Dr. Schroeder van der Kolk on Gases. 189 



the constant greater velocity ; and, thirdly, the friction, in which 

 heat is indeed again produced, but which, as Clausius shows*, 

 partly passes into the sides of the vessel. In our calculation for 

 the case in which the gas issues from a globe into an exhausted 

 one, the first cause only requires to be taken into account; 

 Thomson and Joule's experiments, in which all three causes 

 cooperate, must in any case give a greater cooling, as indeed the 

 above numbers show. 



We might, indeed, consider the difference of the values in the 

 third and fifth column to be the cooling arising from the two latter 

 causes ; I think, however, that these numbers have indeed a qua- 

 litative, but only a very small quantitative value. The question 

 here is as to the difference of two very small magnitudes ; and 

 even if in Thomson and Joule's case the absolute error in the 

 determination of temperature is very small, it might yet rela- 

 tively be considerable. 



The numbers of the third column are only calculated from 

 Mariotte and Gay-Lussac's law, but these might be calculated 

 much more accurately from Regnault's experiments. In the first 

 place, the values are obtained by means of rough interpolation; 

 a more accurate calculation would not be of much use, on account 

 of the cause given in the fourth section. The formula given in 

 § II. for carbonic acid is manifestly only approximate, since the 

 coefficient of (A — l) 2 is found here to be greater than at 3°, 

 which cannot be the case if gases generally approximate to the 

 real condition with increasing temperature. It follows from 

 this that the differences of specific heats, in the case of carbonic 

 acid, change regularly, yet that the differences of these series 

 have not the desired continuity. It would have been better to 

 calculate the formula for carbonic acid at 100° from the coeffi- 

 cient of expansion by means of the method of least squares. 

 But all this only gives greater accuracy in case the fundamental 

 formula of Mariotte's law deduced from Regnault's investiga- 

 tions is more accurate than the one which occurs in his memoir. 

 It follows) further, from the theoretically deduced formulas, that 

 Thomson and Joule's result, that the cooling is proportional to 

 the difference of pressure, is inaccurate. But the deviations are 

 too small to be capable of experimental determination. 



It is interesting to remark that an ideal gas, one therefore to 

 which Mayer's hypothesis applies, would undergo no cooling in 

 the experiment with the globes, but would in Thomson and 

 Joule's experiments; for in an ideal gas the first cause for 

 cooling does not exist, though the two others do, as is easily in- 

 telligible. 



* Clausius, Abhandlungen uber der mechanischen Warmethcorie,]). 107. 



