424 The Travelling Cyclone, 



attention to its main conclusion from another aspect, by way 

 of: paraphrase. Two questions are involved. 11: a vortical 

 system can persist at rest, in an atmosphere rotating with the 

 Earth, can it also persist, slightly modified, with a translatory 

 velocity U ? And if so, how will the distribution of pressure 

 in it be modified ? The equations of fluid motion relative to 

 the ground are (1) and (2) ; in them the last terms Du/Dt and 

 Dv/Dt express the components of relative acceleration, and 

 these are clearly the centrifugal accelerations — J 2 X, — f 2 yin 

 the relative orbits assumed to be circular, as found analyti- 

 cally lower down. On substituting these values, the equations 

 give for Sp an exact differential form which is integrated 

 in (7); therefore a modified motion is possible, and the fiist 

 question is answered in the affirmative, in agreement so far 

 with fact *. The displacement of the pressure-system due to 

 the progressive motion is then examined for two special 

 cases by the formulae (10) and (11), showing also general 

 agreement with fact as regards displacement of the centre of 

 the vortex. But the value of U is not determined by these 

 considerations, wmich refer to frictionless fluid. When 

 viscosity in the fluid is taken into account, the general 

 argument seems to remain applicable ; for the velocity of 

 convection U, being uniform, will not modify the viscous 

 stresses. But, in any case, internal viscosity is negligible in 

 meteorological problems. It is the friction against Jand or 

 ocean, introducing turbulence which spreads upward, that 

 disturbs and ultimately destroys the cyclonic system ; and 

 the high degree of permanence of the type of motion seems 

 to permit that also to be left out of account. As remarked 

 in the postscript, the changes of pressure arising from con- 

 vection involve changes of density, w T hich will modify the 

 motion, but perhaps slightly. There does not seem to be 

 definite discordance with Dr. Jeffreys' detailed discussion.] 



* The conditions of stability for flow of liquid with varying vorticity 

 had been considered in a series of papers, for which reference may be 

 made to the section Hydrodynamics of the catalogue appended to 

 Lord Rayleigh's ' Collected Papers,' vol. iv. 



