Vapour-pressure and the Volumes of Vapour and Liquid. 385 



These three equations are to be employed for the calculation, 

 because from them the values of PC, to, and W for every value 

 of 6 can be determined, which determination further leads to 

 the determination of IT, 10, and W for every value of T also, 

 if 6 is known as a function of T. 



§ 3. If we wished to carry out the calculation with the aim 

 of expressing II, to, and W directly as functions of 0, we 

 should have to treat a transcendental equation which cannot 

 be solved in a closed form. Hence, as Planck rightly says, it 

 is better first to determine all four quantities II, to, W, and 6 

 as functions of a suitably chosen new variable. Planck has 

 selected as such new variable an angular magnitude <£, which 

 he provisionally unites with another quantity r, and, together 

 with this, defines by the following equations : — 



W = ^cos 2 ^-; w=rsm 2 ^. 



I, on the contrary, have chosen, in my calculations, simply 

 the quantity log (W /to), occurring in equation (IIP), as the 

 new variable, which I have denoted by A. 



Before introducing this symbol into the above equations, 

 we w T ill somewhat further transform them. From (I.) and 

 (II.) follows directly: — 



1 27 7 1 27 



w 86><> + 7) 2 W 80(W+7) 2 ' 



and from this we get 



1 _1_ 

 27y _ to W 



$9 _J_ _L ? 



(w + yf (W + 7) 2 

 or, transformed, 



277_ (W + 7)> + y) 2 



86 ~Ww(W + w + 2y) ^ ; 



Inserting this value of 27y/S9 in equation (L), we obtain 



1 (W + 7) 2 



to Wio(W + io + 2yY 



which expression can be transformed into 



n= W + io + 2y\ l ~Ww) * ' * ( 8 ) 

 Lastly, with respect to equation (IIP); which may now be 



