386 



Lord Kelvin 



[April 27, 



above the former is sin — 20 cos 0. By summation for 

 143 flights we have found, 



whence, 



2sin0= 121-3; 2 2 0cos0 = 108-3 ; 

 2sin0 - 22 0cos0 = 13-0. 



This is a notable deviation from the Boltzmann- 

 Maxwell doctrine, which makes 2 (sin — cos 0) equal 

 to 2 cos 0. We have found the former to exceed the 

 latter by a difference which amounts to 10 -7 of the whole 

 2 sin 0. 



Out of fourteen sets of ten flights, I find that the time- 

 integral of the transverse component is less than half the 

 whole in twelve sets, and greater in only two. This 

 seems to prove beyond doubt that the deviation from the 

 Boltzmann-Maxwell doctrine is genuine ; and that the 

 time-integral of the transverse component is certainly 

 smaller than the time-integral of the radial component. 



§ 39. It is interesting to remark that our present 

 result is applicable (see § 38 above) to the motion of a 

 particle, flying about in an enclosed space, of the same 

 shape as the surface of a marlin-spike (Fig. 7). Symmetry 

 shows, that the axes of maximum or minimum kinetic 

 energy must be in the direction of the middle line of 

 the length of the figure and perpendicular to it. Our 

 conclusion is that the time-integral of kinetic energy is 

 maximum for the longitudinal component and minimum 

 for the transverse. In the series of flights, corresponding 

 to the 143 of Fig. 6, which we have investigated, the 

 number of flights is of course many times 143 in Fig. 7, 

 because of the reflections at the straight sides of the 

 marlin-spike. It will be understood, of course, that we 

 are considering merely motion in one plane through the 

 axis of the marlin-spike. 



§ 40. The most difficult and seriously troublesome 

 statistical investigation in respect to the partition of 

 energy which I have hitherto attempted, has been to find 

 the proportions of translational and rotational energies 

 in various cases, in each of which a rotator experiences 

 multitudinous reflections at two fixed parallel planes 

 between which it moves, or at one plane to which it is 

 brought back by a constant force through its centre of 

 inertia, or by a force varying directly as the distance 

 from the plane. Two different rotators were considered, 

 one of them consisting of two equal masses, fixed at the 

 ends of a rigid massless rod, and each particle reflected 

 on striking either of the planes ; the other consisting of 



