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XIII. On the Relation of the Internal Pressure of a Liquid 

 to its Dielectric Capacity and Permeability. By W. C. 

 McC. Lewis, M.A.,D.Sc, Professor of Physical Chemistry 

 in the University of Liverpool*. 



AS a result of the work o£ Perrin, Millikan, Svedberg 

 and others, it is now known that the actual number 

 of molecules in one grammolecule is very nearly 7 x 10 23 . 

 Restricting ourselves to the so-called non-associated or 

 normal liquids, and taking as a particular case liquid fluor- 

 benzene, which according to Young possesses a gram- 

 molecular volume of 91*7 c.c. at 0° C, we find that the 

 volume "occupied" by a single molecule, or using Suther- 

 land's more appropriate term the " molecular domain/'' is 

 1*3 x 10~ 22 c.c. Hence the average distance between the 

 centres of the adjacent molecules of fluorbenzene is 

 7 x 10 " 8 cm. In the case of ethyl ether the value is 

 5xl0~ 8 cm. It follows, therefore, that the distance apart 

 of the molecules in the liquid state is of the same order of 

 magnitude as the diameter of each molecule. Owing to this 

 close packing one may expect very large values for the in- 

 ternal pressure or cohesion (ir). The relation between the 

 pressure and volume of such a system may be written by 

 analogy with the gas equation in the form 



(/>+w)(tv-t*)=BT, 



in which no assumption is made regarding ir as a function 

 of volume and temperature, and further vi denotes the 

 limiting volume " experimentally obtained,''' that is obtained 

 by extrapolating the Cailletet-Mathias linear diameter to 

 absolute zero. As is well known, the b of van der Waals' 

 equation is one-third of the critical volume, whilst the 

 " actual " limiting volume is more nearly one fourth of the 

 critical volume. Berthelot (cf. Kuenen, Die Zustands- 

 gleichung, p. 83) found that for oxygen, chlorine, carbon 

 dioxide, sulphur dioxide, carbon tetrachloride, and benzene, 

 the mean value of vi was 0*26 v c , where v c is the critical 

 volume. Guldberg some years previously had examined a 

 much larger number of substances (76 organic and 13 in- 

 organic), and had found that y c =3*75 vi or vi = 0'27 v c , the 

 mean error not exceeding 4 per cent. 



* Communicated by the Author. 



