46 E. L. Nichols—Optical Method for the 
the intensity of the reflected ray diminishes, and a larger 
ortion of the incident ray is absorbe 
reflexion” occurs, are not included int his argument, since the 
formule do not apply to them. ‘They would have to be con- 
sidered in the lack of further knowledge as possible exceptions 
to the law. 
_ For such bodies MacCullagh,* making use of the hypothesis 
of an imaginary angle of refraction, assumed for r the follow- 
ing expression : 
: sin z a 
sin 7= ~~ cos AX+e/ —1 sin x. (6) 
= (cos *1 + sin’ y) 
which admits of the common definition of n 
: ger PR, 
since even for an imaginary angle, 
cos’ r+ sin? r= 1, 
In a similar manner MacCullagh assumes 
st ae 
cos r= — (cos x’+a/—1 sin 7’), (7) 
where m’ and y’ are functions of m and y. 
Substituting these values in equation (3) we obtain, 
(m”? —m’*)?+4m” m? sin’ (y¥—-1’) 
R,=,f 7s ey as 
(m*+- m"-+ 2m' m cos (y— x’) 
disappear we must set m=m/’ and y=7- 
MacCullagh determined experimentally the values of m and ¥, 
but I know of no researches from which to draw any conclu- 
sions concerning the influence of temperature upon these 
quantities. 
Cauchyt gives for R, the following expression, 
__ , sin’ (i— r)+ y’ sin’ r 
R=, sin’? (¢+r)+y7’ sin’? r’ (9) 
* MacCullagh, Proceedings of the Irish Academy, i, 2, 159; ii, 375. 
+ Cauchy ; Comptes Rendus, ii, 427 ; viii, 553-658 ; ix, 727; xxvi, 86. 
