( 



271 Prof. L. Natanson on the Critical 



is by no means satisfactory, we shall in the following calcula- 

 tion take the value of A deduced for carbonic acid as that 

 which is probably nearest the truth*. 



Could the critical volume of hydrogen be evaluated, 

 equation (3) shows us that the unknown value of the critical 

 temperature of hydrogen would follow at once. In order, 

 then, to estimate the critical volume, observe that between 

 limits from 100 to about 600 atm. hydrogen sensibly obeys 

 " Bernoulli's Law," that is, the relation 



p(v-b)=m, ...... . (4) 



b being a constant quantity. (Of course equation (4) is only 

 an approximation, because otherwise a critical state would be 

 altogether impossible.) But then M. van der Waals' equation 



JP + 3 )(«-&)=» (5) 



may be said to be applicable with due approximation as well, 

 if we agree to select for the constant a some value which 

 sufficiently approaches zero. From (5) we obtain 



r,=36...(«); Pc=5yp...(£)i tc= 2UR'"^ ; ' ^ 



and 



t c ___ 86 ,_v 



p c ~ K *V> 



For hydrogen the constant a cannot be evaluated ; in the 

 particular case of hydrogen, therefore, equations (6/3) and 

 (6y) are of no use ; equations (6 a) and (7), on the contrary, 

 being independent of the value of a, may be taken to hold, 

 even if a = 0. Thus it is seen that a fairly approximate value 

 of the critical volume of hydrogen is to be found in 36. 

 From the compressibility experiments published by M. Amagat 

 in 1881, the value of b for hydrogen has been found by Prof. 

 Witkowski to be *00067 for pressures ranging from 30 to 300 

 metres of mercury, the unit volume being that occupied by 

 the gas at zero Centigrade and one atmosphere pressure; 

 and from M. Amagat's later investigation, which he published 

 in 1893, 1 myself deduced (for zero Centigrade and pressures 

 between 150 and 550 atm.) values included between '00070 

 and '00074. Assuming, then, b = '00070, we find the critical 



* In his celebrated Thesis, M. Tan der Waals has given an equation 

 •which, although in a somewhat particular form, nearly coincides with the 

 above (3). Prof. Sydney Young and M. Guye have given much attention 

 to its verification, and the values of A thus obtained would differ but 

 little from that here adopted. 



