174 Lord Rayleigh on Stresses in Solid Bodies due to unequal 



At the middle surface, where z = 0, the right-hand member 

 of (23) becomes 



Initially 



4 97-8 - 



as was required. If we put «"" p i' = T, (25) may be written 



T(l-D_*l>(l + ^)+ll-(l-4)-.:.; (26) 



and (26) maybe tabulated as a function of T, and thence of t. 

 It vanishes when T = l and when T = 0. The maximum value 

 occurs when T = *747. When T is less than this, which cor- 

 responds to an increased value of t, only the first two or three 

 terms in (26) need be regarded. The above value of T gives 



^ = •292; 



and if, as for glass, the diffusivity for heat in c.G.s. measure 

 be '004, we get 



•292c 2 



T = 



•0047T 5 



(27) 



Thus if a plate of glass be one centimetre thick, so that c= 1, 

 the light seen in the polariscope at the centre of the thickness 

 is a maximum about 7 \ seconds after heat is applied to the 

 faces. 



The following small table will give an idea of the relation 

 between (26) and T. 



T. 



(26). 



T. 



(26). 



00 



o-oooo 



06 



02139 



o-i 



00363 



0-7 



0-2381 



02 



00727 



0-8 



0-2371 



03 



0-1090 



0-9 



0-1823 



0-4 



0-1453 



10 



0-0000 



0-5 



01809 







In his paper above referred to Ilopkinson considered the 

 strains produced by unequal heating in a spherical mass, 



