1893-94.] Prof. Tait on Compressibility of Fluids. 249 
The rest of the paper deals with (unsuccessful) attempts to 
apply, to Amagat’s data, the equation of Yan der Waals : — viz. 
The arguments in consequence of which the constituent was 
originally introduced and, as I have elsewhere* endeavoured to 
show, incorrectly introduced, were specially based upon the pro- 
perties of liquids, rather than of fluids in general ; and it is there- 
fore to be expected that the formula, if valid, should be specially 
applicable to liquids. 
The most valuable characteristic of the equation above, in addi- 
tion to its special merit of giving in certain cases three real values 
of Vj and therefore, in a sense, representing the results of Andrewf' 
and the conclusions of J, Thomson, is its simplicity. But this 
simplicity depends essentially upon the understanding that A, yS, 
and R are genuine constants ; or, at least, may be treated as such 
through moderate ranges of volume : — as, for instance, in the com- 
pression of an ordinary liquid by 3000 atmospheres. The equation 
loses its value (from this point of view) entirely if, as has been 
suggested, y8 is a sort of adjustable constant ! For if it be so, it 
ought to be expressed as a function of or of v and and then 
the simplicity of the whole is gone. 
Selecting, as before, a set of three corresponding pairs of values 
of p and V for any one temperature, we form three equations which 
lead to a quadratic in A, when y8 and R are eliminated. This 
involves heavy numerical work, and the results are so much modi- 
fied by very slight changes in the data (quite within the limits of 
experimental error) that I was fain to try the simpler process of 
assuming tentative values for A, and determining the other con- 
stants from them : — the equations being then linear. But I found 
that very wide ranges of tentative values of A seemed to suit the 
conditions, to the same (extremely rough) approximation. I could 
get nothing satisfactory. The reason is easily found by making a 
case in which the labour of calculation shall be, to a considerable 
extent, avoided. It is clear, from the numbers in the early part of 
* Trans. R.S.E., xxxvi. ii. (1891). See also Correspondence with Lord 
Rayleigh and Prof. Korteweg {Nature^ xliv. and xlv. ). 
