498 REPORT—-1904. 
all mixtures without carrying out special experiments to find the value of ec. Itis, 
therefore, a matter of considerable interest to ascertain whether c is really equal to 
Pa 
mP, + (100—m)Ps 
100 
cation of Brown’s formula, or that of Lehfeldt, or of Zawidski, must be employed to 
calculate the vapour composition, and the constants for those formule must first be 
determined experimentally. 
Other physical properties, such as the refractive power of mixtures, might be 
considered, but I will only refer to the critical temperature and pressure. In 1882 
Pawlewski stated that the critical temperature of a mixture could be calculated 
m6, + (100 — m)6z 
100 : 
is the percentage by weight of A; and G. C. Schmidt, in 1891, carried out experi- 
ments to test the correctness of the statement, purposely choosing substances of 
widely different physical properties. The differences between the calculated and 
observed temperatures were not, as arule, very great, rarely exceeding 4°, and 
Schmidt considered that they might, to some extent, be accounted for by partial 
decomposition of one or other component. 
Such determinations are, however, liable to serious errors. It is exceedingly 
difficult to filla tube with the required amount of a liquid mixture of known 
composition quite free from air, and, although the composition of the very small 
amount of liquid employed might be determined after the experiment from its 
specific refractive power, it would be necessary to know the specific refractive 
powers of the two components and of mixtures of them. Schmidt does not state 
how he prepared his mixtures and determined their composition. 
Again, when a liquid mixture is heated in a sealed tube, fractionation goes on, 
so that the more volatile component tends to accumulate in the upper part of the 
tube, leaving the less volatile component in excess below, and unless a stirring 
arrangement, such as that devised by Kuenen, is employed, many hours would elapse 
before complete admixture by diffusion took place at the critical point. 
By far the most important and accurate experiments on this subject have been 
carried out by past or present pupils of Professor Kamerlingh Onnes, notably by 
Professor Kuenen; and it is quite certain that the formula of Pawlewski cannot be 
generally true for mixed liquids, for, just as we may have mixtures of minimum or 
maximum boiling-point, so also, as Kuenen has shown, mixtures of minimum or 
maximum critical temperature may exist, Thus the critical temperature of carbon 
dioxide is 31°1, and of ethane, 32°:0, but that of a mixture containing 30 molecules 
per cent. of carbon dioxide is 18°8. The question remains, however, whether some 
such law as that proposed by Pawlewski may not hold good for closely related 
substances. In certain cases, when the relationship is very close (for example, 
C,H,Cland C,H,Br), the critical pressures are equal, or very nearly so, and it seems 
probable that the critical pressure would be the same for any mixture as for the 
components. Such a case as this would be likely to give the simplest possible 
relation between the critical temperatures of a mixture and those of its com- 
ponents ; and although the critical temperatures of these substances are incon- 
veniently high, there are, no doubt, others which might be employed—perhaps etbyl 
chloride and bromide, or possibly carbon dioxide and carbon disulphide. I imagine, 
however, that Pawlewski’s formula would be more likely to hold if m represented 
the moleculur percentage, and not the percentage by weight of A. 
In the case of homologous compounds, paraffins, ethers, esters, and so on, the 
critical pressures are not equal, and it would be necessary to find whether the 
mPa + (100 —m)Px 
100 
(where m is the molecular percentage of A), and also whether any such simple 
formula is applicable to the critical temperatures. 
Kuenen has made some observations with mixtures of ethane and butane con- 
taining 2°5 and 5 molecules per cent. of butane, and at the conclusion of his paper 
When the equation P = does not hold good, a modifi- 
from those of the components by the formula 6= where m 
critical pressures of mixtures are represented by the formula P = 
