( 284 ) 



and in the same way 



dp Öpc 



The first conclusion we draw from this is, that at the critical 

 temperature the liquid branch and the vapour branch have always 

 the same tangent, and therefore touch. The initial direction is given 



by the quantity — ^ or by ( — I . But as at the critical temperature 



/öoA rdp\ 



i\ =z V,, the mQan value of -- is equal to the value which ( v" 



has at that volume equal for vapour and liquid. We have therefore 

 at the critical temperature : 



yd.vjT \ilvjT yd.vJoT 

 or 



1 /dp\ _ 1 /dp\ _ 1 /Ö/A _dlpc _ dlT,. dlh 



p \d.v^Ji p \cIv^Jt P \px)rT o.v ' (Ix dx 



The second conclusion we draw is that at the critical temperature 

 1 /Ö/A UllT, 1 dlb\ 



p \OxJcT { dtV b dx] 



which has been put in the preceding communication, but has not 

 been proved there. 



/"dp^ /dp\ /öp-\ 



That at the critical point -— and -r— is equal to v" 



\dxjT \dxjT \dxJ,.T 



we might have immediately concluded, without following the elaborate 



way by which we have now arrived at this conclusion. In the same 



/dp\ /dp\ 

 way that at the critical point [jTpj — I ^ I • 



Let us tirst consider a simple substance. If we pass from one homo- 

 geneous phase to another, at which v is increased by (h, and T 

 by'clT, then 



If I ^] =0, as is the case at the critical point, then : 

 \avjT 



and so every -^ = 1 ^] , also with such a change at which the 

 ^ dT \pTj^ 



