in relation to Pressure, Volume, and Temperature. 397 



Andrews's figure is reproduced with Thomson's supplementary 

 curves added, drawn in dotted lines ; only the external 

 arrangement of the figure is altered, in a way first brought 

 into use by Maxwell. Namely, Andrews represented in his 

 figure the pressures by the abscissae, and the volumes by 

 the ordinates ; but it is now customary, in the mechanical 

 theory of heat, to represent the volumes by the abscissae and 

 the pressures by the ordinates, and the figure is redrawn in 

 accordance therewith. 



In the curves belonging to the temperatures 13°*1 and 

 21°*5, ae and fk are the above-mentioned straight lines cor- 

 responding to the occurrence of condensation, which J. Thom- 

 son has replaced by the dotted curved lines abcde and 

 fghik. 



J. Thomson drew his conclusion respecting the form of 

 these lines merely from the form of Andrews's curves belong- 

 ing to the higher temperatures — tracing how these latter gra- 

 dually change as they approach toward the temperature 31°, 

 and then continuing the same kind of change below 31°. 

 Upon an investigation of the reasons for this peculiar confor- 

 mation of the pressure-curves, and the formation of a mathe- 

 matical expression corresponding to them, he did not enter. 



As regards the latter point (the mathematical treatment of 

 the subject), attempts have been made by various authors, 

 some before and some since Andrews's experimental investi- 

 gation, to express the deviations of the gases from Mariotte 

 and Gay-Lussac's law by an equation. 



Rankine* constructed an equation in place of (1), with 

 which also an equation derived by Sir W. Thomson and Joule f 

 from their experiments on the changes of temperature that 

 take place during the expansion of gases very closely agrees, 

 and which in its simplest form can be written thus, 



P v=m -Tv> & 



in which c, as well as R, denotes a constant. 



HirnJ effected upon equation (1) a transformation, in 

 which the two above-mentioned circumstances that preemi- 

 nently occasion deviation by gases from the law of Mariotte 

 and Gay-Lussac, namely the volume of the molecules and 

 their reciprocal attraction, are taken into account by the in- 

 troduction of special quantities. The equation formed by him, 

 which he says is applicable not merely to gases, but also to 



* Phil. Trans. 1854, p. 336. f Ibid. 1862, p. 579. 



% Theorie mecanique de la Chaleur, 2 e ed. i. p. 195 j 3 e ed. ii. p. 211. 



