188 Mr. Harvey on the Theory of Arhogast. [Sept. 



inversely as the fourth power of the distance, by help of prop. 81 

 example 3, Princip. that force, therefore, which varies inversely 

 as the square of the distance, appears to be the only one that can 

 produce all the observed phenomena of cohesion. 



Article IV. 



On the Theory of Arbogaat respecti?ig the Separatism of the Sym- 

 bols of Operation from those of Quantity. By Mr. G. Harvey. 



(To Dr. Thomson.) 



SIR, Plymouth, June 5, 18^0. 



The celebrated Arbogast has well remarked in the preface to 

 hislearned work " DuCalculdes Derivations," that "lesecretde 

 la puissance de I'analyse consiste dans le choix et I'emploi 

 heureux de signes simple et caracteristique de la chose qu'ils 

 doivent representer." Of the truth and propriety of this remark, 

 an historical review of theprogress of analysis will present many 

 examples ; of the advancement which particular departments 

 have made by the judicious adoption of appropriate symbols; 

 and the way in which other interesting branches of analytical 

 inquiry have been retarded by not attending to this important 

 particular. 



In selecting or contriving a symbol to designate any analytical 

 operation, we shall not communicate to the analysis the full 

 powers of the symbol by regarding it merely as an instrument to 

 facilitate our present inquiries ; or only to estimate its immediate 

 operations on the functions or quantities which it is destined to 

 influence and controul; but in its adoption, to regard its capabi- 

 lities in a prospective as well ae a present point of view ; and to 

 contemplate the possibility of its producing, even from its oicn 

 evolutions, new and enlarged ideas respecting analytical science. 



I need not go far for examples to prove the consistency of 

 these observations. Every one conversant with the progress of 

 analytical inquiry will instantly recollect the facilities and 

 advantages which have resulted to the differential calculus, and 

 the splendid consequences which have been obtained, by the 

 employment of the notation of Leibnitz ; and to the theory of 

 finite differences from the notation of Euler ; not to mention the 

 harmonious character which these possess, with the notation 

 adopted by Lagrange, for his delicate and refined calculus of 

 variations. 



I have been led into this train of reflection by reviewing some 

 of my MSS. on the method first announced by Arbogast respect- 

 ing the separation of the symbols of operation from those of 



