1879.] 071 Molecular Physics in Hiyh Vaoia. 13'.) 



the bees arc numerous tlic mean free path is very short ; when the 

 bees are few the mean free path will be longer, the length being 

 inversely proportional to the number of bees present. Let us now 

 imagine a loose diaphragm to be introduced in the centre of the box, 

 so as to divide the number of bees equally. The same number of 

 bees being on each side, the impacts on the diai)hragm will be equal ; 

 and the mean speed of the bees being the same, tlie pressure will be 

 identical on each side of the diaphragm, and it will not move. 



Let me now warm one side of this division so as to let it com- 

 municate extra energy to a bee when it touches it. As before, a 

 bee will strike the diajDhragm with its normal mean velocity, but will 

 be driven back with extra velocity, the reaction producing an increase 

 of pressure on the diaphragm. It will be found, however, that 

 although the diaphragm is free to move, the extra strength of the 

 recoil on the warm side does not produce any motion. This at first 

 sight seems contrary to the law of action and reaction being equal. 

 The explanation is not difficult to understand. The bees which fly 

 away from the diajDhragm have drawn energy from it, and therefore 

 move quicker than those which are coming towards it; they beat 

 back the crowd to a greater distance, and keep a greater number 

 from striking the diaphragm. Near to the heated side of the dia- 

 phragm the density is less than the average, while beyond the free 

 path the density is above the average, and this greater crowding 

 extends to all other parts of the box. Thus it happens that the extra 

 energy of the im2:)acts against the warm side of the diaphragm is 

 exactly compensated by the increased number of impacts on the cool 

 side. In spite therefore of the increased activity communicated to a 

 portion of the bees, the pressure on the two sides of the diaj^hragm 

 will remain the same. This represents what occurs when the extent 

 of the box containing the bees is so great, compared with the mean 

 free path, that the abruj^t change in the velocities of those bees which 

 rebound from the walls of the box produces only an insensible 

 influence on the motions of bees at so great a distance as the 

 diaphragm. 



I will next ask you to imagine that I am gradually removing bees 

 from our box, still keeping the diaphragm warm on one side. The 

 bees getting fewer the collisions will become less frequent, and the 

 distance each bee can fly before striking its neighbour will get longer 

 and longer, and the crowding in front of them will grow less and 

 less. The compensation will also diminish, and the warmed side of 

 the diaphragm will have a tendency to be beaten back. A point will 

 at last be reached on the warm side, when the mean free path of the 

 bees will be long enough to admit of their dashing right across from 

 the diaphragm to the side of the box, without meeting more than a 

 certain number of in-coming bees in their flight. In this case the 

 bees will no longer fly quite in the same direction as before. They 

 will now fly less sideways, and more forwards and backwards between 

 the heated face of the diaphragm and the opposed wall of the box. 



L 2 



