IN THE THEORY OF DIFFERENTIAL EQUATIONS. 547 



et soient d'ailleurs <b(x, y), X (», y) les deux derivees partielles de la fonction F(x, y) par 



du du 



die dtJ 

 rapport aux deux variables x et y. De Pequation connue — = -^ , en y remplacant u par 



F(x, y), N par l'unite, et M par -f{w, y), on tirera 



/(*> y) 



This means that F(a, y) = C gives F x + F y .y = 0, so that y'= /(a?, y) gives 



F y =-F x : f. 



But the constant substitution, throughout the work, of distinct letters for differential coeffici- 

 ents, has established Mdx + Ndy = as the representative of the differentiation of 



F(x,y) = C. 



If it be thought necessary to mark differentiation by a symbol, an accent may be added, 

 as in y' x used for dy : dx. This accent may be omitted in working or in continuous writing, 

 and may be supplied in revising the manuscript. 



A. DE MORGAN. 



University College, London, 

 March 25, 1854. 



