168 



- = tan ^7 (c) 



X 



holds good ; that is, the resultant force coincides in direction 

 with the diagonal of the rectangle constructed with lines re- 

 presenting X and y as sides. 



The other part of the known law of the composition of 

 forces, namely, that this resultant is represented also inmag- 

 nitude by the same diagonal, may easily be proved by the 

 process of the Mecanique Celeste, which, in the present no- 

 tation, corresponds to making 



x' = X, y' = 1/, x" = />, 

 and therefore gives 



"^ "T" y 2 2 I 2 



p 

 But the demonstration above assigned for the law of the 



direction of the resultant, appears to Sir William Hamilton 



to be new. 



It was resolved, on the recommendation of the Council, 

 to present a congratulatory address to His Excellency the 

 Lord Lieutenant ; whereupon, the Academy having adjourn- 

 ed for a short interval, an address was pi'epared, which was 

 afterwards agreed to. 



A letter was read from M. Moreau de Jonnes, present- 

 ing to the Academy two volumes of the Agricultural Statistics 

 of France. 



DONATIONS. 



Comptes Rendus Hebdomadaires des Seances de r Acade- 

 mic des Sciences, Premier Semestre. 1841. Nos. 17-24. 



Ordnance Map of the Queens County, in 39 sheets, in- 

 cluding Title and Index. Presented by His Excellency the 

 Lord Lieutenant. 



Journal of the Franklin Institute. Vol. I. Third Series. 

 (1841). 



