Variation in the Pressure of Saturated Vapours, 49 



inconsiderable portion of it between the origin of coordinates 

 and the first inflexion, beyond which observations are never 

 carried. Moreover, it must be remembered that the formula 

 under consideration refers only to certain special conditions, 

 one of which is never actually fulfilled, namely — that the 

 volume of a liquid is equal to zero compared to the volume 

 of the vapour formed from it, so that the curve represented 

 by equation (p) serves to express the actual variation of the 

 pressure of a vapour, and would only fully express these 

 variations if the above conditions were strictly observed *. 



The temperature of the first point of inflexion is very high. 

 For water, for instance f, 



R = 5106-2 + 5-294:8 x 343 = 6922-3 ; 



T 6922-3 / 1 \ 



il ~ 5-2948 V 1 " ^5-2948/"^ *' 



The highest temperature of steam attained by Regnault was 

 only 230°. So also it is easy to find that for sulphuric ether 

 the first inflexion of the curve corresponds to 743°'2, for 

 benzene 886°-7, sulphur 1279°. 



With the majority of the substances I calculated for, x is a 

 positive quantity, but it is sometimes negative and may be equal 

 to zero ; R was always positive. If x < 0, when its absolute 

 magnitude > 1, then it is easy to prove, from the above- 

 mentioned equations (p), (pi), and (P2), that as T varies 

 from zero to infinity, the curve diverges continuously from 

 the axis of abscissae, and always turns its convexity towards 

 this axis, without giving any special points. 



We may add that it would be absurd to deduce any 

 properties of a vapour from the properties of the curves and 



* My paper " On Van der Waals' Formula " (Russian Physico-Chemical 

 Society, vol. xix.) proves that for all substances the second differential 



coefficient — S where p is a function of v and t, is greater than zero, and 

 at £2 



that it is only for perfect gases that ^-f =0. This may seem a contra- 



diction to the above, because the value of —£ for the curve (5) is either 



less or equal to zero. In reality there is no contradiction at all. To be 

 concise, 1 will only observe that the curve expressed by equation (p) 

 presents the variation of the vapour-pressure under certain conditions 

 and within certain limits ; in the given instance it only applies for that 

 portion of the curve which lies between the origin of coordinates and the 



first point of inflexion, and then the condition that ~-f >■ is fulfilled. 



t In order to calculate E, and T x it is necessary to know x a i5. T x ; tli6 

 mode of determining these quantities is given below. For water x = 5-2948, 

 T =343° [6]. 



Phil. Mag. S. 5. Vol. 37. No. 224. Jan. 1894. E 



