328 Mr Basset, Reply to a Paper by Mr Bryan. 



In replying to my criticisms, Mr Bryan has neglected one of 

 the cardinal rules of controversy ; that is, to quote your oppo- 

 nent's statements correctly. The passage from his paper which 

 I criticized was the following, "it does not indicate that the 

 spheroid in question is secularly unstable for this particular type 

 of displacement. Its meaning is that the spheroid is more oblate 

 than that form for which the angular velocity is a maximum." 

 And in his reply Mr Bryan has omitted the first sentence, which 

 contains the pith of the whole matter. From the passage at the 

 commencement of § 3 of his paper in the Proc. Roy. Soc.^, I 

 understood him to mean that when a Maclaurin's spheroid is com- 

 posed of viscous liquid, the steady motion will be stable provided 



MOqi(0-t.HOun'(0>o (1), 



and my object was to show that this result was wrong for the 

 simultaneous values of 



s = 0, 71 = 2. 



For a zonal displacement of degree 2, the condition (1) be- 

 comes 



Piqi-p-2q-2>0 (2), 



and the spheroid is well-known to be stable ; whereas for a certain 

 value of the excentricity the above expression, as Mr Bryan has 

 shown, becomes negative. Consequently if the inequality (2) 

 gave the correct condition of stability, the spheroid would become 

 unstable at the critical value of the excentricity which causes 

 the left-hand side of (2) to vanish and become negative. Mr Bryan, 

 being aware that the spheroid is stable for a spheroidal displace- 

 ment, tries to get out of the difficulty to which a wrong result 

 has led him by arguing, that the fact of the left-hand side of (2) 

 becoming negative does not indicate instability, but means some- 

 thing totally different. Under these circumstances I am justified 

 in characterizing his explanation as incorrect. The true explana- 

 tion is that the condition in question indicates instability, but 

 it is an erroneous one. The correct condition, as I have shown in 

 my paper, leads to stability. 



Another misquotation occurs on p. 52, Mr Bryan states that 

 I have said "that the spheroid is secularly stable if the motion 

 when slightly displaced is determined by terms of the form e'''^'-^' ' 

 where a is negative." I have said nothing of the kind. The above 

 definition of secular stability is Poincare's and not mine. I have 

 objected to it, criticized it, and have said that I consider it an 

 inaccurate use of language. What I said was that when the 

 disturbed motion is of this character, the system is absolutely 

 stable. Mr Bryan then goes on to suggest that possibly the 



1 Vol. xLvii., p. 369. 



