﻿Coefficients of Pressure in Thermometry. 377 



sure p. Thus in a shell bounded by S,- and S e under equal 

 uniform pressures jp on the two surfaces, the stresses, and so 

 the strains and displacements, are at every point the same as 

 if Si were an imaginary surface drawn in material completely 

 filling S e , and p were applied over S e only. In particular, 

 the changes in the volumes contained by the surfaces S* and 

 S e must be the same in the two cases. 



In the case of the shell, let SV, and BY e be the increases 

 in the volumes Y { and V e when uniform pressure p is applied 

 over the inner surface only, and let BY" and BY" e be the cor- 

 responding reductions when the same pressure p is applied 

 over the outer surface only. 



In the case of the solid, bounded by the one surface S e , let 

 BY{ be the reduction in the partial volume V,-, and BY e the 

 reduction in the total volume Y e due to uniform pressure p 

 over S tf . Then by what has preceded, since stresses are 

 superposable, 



8V?+(-5V;) = 8V« (12) 



BY !, e + (-BY' e ) = BY e (13) 



But in the case of the complete solid A is uniform, being- 

 given by (10), and so 



l8V,_loT e _l 



p Yi~p Y e ~k U4j 



Thus, substituting for BY { in (12), we get 



i«vj_i«vs_i. 



pYi pYi'r {ld) 



or, after Dr. Guillaume's definition, see (1) and (2), 



1 



the result required. 



Again substituting for BY e from (14) in (13), we get 



isv:_isy;_i 



P Y e p Y e ~k ^ i)} 



Dr. Guillaume had no occasion to arrive at this latter 

 result. To put it in a similar form to the other, let 7,- repre- 

 sent the increase per unit volume of Y e due to unit pressure 

 per unit surface of 8<, nnd let y e represent the reduction per 



