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especially interesting from the point of view of the parts which various nations 

 have played in developing the intercourse up to 191 2. Mr. Mackail deals in 

 succession with the function of a University, the nature of Poetry, the Modern 

 World, Poetry and Science (" The fancied opposition of science to art and letters, 

 and more particularly to poetry, is injurious to the general interest of mankind. 

 . . . The creative instinct, the imaginative impulse, which find expression in 

 poetry, are powerfully reinforced by the discoveries of science and by the growth 

 of the scientific spirit. . . ."), Poetry and Business, and Poetry and Democracy. 

 The lecture by Prof. StOrmer contains a summary of his researches on aurora 

 borealis which were begun in 1904, and the results of which have been published 

 from 1904 to 1912 in various periodicals. 



Two of the lectures by M. Borel and two of those by Prof. Volterra were 

 noticed in the " Recent Advances " of the last number of Science PROGRESS 

 (1918,12, 544). M. Borel's lecture on "Molecular Theories and Mathematics" 

 starts from the reflection that " it was the study of physical phenomena which 

 suggested the notions of continuity, derivative, integral, differential equation, 

 vector, and the calculus of vectors ; and these notions, by a just return, have 

 become part of the scientific equipment necessary to every physicist . . .," and 

 examines the influence which molecular theories may have on the development 

 of mathematics. Indeed, " the points of contact between molecular physics and 

 mathematics are numerous," " mathematicians can only gain by investigating [the 

 analogies] more closely," and " the task . . . cannot long be deferred of creating 

 an analysis adapted to theoretical researches in the physics of discontinuity." 

 Prof. Volterra's lecture on " Henri Poincare" emphasises the very modern aspect 

 of Poincare's scientific work. At the present day scientific work is published 

 chiefly in the form of memoirs in scientific journals, so that work is often published 

 as it progresses. " The proceedings of the academies, short and precise reviews, 

 have appeared. A man reports in a few words every discovery as soon as he has 

 made it. Time presses ; one fears that the next minute the discovery may be lost 

 . . . this development has created a particular state of mind among scientists, and 

 has changed their lives, their ways of working, and even of thinking. There are 

 great advantages in this modern scientific life. Research has become almost 

 collective. The energies of the investigators are summed ; their discoveries 

 follow each other rapidly ; competition spurs them on. Their number increases 

 from day to day. But how many objections we can oppose to these advantages ! " 

 Indeed, the whole aspect of scientific life has quite changed since the tradition 

 created by Gauss's practice of writing "fiauca sed matura? It may be remem- 

 bered that Weierstrass once remarked that the method adopted by the Paris 

 Academy of Sciences for announcing discoveries seemed to him to injure the 

 work of Poincare. However, it does not really seem that the objections urged by 

 Weierstrass had weight against Poincare's best work ; as regards his " philo- 

 sophical " work, certainly much of it gives one the impression of a kind of lively 

 lack of interest in the subject, and consequent carelessness, but the work that 

 Poincare loved preserves a power of stimulating his readers, and, like many 

 Frenchmen, he thought so quickly and accurately in his chosen domain that one 

 can hardly imagine that his work would have been improved by years of silent 

 meditation before it was published. Prof. Volterra gives a very clear account of 

 certain of Poincare's mathematical investigations : on the theory of linear differ- 

 ential equations and " Fuchsian " functions, on mathematical physics, and on 

 dynamics and astronomy. In particular, that investigation is described rather 

 more in detail which concerns the equilibrium of a rotating fluid mass. 

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