Dynamical Theory of Heat and Liyld. 25 



reflection. For each path I cos 20 and I sin 26 were calcu- 

 lated and entered in tables with the proper algebraic signs. 

 Thus, for the whole 600 paths, the following summations 

 were found : — 



2/=3298; %l cos 26= + 128-8; %l sin 20= -201*9. 



Remark, now, if the mass of the moving particle is 2, and 

 the velocity one centimetre per second, 2/ cos 26 is the 

 excess of the time-integral of kinetic energy of component 

 motion parallel to BO above that of component motion 

 perpendicular to BC, and 2 / sin 26 is the excess of the time- 

 integral of kinetic energy of component motion perpendicular 

 to KK' above that of component motion parallel to KK' ; 

 KK' being inclined at 45° to BC in the direction shown in 

 the diagram. Hence the positive value of Si cos 26 indicates 

 a preponderance of kinetic energy due to component motion 

 parallel to BC above that of component motion perpendicular 

 to BC ; and the negative sign of 2/ sin 26 shows prepond- 

 erance of kinetic energy of component motion parallel to 

 KK', above that of component motion perpendicular to KK'. 

 Deducing a determination of two axes at right angles to each 

 other, corresponding respectively to maximum and minimum 

 kinetic energies, we find that LI/, being inclined to KK' in the 



direction shown, at an angle = ^ tan"" - is what we may 



_ U i. u 



call the axis of maximum energy, and a line perpendicular to 

 LI/ the axis of minimum energy ; and the excess of the 

 time-integral of the energy of component velocity parallel to 

 LL' exceeds that of the component perpendicular to LL' by 

 239-4, being \/128*«" + 20ry*. This is 7*25 per cent, of the 

 total of 2 / which is the time-integral of the total energy. 

 Thus, in our result, we find a very notable deviation from the 

 Boltzmann-Maxwell doctrine, which asserts for the present 

 case that the time-integrals of the component kinetic energies 

 are the same for all directions of the component. The 

 percentage which we have found is not very large ; and, 

 most probably, summations for several successive 600 flights 

 would present considerable differences, both of the amount 

 of the deviation from equality and the direction of the axes 

 of maximum and minimum energy. Still, I think there is a 

 strong probability that the disproof of the Boltzmann-Maxwell 

 doctrine is genuine, and the discrepance is somewhat approx- 

 imately of the amount and direction indicated. I am sup- 

 ported in this view by scrutinizing the thirty sums for 



