TRANSACTIONS OF SECTION B, 833 



high ; for acetic aid — and ,- are high, hut — very low. The marked dif- 



<^o 9o . . 9o 



ferences between the alcohols and acetic acid, and the large deviations in both cases, 

 are probably to be accounted for by the fact that the molecules of the alcohols at 

 moderate temperatures are polymerised in the liquid, but not the gaseous state, 

 whilst with acetic acid there is polymerisation in both states. 



The ratios =- at the critical point should, according to Van der Waals, be 



the same for all substances, the molecules of which undergo no dissociation or 

 polymerisation, and he gives the value of this ratio as § or 2"6. Now the ratio 

 depends on the constant b in the equation 



(;,+ ?j)(i>-6) = RT, 



and Van der Waals takes b to be four times the actual volume of the molecules 

 in unit mass of substance ; 0. E. Meyer, however, contends that 6 = 4 x ^2 

 times the volume of the molecules, and it has been pointed out by Heilborn and 

 by Guye that, if that is so, the ratio 2-6 should also be multiplied by \/2, which 

 would give the value 377. It is remarkable that the mean value for the twelve 

 substances in group (1) is 3'77, from which it may be concluded that the 

 molecules of these substances in the critical state are simple like those of the gas. 

 (At the same time it is to be noticed that with the three normal paraffins and 



the two tetrachlorides — , shows a slight increase with rise of molecular weight. 



The ratios for the ten esters are a little higher (3"87 to 3'95) ; decidedly 

 higher for the alcohols, especially methyl -alcohol (4'52— 4-02), and much higher 

 for acetic acid (5'00). It would appear from this that the molecules of the 

 alcohols and acetic acid are polymerised to a considerable extent at the critical 

 point, and this conclusion is supported by the generally abnormal behaviour of 

 these substances, and agrees with that of Ramsay and Shields, that in the liquid 

 state at moderate temperatures their molecules are decidedly complex, whilst 

 those of the majority of the compounds examined by them are probably simple. 



I hope to continue the investigation of the paraffins and other hydrocarbons 

 in order to obtain further light on the points referred to, and it will be of interest 

 to compare the molecular volumes at the critical points, and at a series of reduced 

 pressures. 



The accurate determination of the critical constants is a matter of great 

 importance. It is best to employ an apparatus similar in principle to that of 

 Andrews, in which the temperature, pressure, and volume can be altered at will ;. 

 though the critical temperature may be determined with but small error in a 

 sealed tube, if the quantity of liquid taken is such that its critical volume is 

 approximately equal to the capacity of the tube. V/ith a pure substance, free 

 from air, two independent determinations of the critical temperature should 

 certainly not ditter by 0°1, unless the temperature is above 300°, when the 

 experimental difficulties are greater. The error in the determination of the 

 critical pressure should not exceed 0'2 per cent., but the critical pressure is greatly 

 affected by the presence of even very small quantities of impurity (and, of course, 

 of air) ; and in comparing two specimens of the same substance, one of which is 

 known to be pure, the agreement of the critical pressure is probably the most 

 delicate test of the purity of the other. 



The only method yet known by which the critical volumes can be accurately 

 determined is the indirect one based on the ' law of diameters ' of Cailletet and 

 Mathias. These physicists made the very important discovery that the mean 

 densities of liquid and saturated vapour for any 'normal' substance are a linear 

 function of the temperature (or D =Do— a^ where 13 = the mean density), and 

 since, at the critical point, the two densities are equal — or rather there is only 

 one — the value of D at that point gives the critical density, from whicli the 

 critical volume is, of course, easily calculated. I have been able to show that the 



1898. 3 H 



