19* MAXWELL'S LAW 389 



which was employed in 28 to calculate the values of i. These 

 magnitudes G and 1 bear to the most probable value "FT the ratios 

 given by . 



it hence follows that a volume of gas V at the pressure 



P = ^ 2 = ^P&> 

 as in 27, possesses a capacity for doing work equal to 



which is as great as its kinetic energy would be if each particle 

 moved with the most probable speed W. 1 



A third mean value is also of interest, namely, that which in 

 accordance with the nomenclature adopted by Gauss in the 

 theory of least squares must be termed the mean probable value 

 or the value of mean probability. This value, which I denote by 

 0, is determined by the condition that the cases in which a 

 molecule has a less speed than occur just as often as those in 

 which the speed of the molecule exceeds the mean value 0. 



Since now the probability of the occurrence of the former case 

 is given by 



and that for the second by 



47r-i(fcm)*|" do. 



while the sum of both probabilities is 



it follows that each of the single probabilities possesses the 

 value ^. The mean probable value of the molecular speed will 

 therefore be determined by the formula 



or by 



i,r*= 



o 



1 Saalschiitz, Schr. d. phys.-okon. Ges. zu Eonigsberg, 1878, 19. Jahrg., 

 Sitzungsber. p. 45 



