COMPRESSIBILITY OF METALS. 



229 



With regard to b as a function of 8, we shall content ourselves with 

 the next order of approximation beyond assuming that it is constant, 

 and put 



b = a + j8S. 



Substituting this value back, 



d& a n(a+P&) 

 db ' ' 8 2 ~ 8 n+] 5" 



d 2 <$> 2a ra(re+l) 2re 



8 n+2 



5' 



and the special value of 37 at 5 = 80 gives 



do 



a_ refa+ffio) 



5 2 o n+1 + o n ' 



Now substitute these values for the derivatives of <£, and we get 



dp 4a re(re+3) (ra+2)(re-l) 



rf5 35 5 35 n + 4 



a — 



35 n+3 



A 



352 



X ~ 5 3 



35 5 



w(w+3) (n+2)(n-l) fl - 



4a — — rr - ; — a — - .„ » p 



sn-l 



s;n-2 



In this equation replace a in terms of 8 by the stability relation, put 

 8 = 5o + A5 , where A<5 is small, so that 



and 



. A5 AF 



replace — by 3 — , and substitute back, obtaining 

 00 v 



