the Travelling Cyclone. 423 



showing that the field of pressure, though still circular, is no 

 longer centred at as when U = 0, or even at C, where 

 x= Ul, y = 0, but is displaced sideways to the point where 

 A'=U^ j/ = G>U/(o>f +2? 2 )- Shaw calls this the dynamic 

 centre ; it is the point which is conspicuous on tlie weather 

 map as the centre of the system of circular isobars. 



As a case where the circular motion diminishes to nothing 

 as we go outwards, let us now suppose that f=Z^~ E2/cj2 , falling 

 off slowly at first but afterwards with great rapidity. We 

 have 



§*ZRdR = iZa 2 (l-e- m < a2 ), J R f 2 RdR = iZV(l-<r 2R2 / a2 ); 



and thus from (7) 



£ =Comt.-2a>\Jy-iaXZe- m ' la2 + 2<oy, . (II) 

 P 



where, as usual, R 2 = ?/ 2 + (,r— TJt) 2 . 



May 17th. 



The completion of this paper was interrupted by illness. 



The two-dimensional solution requires a ceiling, as well as 

 a floor, to take the pressure. In the absence of a ceiling we 

 must introduce gravity, and since in the supposed motion no 

 part of the fluid is vertically accelerated, the third equation 

 of motion gives simply 



- = const. — qz. 

 P J 



Thus (10) is altered merely by the addition of the term —gz. 

 I had supposed too that the solution would remain sub- 

 stantially unaltered even though p were variable as a function 

 of p. But these conclusions seem to be at variance with 

 those put forward by Dr. Jeffreys in the January No. of 

 the Philosophical Magazine. I am not able to pursue the 

 comparison at present. 



June 25th, 1919. 



[The following note has been contributed by Sir Joseph 

 Larmor. — Eds. 



This paper was left incomplete on Lord Rayleigh's decease 

 on June 30. It may therefore be permissible to direct 



