Mr. GJ-. J. Stoney on Crookes's Radiometer. 181 



9. Instead of the actual condition of the molecules which 

 come into collision with the heated disk, we may substitute 

 one more convenient for calculation. The resulting pressure 

 will be the same as if some moderate proportion of the mole- 

 cules, say one third of them, had reached it with velocities 

 corresponding to the temperature 15°'l, while the remaining 

 two thirds reached it with velocities corresponding to 15°. We 

 may further regard the increased pressure on the disk caused 

 by the former class of molecules as equal in amount to the 

 portion which is compensated by the slight reductions of 

 density in the neighbourhood of the disk, and by the slightly 

 increased temperature and density elsewhere, which are due 

 to the existence of a portion of the gradient. Under this 

 hypothesis the effect of these molecules may be left out 

 of account. There would, however, remain the augmented 

 pressure arising from the other two thirds of the molecules, 

 uncompensated so far as regions behind the disk are con^ 

 cerned ; and it is the amount of this pressure which we have 

 now to estimate. The molecules in question reach the disk, 

 according to the hypothesis, with velocities corresponding to 

 15°, and are thrown off from it with velocities corresponding 

 to 15°-1. It is easy to see that the augmentation of pressure 

 which they will produce upon the disk, will be half what 

 would arise if they had reached the disk as well as left it with 

 velocities corresponding to the higher temperature. This 

 latter can be calculated by Boyle and Mariotte's law. It is 



two thirds of a decigramme x -^-^ — --, or 0*000,023 of 



a gramme per square centimetre. The uncompensated excess 

 of pressure on the disk will, upon the assumptions we have 

 made, be half of this, or 0*000,011,5 of a gramme per square 

 centimetre, the amount as determined experimentally by Mr. 

 Crookes being 0*000,01. Accordingly an elevation of the 

 temperature of the blackened face of the disk to the extent of 

 about one tenth of a degree above the temperature of the glass 

 and the back of the disk, is enough to account for the observed 

 pressure. 



but it is more active in front of the disk than behind, and causes increased 

 pressure there, because the addition made to the motions by the heated disk 

 has a direction as well as a quantity ; and it has a direction, because cool, i. e. 

 slow-moving, molecules can crowd up to the disk and are thrown off by it 

 with their velocities increased. This does not happen if what I have 

 called the gradient is complete. In that case the swift molecules within 

 the limits of the gradient are sufficiently numerous to be able to keep 

 back the slower-moving molecules beyond ; accordingly the molecules 

 that reach the disk have as high velocities before as after their contact 

 with it ; there is therefore no resultant in any direction of their mo- 

 mentum. In nearly perfect gases this state of things is nearly realized ; 

 and accordingly such gases do not conduct heat. 



