Heating and on Double Refraction resulting therefrom. 177 



the matter. By supposing R = in (38) we get 



(X + 2 M )f =.^-x(g + ^); . . . (39) 



and using this value of dw/dz, 



„ 2\u / du .u\ a du 2fxy6 ,. AX 



p = xT&U + ^) + 2 ^~^ ' • (40) 



Comparing these with (30), (31), we see that the only differ- 

 ence is that \ and y of those equations are now replaced by 



2\ll , 2/u/y 



and 



X -+- 2/j, \-\-2/ju 



Hence, instead of (37), we should have 



*-Q=&i e -i\'* ,dr i' ■ ■ ■ (42) 



A-f-^ r Jo 



and the same general conclusions follow. 



In the preceding calculations we have supposed that the 

 solid is free from stress at a uniform standard temperature 

 when u, v, w vanish. In the case of unannealed glass, it 

 would require a variable temperature to relieve the material 

 from stress. To meet this, 6 in the above equations would 

 have to be reckoned from the variable temperature corre- 

 sponding to the state of ease, rather than from a uniform 

 standard temperature. 



Some of the questions above considered are easily illus- 

 trated experimentally. A slab of glass about 8 cm. square 

 and 1 cm. thick, polished upon opposite edges, when placed 

 in the polariscope shows but little revival of light so long as 

 the temperature is uniform. The contact of the hands with 

 the two faces suffices to cause an almost instantaneous illu- 

 mination, rising to a maximum at the middle of the thickness 

 after a few seconds. Dark bands situated about halfway 

 between the middle and the faces are a conspicuous feature. 

 After about 30 or 40 seconds the light fades greatly, a result 

 more rapidly attained if the hands be removed after 10 or 20 

 seconds' contact. In the earlier stages of the heating the 

 outside layers are the warmer, and being prevented from 

 expanding fully are in a condition of compression. The inner 

 layers at the same time are in tension, a conclusion that may 

 be verified by interposition of another piece of glas c , of which 

 the mechanical condition is known, and of which the effect 

 may be either an augmentation or a diminution of the light. 



