sit Outline of general Methods for the Development 



will probably be totally lost to the public To me, as an in- 

 dividual, they were of no value, as I preserve no collection, 

 and as I have no occasion to convert them into money. 



In February 1815 I embarked for Eurojoe, and in Septem- 

 ber presented my whole collections to the Court of Directors, 

 with an order from the Lords of the Treasury for their being 

 deUvered free from duty, — an order which was granted with 

 ^he utmost liberality and urbanity. 



LV. Outline of general Methods for the Development of certain 

 Branches of Analysis. By A Corrkspondent. 



To the Editor of the Philosophical Magazine and Journal. 



Sir, 



ALTHOUGH the superiority of analytical methods of in- 

 quiry is now generally recognised, and such methods al- 

 most universally adopted, it is still frequently to be observed, 

 that the change which has thus been effected in many investi- 

 gations is more in the mere form than in the spirit. The 

 essential character of the algebraic analysis consists in the ex- 

 treme generality with which it regards every object it con- 

 templates. It is this which raises it so infinitely above the in- 

 vestigations of geometry. These are necessarily confined to 

 the contemplation of particular cases, and proceed by methods 

 which might almost be termed tentative. Now the mere be- 

 stowing upon such methods the appearance of algebraic in- 

 vestigation, or the mere substitution of symbolic characters 

 for words, does not constitute an analytical procedure. Before 

 the subject can partake of the true spirit of analysis, tentative 

 methods must be banished entirely — the reasoning as well as 

 the result must be generalized — and all the widely different 

 processes by which the particular truths of one family were 

 formerly obtained, must be condensed into one sweeping march^ 

 of symbolic transformations. I have said that this spirit of 

 generality is not yet bestowed upon many investigations pro" 

 fessedly analytical ; and I refer in proof of my assertion to the 

 common modes of treating the arithmetic of sines. The in- 

 quirer leads us on, throughout the elementary formulae, by an 

 algebraic synthesis, which like the geometrical appears natural, 

 and is easily followed, so long as it merely regards the ele- 

 mentary formulae ; but the instant that he passes beyond the 

 mere elements, and attempts to develope the remoter series, 

 he is compelled to resort to methods of a varied and tentative 

 character, that are quite unknown in a truly analytical in- 

 quiry. 



