Mar. i6, 1874J 



NA TURK 



401 



Todhunter gives no account of this work : it is apparently 

 a translation of the work described in § 9S4. 



The following work by Delambre and Legendre (will 

 thisthrowlight on § 1,146?) does not seem to be described : 

 it is " Methodes analytiques pour la determination 

 d'un arc du mdridien precedees d'un memoire sur 

 le meiie sujet," par A. M. Legendre. Paris, 1799. 

 4to.) In note ii. to " Methode pour determiner la 

 longueur exacte du quart du nieridien," par A. M. L. occurs 

 LegendrJ's Theorem. There are 176 pp., 16 pp. of tables 

 at the end, 5 pp. of " Observations sur quelques endroits 

 du memoire du cit. Delambre," par A. M. Legendre ; 

 2 plates, 7 pp. oi avertissement, and 4 pp. of contents. 



We now close our notes with a few remarks.on §§531,682, 

 and 1,584. The memoir, which neither Playfair nor Mr. 

 Todhunter have been able to procure a sight of, is to be 

 met with in vol. i. of the Giuliani memoirs cited above, 

 consequently its date is antecedent to 1743. It occupies 

 pp. 65-88, and is entitled " Problema mecanicum de 

 solido maxima; attractionis solutum, a P. Rogerio Josepho 

 Boscovich." The problem is, " Data quantitate materia: 

 punctum attrahentis, in quacunque lege distantiarum in- 

 venire solidum ipsum continens, quod maxime omnium 

 attrahat ipsum punctum positum inaxesolidi producto ad 

 datam distantiam ob ipsius solido vertice propiore." The 

 author gives a geometrical and an analytical solution of the 

 problem, and concludes, '• Solutio geometrica in eo huic 

 posteriori pncstat quod ibi determinatur solidum maximic 

 attractionis etiam inter solida omnia irregularia, hie 

 tantum inter solida genita rotatione curva: circa axem." 



The greater part of this second volume is taken up 

 with the important writings of Laplace, Poisson, Gauss, 

 Ivory, and Plana. 



In the case of Laplace, who was, like some other 

 writers, not in the habit of acknowledging his indebted- 

 ness to preceding authors, the result of the investigations 

 is to restore his reputation to its proper eminence. " In 

 the present history, and in that of Probability, I have gone 

 over a third part of the collected mathematical works of 

 Laplace ; and to that extent the evidence of his great 

 powers and achievements is, I hope, fully and fairly 

 manifested." 



Our work is now nearly done ; were we to make use of 

 all our notes, we might easily double and treble what we 

 have written.* We have noted upwards of filty articles 

 which are interesting as sidelights : thus, § 227, Bouguer's 

 remarks on what we now call the " personal equation ;" 

 § 710, transformation of variables in a triple integral, and 

 many others. The value of the index would have been 

 enhanced had reference been made to these ; as it is, the 

 index is much fuller than in the earlier volumes, and we 

 have detected but few errors. Thii is no new feature, for 

 all Mr. Todhunter's books are most carefully got up in 

 this respect, and we have not met with a single important 

 error in the mathematical work ; the few mistakes we 

 have come across are easily corrected. 



There are indications here and there throughout the 

 volumes that, should the writer be able to secure the re- 

 quisite leisure, he will not want for subjects to exercise 

 his special gifts upon. We sincerely hope that he will do 

 so at an early date, and that it may be our lot to read the 



* In our remarks we have preferred to treat the subjects from an histori- 

 •cal rather than from a'mathematical point of view. 



results. In the course of the preparation of the present 

 work Mr. Todhunter has published, in the Royal and 

 other Societies' proceedings, \-ariou5 papers which have 

 grown out of his investigations in the history of our two 

 subjects.* R. Tucker 



TRAINING 



Training in Theory and Practice. By Archibald 

 Maclaren. Second Edition. (Macmillan & Co., 1874.) 

 ry-HEREVER we go, " The Boat Race " is the topic 

 of the hour. Opinions are freely expressed as to 

 the relative merits of the rival crews; and the risks and 

 dangers incurred during the process of training, sturdily 

 insisted on by some, are as obstinately denied by others. 

 The respective values of the slow and quick stroke — the 

 American fashion of '" sliding-seats," and a variety of 

 kindred questions, are eagerly debated, occasionally by 

 men who really understand what they are talking about, 

 but more frequently in order to make conversation, or, as 

 the phrase goes, '" for the sake of something to say." 



In such a state of the public mind, it has by a happy 

 chance been so ordered that the second edition of Mr. 

 Maclaren's well-known work on Training should appear, 

 at a moment when all will take unusual interest in its 

 contents. 



From a perusal of this treatise everyone may gather 

 information calculated to be of service to him, not 

 only for the time being but for the future. The 

 man who likes to know a little of cverthing, may 

 with advantage indulge his curiosity about a subject 

 which has perhaps hitherto been out of his line ; 

 while the father with a son in " the eight," and 

 whose mind has been disturbed by letters in the papers, 

 hinting at dire mischief as the outcome of training, may 

 find substantial comfort in its pages. All those who, either 

 from necessity or for amusement, undergo much physical 

 exertion, will do well to mibue themselves with the author's 

 teaching ; and the " man of case " or of sedentary occupa- 

 tion will find hints for health or sanitary lessons of a de- 

 scription which, if honestly carried out, would cause the 

 ruin of half the doctors in London. 



Mr. Maclaren uses "rowing" as the peg on which to 

 hang his theme, and the reason he gives for so doing is as 

 follows : — 



" It is the exercise most susceptible of being influenced 

 by a judicious system of bodily preparation, being at 

 once an act of considerable intricacy, demanding long 

 and assiduous practice, and an exercise of considerable 

 difficulty, involving the possession, although not in an 

 equal degree, of both muscular and respiratory power, to 

 promote which is the object of all training.' 



The question, what is training ? and what is it meant to 

 do ? he answers thus : — " It is, to put the body with 

 extreme and exceptional care under the influence of all 

 the agents which promote its health and strength, in 

 order to enable it to meet the extreme and exceptional 

 demands upon its energies." There can be no doubt that 

 the essence of this paragraph is contained in the words 

 "extreme and exceptional c.nre ;" — for without such care, 



* Possibly some further memoirs of use might be found in the '* Libro- 

 rum in Bibliotheca Specula: Pulcovensis, anno 1858, excunte contentorum 

 catalogus systematicus," by Otto Struve. Petropoli, 1S60. 



