\I1SKR 26, K) I 8 



NATURE 



69 



In his conclusions the author finds that, for 

 remedial action, two fundamental necessities exist. 

 There is the need for further financial assistance; 

 there is the need for guidam < and direction. The 

 first implies substantia] aid from the State; for 

 the second, trust is placed in "the predominant 

 authority of the university ... as against the 

 claim of proprietary interest," the State assuming 

 only the functions ol supervision and advice, "with 

 due regard to the freedom of the university." 

 How far such "due regard " can persist side by 

 side with subvention and supervision it is not easy 

 to say. lint if departments and officials were 

 endowed with Sir (ieonje Newman's knowledge, 

 and imbued with his temper of sweet reasonable- 

 ness, ,1 way would be found of reconciling the 

 bureaucratic and the academic points of view. That 

 a way must be found for advance, along the lines 

 of his vividly clear and deeply wise survey, is 

 certain, unless England is, in the Reconstruction, 

 to lose her opportunity and miss the lessons of her 

 time of trial and testing. 



THE DYNAMICS OF CYCLONIC 



DEPRESSIONS.* 



T^Ili-. publication in 1906 of Shaw and Lemp- 



•*• fert's " Life-History of Surface Air- 

 Currents " marked the passing of a milestone in 

 the progress of our knowledge concerning the 

 mechanism of travelling cyclonic depressions, and 

 it is a matter of surprise that so little further 

 advance along the same lines has been made since 

 that time. This lack of progress obviously could 

 not continue for ever, and two recent, publications 

 by Sir Napier Shaw suggest that the next mile- 

 lias now been passed. 

 In the earlier of the two papers 2 a travelling 

 rotating disc of air was considered in which all 

 the air particles had the same relative tangential 

 velocity around the centre. This hypothesis led 

 to valuable conclusions concerning the "secon- 

 daries" which so frequently form upon the 

 southern side of the centre, but did not throw- 

 much light upon the cyclone as a whole. On con- 

 sideration it became evident thai the mathematics 

 would be much more manageable if the disc of air 

 were assumed to have uniform vorticity £, so that 

 the relative velocity w = £.r, and, working on this 

 assumption, valuable results have been obtained. 



This hypothesis implies a disc of air revolving 

 about its centre as a solid like a cartwheel, and 

 the "normal cyclone" considered in the present 

 paper has within itself a circulation of this type. 



The air particles will trace out trochoids formed 

 by the rolling of the disc of relative motion along 

 the line of motion of the inst ai>' .meous centre, and, 

 if sufficiently extended in all directions, the mass 

 will possess intrinsically two centres, (1) a centre 

 of instantaneous motion, or kinematic centre, 

 about which the resultant winds shown upon the 



1 "The Travel of Circular Depressions and Tornadoes and the Relation 

 of Pre^urc 10 Wind for Circular Isobars. ' By Sir Napier Shaw, Meteoro- 

 Bee. Geophysical Memoirs, No. t-\ 1918. 



- " Revolving Fluid in the Atmosphere." Froc. Roy. Soc, A, vol. xciv., 

 p. 34. 1917. 



XO. 2552, VOL. I02] 



map at any instant will be revolving (surface in- 

 curvature being neglected), and (2) a centre of 

 tvolving fluid or ntre — that is, the 



1 -ntre of the "cartwheel " — which is found at a 

 distance V /£ on the righ r>l the path of 



the instantaneous centre, where I is the velocity 

 of travel of the depression as a whole. 



The "normal cyclone " has, however, yet a third 

 centre. If upon the pressure field of a stationary 

 circular depression a uniform pressure gradient 

 from N. (high) to S. (low) be superposed, it is 

 shown that even- air particle will commence to 

 follow its appropriate trochoid curve, and 1 t 



will be that the depression will advance aci the 

 map from W. to E. with a speed V, while- 

 same time the system of isobars will be displaced 

 a distance V/(2<o. sin<£ + £) to the south from the 

 centre of instantaneous motion (u) equals angular 

 velocity of the earth, 4> equals latitude). This 

 centre of isobars is termed the dynamic centre, 

 and forms the third centre of the travelling de- 

 pression. As a numerical example, if the rotation 

 of the disc be such that a velocity of 20 m./sec. 

 (gale force) is found 200 km. from the centre of 

 instantaneous motion, and if the eastward speed 

 of progression of the depression be 10 m. , sec. in 

 our latitude, the tornado centre will be 100 km., 

 and the dynamic centre 45 km., to the south of the 

 instantaneous or kinematic centre. 



Viewed in another way, the pressure system may 

 be taken to be compounded of a set of circular 

 isobars round the tornado or "cartwheel" centre, 

 and a uniform pressure gradient from S. to N., 

 when the rate of advance V of the depression 

 will equal the geostrophic wind corresponding with 

 this field. Since this superposed field may reason- 

 ably be taken to be the same as the general field 

 surrounding an isolated cyclonic depression, the 

 conclusion is reached that the speed of progression 

 of such a depression will depend directly upon 

 the strength of the surrounding field, and in 

 certain examples shown this is satisfactorily con- 

 firmed. One of the most interesting results 

 reached is undoubtedly that the winds shown on 

 a map for an eastward moving depression will 

 circulate, not about the isobaric centre, but about 

 a point to the north which may be of the order 

 of 50 km. distant. Practical examples of this are 

 also adduced. Other conclusions of importance, 

 such as the probability of secondaries developing 

 at the tornado centre, cannot be more than alluded 

 to in a short notice like the present. The 

 demonstration of the fact that a normal travelling 

 cyclonic depression has three distinct "centres " 

 is the outstanding feature of the paper. 



To the re.ulc: the treatment appears a little dis- 

 jointed and to lack mathematical sequence, but 

 the author has forestalled criticism on this point 

 bv explaining that he considered it better to set 

 out tin matter in the order in which it was 

 developed, since this method would brii 

 under review the various aspects of the subject 

 r ii are presented to the student " j her maps. 



A straightforward theoretical discussion would 

 la k this advantage. .1- S. D. 



