306 Mr. S. H. Burbuiy on some Problems 



u mass motion.'" I prefer to call it a motion of simple trans- 

 lation. Since the equation ¥ F f p = F P //yis satisfied by such 

 a motion, the distribution of velocities is unaffected by en- 

 counters. As is otherwise also evident, because the motion 

 of translation does not affect the relative velocities, it is not 

 necessary that u should be small. It may, for instance, be the 

 earth's motion in space. If, however, u be very small in a 

 motion of this kind, the number per unit of volume of mole- 

 cules of mass M whose velocities are between co and co + dco in 

 direction X//,vcZS is 

 /AM\f 



M W ) 6 ~ Mfw2(y2 d «> <*S(1 + 2XAM«m), 

 the direction of u being taken for axis of x. 



On Disturbed States of a Gas. 



11. Thus far we have treated only of a gas at rest or in 



simple translation, in both of which cases— =0. Both may 



be regarded as normal states. We come now to consider cer- 

 tain disturbances in which, by the action of external causes, 

 the gas is maintained in a state differing from the normal state. 

 We might suppose generally the number per unit of volume 

 of molecules of mass M having velocities Xfjuvco 2 dco <iS 

 to be 



F{cD)G> 2 dG>dS, 



and 



FW=N (™)V" M » 2 { 1 + 2C« Y<}, 



where the Y's are any spherical harmonic functions referred 

 to the origin, the C's functions of co, and 2C,Y t - is supposed 

 very small compared with unity. In the problems with which 

 we shall deal the harmonics will be of the first and second 

 orders only. 



12. In such a system H differs from the minimum value 

 which it would have were there no external disturbing causes. 

 Encounters between the molecules tend to diminish H, and 

 so to reduce the system to the normal condition, and the rate 

 of diminution of H increases with the increase of the distur- 

 bance. If there be an external cause always producing the 

 disturbance at a constant rate, a state of steady motion will 

 be reached in which the disturbance is diminished by encoun- 

 ters as fast as it is increased by the operation of external 



7TT 



conditions. We shall denote by — the time- variation of H 



