Birefringent Action of Strained Glass. 333 



the retardation H' in the same two cases of air and liquid 

 respectively, then, 



e&m+(m- 1)8^=6, (5) 



eflm+ {m — m)he=-U (6) 



Eqs. (5) and (6) give an expression for eS'm and a second 

 expression for (m — 1) Be, both involving measured quantities 

 only ; but if the quantities a and a' have been measured 

 accurately, the difficult and very tedious measurements of 

 /> and V can be avoided in a way that seems to be quite safe 

 though circuitous ; for by eqs. (1) and (5), and by prop. iv. 



e$'m—e&m = b — a=—-n (7) 



The solution of our problem is contained in the equations (3), 

 (4), (7), or in the three following : — 



(m— l)8e= —. — -(a— a 1 ). 

 7 m — 1 



ehn = a — (m — l)8e, 

 eS'm = e8m — -. 



We come now to the measurements. 



Proposition VII. 



If a winged plate, whose index of refraction* is 1*53, be 

 immersed successively in atmospheric air and in water, the 

 differences of retardation of V through strained pillar and H 

 through unstrained wing , produced by the same vertical strain 

 in the two cases, are sensibly as 100 to 69. 



In other terms, and in the notation of last article, if m = 1*53, 

 and »w'=l*33, then a—a' = '3la. 



13. Winged plate and refractor are used as before, but 

 there are some new arrangements. Two strong wooden posts 

 are erected on opposite sides of the optical bench; they are 

 bound together at their lower ends, and bracketed to the 

 table, so as to form one rigid piece with it ; and they are 

 connected at their upper ends by a massive bar of iron, which 

 is directed horizontally at right angles to the optic bench. 

 Projecting vertically downwards from the middle of the iron 

 traverse, and forming one piece with it, there is a strong 

 rectangular frame of metal, which serves as a stand and press 



* Measured on a small prism taken from the same piece as the winged 

 plate, and certainly true to less than -3 per cent. 



