'Theory of Surface Forces. 155 



By differentiation of (58) : 



.... (59) 

 Now we had : 



fR K -R,dS=id((W + rf|^ --t,^ 8 }. (55) 



I. £., if the temperature is changed by constant value of R, 

 we have : 



Sd(R K -R) = SdR K =0. 



If R= — ^ — - remains unchanged so does also the Kelvin 



quantity R K . At the critical temperature : 



j5=£l+£? an d Pl _p 2 =:0. 



Hence: P1 + P2 d f- P1 + P2I 



P 2 rfTl' 5 --^-} 



IS 



Pi— P2 d(p 1 -p 2 ) 



dT 



In the neighbourhood of the critical temperature the 



difference p— pl 9 p2 is always small, and ^m(p-- „ ) ; 



therefore a£ the critical temperature null or finite. Further 

 we have at the critical temperature : 



<&-„„ and ^-zo 

 dT - oc and dT -*. 



Hence : 



x P1 + P2 d f- Pi + P*\ 



,. P 2 dT\ P 2 J null or finite A 



lim. = -77 c = =0. 



P1-P2 d( Pl -p 2 ) -co -co 



dT 



The equation (57) becomes, therefore, at the critical 

 temperature : 



Rk-R=|^, (60) 



where f K denotes the thickness of the capillary layer at the 

 critical temperature. 



