1904.] Physical Constants at Low Temperatures. 259 



range from that of carbonic acid to that of hydrogen ; and came to the 

 conclusion that the co-volume is one quarter of the critical volume, at 

 least for low pressures. 



Guldberg* from a careful graphical discussion of Young's results 

 arrived at the conclusion that the critical volume is 3 '55 times the 

 volume at absolute zero. 



An independent examination of the reduced curve for Young's fluor- 

 benzene showed that the reduced volume for a reduced pressure 

 between * 05 and • 10 is very approximately • 4, in other words, that 

 the critical volume is two and a half times the co-volume. And it is 

 to be noted that the variations of the reduced volume in this neighbour- 

 hood are very slight compared with the change of the reduced pressure. 

 Further, this range of reduced pressure will cover the extent of the 

 present experiments whatever may eventually prove to be the value of 

 the real critical pressure. My old experiments gave as a maximum a 

 critical pressure of a little over 15 atmospheres. 



Hence taking Van der Waals's 5=12 for hydrogen, these results give 

 respectively 48 c.c, 42 "6 c.c. and 30 c.c. as the critical volume, with the 

 corresponding critical densities, 0*0208, 0*0235, and 0*033. 



What further considerations can be brought to determine between 

 these results 1 Van der Waals gives, for corresponding states of two 

 bodies, the equation! 



<L = ML IL C 1 

 d' M! t e p'c 9 



where d is density and M is molecular weight. Now in the liquid 

 states for moderate pressure, the density changes but slightly, hence 

 we may assume with very little error that the boiling-point densities 

 belong to corresponding states. Comparing, therefore, hydrogen with 

 oxygen, we get : — 



0j070 = 2_ p e 155 U = o. 15 . 

 1*138 32 t e 50 p c 



and comparing hydrogen with nitrogen we have, 



0*07 _ 2 p c 127 Qr t c 2 . 93 

 0*79 28 t c 35 p e 



hence, taking the mean, we have for hydrogen t c /p c = 3*04. Now, 

 Van der Waals's theory makes p c v c lt c = § R, but experiment seems to 



require pcVcjU to be equal to — ^ E, and when p is measured in 

 atmospheres, R = 41*0183 for hydrogen, for which, therefore, 



PcVc = 41*0183 

 t e ' 3*77 



10*8801. 



* Loc. ext. 



f "'Continuity, &c." (English, translation), p. 491. 



