OBSERVATIONS 



RELATIVE TO 



THE FORM OF THE 



ARBITRARY CONSTANT QUANTITIES 



THAT OCCUR IN THE INTEGRATION OF 



CERTAIN DIFFERENTIAL EQUATIONS ; 



AND, AXSO, IN THE INTEGRATION OF A 



CERTAIN EQUATION OF FINITE DIFFERENCES. 



By THE Rev. JOHN BRINKLEY, D. D. F. R. S. M. R. I. A. 



AND ANDREWS' PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF DUBLIN. 



Read, June 23, 1817 



It is well known that the integral of a differential equation 

 of any order will contain as many constant arbitrary quanti- 

 ties as the order contains units, and it is generally assumed 

 that tliey are entirely arbitrary, as well in form as in quantity. 

 But making them arbitrary as to form, oftentimes makes them 

 less comprehensive than they would otherwise be. 



