Elastic Solids to Metrology. 595 



where P is the pressure in the medium at the level o£ the 

 divided surface, and k is the bulk-modulus. 



When the prism is not of rectangular section, or when, 

 being of rectangular section, it is supported on points or 

 roller surfaces situated in a horizontal plane, we have to 

 content ourselves with the mean change in the length of the 

 longitudinal "fibres." For this we find from (1), H being 

 the height of the C.Gr. of the section above the supports, 



8L/L= -(l-2,)(^/E)+,5r(p-pO(H/E) : 



(68) 



where p is the pressure in the surrounding medium at the- 

 height H. 



In the case of the rectangular section, with the base- 

 uniformly supported, it follows from (66) that the mean 

 change in the length is the change actually occurring at the 

 level of the C.Gr. ; but we are not entitled to assume that this 

 is true generally. This is a question of some theoretical 

 importance in view of the now common practice of dividing 

 standards of length along the so-called " neutral " surface, 

 i. e. the horizontal plane containing the C.G. 



§ 20. To afford a more exact idea of the problems actually 

 arising in metrology, I give in fig. 1 some representative 



Fig. 1. 



39-0 





in 







8-2 



m 

 <* 





5-8 



forms of cross section in standards of length. The sides 

 shown vertical in the figure are vertical in ordinary use ; 



