ON SIR ISAAC Newton's first solution of the pro- 

 blem TOR finding the relation between resis- 

 tance AND GRAVITY, THAT A BODY MAY BE MADE 

 TO DESCRIBE A GIVEN CURVE; AND THE SOURCE OP 

 ERROR IN THAT SOLUTION POINTED OUT. 



BY THE REV. J. BRINKLEY, D.D. F.R.S. <S* M.R.I.A. 



ilNDREWS PROFESSOR OF ASTRONOMY IN THE UNIVERSITY OF DUBLIN. 



READ, MAY 25, 1307. 



It is well known, that Newton's investigation of this pro- 

 blem, as published in the first edition of the Priiicipia,* is 

 erroneous. In the subsequent editions, the illustrious author 

 has given an accurate solution, by an entirely different me- 

 thod, and without adverting to the former solution. John 

 Bernouilli seems to have been the first who pointed out the 

 erroneous conclusion in the first edition .-j- Nich. Bernouilli 

 imagined he had discovered the source of error in the New- 

 tonian solution. His opinion seems to have been generally 

 acquiesced in till lately, when the celebrated Lagrange, in 

 his ingenious work, entitled " Theorie des Fonctions ana- 

 lytiques," remarked, that Newton's solution is accurate in 

 the part in Avhich N. Bernouilli had thought it erroneous. 

 Indeed had the error been such as was pointed out by N. 



Bernouilli, 



* Lib. II. Prob. 3. 



t Mem. Acad. Scien. nil. & Tom. I. opera Bernouilli. 



