Miscellanies. 347 



P P 



4+2nP /4+2nP 



that is we shall have =6 ; .'.by (6) z cos. I ~ 



z COS. 6 = z decomposed in the direction of x, =a:; or z cos. 6 =x, 



P /P \ 



(7); and by changing 6 into ^ — 6, we have 2; cos. [q —&j =z sin. 



6=y, (8); by adding the squares of (7) and (8), since cos.^^ + 

 sin.2^ = l, we have z'^ =x- ^y"^, (9) ; hence by (7), (8), (9), two 

 forces X and y, whose directions form a right angle, have for their 

 resultant the diagonal of the rectangle, of which they are the adja- 

 cent sides. The usual rules for compounding and resolving forces, 

 can now be easily obtained, but for these, we must refer to Vol. 

 XXVI, No. 2, Art. V, of this Journal, to which this paper is in- 

 tended as a supplement. We will add that the method here given is 

 new to us, and if we do not greatly err, it is as simple as the nature 

 of the subject admits. 



Note. — We have in this paper used (for brevity,) the term angle, 

 to denote arcs, whether they are greater than two right angles or not. 



MISCELLANIES. 



FOREIGN AND DOMESTIC. 



1. Fifth Meeting of the British Association for the Advance- 

 ment of Science at Dublin, Ireland, July, 1835. — In our No. for 

 April, 1835, we gave some account of the proceedings of the Brit- 

 ish Association for the advancement of Science at Cambridge Uni- 

 versity in 1833, and at Edinburgh in 1834. The recent meeting 

 at Dublin, (August, 1835,) api)ears to have been equally spirited 

 and interesting, as its predecessors, and we are indebted to the Lon- 

 don Atheneum for a detailed account, from which we have room to 

 extract only a few notices. 



The President of the Association, was the Rev. Dr. Lloyd, Pro- 

 vost of Trinity College, Dublin. 



Vice Presidents, Lord Oxmantown and Rev. Wm. Whewell, of 

 the University of Cambridge. 



Secretaries, W. R. Hamilton, astronomer Royal of Ireland, and 

 Rev. W. Lloyd, Prof, of Nat. Philos. • 



Treasurer, Henry Aspen, M. D. 



