SCIENCE PROGRESS 



RECENT ADVANCES IN SCIENCE 



PURE MATHEMATICS. By Dorothy M. Wrinch, D.Sc, Member 

 of the Research Staff, University College, London, and Fellow of Girton 

 College, Cambridge. 



Some remarkable problems of a new type arise in a paper by 

 Messrs. R. H. Fowler, E. G. Gallop, C. N. W. Lock, and H. W. 

 Richmond, devoted to the analysis; — theoretical and experi- 

 mental — of the aerodynamics of a spinning shell {Phil. Trans., 

 A, vol. ccxxi, pp. 295-387). The subject is, by its nature, 

 remote in certain aspects from the interests of the pure 

 mathematician, but there are other aspects which appear to 

 indicate a large field of future work. The general problems of 

 dynamics have previously suggested or made necessary some 

 large fields of modern analysis, and in our view this problem will 

 prove to be one of the sequence. Hitherto it has been quite 

 untractable, but the combined experimental work and theoretical 

 suggestions of the present authors clearly succeed in paving the 

 way to an ultimate solution, while at the same time bringing 

 clearly into view many points which may prove the determining 

 factor in the future lines of development of, for instance, detailed 

 discussion of solutions of specific differential equations. Applied 

 mathematics has usually in the past dictated the choice of the 

 differential equations whose solutions are worthy of detailed 

 examination, as, for instance, in classical cases such as Legendre's 

 or Bessel's equations, which afterwards take on an important 

 role in function-theory quite independently of their historical 

 origin. The general hypergeometric function has begun recently 

 to play a similar important part in applied mathematics, its 

 history being thus, in a certain way, the converse of that of such 

 functions as those of Legendre and Bessel. 



We cannot here enter into the more practical side of the 

 paper under consideration, for it is outside our legitimate 

 province. But it deals with shells which can have a velocity 

 greater than that of sound — a significant advance in itself — 

 and seeks to find the forces and couples acting on the shells 

 during their motion. The drag, in the case of symmetry, is 

 taken as ,y. 



where {v, a) are the velocities of the shell and of sound in air, 

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