}'. . (68) 
N, and N, being the refractive indices at right angles to the axis, and k, 
a constant on which the rotatory power depends. For ordinary active 
media the law of the rotation is 
The rotation in a magnetic medium is given by Q= af 
Ost > + “4, ete. : é -" \€69) 
It will be noticed that in the theories of both Lommel and Ketteler the 
rotatory terms are introduced into the equations of the matter particles, 
and affect the ether only indirectly through the values of 1, v, and w. 
§ 3. Voigt’s work? embraces double refraction and circular polarisa- 
tion. The existence of three principal axes is assumed, and for these the 
coefficients o and s in the values of f, and f,* of equations (53) vanish. 
The values of f; and /, are written down with coefficients a,, do, etc., and 
a,', ao’, etc., respectively, and finally the equation of motion for w is 
obtained in the form— 
dp d 
—— 1,U + a, 
da? : d?u du 
(m +71) Fa Sev ut = + dy. 2 
estes SS ei ee 
a dep” Oa 
+ (c3 + b3) oe + (¢y + by) wath + La [similar terms with a,’, etc.] (70) 
dady dadz dt? i 
It will be seen that there are enough coefficients here to give any 
imaginable theory of double refraction. 
Put m+7,; =, etc. Then the equations may be written 
d? du du d?u , dP 
(mate )u= aio Bis ati aati tedat . (71) 
* Ketteler, ‘ Theorie der circularen und elliptischen polarisirenden Mittel,’ Wied. 
Ann. t. xvi. p. 86. 
* ‘Theorie des Lichtes fiir vollkommen durchsichtige Medien,’ Wied. Ann. t. xix. 
p. 873. * See p. 231. 
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