16 Mr. G. F. Fitzgerald on the Mechanical 



could not possibly be the source of such a force as would ex- 

 plain the motion of the arms of a radiometer. 



In amplification of a letter I wrote to ' Nature ' on the 17th 

 of December 1877, and which was published on the 4th of 

 January, 1878, I now intend to prove that such a state of 

 stress as Mr. Stoney' s theory requires would exist under the 

 assumed conditions. My letter contains a proposed applica- 

 tion of Clausius' investigation for finding the conducting- 

 power of a gas, as published in the Philosophical Magazine, 

 vol. xxiii. 4th series. Mr. Stoney, in a paper read before the 

 Royal Dublin Society on Monday, the 18th of February, 1878, 

 [Phil. Mag. Dec. 1878, p. 401] has obtained results some- 

 what like those obtained by my method by applying a method 

 similar to one he originally employed. 



I may first observe that the only way in which a state of 

 other than uniform stress can exist in a gas is by the distribu- 

 tion of the mean velocities, and number of molecules, being 

 different in different directions, or, as Mr. Stoney has called 

 it, by the gas being polarized. That the distribution is not 

 uniform when heat is being conducted through a gas has been 

 pointed out long ago by both Clausius and Maxwell ; and what 

 is required is, to show that the distribution will then be such as 

 to develop a force like Crookes's. 



Following the method adopted by Clausius in his paper 

 already referred to, I assume that the mean velocity of a mo- 

 lecule is a function of its direction of motion, and that the 

 number of molecules in the unit volume moving in a given 

 direction is also a function of that direction. If, then, we 

 define the direction by means of fi, the cosine of the angle it 

 makes with a given direction, <j> the angle the plane of these 

 two directions makes with a fixed plane through the given di- 

 rection, we may evidently assume 



where v and n are the mean velocities and number of mole- 

 cules moving in this direction, and v and n are certain given 

 values of v and n when / and F are unity. Now we may evi- 



dently in addition take n = j— N dfi d<j>, where !N" is the total 



number of molecules per unit of volume; so that we have, 

 generally, 



The quantities I intend to calculate are — the number of mo- 

 lecules carried through the unit area in any direction, the total 



