1904.] Physical Constants at Low Temperatures. 



261 



when the pressure is great, the ratio bjv cannot be neglected and the 

 critical temperature is a greater multiple of the temperature of 

 inversion. The second of these equations shows that the initial 

 pressure must not exceed nine times the critical pressure. Assuming 

 a critical pressure of 16 atmospheres for hydrogen and taking 

 p =117 atmospheres and t = 192°, this equation gives the critical 

 temperature as 42° absolute. Again, for^> c =15 atmospheres, t c = 46° 

 and f or t c = 32°, p c = 41 atmospheres. 



Results derived from a discussion of similar equations depending 

 on Clausius's formula, Berthelot's " modified " Van der Waals's, or 

 Reinganum's formula, are still farther from the value we expect. 



In part explanation of this failure it is to be noted that these 

 formulae are but the best theoretical approximations we have at hand, 

 and while they are useful within short ranges, we can hardly expect 

 the same accuracy over a temperature range of five or six times the 

 critical temperature. 



Again, for a very large number of bodies the product of a, the 

 co-efficient of expansion at the boiling point, and the critical tempera- 

 ture is constant and about 0'6 to 0*7. 



Thus for oxygen from equation (2), we have cd c = 0*61. For 



nitrogen we get at c = x 127 = 0*79, but for hydrogen 



we have — 0054 x 34 = 0*45 and even if we take the critical tem- 

 0-07 x 5-8 



perature as high as 42, oct c only reaches 0'56. 



7. There are, therefore, as far as we can see at present, and as far 

 as theoretical considerations can aid us, great departures shown by 

 hydrogen from what are fairly general results. Van der Waals's / 

 and Trouton's constant are each only about half the usual values ; and 

 we have now found, from the consideration of the point of inversion 

 of the Joule-Thomson effect, and of the product at c , variations greater 

 than the average from the values we should have expected. Further 

 experiment will be necessary before these discrepancies can be 

 cleared up. 



VOL. LXXIII. 



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