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' zz the maximum tints of the two plates. 

 B B'~ the breadths of the plates. 

 x zz the distance from the centre of the plate of 

 any point where the resulting tint is required. 

 y zz the distance of the same point from the centre 



of the other plate. 

 t t' zz the tint produced by each plate separately at 

 the distances x and y, and 

 r zz the resulting tint. 



Then, substituting .312 B instead of its equal D, we have 



tzzT———^, and t'-T IV . 



.312 B 2 ' .312 B' 2 



But, since the resulting tint r arising from the combination 

 is equal to the difference of the two tints, we have 



T' v 2 T x 2 



T .312 B' 2 "*" .312 B 2 » and 



T— T — A , T.312B' 2 * 2 



^ = .312B*(1^^) + 



T'.312B 2 * 



Consequently, the lines of equal tint are Hyperbolas. When 

 T zz T, and B zz B', the hyperbolas are equilateral, and 



y zz .312 B' 2 (-^ 



+ x 2 . 



When a plate whose principal axis is negative, is crossed 

 with a plate whose principal axis is positive *, the resulting 



tint 



* Phil. Trans. 1816, vol. II. fig. 8. 



