394 



Sir "W. E. Hamilton, LL. D., read a paper (previously communicated 

 to the President) — 



On a Geneeal Centke of Applied Fokces. 



Observatory, May 25, 1863. 



Sir W. R. Hamilton wishes a note to be preserved in the " Proceed- 

 ings" of the Eoyal Irish Academy, that on recently reconsidering an 

 application of Quaternions to the Statics of a Solid Body, some account 

 of which was laid before the Academy many years ago (see the Pro- 

 ceedings"*- for December, 1845), he has been led to perceive the theore- 

 tical (and to suspect the practical) existence of a certain Central Point 

 for every system of applied forces, not reducible to a couple, nor to zero : 

 which generally new point, for the case of parallel forces, coincides with 

 their well-known centre. 



An applied force AB, acting at a point A, being said to have a qua- 

 ternion moment, equal to the quaternion product OA . AB, with respect 

 to any assumed point 0, the sum of all such moments, or the quaternion, 

 Qr=^{OA . AB) = OA .AB+ OA' . A^B' + &c., is called the total 

 quaternion moment of the applied system with respect to the same point 

 0. 



This total moment Q varies generally with the point to which it is 

 referred ; and there is one point G, or one position of 0, for which the 

 condition 



TQ - a minimum, 



is satisfied, with the exceptions (of couple and equilibrium) above alluded 

 to. 



It is this point C, which Sir W. E. H. proposes to call geyierally the 

 Centre of a System of Applied Forces. 



In the most general case of such a system, he finds it to be situated 

 on the Central Axis, the minimum TQ representing then what was called 

 by Poinsot the Energy of the Central Couple. 



Por the less general case of an unique resultant force, the quaternion 

 Q reduces itself to zero at the new Central Point C, which is now situ- 

 ated on the resultant, and determines its line of application. 



Sir W. E. Hamilton read a communication On the Locus of the 

 Osculating Circle to a Curve in Space." 



The President exhibited a copy of Letters Patent granted by Queen 

 Elizabeth, in the 37th year of her reign, to the Provost and Pellows of 

 the newly founded University of Dublin, committing to them the custody 

 of the temporalities of the See of Tuam, then seised to the Crown, by 

 reason of the death of Archbishop "William Lally, or Mulally, and to be 

 accounted for into the Exchequer according to the true annual value. 



John Anster, LL. D., on the part of Lieut. -Colonel Prench, presented 

 to the Academy a large collection of East Indian musical instruments. 



The thanks of the Academy were voted to the donor. 



* See " Proceedings of the Royal Irish Academy," vol. iii., Appendix, pp. Ivii., Iviii. 



