62 
MR. J. J. WATERSTON ON THE PHYSICS OF MEDIA COMPOSED OF 
From this we may eliminate G by trial and error. The shortest way of making this 
computation is, perhaps, the following :— 
Assume any value A for G, and substitute it in (5), and compute the corresponding 
value of R, which let us denote by N. If we make the proportion, as the differential 
of N is to the differential of A, so is the difference between N and It to 8, the difference 
between A and G, we have 
i {(v+ - A)« - (A - A)°} - {(x/t - A)« - (xA, - A) 6 } R 
6 {(x/t - A ) 5 - (+q - A) 5 } N - IGA - A ) 5 - (A - A)G 
8, and A — 8 = A 1? 
which approximates nearer to G. Substituting this value in the place of A in the 
above equation, we obtain the next value of 8, which call S 1( and A Y — — A 2 , which 
approximates still nearer to G. 
We arrive more quickly at the exact value of G by making A — - 8 = A l5 and 
N 
A l — — 1 8j = A. z . Having thus found A l5 A.,, N, N 1? N s , we may lay off A as the 
_Llr 
ordinate to N, A : to N l5 and A. 2 to N 2 , then, drawing a curve through these points, 
the ordinate to it opposite It is G, which, in this way, may be obtained very exactly. 
As an example the following three observations are taken from Professor Magnus’s 
experiments on the elastic force of steam, that have recently appeared in the 
I4th number of the ‘Scientific Memoirs.’ 
e 0 = 0-178 t 0 =493 =(461 + 32) 
e = 3793 t = 585-1 = (461 + 124-1) 
e 1 = 29-920 q = 673 = (461 + 212) 
Computing the preceding formulae with these data, a few trials give G = 19"625. 
Then, by (3) or (4), we get H = 10"62, and by (2), from the first experiment at the 
lowest temperature, we obtain the value of F 6 , and thence F 6 (51 + 461) = 0"08, or 
3 +§-th part of an atmosphere of permanently elastic matter at 51° Fahr. 
The line on the chart which answers to the experiments of Southern and the 
French Academy has G = 19"492, and H = 10"83. 
It is obvious that one of the experiments ought to be taken at as low a tempera¬ 
ture as possible, and that F 6 should be computed from its data. 
The general formula for vapour, t = e ’ * s eas 7 f° compute when the 
tension for a given temperature is required ; but when the temperature that corre¬ 
sponds to a given tension is sought, the equation does not admit of direct solution. 
The following is, perhaps, the simplest method of overcoming the difficulty. It is 
founded on the property of the tangent to the curve of constant pressure, alluded to 
in Note B. 
