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XLI. On Periodic Convection Currents in the Atmosphere 

 (Second Paper.) By Harold Jeffreys, M.A., JJ.Sc, 

 Fellow of St. Johns College, Cambridge*. 



IN a recent paper f the present writer has considered 

 the motions that arise when a portion of the earth's 

 surface, with the atmosphere above it, is periodically 

 heated and cooled, symmetry about an origin being main- 

 tained throughout the changes. The main object of the 

 investigation was to ascertain whether the usual assumption 

 that the velocity can be neglected in the equation of vertical 

 motion is valid, and it was found to be so provided the 

 radius of the heated area is large compared with the vertical 

 range of the temperature variation. Several restrictions 

 were, however, imposed on the problem, namely : 



(1) The atmosphere was replaced by an incompressible 



fluid of finite depth. 



(2) The depth was supposed to be great compared with 



the radius of the heated area. 



(3) The rotation of the earth was neglected. 



(4) Second order terms were neglected. 



Subject to these restrictions, an exact solution of the 

 special problem was obtained. In the present paper the 

 second and third restrictions are removed, and the last 

 is shown to be justifiable. The inclusion of rotation on 

 the whole simplifies the problem, for two reasons. First, 

 the speed of the variations usually enters in combination 

 with the speed of rotation, and as the latter is a fixed 

 quantity approximation can be resorted to at an earlier 

 stage. Second, in the former problem the variation of 

 velocity with height depended on a differential equation 

 one of whose complementary functions varied with height 

 in the same way as one of the terms in the acting force, 

 so that this term in the force required special treatment. 

 The depth is now supposed small compared with the hori- 

 zontal extent of the temperature variations, while no 

 assumption is made about the relation between their vertical 

 extent and the depth. The actual conditions are thus much 

 better represented. The results obtained are summarized in 

 the last two sections and agree with observation so far as 

 comparison is possible. 



* Communicated by the Author. 



t Phil. Mag. vol. xxxiv. 1917, pp. 112-128. 



Phil. Mag. S. 6. Vol, 34. No. 203. Nov. 1917. 2 I 



