EXPERIMENTAL KNOWLEDGE OF THE PROPERTIES OF MATTER. 129 



■some one substance. The results of these can then be used to enable us 

 to calculate for a large variety of substances and circumstances, numerical 

 data which could not otherwise be got without the most laborious and 

 tedious investigations. 



One case of this is that of Clausius' formula ' u= — for 



^ v-a T (v-fiy 



the relation between the pressure, volume, and absolute temperature of a 

 gas ; Sarrau ^ has determined the constants in this equation for several 

 gases by Amagat's results, and has deduced the critical temperature, 

 pressure, and molecular volume for oxygen, carbon dioxide, nitrogen, 

 and marsh-gas. 



In 1873 Van der Waals first published at Leiden his dissertation ' On 

 the Continuity of the Gaseous and Liquid States,' in which he predicts 

 some of the most striking of the results which Amagat five or six years 

 afterwards firstpublished, and long before his most complete and exhaustive 

 treatment of the gases he examined was concluded ; and in this disserta- 

 tion, of which a German edition was published at Leipzig in 1881, he 



proposed a formula (p + ^^ (v-h) =U{l + at) (p. 62, Leipzig edition) 



as a general relation between volume, pressure, and temperature for a 

 gas ; the constants in the equation must of course be determined for each 

 gas.^ Baynes calculates from the formula a series of values of pv for 

 ethylene,_ which agree remarkably with the numbers found by Amagat 

 by experiment. Amagat applies Clausius' and Van der Waals' formulae 

 to the case of COj, and finds'* a portion of the gas well represented by 

 calculations from their formulae, but that neither his nor Clausius' formula 

 represents the whole of his curves. 



Critical Temperatures and Pressures. 



Faraday having shown how certain gases might be liquefied, and 

 liaving himself liquefied a number of those which under ordinary condi- 

 tions are gases, Cagniard de la Tour ^ showed that when certain liquids 

 were gradually heated in a sealed tube partly filled, suddenly at a certain 

 temperature the line of demarcation between liquid and vapour dis- 

 appeared, and there was nothing to distinguish one part from another 

 part of the tube. 



Thilorier had noticed ^ that COg liquid from 0° to 30° expands four 

 times as much as COg gas between the same temperatures. 



Andrews ^ investigated the efiecta of pressure on COj at different 

 temperatures, and arrived at the conclusion that above the temperature 

 •30-9° C. no pressure however great can liquefy the gas, that is, separate 

 it in the tube in which it is confined into two portions, one denser than 

 the other, separated by a line of demarcation. 



At any temperature below 30-9° he showed that by some pressure 

 under 74 atmos the gas can be liquefied; and at a temperature the 



* Wled. Ann. 1879, t. ix. p 127 ; Annales de CJtim. 1883, xxx. p, 358. • 

 - C.R. xciv. pp. 639 and 718 ; J.C.S. Aba. 1882, p. 686. 



^ See Baynes on ' Critical Temperature of Ethylene ' in Nature, vol. xsiii. 18S0-1, 

 < Annales de dhlmie et de Physique, 1883 (5), xxviii. pp. 500-502. 



* Ibid. (2), xxi., xxii. 



* Ilnd. 1835 (2), Ix. p. 427. ' Phil Trans. U.S. 1869. 

 1886. 



