February 29, 191 2] 



NATURE 



58, 



^ being- done by those English mathematicians who, 

 . denying themselves the luxuries of life, or other- 

 wise, are able to give time and thought to original 

 work. Applied mathematics Is only represented by 

 Dr. Nicholson's paper on scattering of light by a con- 

 ducting sphere, and Mr. F. B. Pidduck's note on 

 stability of rotating shafts. The most substantial con- 

 tribution to pure mathematics is Dr. W. H. Young's 

 series of seven papers dealing with various points 

 regarding the foundations of the differential and 

 integral calculus. At a time when the teaching of this 

 subject to elementary classes is receiving so much 

 attention, it is most fortunate that our country has 

 been able to produce a mathematician like Dr. A^oung, 

 who is underpinning this structure with a foundation 

 of rigorous reasoning. For example, one paper is 

 called "A Note on the Property of Being a Differ- 

 ential Coefficient," while in another paper on " A 

 New Method in the Theory of Integration," the author 

 proves a number of interesting results, such as that 

 "an upper-upper-lower-upper (lower-lower-upper-lower) 

 semi-continuous function is an upper-lower-upper 

 (lower-upper-lower) semi-continuous function." 



Lieut. -Colonel x\llan Cunningham writes " An 8-vic, 

 i6-ic, . . . , Residuacity," while it may be desirable 

 to explain that Mr. G. T. Bennett's note on "The 

 Double Six " refers to certain lines associated with 

 quadric and cubic surfaces. We have one fault to 

 find with the binding ; the top edges of the pages are 

 cut, but the outside edges are left rough, and are 

 very uneven, consequently the pages soon get to look 

 untidy ; and, furthermore, the book always opens at 

 certain pages and never can be opened at others. 



One cannot, however, help regretting that there 

 are probably many hundreds of persons in this country 

 engaged in teaching mathematics who are ignorant 

 of the very existence of these Proceedings. It would 

 be a great advantage in this respect if the London 

 Mathematical Society and the Mathematical Associa- 

 tion could be amalgamated so that the educational 

 and " original work " aspects of mathematics could 

 be brought into closer touch with each other, as 

 appears to be done in the American Mathematical 

 Society. A very similar fusion of theoretical and prac- 

 tical interests has just been effected in the Aeronautical 

 Society. 



(12) One thing further is needed, namely, 

 the publication of a summary of current mathematical 

 literature, with abstracts of the principal papers. This 

 is furnished by the Bulletin of the Calcutta Mathe- 

 matical Society, which, in addition to original papers 

 by Cullis and Mukhopadhyaya, contains a summary 

 of the principal mathematical journals, reviews, lists 

 of papers under " Societies and Academies," " Notes 

 and News," " New Publications," and an obituary 

 notice of Prof. Simon Newcomb. 



Assuming that the Calcutta society is sufficiently 

 powerful efficiently to continue the publication of these 

 notes and abstracts, it is surely somewhat humiliating 

 to think that the mathematicians of a Western civilisa- 

 tion should have to send to Calcutta for a list of the 

 papers which they themselves have written. But as 

 it is stated that the Bulletin will appear four times 

 a year. \Vhile the number before us for October, 1909, 

 NO. 2209, VOL. 88] 



bears the date of printing 191 1, and was only received 

 for review on October 14 last, we have some fears 

 lest the task which these Calcutta mathematicians 

 have undertaken may have proved too heavy for them. 

 If so, we hope that European mathematicians will 

 take steps to ensure the continuation of a chronicle 

 which is unique of its kind. 



(13) Although it has been mentioned in the "Notes" 

 column of a previous issue of Nature, the Spanish 

 society's " Revista " may with advantage be referred 

 to in this connection as showing that Spain has ob- 

 tained an amalgamation between theory and practice 

 of the kind which we in England have hitherto failed 

 to attain. On the theoretical side we have papers 

 on such questions as summation of series, polygonal 

 numbers, generalisation of the nine-point circle, 

 meridian arcs, and equilibrium of a moving chain 

 (the figures, however, show the rubber belt of the 

 barber's hair-brushing machine upside down, and 

 the wheel moving in the opposite sense to the 

 belt). On the more popular side we have biographies 

 of Fermat, Nunez, Benaflah, and Siliceo, a history 

 of Spanish mathematics, reviews, notes and news, 

 and notes and queries columns. In addition, the 

 society is drawing up a vocabulary of Spanish mathe- 

 matical terms. We cannot better close this review 

 than by quoting an extract from the article, " Sursum 

 corda," by Captain Dur^n Loriga, on the functions of 

 the newly founded society, in which he says, "The 

 first which imposes itself is to create a mathematical 

 atmosphere (ambiente matemdtico), in particular to 

 convince the whole world that without that great 

 science it would be impossible to approach the study 

 of natural and physical sciences, which daily tend 

 more and more to assume a mathematical form." 



This quotation is not the only or even the most 

 powerful argument in Captain Loriga 's article, which 

 further refers to the epoch-making discoveries of Abel 

 (who lived and died in great poverty), Kowalewski, 

 and others, and their influence on the progress of 

 applied science. But his notion of an "ambiente 

 matem^tico" should be kept prominently in mind by 

 all mathematicians who are able and willing to take 

 part in the campaign which in our country requires 

 to be waged against "England's neglect of mathe- 

 matics." This campaign can only be successful if 

 everyone who is interested in the progress of pure 

 science lends a helping hand. If they will not, then 

 we must let the coming generation make the best it 

 can of the knowledge which it has inherited from 

 its forerunners, and leave posterity to fend for itself. 



G. H. Bryan. 



OUR BOOK SHELF. 



The Principle of Individuality and Value. The 



Gifford Lectures for 191 1, delivered in Edinburgh 



Universitv, bv Dr. B. Bosanquet. Pp. xxxvii + 409. 



(London :' Macmillan and Co., Ltd., 1912.) Price 



\()S. net. 



Tins mav be described as a reply to the critics of 



.Absolutism, mainly, of course, the late Prof. James. 



Dr. Bosanquet is always as readable as the difficulty 



of his subject permits, and his rejoinders are always 



moderate and courteous. The reader feels that the 



