290 Notices respecting New Books. 



perspicuous detail of the logic of the science, and the practice of the 

 art. This is precisely the purpose by which Mr. Young seems to have 

 been directed. There arc no affected changes of method : there is 

 no parade of original plan, or of novelty of principle ; and yet there 

 is much original matter, much original reasoning, and, what is of 

 more value than all questions about originality in an elementary 

 treatise, there is a perspicuity, a unity of method, prevailing in all 

 its jjarts, that renders it, more than any book we have seen, peculiarly 

 adapted to instruction. It is professedly composed " for the Use of 

 Students in Schools and Universities ■" and we think the science is 

 brought more nearly to the level of school-boy capacities, than any 

 work we have consulted brings it to the understanding of a University 

 two-year man. We are |)ersuaded that with due attention to the 

 steps of explanation and demonstration, any student with ordinary 

 powers of mind, and tolerably familiar with elementary algebra, may 

 master the difficulties of the Differential Calculus by means of this 

 work with very great facility ; and this once effected, he will jjroceed 

 to its diversified applications with a success that can never attend 

 the labours of those who take first principles upon trust, and lean 

 for the truth of the processes themselves, upon the authority of an 

 imperfect evidence. 



It is not, however, as an elegant and perspicuous development of 

 the first principles of the Calculus, merely, that we have admired, 

 and therefore recommended, Mr. Young's little work : we havefound 

 much to commend in it of a more profound character; much that we 

 look for in vain in larger works, and indeed, in all English works. 



We have already occupied so much of the room that we can devote 

 to this notice, that we cannot possibly enter into particulars; and, 

 indeed, we have greatly exceeded the limits of our plan, so that no 

 apology will be expected from us if we refer those readers who are in- 

 terested in this branch of mathematics, to the book itself, rather than 

 transcribe it into our pages. We feel, however, that we should appear 

 too abrupt to our readers and unjust to Mr. Young in closing without 

 noticing one or two of his chapters. One is the discussion of the 

 failing cases of Taylor's theorem (p. 98.) : a chapter which offers a 

 fair specimen of that happy facility in the discussion of an intricate 

 and embarrassing question, which pervades the work, and which we 

 think marks the perfection of didactic writing. This theorem, the mere 

 accidental notice of which has conferred immortality on its author, is 

 made the basis of almost all those mathematical processes employed in 

 physical inquiry which in any way involve the Differential Calculus; 

 and it has been aptly denominated by the late lamented namesake of 

 the gentleman whose work we have now under review, (Dr. Thomas 

 Young,) " a universal Solvent of Analytical difficulties." Whether 

 this appellation be too strong or not, we shall not here inquire ; but 

 it has long been known, that as a general expression, it is subject to 

 some limitations in its application. The knowledge that such limita- 

 tions did exist, and our ignorance of any test by which their presence 

 might be recognised, has long rendered the settlement of this ques- 

 tion a matter of anxious interest to the mathematician and philoso- 

 pher. 



