48 THE VOYAGE OF H.M.S. CHALLENGER. 



It appears from the Kinetic Theory of Gases, in which the particles are treated as 

 hard spheres, whose coefficient of restitution is 1, and which exert no action on one 

 another except at impact, that the pressure and volume of the group at any one 

 temperature are connected by a relation approximately of the form 



p (v — a) = constant. 



The cpiantity a obviously denotes the ultimate volume, i.e. that to which the 

 group would be reduced if the pressure were infinite. 



I have pointed out * that this expression coincides almost exactly with the results 

 of Amagat's experiments on the compression of hydrogen. The introduction of an 

 attractive force between the particles, sensible only when they are at a mutual 

 distance of the order of their diameters, merely alters the constants in this expression. 

 Let us see what interpretation it will bear if, for a moment, we suppose it roughly to 

 represent the state of things in water. 



The average compressibility of such a group of particles, between the pressures 

 ■m and vs+p, viz., 



where v is the volume at m, and v that at m+p, is easily shown to be 



Compare this with the empirical expression above for the compressibility of water 

 say at 0° C. (per ton weight on the square inch) — 



152-3 x 0-00186 _ 0-283 

 36 +p 36 +p 



and we see that they agree exactly in form. If, then, the results of the kinetic theory 

 be even roughly applicable to the case of a liquid, we may look upon the 36 in this 

 expression as the number of tons weight per square inch by which the internal pressure 

 of water exceeds the external pressure. And the corresponding empirical expression 

 for the compressibility of a solution of common salt may be interpreted as showing 

 that the addition of salt to water increases the internal pressure by an amount simply 

 proportional to the quantity of salt added. 



That liquids have very great internal pressure has been conjectured from the results 

 of Laplace's and other theories of capillarity, in which the results are derived statically 

 from the hypothesis of molecular forces exerted intensely between contiguous portions 

 of the liquid, but insensibly between portions at sensible distances apart. A very 

 interesting partial verification of this proposition was given by Berthelot 2 in 1850. By 



1 Trans. Roy. Soc. Edin., vol. xxxiii. p. 90, 1886.] 2 Ann. de Chimie, tom. xxx. p. 232. 



