38 



On the 13th of December, 1847, while walking on the 

 South Circular Road, near the Richmond Penitentiary, about 

 11 o'clock at night, he observed a remarkable meteor ; it first 

 appeared in the west, very brilliant, and about 30° above the 

 horizon ; it moved rapidly towards the observer, passing 

 between him and the above-named building, in an easterly 

 direction ; disappeared about 500 yards off, and a slight noise 

 from it was distinctly heard as it passed. 



The evening was rather cloudy ; wind southerly. 



Barometer, 29.716 



Thermometer, ^3° 



Sir William Rowan Hamilton gave an account of some 

 applications of Quaternions to questions connected with the 

 Rotation of a Solid Body. 



I. It was shown to the Academy in 1845, among other 

 applications of the Calculus of Quaternions to the fundamental 

 problems of Mechanics, that the composition of statical couples, 

 of the kind considered by Poinsot, as well as that of ordinary 

 forces, admits of being expressed with great facility and sim- 

 plicity by the general methods of this Calculus. Thus, the 

 general conditions of the equilibrium of a rigid system are 

 included in the following formula, which will be found num- 

 bered as equation (20) of the abstract of the Author's com- 

 munication of December 8, 1845, in the Proceedings of the 

 Academy for that date : 



In the formula thus cited, a is the vector of application of 

 a force denoted by the other vector /3; and the scalar symbol, 

 - c, which is equated to the sum ajS -f a'/3' + . . of all the qua- 

 ternion products aft, aft', . . of all such pairs of vectors, or 

 directed lines a and ft, is, in the case of equilibrium, indepen- 

 dent of the position of the point from which all the vectors 



