220 



NATURE 



{July 18,1872 



OUR BOOK SHELF 



T/u Mcss:-if^cr nf .'\fa//ic:m.iliLS. New series. Edited by 

 Messrs. Whitworth, Taylor, Lewis, Pendlebury, and 

 Glaisher. Vol. i. (Macmillan and Co., London, 1872.) 

 The twelfth monthly number of the ne^r series of the 

 "Messenger of I\Lathematics " has just been published. 

 This offers a convenient epoch for estimating the aims and 

 achievements of this new mathematical periodical. 



The principal ann of the editors was stated in their 

 introductory note to be the fostering of a continuous and 

 ample supply of original investigations into the more and 

 more specialised branches of mathematics. This origi- 

 nality was to be welcomed from whatever quarter it came 

 — whether from mathematicians of established reputa- 

 tion or from junior students of the science ; whether from 

 the Universities of this country or from more distant 

 centres. 



The intentions of the editors have been fully realised 

 by the publication of the twelve numbers now before us. 

 The list of the contributors to these numbers contains 

 nearly twice as many names as there are numbers of the 

 magazine. And while in that list we find the names of 

 some of the foremost mathematicians of the age, such as 

 Messrs. Cayley, Routh, Stokes, and Townsend, we find 

 also a considerably greater number of the names of junior 

 students, some of whom have only recently graduated. 

 The localities of the contributors are also as various as 

 was intended, one of them, for example, writing from 

 Queensland. 



As regards the articles themselves, there are about four 

 times as many on pure mathematics as there are on ap- 

 plied mathematics. Among the former we find, for 

 example, such a simple matter as a very elegant proof, 

 by Mr. Taylor, of Euclid, ii. S, in which he mikes a 

 further step towards the elimination of the diagonals from 

 the diagrams of the Second Book of Euclid. This 

 construction is recommended to the attention of the 

 Association for the Improvement of Geometrical Teach- 

 ing. We find also such interesting contributions to the 

 study of the higher geometry as Prof. Cayley's articles on 

 the " Theory of Envelopes," and on " Penultimate 

 Quartics ; " Mr. Merrifield's article on " Families of Sur- 

 faces ; " and Mr. Townsend's on " Confocal Ouadrics." 

 The articles on other branches of pure mathematics are 

 as varied and as instructive as those on geometry. There 

 is, for example, a spirited controversy between Prof 

 Cayley and Mr. Wilkinson, about the quantitative limita- 

 tions which have, in more recent times, been imposed on 

 the generality of Taylor's theorem. Prof. Cayley's 

 plea for greater liberty of interpretation, and against con- 

 fining our symbols in mathematics so exclusively to 

 quantity, is especially effective and well-timed ; for the 

 more liberal our interpretations the vaster will be the 

 domains we can overrun and occupy by means of our 

 symbols, and the greater will be the tendency to that 

 speciahsation of efforts, or division of labour, which is so 

 characteristic of modern mathematical research, and which 

 the publication before us aims to combine by co-operation. 

 Then there are " Exercises on the Integral Calculus," by 

 Sir John Cockle, and papers on " Definite Integrals," by 

 Glaisher ; besides articles treating of many other subjects, 

 too numerous to mention. 



Among the articles on appHed mathematics we find one 

 by Prof Stokes, on the " Compound Pendulum ;" two by 

 Mr. Routh, on the " Oscillations of a Heavy String," and 

 an improved solution of a problem in the Astronomer 

 Royal's " Undulatory Theory of Optics ; " one by M. 

 Leclert, on " Naval Geometry ; " two by Mr. Hopkinson, 

 on " Electricity ; " and so on. There is also a most 

 elegant model of mathematical style, especially suitable 

 for intending competitors in mathematical examinations, 

 namely, the solutions, by Prof Cayley, of the whole of a 

 Smith's Prize Paper, which are of the stiifest ever set. 



With all its variety of contents, this magazine is still 

 eminently readable, principally on account of an utter 

 absence of that tendency to riot in new terminology, or 

 scientific slang, which disfigures the pages of some 

 modern mathematical writers. The typography is also 

 very good. 



We shall be well satisfied if vol. ii. maintains the high 

 standard set by vol. i. ; but we should be pleased to find 

 in it a little larger proportion of articles on applied mathe- 

 matics. There is much interest felt at present in such 

 su'ojects as molecular mathematics ; the theory of elec- 

 tricity and magnetism ; the determination of the centres 

 of gravity of ships ; and such like problems in advanced 

 theory or in complicated practice. We should be glad to 

 see the miscellaneous portion of the magazine, containing 

 notices and reports of the meetings of mathematical 

 societies, reviews of books, &c., somewhat extended, even 

 if the present very moderate charge of a shilling a number 

 was somewhat exceeded in consequence. There has 

 been, for example, no notice of the large and influential 

 meeting held last January by the Association for the Im- 

 provement of Geometrical Teaching. Now, in that asso- 

 ciation the want of a monthly organ is much deplored. 

 Why should not the " Messenger " fill that void .' Per- 

 haps, also, if the size of the " Messenger" were increased, 

 space might be found for queries and notes from cor- 

 respondents ; and the name might be advantageously 

 altered to " The Mathematical Magazine." But, in any 

 case, every student who wishes to keep abreast of the 

 current of contemporary mathematical thought should 

 subscribe to this excellent little periodical. 



LETTERS TO THE EDITOR 



[ T/te Editor does fiot hold himself responsible for opinions expressed 

 by his correspondents. No notice is taken of anonymous 

 communications. ] 



Spectrum of Lightning 



0.\ the nth inst. there was a considerable thunderstorm in 

 Patlerdile, and I was again able to observe the lightning spec- 

 trum. Among other lines I saw one repeatedly near Dj and about 

 t'le centre of the bright yellow band between the two masses of 

 atmospheric absorption lines in that neighbourhood. I also saw 

 the hne near /'. Both correspond in position with principal air- 

 lines. 



But besides this line spectrum I repeatedly saw a continuous 

 spectrum with bright bands, which might have been the low 

 temperature nitrogen spectrum, though I feel no certainty that 

 sucli was the case. There seems, however, no doubt that light- 

 ning; gives two different spectra, one of bright lines, and the other 

 continuous ; unless indeed the latter be identical with the 

 former, but with the lines much expanded. I do not think this 

 is the case. 



Henry R. Procter 



P. S. — Since writing the above there has been another thunder- 

 storm, during which I more distinctly saw the band spectrum. I 

 find that it is not the ordinary nitrogen band spectrum, but might 

 be a very much expanded line spectrum. It is however difticult to 

 understand the cause of so great a ditTerence, for the line spectrum 

 was very sharp and well defined. 1 thought I was able to recog- 

 nise that the latter corresponded to the shorter and sharper peaJs 

 of thunder. The spectrum showed no connection with the 

 brilliancy of the ll.ish. I recollect that in a brilliant thunder- 

 storm which I lately witnessed at night in Syri.a, some flaslies 

 liglited up the dull foliage of the prickly pear to a vivid green ; 

 wliile others, showing the form of the landscape with nearly 

 equal distinctness, left it almost colourless. I had then, un- 

 fortunately, no spectroscope. 



Patterdale, Penrith, July 12 



Aurora of July 7 



The very fine aurora of Sunday night, July 7, was well seen 

 near Leenane, on Killaiy Harbour (lat. 53" 36', long, cj' 45', 

 nearly), in the west of Ireland. Probably this is the most 



