28 



Lord Kelvin on the 



§ 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 perpen- 

 dicular 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, corre- 

 sponding 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, 



§ 10. The most difficult and seriously trouble- 

 some statistical investigation in respect to the 

 partition of energy which I have hitherto 

 attempted, has been to find the proportions of 

 translation al 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 two masses, 1 

 and 100, fixed at the ends of a rigid massless 

 rod, the smaller mass passing freely across the 

 plane without experiencing any force, while 

 the greater is reflected every time it strikes. 

 The second rotator may be described, in some 

 respects more simply, as a hard massless ball 

 having a mass = 1 fixed anywhere eccentric- 

 ally within it, and another mass = 100 fixed at 

 its centre. It may be called, for brevity, a 

 biassed ball. 



