Variation in the Pressure of Saturated Vapours. 61 



has already been explained that T is also not arbitrary, 

 because this number has a physical significance, and r and 

 p , being dependent upon T , are therefore also not arbitrary. 



Thus, as was said above (§ 1), formula (5) does not contain 

 any arbitrary quantities. 



9. I foresee the possibility of yet another objection. Let 

 us imagine two curves of a different nature, and, by the aid 

 of differential coefficients, bring three points of one curve 

 into coincidence with three points of the other curve ; and 

 let us, moreover, assume that these common points approach 

 each other for an infinitely small, or at least exceedingly 

 small, distance. According to the common property of 

 curves, they diverge very gradually as they pass from the 

 three common points, and only diverge to a great extent at 

 a very remote distance from the common points. From 

 this it might be concluded that the fact of the curve (7) and 

 the curve of the actual vapour-pressures being near each 

 other about the common points, and even at a considerable 

 distance from them, does not prove the truth of the above 

 theory. Such a view would be unfounded. In order to 

 prove this, let us take any formula with three arbitrary 

 coefficients, for instance the parabolic formula 



p = a + a 1 T + a 2 T 2 , ..... (5J 



and assort the constants a, a^ and a 3 in such a manner that 

 the formula would satisfy temperatures 65°, 70°, and 75° ; 

 t. e. so that the curve expressed by formula (5i) would pass 

 through three points lying on the curve (5) and on the curve 

 of the actual vapour-pressures. It is then seen that 



a=18513*75, a^l.16-7576, a 2 = O185020. 



The vapour-pressures calculated according to formula (5 X ) are 

 given in the 5th column of the preceding table. We see that 

 even at temperatures near 70°, for example at 40° and 100°, 

 the figures in this column differ considerably from those of 

 observation, and at remote temperatures, for instance 20° and 

 220°, there is not the slightest analogy. Thus formula (5^ 

 has nothing in common with that function which expresses 

 the dependence of a vapour in a state of saturation on the 

 temperature. 



The properties of Roche's formula (§ 2) are different; having 

 a theoretical basis, it somewhat closely satisfies the results of 

 observation. A formula analogous to it may, as we saw, be 

 obtained from the equation 



log jr"Ki~T)- 



