38 Prof. Tait on the Motion 



Let / 



- = COS a, 



e ' 



sin B 



tan y = = • 



* /3 + « /3-a 

 2 cos — - — cos — 5 — 

 2 'id 



There may be transmission of power from the source of e to 

 the source of/ even when /> e, provided that /cos is not > e; 

 as would appear at once from a geometrical construction on 

 the plan given above, and in any case the condition of maxi- 

 mum efficiency is one of stability. 



V. Note on the Motion of a Gas " in Mass." 

 By Professor Tait*. 



THE objections raised by Mr. Burbury and Prof. Boltz- 

 mann to certain parts of my first paper on the Kinetic 

 Theory of Gases were such as 1 could understand ; and my 

 reply to them seems to have been accepted as sufficient. 



Mr. Burbury now (Phil. Mag. Dec. 1887) raises an objec- 

 tion, which I do not understand, to an assumption made 

 (after Clerk-Maxwell and Clausius) in my second paper. This 

 objection is based upon a Theorem which Mr. Burbury sup- 

 poses to have been established by Prof. Boltzmann. The 

 passage objected to is as follows (the italics are not in the 



original) : — " except in extreme cases, in which the 



causes tending to disturb the ' special ' state are at least nearly 

 as rapid and persistent in their action as is the process of 



recovery, we are entitled to assume that in every part 



of a gas or gaseous mixture a local special state is maintained. 

 And it is to be observed that this may be accompanied by a 

 common translatory motion of the particles (or of each sepa- 

 rate classy of particles) in that region ; a motion which, at 

 each instant, may vary continuously in rate and direction 

 from region to region ; and which, in any one region, may 

 vary continuously with time. This is a sort of generalization 

 of the special state, and all that follows is based on tJie assump- 

 tion that svch is the most general kind of motion which the parts 

 of the system can have, at least in any of the question* hen 

 treated. Of course this transactional speed is not the same for 

 all particles in any small par* of the system. It is merely an 



* Communicated by the Author. 



f The " classes " here spoken of are different kinds of gases, not (as in 

 Mr. Burbury's paper) groups of particles of one gas which have nearly 

 the same speed. 



