Variation in the Pressure of Saturated Vapours, 55 



values is taken, but still it is far from being the true value, 

 and the difference is greater the more rapidly p varies. In 

 order to lessen the error it is necessary to make use of more 

 or less complex interpolation formulae. Let 



p=a + a 1 T + a 2 T 2 , 



where a, %, a 2 are arbitrary constants which may be calculated 

 from three observations. Hence 



dp _ 



dt 



= a + 2a 2 V ; 



this equation only leads to the above method, which, as we saw, 

 was not sufficiently accurate. In order to attain a greater 

 degree of accuracy, let us take the more complex formula 



p = a + a 1 T+a 2 T 2 + a B T d ; 



(T) 



the four arbitrary constants are determined from four ob- 

 servations. Hence we have 



^=a 1 + 2a 2 T + 3a 3 T 3 . 



Let the vapour-pressures corresponding to the temperatures 

 T x , T 2 , T 3 , and T 4 be p ly p 2 , p% } and p± ; we will denote the 

 differential coefficients corresponding to these pressures thus : — - 



dpi dp 2 dp% dp± 

 ~dt' ~df f ~di y ~dt' 



We will assume that tables of vapour-pressures are formed for 

 equal intervals of temperature, so that 



T 4 -T 3 =T 3 «T 2 =T 2 -T 1 =A. 



On substituting the pressures p lf p 2 , p 3y and p 4 with their 

 corresponding temperatures in equation (T), we obtain four 

 equations, from which, after a very easy transmutation, we find 



2(p 4 — Ps) — 7(ff 3 — P2)+ll (p 2 —pi) 



dpi 

 dt 



dps 

 dt 



dps 

 dt 



dp± 



~dt = ~ ~6A 





6A 







-O*- 



-p?d+3(ps- 



7>a)+ 2 (iV 



-pi) 





6A 







2(p±- 



-Pz)+Kpz~ 



•Pa) — (P3- 



-Pi) 





6A 







UCp 4 



-P3)—7(Pz- 



-p 2 ) + 2(p 2 - 



-Pi) 



y. • (ii) 



