Theory of Surface Forces. 347 



pressure and the reciprocal value of the density for every point 

 of the capillary layers which envelop the spherical drops and 

 the spherical vapour-bubbles, the minima of these curves present 

 exactly the unstable part A^B^ of the theoretical isotherm 

 of James Thomson. 



In the case that the liquid drop has its minimal size the 

 pressures p^ q . and p vap . have their maximum value, and are 

 thus given by the ordinates of the points A 8 and C H , while 

 the abscissas of these points denote respectively the reciprocal 

 values o£ the densities of the liquid and the vapour which 

 surround the spherical capillary layer. Since we do not seek 

 an exact value but only the order of greatness of R, we may 

 use for the homogeneous phase the equation of state of 

 van der Waals. The equality of the thermody mimical 

 potentials in the points A 8 and Cg gives approximately : 



2(>iiq.— Pi)v x = (pvap.— Pi)(r 2 + *W.) • • (16) 



pii q . and ^?vap. have the known significations, v 2 and i\ are 



respectively the abscissas of K and H, and denote therefore 

 respectively the ordinary vapour- and liquid-volume. Further, 

 *Vax. is the abscissa of C 8 , while the abscissas of A 8 and H are 

 considered to be equal. 



We shall at first make the calculation for ether at the 

 temperature for which the isotherm touches the axis of 

 volume; that is for the temperature T = 0'84:4:T* *. This 

 temperature is for ether, 121°*5 Celsius. The equation of 

 state of van der Waals gives for the sum of the three 

 densities which correspond to a definite pressure: 



P1+P2 + P:, = 3/o* (.17) 



For the ordinary vapour-pressure p { we have : 



I?, = — = 1*7 cm. 3 , /*., — = 27*3. and um = 3*8 cm. :; 

 Pi Pi 



Hence, r 3 = = l.j'12. The ordinary vapour-pressure p\ 



Po 



of ether at 121°'5 Celsius is 7896*2 mm. = 10*528 x 10 6 

 dyne per em. 2 



The rule of Maxwell- Olausius gives further as a first 

 approximation, p mm , being null : 



* J. D. van der Waals, Kontinuitat, p. 105 (1890). 



t We seek only the order of greatness of It and make no pretence to. 

 gixe an exact value. 



