240 REPORT—1885. 
These become MacOullagh’s and Neumann’s formule on the assumption 
that 
M, +7) =M,+75 ) 
(75) 
Ny, = Ng ) 
They become Fresnel’s if 
€) +a, =e, + a5 
bea tani aet °? i odd a aed 
a’, =a, 
for these equations lead—remembering the value of the velocity—to the 
condition— 
m,+r;—n,7? __ sin’, 
My+%g—Ngi2 sin?d, 
For the vibrations in the plane of incidence the results of the first and 
second principles are inconsistent with that of the third, For the first 
and second give 
E,+R,) cos¢, =D, cos¢ ) 
( v ») pil Pp a 2 , : (77) 
m,(H, —R,) sing; =m, D, sing, ) 
while the first and third give, instead of this second equation, 
(m, +7; — 7,77) (EB, — R,) sind, = (my + 72 —Ng7”) D, singg. (78) 
They become consistent if we assume m, =, and, adopting Neu- 
mann’s hypothesis, 
F : r, =1o, nN, = No, 
or, adopting Fresnel’s, 
€; + a, = ey + Ag, a, =o. 
Tn another paper! it is shown that Kirchhoff’s principle, when applied 
to circularly polarising media, leads to an impossible result, and the 
principle is modified by the supposition that the work done is a function 
of the time only, and not zero. 
The theory of ordinary absorbing media is developed? from the 
supposition that terms involving a loss of energy may come in through 
the mutual reaction of the ether and matter, and it is shown that these 
would lead to terms of the form—1 +¢V tee in the equation for 
6 
u, which merely becomes, for waves travelling parallel to z, 
d?u d?u du du 
A — . - ; 
hags icc ae aie ae OA aD (79) 
where 
M,=*#, +7) —7,7? 
/! : : ; - (80 
In considering the problem of reflexion in this case, Voigt assumes 
that the plane zy being the face of incidence, Mw is continuous. The 
1 Voigt, ‘Das G. Kirchhoff’sche Princip und die Theorie der Reflexion und 
Brechung an der Grenze circular-polarisender Medien,’ Wied. Ann. t. xx. p. 522. 
2 Voigt, ‘ Theorie der absorbirenden isotropen Medien,’ Wied. Ann. t. xxiii. p. 104. 
