256 Mr. W. Sutherland on Molecular 



attractional potential energy has for the liquid state half the 

 value for the gaseous. These points and many others will 

 be cleared up only by a kinetic theory of liquids worked out 

 as completely as the kinetic theory of gases. It is because 

 of this form l\(v + k) involving change of I from I to lj2 that 

 I retain I as the symbol for a quantity, standing for the K of 

 Laplace who puts p = l, and the a of van der Waals. 



8. Surface energy of a liquid and its vapour 

 (continued from 6). 



Having satisfied ourselves that for the element gases and 

 CH 4 the value of e 2 s 2 may be taken to be the same in the 

 states of liquid and vapour, we can write for them the equation 

 for surface tension « 



3 a /4 = A-'{l/R 1 5 -(l/R 1 2 + l/E 2 2 )/ 1 R i! 3 + l/R 2 5 }. . (8) 



For a typical compound, if we express the various effective 

 values of es in terms of that for the vapour when v — go or 

 p = Q denoted by e g s ffi then for the liquid e 2 s^ = e^j2, and for 

 the vapour e 2 s-~e 2 g s 2 g v\(v + k) =^/(l + kp), so 



3«/4 = 4s|{l/21V - (1/Bjf + l/R^R^l + k P )h 



+ l/R/(l + *p)}. . . (9) 



Though empirically k = 6v c j7 = 6j7p c , where p is the critical 

 density, it simplifies matters to assume that in this connexion 

 k can be replaced by l/p c , and then 



3«/4=«V{l/2R l 5 - (1/B 1 *+1/Bi0/ 1 B,«2»(1 +^ )» 



+i/R/(i+/>K>}. . (io) 



This vanishes at the critical point, as it ought. 



For the further development of this equation we can 

 proceed as in the Boltzmann Festschrift, but more definitely 

 and rigorously. Let us consider two typical neighbour 

 molecules as regards the relative motion of approach and 

 departure. Suppose one fixed while the other performs the 

 relative motion. Its kinetic energy may be such as will just 

 carry it to rest at infinity, or it may be more or less than 

 that amount. The relative orbit may be one of infinite range 

 with finite or zero velocity at infinity, or one of finite range. 

 The most beautiful and familiar instances of these three 

 classes of relative orbits are those described under a force 

 varying inversely as the square of the distancej as in the 

 case of comets under the influence of the sun. The hyper- 

 bola is the orbit open at infinity on account of there being 



