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eminently gifted, in improving, by means of it, every subject he 

 ever handled. There is no one capable of appreciating such subjects, 

 who will not agree with me, that during the several years of his 

 purely mathematical lectures nothing could exceed the depth, or 

 surpass the exquisite taste and elegance, of all his original concep- 

 tions, both in analysis and in the ancient geometry in which he 

 delighted. Nor will it be denied, by any one who was so happy 

 as to possess the opportunity of judging, that during the last three 

 years and a half in which he filled the chair of Natural Philosophy, 

 his earnest endeavour was to instil sound and accurate physical 

 conceptions into the minds of his hearers, and to array them, when 

 stated into mathematical language, in all the charms which result 

 from true taste and refinement. 



" In his first course of lectures (on the Eotation of a solid Body 

 round a fixed Point), he completely solved the case of a body aban- 

 doned to its own motions, on receiving a pruiiitive impulse in any 

 direction, under the action of no accelerating forces. This prob- 

 lem he had finished several years before, and was preparing it for 

 publication, when he was anticipated by Poinsot, who published a 

 very elegant tract on the subject. Both theories are founded on 

 the same principles, and exhibit the effects of the forces in diffe- 

 rent positions of the body, as well as the actual motions of the 

 body itself, by means of an ellipsoid described round the fixed 

 point as a centre. But they differ in employing, not the same but 

 reciprocal ellipsoids, which, though seemingly unimportant, makes 

 this difference, that Mac Cullagb's method, although not superior 

 in clearness or elegance, had the prodigious advantage of enabling 

 him to throw his geometry into the analytical form, and to deduce, 

 from the simplest geometrical considerations, the elliptic integrals 

 which expressed the circumstances of the motion, such as the times 

 of oscillation, revolution, &c. This method also enabled him to find 

 several interesting properties, which Poinsofs mode of treating the 

 question did not so readily exhibit, and which Poinsot had in fact 

 omitted to notice. Some of these results were since published by 

 Professor Mac Cullagh in the Proceedings of the Academy. Indeed 

 the whole discussion, which is in existence in its first form, as de- 

 livered by himself, is highly original, interesting, and instructive, 



