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XXXII. On the Use of Analysis in i?ivestigating the Elementary 

 Relations of Figure and Forces. By A Correspondent. 

 To the Editor of the Philosophical Magazine and Journal. 

 Sir, 

 ¥ N a former short paper I pointed out a method by which 

 "■■ some objections to Legendre's mode of evolving the pro- 

 perties of figure from functional equations might be obviated ; 

 and I resume the subject in the hope of clearing away certain 

 misrepresentations, by means of which a sect of our philoso- 

 phers have sought to bring the principles of such methods 

 of inquiry into discredit. There is amongst one class of sci- 

 entific men in this country a violent prejudice against the use 

 of analysis, either in the elements of geometry or of mechanics. 

 They regard it, not as the mere substitution of one mode of 

 reasoning for another, but as a dangerous attempt to remove 

 from the view the experiments upon which these sciences are 

 built, and to revive the justly exploded philosophy of Leibnitz 

 and his immediate successors. I will not stop to speculate re- 

 specting the secret biases on which this prejudice rests, al- 

 though such speculation might be productive of some amuse- 

 ment, but hasten to examine the character of its ostensible 

 foundation. It may be found now and then appearing in the 

 Edinburgh Review*, in the shape of invective against the ge- 

 neralizations, &c. of the continental mathematicians : but it is 

 preferable to apply at once to the fountain head, and to seek 

 an official indication of it in the works of the great leader of 

 this sect, Professor Leslie. From them the spirit will be ob- 

 tained in its wildest and most unrectified state, and the ex- 

 emplifications of it are as numerous as it is wild. 



The following three sentences of the concluding paragraph 

 of his note respecting Legendre will amply serve my purpose. 

 " In this abstruse research assumptions are still disguised 

 and mixed up with the progress of induction. Such indeed 

 must be the case with every kind of reasoning on mathemati- 

 cal or physical objects which proceeds a priori^ without ap- 

 pealing at least in the first instance to external observation. 

 Of this kind are some of those ingenious analytical investiga- 

 tions respecting the laws of motion and the composition of 

 forces." With the second sentence of this extract I conceive 

 that every philosophic mind will now-a-days concur. There 

 cannot be evolved from any train of reasoning one single 

 truth which was not previously infused into it. Reasoning 



• See, amongst other places, the notice of a memoir nf l.aplace's in the 

 ■econd volume of the Memoiret lie la Sociele (PAi-ctu-U. I might also have 

 referred to »om'; papers in the Supplement to the Eurycl. Britannica. 



B b 2 merelv 



