M. Achille Cazin on Internal Work in Gases, 207 



If these effects be compared with what is known of the velocity 

 of the efflux of these gases, it will be found that the gr :ater the 

 velocity the smaller the abscissa of; hence the idea of a rela- 

 tion of cause and effect between this velocity and the depression 

 observed in my experiments. We have thus a confirmation of 

 the opinion advanced in Sections X. and XI. The depression 

 is due to the velocities acquired during the expansion. If it is 

 due to this cause alone, it must disappear simultaneously with 

 the velocities; and the prompter the extinction of these velocities, 

 the closer the point h will be to the origin of coordinates, o. 



The mobility of hydrogen is certainly greater than that of 

 carbonic acid. The molecules of hydrogen are to those of car- 

 bonic acid as a very elastic ball is to one which is but slightly 

 so. Consequently the agitation, the whirlings, which gradually 

 destroy the motion in reservoir B, must continue longer with 

 hydrogen than with other gases. On the other hand, the velo- 

 cities acquired at the moment when the expansion ceases are 

 greater for the former gas. This tends to increase the duration 

 of the agitation. Since, according to my experiments, the du- 

 ration of the depression is, on the contrary, for this gas less than 

 half of that for carbonic acid, it must be admitted that some 

 other cause influences this effect. 



We cannot find it in the action of the sides, because the line 

 X X rises less above the axis of the abscissa? for hydrogen than 

 for the other two gases ; so that the excess of heat given out over 

 that withdrawn by the sides is the least for hydrogen. Now a 

 diminution of this excess can only cause the point h to recede. 



But this effect is explained very well by a spontaneous cooling 

 which is greater for carbonic acid than for air, and independent 

 of the velocities acquired during the expansion, because the 

 sides must take so much more time to let the cooling disappear 

 the more considerable it is. Hence the question is resolved in 

 the same way as that which has occupied Messrs. Joule and 

 Thomson; but the method which I have employed enables us 

 to distinguish the influence of each of the circumstances which 

 play a part in the phenomenon ; and it is that which must be 

 done when it is impossible to eliminate them. I think the same 

 circumstances must present themselves in the experiments of 

 the English physicists, and that their method, more simple in 

 appearance than mine, cannot give exact quantities. 



The experiments which I have described do not prove that 

 there is a spontaneous cooling in hydrogen ; but they demonstrate 

 that there is in air and carbonic acid. As to the numerical 

 values, they can only be obtained approximately, as we shall 

 presently see. 



We have now to examine the differences which the parts of the 



