¢ 
% 
IN PLATES, TUBES, AND CYLINDERS OF GLASS. 357 
tint will be found to be Hyperbolas, Circles, Ellipses, Straight 
Lines and Parabolas. 
Let us now suppose, 
T T’= the maximum tints of the two plates. 
B B’= the breadths of the plates. 
x =the distance from the centre of the plate of 
any. point where the resulting tint is required. 
y = the distance of the same point from the centre 
of the other plate. 
t ¢ = the tint produced by each plate separately at 
the distances « and y, and 
¢ = the resulting tint. 
. 
Then, substituting .312 B instead of its equal D, we have 
: Tax 2 q’ 2 
i Pe al fue dy eet 
312 Be?“ 312 B®’ 
But, since the Bie eye tint + arising from the combination 
is equal to the difference of the two tints, we have 
Pgh Lig* 
312 B2 + —— 312 312 B® 9 and 
me yh ws =") T .312 B? x’ 
sige ak (= TT" 312 Be 
z— T’—T— 
Consequently, the lines of equal tint are Hyperbolas. When 
feed yl and.B = B, the Sik ae are equilateral, and 
of = .312 B? +a%. 
When a plate whose Same axis is negative, is crossed 
with a plate whose principal axis is positive *, the resulting 
tint 
* Phil. Trans. 1816, vol. II. fig. 8. 
