Notices respecting Neio Books. 307 



Now, putting out o£ the question the curious clerical error — for 

 such we suppose it to be — of calling B the axis of greatest or least 

 moment of inertia, we cannot help thinking that if we were to 

 write down all the steps needed to justify the conclusion, it would 

 appear that most of them are suppressed, and that even if only the 

 principal steps were indicated, still the paragraph would need con- 

 siderable expansion. The aboAe extract, it must be remembered, 

 occurs in one of the articles designed for students to whom the 

 subject is entirely new. We cannot help thinking that such a 

 student might spend a long time over it, and have after all to get 

 help from his private tutor before fairly making out its meaning. 



The merits of Mr. Routh's Treatise are so great and so generally 

 acknowledged, that we are sure the purpose of our remarks will 

 not be misunderstood. It is merely this, that the above-quoted 

 passage leaves too much to be made out by the unaided sagacity of 

 a student who is just beginning a difficult part of a difficult sub- 

 ject. We suspect that a careful examination of the volume would 

 reveal other points hi which greater fulness of exposition would be 

 of advantage to the student. 



An Elementary Treatise on tJie Integral Calculus, containing Appli- 

 cations to Plain Curves and Surfaces ; ivith Numerous Eccamples. 

 By Beis-jamin AVilliamsois", M.A., Fellow and Tutor, Trinity 

 College, Dublin. Second Edition, Revised and Enlarged. London : 

 Longmans, Green, and Co. 1877. (Crown 8vo, pp. 348.) 

 We gave a brief account of this work on the appearance of its 

 first edition (vol. xlix. fourth series, p. 319), and what we then said 

 of it is applicable to the present edition — except that we have to 

 notice the addition of two chapters, which together increase the 

 volume by more than a fourth part. The first of these chapters is 

 on " Moments of Inertia." It contains not merely an account of 

 the methods of determining the moments of Inertia of bodies with 

 reference to given axes, but also enters into the determination of 

 products of Inertia, and questions connected with the momenta! 

 ellipsoid and principal axes of a solid. In fact, its contents coincide 

 pretty closely with those of the chapter on moments of Inertia and 

 principal axes, which usually forms part of a treatise on the motion 

 of a rigid body. For the methods adopted in the chapter the author 

 is " indebted to the kindness of Professor ToMTisend." There is, 

 we conceive, a distinct advantage in making such a chapter part of 

 an Elementary Treatise on the Integral Calculus ; but we think 

 the author might have gone further, and should have inserted a 

 chapter on the determination of centres of gravity. These deter- 

 minations, like those of moments of Inertia, form a branch of 

 Geometry which it is a gain for the student to understand, and to 

 have had practice in, before entering on the more advanced parts of 

 Mechanics. 



The second chapter peculiar to the present edition is on " Mean 

 Value and Probability," and, of course, relates to those cases in 

 which the magnitude to be considered is subject to continuous 



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