2 Dr. Harold Jeffreys on 



wave velocit} r is very small, or, what is equivalent, that 

 the acceleration terms in the equations of motion of the air 

 can be neglected. If (u, v, w) be the components of velocity 

 of the air at the point [x, y, z), at time t, the axis of z being 

 vertical, the equations of motion take the form * 



du 1 "dp' 



-rr —2cov= ^ /L 



at p o% 



£+*■■— ;%►• — (i > 



dw 1 dp 



dt 9 p dz ^ 



dt ot on oy oz 

 p is the pressure, 

 p is the density, 



g is the acceleration due to gravity, 

 and g) is the component about the vertical of the earth's 

 angular velocity of rotation. 

 Friction, which is only effective in the surface-layers, is 

 ignored. 



It is assumed first that the vertical velocity can be 

 neglected. The writer has shown elsewhere that | this is 

 justifiable in problems of winds caused by temperature 

 variations of horizontal extent large compared with the 

 height of the atmosphere, and as an average cyclone is of 

 the order of 1000 km. across the same is probably true here. 

 The assumption must not, however, be pushed too far; it 

 would be in serious error for small islands, and probably also 

 for land and sea breezes of the usual diurnal type. For the 

 ordinary widespread depression, however, it is probably 

 correct, and the third equation of motion becomes 



=r 



gpdz (2) 



The assumption that the disturbance is permanent gives 

 at once that ^— - and =r- are zero ; hence the two equations 

 of horizontal motion become 



ou ~du 

 0% oy 



o^ oy 



* Cf. Lamb, ' Hydrodynamics,' p. 302. 



t Phil. Mag. vol. xxxiv. pp. 449-458 (1917). 



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