228 BRIDGMAN. 



one on b. Born has availed himself only of the check on n given by 

 compressibility measurements. 



All the following considerations take no account of temperature; 

 they hold rigorously at absolute zero, but approximately at higher 

 temperatures, because compressibility does not greatly depend on 

 temperature. 



Given a structure with a potential, like the above, and subjected to 

 external pressure, then a necessary condition of equilibrium in general 

 is that 



$ + p8 3 



shall be a minimum for changes of 5, or 



d$ 



M + ^ = °' 



In particular, when there is no external pressure, and 8 = 5 , 



d$\ 



m\ =0 - 



The compressibility we define in accordance with the experimental 

 usage above as 



J_ dV _ 35* d8_ 

 <5 3 dp d 3 dp ' 



d8 



We can get — by differentiating the equation of stability, which 



is, solved for p, 



1 ^ 



V ~ ~ 36 2 db " 



Hence 



dp 2 d<P 1 (P$> 



do' : 35~ 3 dl ~ 35~ 2 dJ 2 ' 



We must next evaluate the derivatives of <£. 



r/<& a nb 1 db 



lb 7 ' 8 2 " 5"+i + 6" ~d8 ' 



<m> 2a n(n+l)b 2n db lffl 



dS 2 ~~ ~ 5 3 + 8 n+2 ~ 8^dS + 8"dJ 2 



