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XXXVIII. Notices respecting New Books. 



An Eleme7itary Treatise on the Differential Calculus : comprehending 

 the complete Theory of Curve Surfaces and Curves of Double Cur- 

 vature. By J. R. Young. 



HOW cursory soever be the survey we take of the present state 

 of physical science, we must be convinced how extensively 

 dependent it is upon the Differential and Integral Calculi, in some 

 or other of their varied modifications. So complete, indeed, is this 

 dependence, that he who attempts to pursue any one branch of 

 physical inquiry beyond its simplest and most elementary state, will 

 find his progress at once arrested, if he be not provided with this 

 apparatus of research : and those who have penetrated most pro- 

 foundly into the arcana of nature and of nature's laws, have uni- 

 formly concurred in the statement — that the principal desiderata 

 are improved methods of effecting the mathematical processes to 

 which the individual inquiries give rise. Several branches of philo- 

 sophical investigation, indeed, seem to admit of no boundary, save 

 that which the imperfection of our mathematics impresses on them ; 

 and every improvement which the calculus receives is sure to open 

 new facts and new views, and often new paths of inquiry, which the 

 mere experimentalist could never have suspected. The time may 

 come, too, when sciences which as yet seem to acknowledge no dis- 

 coverable quantitative laws, and especially with respect to the modi- 

 fication in the intensities of the producing forces, shall offer a splen- 

 did triumph to human perseverance, and fall as completely under 

 the dominion of the symbolic methods, as the system of the celestial 

 motions in the writings of Laplace can exhibit in our own time. This 

 consummation is neither so visionary nor so remote as to discourage 

 our hopes or paralyse our exertions : it rather, on the contrary, ani- 

 mates us with redoubled assiduity, whilst it offers the most cheering 

 encouragements to future labourers. Already some gifted minds are 

 intent upon marking the probable boundaries, and the proper route 

 to be pursued 3 others are penetrating the dense and tangled masses of 

 foliage, with which the baneful tree of error has overrun the soil, 

 and intercepted our view of the recesses of nature's works ; while 

 others again, more'humbly but not less usefully perhap.^, stand at the 

 entrance to encourage the young adventurer, and to point out to him 

 the surest and the most successful route he can pursue. It falls to 

 the lot of few to open new paths ; but every man of science may 

 more or less contribute to the ulterior object of all their exertion, and 

 facilitate the progress of the young philosopher by removing the ob- 

 KtaclcB that would arrest his career. It is true, that in the capacity 

 of elementary writers or scientific lecturers, all men will not be alike 

 successful, whatever their actual attainments may be; for the peculiar 

 faculties of the mind are as much displayed in tlie composition of an 

 elementary book, in the verbal explanation of a process, or the illus- 

 tration of a principle, <is in any liiglicr order of intellectual exertion. 

 Hlgiier, indeed, we have called it ; but we are not sure tliat there is 

 less loftiness of view, whilst we are certain that there is often much 



