Dynamical Theory of Heat and Light. 21 



out of the 199 points dividing AB into 200 equal parts. 



This was done by taking 100 cards*, 0, 1 98, 99, to 



represent distances from the middle point, and, by the toss of 

 a coin, determining on which side of the midd'e point it was 

 to be (plus or minus for head or tail, frequently changed to 

 avoid possibility of error by bias). The draw for one of the 

 hundred numbers (0 . . . . 99) was taken after very thorough 

 shuffling of the cards in each case. The point of entry having 

 been found, a large-scale geometrical construction was used 

 to determine the successive points of impact and the inclina- 

 tion of the emergent path to the diameter AB. The inclina- 

 tion of the entering path to the diameter of the semicircular 

 hollow struck at the end of the flight, has the same value 0. 

 If we call the diameter of the large circle unity, the length 

 of each flight is sin 0. Hence, if the velocity is unity and 

 the mass of the particle 2, the time-integral of the whole 

 kinetic energy is sin ; and it is easy to prove that the time- 

 integrals of the components of the velocity, along and per- 

 pendicular to the line from each point of the path to 

 the centre of the large circle, are respectively cos 0, and 

 sin — 0cos 0. The excess of the latter above the former is 

 sin — 20 cos 0. By summation for 143 flights we have 

 found, 



2sin0=121-3 : 2X0 cos 0=108-3; 



whence. 



S sin 0- 210 cos 0=13-0. 



This is a notable deviation from the Boltzmann-Maxwell 

 doctrine, which makes 1 (sin — cos 0) equal to 1.0 cos 0. 

 We have found the former to exceed the latter by a difference 

 which amounts to 107 of the whole £ sin 0. 



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

 integral of the transverse component i> 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. 



* I had tried numbered billets (small squares of paper) drawn from a 

 bowl, but found this very unsatisfactory. The. best mixing we could 

 make in the bowl seemed to be quite insufficient to secure equal chances 

 for all the billets. Full sized cards like ordinary playing-cards, well 

 shuffled, seemed to give a very fairly equal chance to every card. Even 

 with the full-sized cards, electric attraction sometimes intervenes and 

 causes two of them to stick together. In using one's fingers to mix dry 

 billets of card, or of paper, in a bowl, very considerable disturbance may 

 be expected from electrification. 



