114 M. R. Clausius on the Moving Force of Heat, 



calculated must not however be regarded as expressing literally 

 the same thing as the coefficient of expansion, which latter is 

 obtained either by suffering the volume to expand under a con- 

 slant pressure, or by heating a constant volume, and then obser- 

 ving the increase of expansive force ; but wc are here dealing 

 with a third particular case of the general differential quotients 



-f7\—)f where the pressure increases with the temperature in 



the ratio due to the vapour of water which retains its maximum 

 density. To establish a comparison with carbonic acid, the same 

 case must be taken into consideration. 



At 108^ steam possesses a tension of 1 metre, and at 1.29^° 

 a tension of 2 metres. We will therefore inquire how carbonic 

 acid acts when heated to 21^°, and the pressure thus increased 

 from 1 to 2 metres. According to Regnault*, the coefficient 

 of expansion for carbonic acid at a constant pressure of 760 

 millims. is 0*003710, and at a pressure of 2520 millims. it is 

 0*003846. For a pressure of 1500 millims. (the mean between 

 1 metre and 2 metres) we obtain, when we regard the increase 

 of the coefficient of expansion as proportional to the increase of 

 pressure, the value 0'003767. If therefore carbonic acid were 

 heated under this mean pressure from to 21|°, the quantity 



^ would be thus increased from 1 to 1 + 0003767 x 21-5 



=s 1*08099. Further, it is known from other experiments of 

 Regnault t, that when carbonic acid at a temperature of nearly 

 0°, and a pressure of 1 metre, is loaded with a pressure of 

 1*98292 metre, the quantity j^v decreases at the same time in 

 the ratio of 1 : 0*99146; according to which, for an increase of 

 pressure from 1 to 2 metres, the ratio of the decrease would be 

 1 : 0*99131. If now both take place at the same time, the increase 

 of temperature from to 21^, and the increase of pressure from 



1 metre to 2 metres, the quantity ^ must thereby increase 



very nearly from 1 to 1*08099 x 0*99131 = 1*071596; andfrom 

 this we obtain, as the mean value of the differential quotients 

 d_/pv_\ 

 dt \pvj' 



We see, therefore, that for the case under contemplation a value 

 is obtained for carbonic acid also which is less than 0*003665 ; 



* M^m. de VAcad.y vol. xxi. Mem. I. f Ibid. Mem. VI. 



