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THE TRAVELLING CYCLONE. [Philosophical Magazine, Vol. xxxvm. pp. 420 — 424, 1919.]
[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. — EAYLEIGH.]
ONE of the most important questions in.meteorology is the constitution of the travelling cyclone, for cyclones usually travel. Sir N. Shaw* says that "a velocity of 20 metres/second [44 miles per hour] for the centre of a cyclonic 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 comparatively 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 treatment is desirable, which shall allow us to suppose a gradual falling off of rotation as the distance from the centre increases ; and I propose to take up the general problem in two dimensions, starting from the usual Eulerian equations as referred to uniformly rotating axesf. The density (/D) is supposed to be constant, and gravity can be disregarded. In the usual notation we have
where D/Dt = d/dt + ud/dss + vd/dy ...................... (3)
* Manual of Meteorology , Part iv. p. 121, Cambridge, 1919. f Lamb's Hydrodynamics, § 207, 1916.turn out to be, and our efforts to attain it should have the sympathy of all, and I would add especially of scientific men.ies besetting the acceptance of telepathy, biit I fully recognize that a strong case has been made out for it. I hope that more members of the Society will experiment in this direction. It is work that can be done at home, at odd times, and without the help of mediums, professional or other. Some very interesting experiences of this kind have been recorded by a former President, Prof. Gilbert Murray. With perhaps an excess of caution, he abstained from formulating conclusions that must have seemed to most readers to follow from the facts detailed. I trust we may hear still more from him.