90 Prof. L. Boltzmann on some Questions 



stand the probability that the component velocities of a 

 molecule estimated along the axes of coordinates lie respec- 

 tively between x and x + dx, y and y + dy, and z and :+</;. 

 But in what Prof. Tait has recently said in his second paper 

 on pp. 252 and 253, I see anything but an exact and cogent 

 proof of this. That that group of molecules which he 

 designates as the minority would behave exactly as if it 

 alone were shut in between two material planes, and as if all 

 lines of centres were parallel to these planes at the moment of 

 impact, is indeed asserted by Prof. Tait, but without the least 

 proof ; for since a molecule of this minority must come into 

 collision with a molecule of the majority infinitely oftener than 

 with another molecule of the minority, in which continually 

 the x-, y-, and ^-components of the velocities are exchanged. 

 it is inconceivable why the molecules of the minority should 

 behave as if they alone w r ere present, if we do not assume 

 Maxwell's law of distribution of velocities as already proved. 

 The condition of the molecules of the minority will no 

 doubt be stationary, but also dependent upon the condition 

 of the molecules of the majority. But the relative motion of 

 the molecules of the minority with reference to those of the 

 majority is different for different values of the velocity x. with 

 which very nearly all the molecules of the minority move 

 parallel to the axis of abscissas. Hence the relative pro- 

 bability of the different values of the y- and c-components of 

 the velocity might also quite well depend upon the value of x 

 for the minority-molecules in question. 



Let us suppose, to take a case chosen at random, that as is 

 equal to twice the mean velocity of a molecule, or even some- 

 what larger. Then there wall be very few molecules of the 

 majority which have small velocities relatively to those of the 

 minority. Relative to each molecule of the minority, more 

 than half the molecules of the majority will move with a 

 velocity which is equal to the double mean velocity, or still 

 greater. Since this large relative velocity in the impacts is 

 continually transformed into velocity parallel to the Y- and 

 Z-axis, it might quite well be possible that for so large a value 

 of x amongst the molecules of the minority, large velocity- 

 components in the Y and Z direction would prevail ; whereas 

 for small values of x among the molecules of the minority, the 

 small y- and --components of velocity would predominate. 

 From the behaviour of the different groups of a communitv, 

 we can therefore only conclude that the number of those 

 molecules of the minority for which the velocity-coin ponents 

 estimated along the Y- and Z-axis lie between y and y + dy or 

 z and z + dz } as the case may be, always remains the same on 



