polarisation of light by reflexion from transparent bodies . 157 
whole refraction to which the dispersion, or the distance be- 
tween the extreme rays is equal, the formulae will become 
tang A. 
j 3 + 
/ tang. A' J 3 
( tang. A* 
\m — \dm 
\m — \ dm l 
U — -dm 
1 
|’ + 
1 1 
i 
( m + -dm^ 
lm + idmy 1 
dm 
\ tang, a 
\ tang, at 1 
tang, a " 
If the angles are partly above, and partly below the pola- 
rising angle, for example, at the angles A, a , a! ' A " then the 
formula will become 
/ tang. A ^ 
> + 
’ m + \ dm 
1 ^ m + idmf I | tang. A" j 
\m — f- dm 
tang . a 
tang, a' 1 \ m — £ dm l 
Scholium. 
I have determined the values of dm for 151 different sub- 
stances, and have published a Table containing 137 of these 
in my Treatise on New Philosophical Instruments , p. 315. The 
value of m or the mean index of refraction, was found in the 
common w 7 ay by measuring the angle of deviation produced 
by a prism of the substance under examination. The values 
of dm were computed, from measures taken with a new in- 
strument, by means of a formula investigated by Boscovich, 
and used in the reduction of all his valuable experiments. 
This formula requires that the ray should be incident perpen- 
dicularly upon the first surface, but it will be found in prac- 
tice that the dispersion of the prism under examination is 
equally corrected by the standard prism, when the ray is 
incident several degrees on either side of the perpendicular. 
I have thus endeavoured as briefly as possible, and perhaps 
