378 



NATURE 



[Mar. 19, 1874 



present time ab^tncts of about 4,000 papers, all of later 

 date than ihote noticed in the last German Jalireshericht. 

 Our German fellow-workers may therefore, with advan- 

 tage to themselves, give their support to this English work. 

 We trust that the appreciation of all interested in 

 chemical science for this most useful work will be so 

 decidedly shown that the Chemical Society will soon have 

 no further anxiety as to the success of their undertaking. 

 The circle of readers appealed to is a very wide one ; 

 not only is it an absolute necessity for those who work at 

 Science and those who profess it, but the medical man, 

 the agriculturist, the manufacturer, and the geologist will 

 all find an abundance of matter interesting to their special 

 pursuits. 



^1 



TODHUNTER'S "MATHEMATICAL 

 THEORIES OF ATTRACTION" 

 A History of the Mathematical Theories of Attraction 

 and the Figure of the Earth from the titne of Newton 

 to that of Laplace. By I. Todhunter, M.A., F.R.S. 

 Two vols. (London; Macmillan, 1874.) 



I. 

 'HE late Prof de Morgan, in his " References for the 

 History of the Mathematical Sciences," divides 

 the written histories into two classes, those which are 

 written on the plan of Montucla, Bossut, &c., in which a 

 general account is framed out of the writer's notes or 

 remembrances of miscellaneous reading ; or in that of 

 Delambre, Woodhouse, &c., in which the successive 

 writings of eminent men are examined and described one 

 after the other, so that each chapter or section is a 

 description of the progress of Science in the hands of 

 some one person, and is complete in itself This latter 

 plan is the one he considers the most favourable to accu- 

 racy and the most interesting to students who are desirous 

 of being the critics of the historians, and of amending 

 their works, if need be. The admirable two volumes 

 before us would certainly be placed under this head. As 

 to the utility of such works, our author remarks: "A 

 familiarity with what has been already accomplished or 

 attempted in any subject is conducive to a wise eco- 

 nomy of labour ; for it may often prevent a writer from 

 investigating afresh what has been already settled ; 

 or it may warn him, by the failure of his predecessors, 

 that he should not too lightly undertake a labour of well- 

 recognised difficulty." Mr. Todhunter is no novice in this 

 style of writing ; his "History of the Calculus of Vari- 

 ations " appeared in 1861, and at once placed him in the 

 foremost rank of mathematical historians ; this work was 

 followed, in 1865, by the " History of the Theory of Pro- 

 bability." The principles upon which these earlier works 

 were written have been adopted in the work under con- 

 sideration. Experience has improved his already first- 

 rate powers of analysis and of graphic representation of 

 the contents of the works he considers ; all that he wants 

 is leisure ; possibly a time may come when the University 

 of Cambridge will appoint an historian (or historians) to 

 fill up the painfully patent void which now exists in this 

 department of literature. The acknowledged high merits 

 of his published histories would suggest Mr. Todhunter 

 as a most fitting first occupant of such a chair ; the libe- 

 rality of the syndics of tlie University Press in defraying 



the expenses of the printing of this last work affords evi- 

 dence that the work is appreciated. In his recent volume 

 of " Essays" (p. 151), our author mentions his taste for 

 the history of Mathematics ; we heartily hope that the 

 union of such taste and mathematical powers will result 

 in the begetting a numerous progeny all equally comely 

 with, and of as good disposition as, the elder members of 

 the family. 



There is one feature in these histories that especially 

 commends them to our own mind, and that is the writer's 

 candotcr. We cannot better express our own views upon 

 this point than by citing the following passage from the 

 late Sydney Smith's writings : " There is nothing more 

 beautiful in science than to hear any man candidly own- 

 ing his ignorance. It is JO Tittle the habit of men who 

 cultivate knowledge to do so — they so often have recourse to 

 subterfuge, nonsense, or hypothesis, rather than to a plain 

 manly declaration, either that they themselves do not un- 

 derstand the subject, or that the subject is not understood 

 — that it is really quite refreshing to witness such in- 

 stances of philosophical candour, and it creates an imme- 

 diate prepossession in favour of the person in whom it is 

 observed." * It is the absence of this candour which has 

 been productive of so much confusion in this subject of 

 mathematical history : the straining after completeness 

 leads to the insertion of second- and third-hand descrip- 

 tions ; the right rule seems to be that of De Morgan and 

 our author, " to give no opinion or account of any book 

 whatever unless such as is derived from personal ac- 

 quaintance with its contents." Extreme care and pains- 

 takingness are manifest throughout without any sign of 

 flagging. Interesting as Mr. Todhunter's histories are, 

 even to the general student, from the many " sidelights ' 

 they contain, and which are especially numerous in the 

 present work, they are exceedingly valuable to the special 

 student, on account of the investigations with which they 

 abound. These are not mere reproductions, but they 

 translate, as it were, the old and now almost obso- 

 lete language of the earlier writers into the lan- 

 guage of modern analysis : thus in § 443 it is remarked 

 of D'Alembert's notation, " It is not very inviting, and he 

 leaves it to explain itself" Some idea of the extent of 

 these investigations may be got from the fact that 475 out 

 of the 1,632 articles are devoted to them. 



The author's design is to write the history of the Mathe- 

 matical Theories of Attraction and of the Figure of the 

 Earth ; for this purpose, he says, he has endeavoured to 

 include all the memoirs and works which relate to these 

 subjects. Such has been his diligence in his seven years' 

 research, that we should suppose few books have escaped 

 his notice : certainly none that would materially aftect 

 the conclusions he has arrived at. That he would have 

 added a few to his list had he consulted the British Mu- 

 seum library, or had access to that bequeathed by the 

 late Mr. Gravest to University College, we shall probably 

 show in the course of this notice. 



Mr. Todhunter shows that the subjects treated of are 

 of no common importance and influence. Researches 

 into both theories have been fertile in yielding new re- 

 sources for mathematicians : it will suffice to instance 



* • ' Conduct of the Understanding." 



t We are inlormed that the liberality of a gentleman who has already 

 been a great benefactor to tne College will shortly enable students to get an 

 accurate idea of the treasures contained in the above library. 



