38 



LORD RAYLEIGH. 



aiid if, as for giass, the ditt'usivity for lieat in c.g..s. ineasure be "004, 

 Ave get 



7'=^^— (27) 



Thus if a plate of glass be one centimètre tliick, so tliat c = 1, the 

 light seen in the polariscopc at tlie centre of the thickness is a maximum 

 about 7^ seconds after beat is apjilied to the faces. 



The following small table will give an idea of the relation betweeu 

 (26) and T. 



In bis paper above referred to Hopkinson considered the strains pro- 

 dnced by unequal heating in a spherical mass, under the supposition 

 that the température was everywhere the same at the same distance from 

 the centre. A similar analysis ap])lies in the two-dimensional problem, 

 which is of greater interest from the présent point of view. We suppose 

 that everything is symmetrical with respect to an axis, taken as axis of 

 z, and that ô is a function of r, equal to Y {■f--\-y-), only. ïlie displa- 

 cements in the directions of z and r will be denoted by w and w; in the 

 tliird direction, perpendicular, to - and /•, there is su2)posed to be no 

 displacement. 



We may commence with the strictly two-dimensional case where 

 10 = throughout. Tliis implies a stress Jî whose magnitude is given by 



2i = 



in which 



(2+d- 



du II 

 Jr ' V 



■yù,. 



■281 



(29) 



represcnts the dilatation. 



