13 PRESSURE OF GASES 25 



given circumstances is 773*3 times lighter than water at 

 4 C., 1 we must put 



p = s/773-3, 



where 5 is the specific gravity of the gas. We obtain in 

 this manner, according to Clausius's calculation, a general 

 formula for the value of the mean molecular speed of a 

 gas at 0C., which we will denote by , viz. 



($5 = 485 j\/s metres per second, 2 



which holds good for all pressures and places, though the 

 special circumstances of Eegnault's observations were 

 employed in its calculation. 



From this formula Clausius 3 has deduced the follow- 

 ing values for the mean molecular speeds of atmospheric 

 air and other gases at C. in metres per second : 



Values of & 



Air 485 



Oxygen 461 



Nitrogen 492 



Hydrogen , . . 1844 



The surprising magnitude of these numbers may serve 

 as new evidence of the degree in which heat, the cause of 

 these rapid motions, is superior to the mechanical forces 

 which are at our disposal in capability for doing work ; and 

 they further justify the assertion in 4, which is there 

 not proved, that the speeds produced by gravity in short 

 periods are too small in comparison with these speeds to 

 cause any sensible parabolic curvature in the paths of the 

 molecules. 



But, on the other hand, these molecular speeds are not 

 so great that in comparison with them gravity can be abso- 

 lutely neglected. If this were so, the continuance of an 

 atmosphere about the earth would be impossible, as all the 



1 Eegnault found p = 0-00129321 = 1/773-270, and Broch (Trav. et Mtm. 

 du Bureau Int. des Poids et Mes. 1881, pt. i. p. 49) p = 0-00129305 = 1/773-365. 



2 [Kegnault's value of p gives 484-898, and Broch's 484-928, and the 

 number 773-3 for the value of s/p gives 484-907. TB.] 



3 Pogg. Ann. c. 1857, p. 377 ; Abh. u. Warmetheorie, pt. ii. 1867, p. 256 ; 

 Mechanische Warmetheorie, 1889-91, 2nd ed. iii. p. 35, edited by Planck and 

 Pulfrich. 



