7-0 Dr. T. J. Fa. Bromwich on Kinetic Stability. 



"end-on" to " broaclside-on " increases the surface conduc- 

 tivity by 34 per cent. 



The thanks of the author are due to Mr. Gold for sug- 

 gesting some of tbe problems, and to Mr. G. M. B. Dobson 

 for many valuable suggestions and kind cooperation in 

 numerous ways. 



Koyal Aircraft Establishment, 

 Farnborough, 



Sept. 1919. 



V. Kinetic Stability. 

 To the Editors of the Philosojyhical Magazine. 

 Gentlemen, — 



ALTHOUGH the idea of Kinetic Stability appears to 

 . be of considerable importance in certain Dynamical 

 investigations, yet there are misunderstandings to be found 

 in even some of the best text-books ; and at the moment I 

 am aware of only one book * which contains a good account 

 of the theory accompanied by two or three well-chosen 

 examples. 



Still I should hardly have troubled you with these remarks, 

 if I had not chanced to come across a very misleading 

 statement on the subject of Kinetic Stability in Mr. 

 Jeans's recent Adams Prize Essay j\ On account of the 

 author's reputation, and of his very attractive presentation 

 of the subject-matter, it seems likely that this Essay will 

 soon be one of the standard sources of information on cosmical 

 mechanics. It therefore seems desirable to warn readers 

 against the oversight, so that they may not be misled in similar 

 investigations. 



The passage in question will be found in Art. 27 J. 

 Summing it up into a brief statement, it implies that when a 

 dynamical system is referred to axes rotating uniformly, an 

 instability is introduced ; but this is plainly absurd, for if we 

 make the change of variables 



X=a? cos cot—y sin cot, Y = .r sin cot+y cos cot, 



where x = SA r sin (cr r t + a,.), y = 2B r sin (<r r t + r ), 



then the new variables will remain as simple harmonic 



* Lamb's ' Higher Mechanics/ (See Oh. xi. Arts. 98, 99). 



t 'Problems in Cosmogony and Stellar Dynamics.' Cambridge. 



% See the foot of p. 29 and the first half of p. 30. 



