Laws of Molecular Force. 231 



The agreement here is again satisfactory, and we have now 

 seen that our form, with only two constants in addition to 

 those characteristic of the gaseous state, can give both the 

 expansion and compression of the liquid at low pressures ; 

 but Amagat has measured these also at high pressures up to 

 2000 and 3000 atmos. (Compt. Rend. ciii. and cv.), and the 

 following Table compares first his values of the mean co- 

 efficient of expansion between 0° and 50 c at pressures from 

 76 up to 2280 metres with those given by the equation, and, 

 second, his values of the mean compressibility at 17°*4 and at 

 pressures up to 1500 metres with those given by the equation. 

 If t\ and v 2 are the volumes at p 1 and p 2 , then the mean com- 

 pressibility is taken as {v 1 — v 2 )/v l (p 2 — pi). The apparent 

 compressibilities given by Amagat are converted to true values 

 by adding "000002, which he has since given as the com- 

 pressibility of glass. 



Table XVIII. 

 Mean Coefficient of Expansion at high pressures. 



p in metres ... 76. 



Amagat '00170 



Equation -00170 



Mean Compressibilities at high pressures. 



join metres ... 76 to 114 to 366 to 654 to 933 to 1218 to 1500 



I i I I I I 



Amagat '000208 '000143 '000112 '000086 '000070 '000062 



Equation -000197 '000128 -000085 '000060 '000046 '000037 



As regards expansion the equation goes fairly near to the 

 truth ; except at the lowest pressures, it gives coefficients 

 somewhat smaller than the experimental, but it parallels 

 closely the main phenomenon of the rapid diminution of the 

 coefficient with rising pressure. But in the compressibilities 

 there is an increasing divergence between experiment and 

 equation with increasing pressure, although again the equation 

 is true to the main fact of the rapid diminution of compres- 

 sibility with increasing pressure. We may conclude from the 

 last table that our equation holds within the limits of experi- 

 mental accuracy up to 760 metres ; beyond that it begins to 

 fail. A simple empirical modification would adapt the form 

 to the whole of Amagat's range, but as it stands it will be 

 found good enough for our applications. 



We will now consider briefly how this form applies to car- 

 bonic dioxide below the critical volume ; and the comparison 



380. 



760. 



1140. 



1520. 



1900. 



2280. 



00112 



■00091 



•00077 



•00070 



•00063 



•00056 



00101 



•00076 



•00066 



•00056 



•00050 



•00047 



