Notices respecting New Books. 291 



pher. Many explications and discussions have appeared at different 

 times, more or less converging towards a correct theory of these 

 cases ; and we think the doctrine may be called complete as it ap- 

 pears in the work of Mr. Young*. 



The doctrine of curves and curve surfaces is also developed with a 

 neatness and elegance which We do not recollect to have seen in any 

 English work ; and though Mr. Young refers to Monge and Leroy as 

 the authors whom he has principally had in view as models, yet upon 

 looking into the work of the latter, we remark several great improve- 

 ments in the execution; and as to that of the former, the portions which 

 it could contribute to any elementary work are necessarily very few. 

 We were particularly pleased with the demonstrations of the theo- 

 rems of Euler and Meusnier upon the curvatures of surfaces, and with 

 the somewhat novel way in which the evolutes of curves of double 

 curvature are explained (p. 224.). Regard, however, must be had 

 to a little correction on p. 22.5, as supplied in the Errata. VVe have 

 remarked a few typographical errors in other parts of the work which 

 it would be well to annex to the list already given, and which we 

 hope the publisher will do. The paralogisms of some other writers, 

 — distinguished ones too — are pointed out in the Preface, and in the 

 body of the work ; and many steps which have hitherto been deemed 

 unquestionable, have been shown by Mr. Young to be altogether 

 fallacious. We wonder, indeed, when we see them pointed out, why 

 they did not occur to ourselves nor to anybody else till now ; and 

 we look upon the aptitude displayed in these detections to be highly 

 characteristic of a mind which looks with a laudable anxiety to the 

 purity of the fundamental principles of science. 



The advantages furnished by the Syndics of the Cambridge Univer- 

 sity press in bringing out mathematical books, amounts almost to a 

 monopoly ; and the general prepossession of the public in favour of 

 Cambridge men actually completes that monopoly, and shuts the 

 door against all competition from mathematicians less advantageously 

 situated t- Taking all circumstances into account, we doubt whe- 

 ther 



• We would suggest to Mr. Y. that the remark at p. 106, needs no qua- 

 lificEtion, the same remaining true from h=. to h = a, both inclusive ; 

 for when h = a, although the expression becomes then 



c = e + »J~u . rt« + - — =^ • a' + 



it nevertheless continues true, because all the imaginaries on the right side 

 will destroy each other. 



Mr. Young has established, too, that when negative powers of h enter 

 into the development, the terms which precede the first such power of A, 

 is the true expansion : and it seems, we would hint, to depend on the same 

 principle, viz. that all the infimlcs neutralize each other. 



t " It is very easy to account for the appearance of more mathematical 

 publications from (."ambridgc," says Dr. Abram Robertson, " than from any 

 otiier place in this kingdom. The members of that University, who persevere 

 in the study of science, and who are conscious of their ability cither to 

 elucidate its truths, or enlarge its boundaries, can look with confidence to 

 the syndics of the press for assistance, to render their writings profitable to 

 themselves, and useful to the public. All apprchcni-ion as to the pecuniary 

 2 P 2 risk 



