26 MAXWELL'S LAW 53 



limits that the variable values lying between them give the 

 same mean kinetic energy as if all the values are possible. 

 We have merely to take one limit on the ascending and the 

 other on the descending branch of the curve at corresponding 

 places. 



/The probability that the speed of a molecule lies between 

 Aveu limits is represented on the figure by the area included 

 '^between the curve, the axis of abscissae, and the ordinates 

 corresponding to the limits. In this way we find, for instance, 

 that the probability of a value between O9 and 1-1 of the 

 most probable value is given by 0'2 x 0*8 = O16 ; that is, 

 16 molecules out of every 100, or 1 out of every 6, have 

 speeds which deviate less than 10 per cent, from the most 

 probable value. There are, on the contrary, as we similarly 

 find, about 9 molecules in every 100 which possess within 

 10 per cent, of half the most probable value, and about 11 

 in 100 with a speed equal, within the same limits, to 1J times 

 this value. There are, further, but 3 in 100 with a speed 

 4 times less than, and scarcely more than this number with 

 a speed twice as great as, the most probable. 



27. Mean Value of the Speed 



These numbers teach us, as indeed does a glance at the 

 curve, whose ascending branch is steeper than its descending, 

 that the number of particles, whose molecular speed is greater 

 than the most probable, surpasses that of the particles which 

 move with a speed less than the most probable. The most 

 probable speed is therefore not also the arithmetical mean 

 of the various speeds, but the mean value of the speed is 

 greater than the most probable. Similarly the mean value 1 

 of the,_molecular energy_Js__reater than the energy of a 

 molecule which moves with the most probable speed. 



The values of the molecular speed, which we have calcu- 

 lated in 13 by Joule and Clausius' method, from the 

 pressure exerted by gases, are, therefore, not at all the most J 

 probable values of the speed of the molecular motion. ^ 

 Indeed, we cannot strictly regard them as correct means 

 of the various speeds ; at least, they are not the arithmetic 



