Transition Layer of a Liquid on its Surface Tension. 879 



and passing through the zero. We then have similarly as 

 before 



9 f dXx 



" t dx 



+ d[2x) H " ~d$x) ^ ' " j ~ \^ + 2^ + 3~^T + ' " j 



(4) 



where a? denotes the distance of separation of the molecules 

 in the liquid. The intrinsic pressure P m of the liquid is 

 given by 



P n =i-(F X +F 2 , + F 3 ,+ ...) J .... (5) 



and the surface-tension A, 2 , on the supposition that no 

 transition layer is formed, is given by 



^2 = ~~2 0^ x + ^ + ^3z + • • • ), (6) 



where the factor — 9 denotes the number of rows of molecules 

 or 



standing on one cm. 2 . 



If the law of molecular attraction were exactly known we 



could express the quantities \ x , X 22r , . . . . , in terms of the 



attraction constant of the molecules, that is, we could deduce 



a number of relations of the form 



Kx=fi(r,x,k), (7) 



where k denotes the molecular attraction constant. On 



substituting for \ nx in equations (4) and (6) from the above 



equation, we obtain two equations from which k may be 



eliminated. The resultant equation and equation (5) give 



an equation containing P„, X 2 , and x, only. The form of 



this equation depends on the form of the function ^(nx^k). 



A form of the equation which very approximately represents 



the facts is obtained from the following considerations. 



Let us suppose that the attraction between two molecules 



k 

 is given by an expression of the form— -, where z denotes 



the distance of separation of the molecules, and k and m are 

 constants. From equation (7) we then have 



\i X =\ x c n (8), 



where c n is a function of n and m. Equations (4), (5), and 



3M2 



