166 



country, of pursuing an inquii'y of deep historical interest; 

 ■which if they were to occur at the other side of the Irish 

 channel, would be grasped at with avidity by the untiring 

 zeal of many an English antiquary, who, while he cultivates 

 assiduously, and under circumstances of extreme difficulty, 

 the meagre opportunities which England affords to the 

 study of ancient British and Celtic remains, cannot but look 

 with a feeling of astonishment (akin perhaps to contempt), 

 on the apathy with which in Ireland we suffer daily the tan- 

 gible and unquestionable proofs of the early civilization of 

 our country, to which we have long proudly laid claim, ac- 

 tually to perish before our eyes, from the most disgraceful 



The Chair having been taken, pro tem2)ore, by the Rev. 

 J. H. Todd, D. D., V. P., the President communicated the 

 following proof of the known law of Composition of Forces. 



Two rectangular forces, x and ij, being supposed to be 

 equivalent to a single resultant force p, inclined at an angle 

 V to the force x, it is required to determine the law of the 

 dependence of this angle on the ratio of the two component 

 forces X and y. 



Denoting by p' any other single force, intermediate be- 

 tween X and y, and inclined to x at an angle v', which we 

 shall suppose to be greater than v ; and denoting by x' and 

 y' the rectangular components of this new force p, in the 

 directions of x and y, we may, by easy decompositions and 

 recompositions, obtain a new pair of rectangular forces, x" 

 and y", which are together equivalent to />', and have for 

 components 



x" zz- x' + ^y'; 

 p p 



y"=-y'~y-a:'; 

 P' P 



