4S4 



NA TURE 



[March 21, 1895 



no allusion to any such theory. We wish that she had 

 found i: possible to introduce a brief notice of the 

 analytical theory in which the circle is taken as the 

 primary element in view of the fact that most of the 

 properties of an important class of curves— bicircular 

 quartics — are best discussed by expressing the equations 

 of these curves in terms of circular coordinates. 



It is also a matter of regret that the use of trilinear 

 coordinates is retained, although results are usually 

 given in terms of areal coordinates as well. The use of 

 both systems is confusing to students, and the use of 

 the areal system has a double advantage ; firstly, the 

 fundamental metrical formula are more easily proved, 

 and secondly, the areal system is intimately connected 

 with the tetrahedral system in solid geometrj'. For the 

 latter reason, if for no other, it is very desirable that the 

 use of trilinear coordinates should disappear from our 

 text-books on plane geometry. In this book the proofs 

 of two fundamental results (§§ 20, 21) are long and 

 tedious. 



The only other point we have to find fault with is that 

 harmonic relationship and involution are introduced as 

 particular cases of cross ratio and homography. The 

 author herself admits (p. 160) that this view disguises 

 the real difference between the two conceptions, and ex- 

 plains that while cross ratio and homography relate to 

 different spaces, harmonic relationship and involution 

 relate to pairs of elements in the same space. The 

 theories are developed independently, but we should 

 have preferred that the theory of harmonic groups and 

 the theory of involution should have been developed 

 before the introduction of the idea of cross ratio and 

 homography. 



The examples chosen by the author to illustrate 

 various theorems have been very carefully selected, and 

 should be found quite sufficient for the use of students. 

 .Among them will be found many theorems of inde- 

 pendent importance, which could scarcely be said to come 

 within the scope of the book. We may add that an 

 excellent index is provided. R. L. 



ObR BOOK SHELF. 



Les Aurores Polaires. By Alfred Angot. Pp. 31S. 



(Paris: Felix Alcan, 1895.) 

 France has made two important contributions to the 

 knowledge of aurorae. Perhaps the first work devoted 

 entirely to the study of auroral phenomena was the 

 " Trait'j physique et historique dc 1 aurore bor<-ale," by 

 Mairan, published by the Paris Academy of Sciences in 

 1733. A century later a volume was published containing 

 the results of aurora observations made on the Recherche 

 during the scientific expedition to Lapland. The plates 

 which illustrated the observations then made have been 

 laid under tribute by M. Angot for the present volume. 

 .Since the publication, however, of the "Aurores 

 Horcales ' which resulted from the 1S3S-39 expedition, 

 we have it on the authority of M. .Anj^ot that no work 

 dealing wholly with the subject has appeared in France. 

 This volume, therefore, stands as practically the only one 

 in which our neighbours on the other side of the Channel 

 can find a popular account of aurorx, written by one of 

 their own countrymen. 



M. Angot has treated the subject lightly, yet scien- 

 tifically. He traces the history of aurora observations 



NO. 1325. VOL. 51] 



from the time of Aristotle ; describes the apparently 

 adventitious forms assumed by the phenomena ; explains 

 the facts as to the extension, position, frequency, and 

 periodicity of aurorae ; develops the relations between 

 auroral and terrestrial magnetism and electricity, and 

 connects them with meteorological phenomena; and, 

 finally, he presents the cosmical, optical, magnetic, and 

 electrical theories put forward to account for the pheno- 

 mena. 



\ list is appended, giving in chronological order all 

 the aurora: seen in latitudes above 55' North from 1700 

 to 1890, with the names of the places at which obser- 

 vations were made. Eighteen rather coarse illustrations 

 are distributed through the book. Altogether, the volume 

 is a valuable summary of the growth of knowledge of 

 auroras. 



A Fc-iu Chapters in As/ronomy. By Claudius Kennedy, 

 M.A. (London : Taylor and Francis, 1S94.) 



In these 150 pages are discussed four or five of the 

 numerous problems in astronomy, and these are handled 

 in such a manner as to make them full of interest, both 

 for the general reader and for the student. This book, 

 unlike many others, is not written for the sole purpose 

 of pouring condensed knowledge into the student's head, 

 but for those who wish to sit down for half an hour or 

 so and read for recreation, and so gain a fair under- 

 standing of some of the discussions contained in them, 

 without going into too great detail. The points chiefly 

 referred to, are, visual illusion affecting certain astro- 

 nomical phercmena : the effect of theeaith's lotaticn on 

 certain moving bodies, as projectiles, paths of projectiles, 

 Foucault's Pendulum and the Horizontal Pendulum ; the 

 causes of the tides ; the moon's variation ; and the 

 parallactic inequality. In the last two chapters the text 

 is accompanied by several figures. 



As a supplement to the ordinary text-books on astro- 

 nomy, this small volume will be found especially useful, 

 as it deals with subjects not generally referred to in them, 

 or at least only briefly mentioned. 



Mechanics for Colleges and Schcols : Sialics. Bv R. T. 

 Glazebrook. M.A., F.R.S. Pp. 180. (Cambridge 

 University Press, 1895.) 



This addition to the physical series of the Cambridge 

 Natural Science Manuals will haidly add to the 

 lepiitaticn of the assistant diiector of the Cavendish 

 Laboratory. The only noteworthy feature is the pro- 

 minence given to the experimental verification of statical 

 principles ; but excepting this, little can be found to 

 distinguish the book from others of a similar type. 

 Many oi the experiments described are intended to be 

 performed by the students, and the theoretical con- 

 sequences are, when possible, deduced frcm experi- 

 ments. This is undoubtedly the right line to go upon, 

 but we are afraid that few of our schools or colle^'es 

 possess at present sufficient apparatus for the laboratory 

 work described. The text is clear and concise, and 

 sufficiently illustrated ; and the examples are numerous. 



The Telegraphist's Guide. By James Bell, A.I.E.E. 

 Pp. loi. (London : Electricity Office, 1895.) 



Tei.kckaphists in the Government service have now to 

 submit themselves to a technical examination before they 

 can obtam promotion. Herein we have a guide in which 

 the subjects of the new examination arc considered in 

 the order laid down by the Postmaster-General. The 

 aspiring telegraphist will find the book a means of 

 acquiring the knowledge he needs; and students of 

 lelegraphy not directly cornecled wilh the service, ma; 

 obtam fum it useful inloriralion on the practical work 

 ing oftelegraphic systems. 



