M. Achille Cazin on Internal Work in Gases. 271 



and by introducing this value in equation (5), we obtain 



'hence 



,_ 2Aap vlf 1 J_\ 



T '=^- N V(y- N ) 2 + N ' 



N= Aqp t*; 



ktV 



Kz;' 



(?) 



The calculation is, as may be seen, very easy. 



Before applying formula (7) numerically, it is important to 

 see how formula (6) satisfies the various experiments of M. Reg- 

 nault on the compressibility and dilatation of carbonic acid. 



Mr. Rankinetook = 1*9; but I found, when all the experi- 

 mental data of M. Regnault were taken into consideration, that 

 the value a = 1*6 was more suitable. The reader will be able to 

 decide the question from the following reasoning. 



In his memoir on the density of gases*, M. Regnault says 

 that a glass globe of 9*881086 litres at zero contained 19*539 

 grms. (mean of five experiments) of carbonic acid gas at zero and 

 under the pressure of one atmosphere • from this may be deduced 

 the volume of one kilogramme of gas under normal circum- 

 stances, 



i? =0-50571 cub. m. 



By means of the Table on page 236 of vol. xxvi. of the Me- 

 rnoires de VAcademie des Sciences de Paris, we obtain 



v =0*38307 cub. m. 



at zero, under the pressure of 1000 millims. of mercury. The 

 specific volume at zero and under various pressures may after- 

 wards be calculated by means of the formula on page 426, vol. 

 xxi. of the same Memoires, which gives the results of experi- 

 ments made on carbonic acid at about 3°; at zero the same for- 

 mula is admitted. Finally, in the memoir on the dilatation of 

 gasf, we find (p. 112) that, under the pressure of 3589 millims. 

 of mercury, the binomial of dilatation at constant volume from 

 0° to 100° is 



1 + 100 « = 1*38598, 



* Mem. de VAcad. des Sciences de Paris, vol. xxi. pp. 147 & 155. 

 t Mem. de I' Acad, des Sciences de Paris, vol. xxi. 



