1904] 



the Volume Elasticity of Elastic Solids. 



(ii) 

 (iii) 



Pv=-p e v e 



81/1 = - 



Here 

 Noticing that 



523 



(20), 

 (21); 



( 2 3). 

 (24). 



Cross-section within 



v Section of prism wall ' 



and similarly for v et it is obvious that Cases (i) and (ii) answer 

 respectively to uniform internal and external pressures in a hollow 

 prism whose ends are covered by caps. 



The above results are true under the same limitations as for the 

 isotropic cylinder whatever be the shapes of the prismatic sections, 

 and irrespective of whether they be similar to one another or not. 

 If, however, the prismatic walls be thick, or the contours of the cross 

 sections be irregular and dissimilar, there may be, so far as the above 

 proof is concerned, considerable differences between the longitudinal 

 alteration of different " fibres," and to obtain a satisfactory observational 

 value for 8l might be troublesome. 



In the case of a right circular cylinder whose two surfaces are 

 co-axial there cannot, of course, be any buckling, and if the walls are 

 thin, 81 will be given satisfactorily by measurement of a single 

 generator. 



The elastic modulus k s defined by (24) represents (mean surface 

 pressure -r reduction in volume), in a unit cube when only the faces 

 perpendicular to z are under pressure, the remaining four faces being 

 unstressed. It is distinct from the true bulk modulus k, answering 

 to uniform pressure the same in all directions, which is given by 



1 _v_i\ 

 E' 1 IV 



(25), 



or 



1^-1^1 (26). 



