During his residence at Bath, although greatly occupied with professional engagements, the time he devoted to his mathematical studies was surprising. Often, we are told, after a fatiguing day’s work of fourteen or sixteen hours among his pupils, he would, on returning home at night, repair for relaxation to what many would deem these severer exercises. In this manner, in the course of time, he attained a competent knowledge of geometry, and found himself in a condition to proceed to the study of the different branches of physical science which depend upon the mathematics. Among the first of the latter that attracted his attention, were the kindred departments of astronomy and optics. Having applied himself to these sciences, he became desirous of beholding with his own eyes those wonders of the heavens of which he had read so much, and for that purpose he borrowed from an acquaintance a two-feet Gregorian telescope. This instrument interested him so greatly, that he determined to procure one of his own, and commissioned a friend in London to purchase one for him, of a somewhat larger size. But he found the price was beyond what he could afford. To make up for this disappointment, he resolved to construct a telescope for himself; and after encountering innumerable difficulties in the progress of his task, he at last succeeded, in the year 1774, in completing a five-feet Newtonian reflector. This was the commencement of a long and brilliant course of triumphs in the same walk of art, and also in that of astronomical discovery. Herschel now became so much more ardently attached to his philosophical pursuits, that, regardless of the sacrifice of emolument he was making, he begun gradually to limit his professional engagements, and the number of his pupils. Meanwhile he continued to employ his leisure in the fabrication of still more powerful instruments than the one he had first constructed; and in no long time he produced telescopes of seven, ten, and even twenty feet focal distance. In fashioning the mirrors for these instruments, his perseverance was indefatigable. For his seven-feet reflector, we have been informed that he actually finished and made trial of no fewer than two hundred mirrors before he found one that satisfied him. When he sat down to prepare a mirror, his practice was to work at it for twelve or fourteen hours, without quitting his occupation for a moment. He would not even take his hand from what he was about, to help himself to food; and the little he ate on such occasions was put into his mouth by his sister. He gave the mirror a proper shape, more by a certain natural tact than by rule; and when his hand was once in, as the phrase is, he was afraid that the perfection of the finish might be impaired by the least intermission of his labours.