658 THE TRAVELLING CYCLONE [444
then examined for two special cases by the formulas (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, which 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 land 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 convection involve changes of density, which will modify the motion, but perhaps slightly. There does not seem to be definite discordance with Dr Jeffreys' detailed discussion.] Rayleigh's decease on June 30. It may therefore be permissible to direct attention to its main conclusion from another aspect, by way of paraphrase. Two questions are involved. If 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 Da/Dt and Dv/Dt express the components of relative acceleration, and these are clearly the centrifugal accelerations — £-X, - t?y in the relative orbits assumed to be circular, as found analytically lower down. On substituting these values, the equations give for Bp an exact differential form which is integrated in (7); therefore a modified motion is possible, and the first question is answered in the affirmative, in agreement so far with fact*. The displacement of the pressure-system due to the progressive motion is