APPENDIX B. 



EELATION BETWEEN TRUE AND AVERAGE COMPRESSIBILITY. 

 The average compressibility per ton for the first p tons of additional pressure is 



where v is the initial volume, and v is the volume at p additional tons. 

 The true compressibility at p additional tons is 



dv 

 vdp 



Hence, if one of these quantities is given as a function of p, it may be desirable to find 

 the corresponding expression for the other. The simplest example, that on p. 30, 

 will suffice to show the principle of the calculation. Let 



V -^ = e(l-M; ....(1) 



where e is, in general, a much smaller quantity than/! We have 



-= 1 - ep + efp\ 



whence 



_^^ e(l-2M ...).... (2) 



vdp 1 - ep + efp- \ w / -r 



where the expansion may be easily carried further if required. 



If the terms in the second and higher powers of p are to be neglected, (1) and (2) 

 as written show at once how to convert from true to average compressibility, or 

 vice versd. 



(PHYS. CHEM. CHALL EXP. — PAKT IV. — 1888.) 



