1820.] Mr. Harvey on the Theory of Arbogast. 189 



quantiti/ ; and the elements of which, adapted to his " Signes 

 des Derivations," may be seen in the second general article of 

 his work ; together with its application to the symbols of the 

 differential calculus and finite differences in Articles 371 and 

 442. 



The remarkable simphcity attendant on many of the investiga- 

 tions of analysis by the method just alluded to, and the concise 

 and beautiful demonstrations it affords of many interesting and 

 important formula), renders the inquiry peculiarly instructive 

 and pleasing. 



We well know that the generality of functions often disclose 

 by the successive and varied eifects of the symbols of operation, 

 new, and remarkable laws ; but to mark the changes which the 

 symbols themselves undergo in these operations ; and to draw 

 from their characteristic forms, the elements of almost a new 

 analysis, is an idea, original in its kind, due to Arbogast alone, 

 and owes its origin to the happy adoption of the differential 

 notation. It was this view of the subject doubtless which 

 induced a learned and skilful analyst* to I'emark, that the 

 system of notation resulting from the theory of Arbogast "seems 

 to unite in the most perfect manner the properties of conciseness, 

 simplicitj', and elegance, and appears pecuharly well adapted to 

 open new and enlarged views of the extent and' meaning of ana- 

 lytical operations." 



Mr. Woodhouse in his admirable work on the " Principles of 

 Analytical Calculation," and ftlr. Herschell in the treatise just 

 alluded to, are the only analysts, as far as I am aware, who have 

 directed the attention of our younger mathematicians to this 

 important subject. And as it is the object of a periodical work 

 like the Annals of Philosophy, not only to be the repository of 

 the new and original views which men of genius are continually 

 producing ; but also to give a wide circulation, and an accele- 

 rated effect, to truths which have hitherto been confined to 

 treatises accessible only to a i&\\, I have conceived that some 

 elementary remarks on the theory of Arbogast, and some illustra- 

 tive examples, may not only be of immediate benefit to the 

 young analyst, but may also induce him to extend his inquiries 

 to the authors above-mentioned ; and thus to diffuse in a wider 

 degree the taste for analytical researches, which now seems so 

 rapidly forming in this island. f 



• Mr. Ile^^clleIl in his Appendix to the translation of La Croix's Differential 

 Calculus, p. 479, 



t The future historian of an^l^sis will probably trace to Mr. Woodhouse's 

 Ircatisc on analytical calculation, the dawn of those just and enlajrged views of (lie 

 iiaturc of analysis in general, now so widely ditl'used among the self-laught mndie- 

 iiiaticians of this island. And to the same work we may allrlbiitc the popularity 

 which the calculus of functions is so rapidly acquiiing; and by means of which 

 the student may he conducted " from the unalijsis offinlle (/iiaiUUies into tlic nnali/fii 

 of injiiiilc n-ilhoul formaUi) announcing to him his arrival on Ihcir boundaries, or rcginr- 

 ing him ubrnpllij to passthem,"—{yi ooAho\ise, ibid. p. 72.) 



