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XXXVIII. The Travelling Cyclone. 

 By the late Lord Rayleigh, O.M., F.R.S* 



[Note. — The concluding paragraphs of: this paper were 

 dictated by my father only five days before his death. The 

 proofs therefore were not revised by him. The figure was 

 unfortunately lost in the post, and I have redrawn it from 

 the indications given in the text. — Bayleigh.] 



ONE of the most important questions in meteorology is 

 the constitution of the travelling cyclone, for cyclones 

 usually travel. Sir X. Shaw f says that "a velocity of 20 

 metres/second (44 miles per hour) for the centre of a cy- 

 clonic depression is large but not unknown ; a velocity 

 of less than 10 metres/second may be regarded as smaller 

 than the average. A tropical revolving storm usually travels 

 at about 4 metres/second." He treats in detail the com- 

 paratively simple case where the motion (relative to the 

 ground) is that of a solid body, whether a simple rotation, or 

 such a rotation combined with a uniform translation ; and 

 he draws important conclusions which must find approximate 

 application to travelling cyclones in general. One objection 

 to regarding this case as typical is that, unless the rotating 

 area is infinite, a discontinuity is involved at the distance 

 from the centre where it terminates. A more general treat- 

 ment is desirable, which shall allow us to suppose a gradual 

 falling off of rotation as the distance from the centre in- 

 creases ; and I propose to take up the general problem in 

 two dimensions, starting from the usual Eulerian equations 

 as 'referred to uniformly rotating axes|. The density [p) is 

 supposed to be constant, and gravity can be disregarded. In 

 the usual notation we have 



1 dp 9 Du . 



p CUV \)t 



1 dp 2 \)v 



p dy J Dl' V 



where 



fyDt=d/dt + vd/dx + rdldi/ (3) 



Here ,v, y are the coordinates of a puint, referred to axes 



* Communicated by the Author. 



f ' Manual of Meteorolojrv," Part iv. p. 121, Cambridge, 1919. 



\ Lamb's ' Hydrodynamics,' § 207, 1916. 



