364 Reviews, and Notices respecting Nero Books. 



between the arithmetical operation and the formula which closed 

 the algebraical investigation. The purposes of an investigation 

 were never lost sight of, and the mere transformations of an equa- 

 tion were only considered valuable as they tended to a more facile 

 determination of the numerical result. Algebra was viewed as a 

 universal arithmetic, only because the laws of its changes were iden- 

 tical with those of arithmetic, and because it thereby became, in 

 fact, a part of the process of finding the solution of an arithmetical 

 problem. 



We do not deny that this arithmetical purpose, as thejinal one, 

 of algebraical research, may be productive of confined views of the 

 nature and purposes of that most extraordinary instrument of the 

 human mind, nor do we wish to see any of the delicate and subtle 

 abstractions that characterize our modern algebra, less valued than 

 they are in our own day ; but we must enter our protest against 

 the almost universal neglect of the numerical part of the processes 

 that have been derived from algebraical investigations (in our ele- 

 mentary works on almost every branch of physical and mathema- 

 tical science) which is becoming every succeeding day more and 

 more prevalent. If formulae be intended to exhibit the curious and 

 diversified relations of figure or number, then, indeed, the deriva- 

 tion of the formulae may properly be considered the final object, — 

 and we think that in pure mathematics there cannot be a more in- 

 teresting employment than this ; but if the investigation relates to 

 the phenomena of nature or the actual value of the unmeasured 

 parts of measured figures, we hold that the method of conducting 

 the whole investigation, from its measured parts to the determina- 

 tion of the calculable parts, ought to be clearly and completely 

 taught in every elementary book on those particular subjects. 

 How imperfectly this is done in our most modern elementary trea- 

 tises on Trigonometry, Mechanics and Physical Astronomy, we 

 need not particularly specify ; nor can it be doubted that the many 

 excellences transplanted from our foreign mathematical cotempo- 

 raries, have been much diminished in their real value by our servile 

 imitation of them in keeping aloof from the vulgarity of numerical 

 application. The time to acquire these habits of numerical accu- 

 racy and expedition is, when the method of deriving the rules is 

 first acquired j and it is to the neglect — the culpable neglect — of 

 this practice, in our modern systems of mathematical education, 

 that we owe the discreditable fact, — the too frequent incompe- 

 tency of our most distinguished academic youth, to proceed from 

 the observed elements to the numerical result of a physical pro- 

 blem, if that problem but very little exceeds the most common 

 degree of difficulty. A parade of symbolic abstraction and a fond- 

 ness for algebraical conundrums, are too prevalent amongst the 

 mathematicians of our own day, — infesting our seats of learning to 

 a degree that almost defeats the useful purposes which mathematics 

 as a branch of general education is calculated to afford. " More in 

 sorrow than in anger" do we mention this ; but we cannot shut our 

 eyes to the melancholy fact, nor yet to the melancholy conse- 



