to give us much information respecting them. We think that such minds are in general too reserved in relation to leaving us a correct account of all the trials of their early history. As Laplace says, "The knowledge of the method which has guided a man of genius is not less serviceable to the progress of the science, and even to his own glory, than his discoveries;" and since the method which he has pursued is often experimental and is marked by repeated failures, the record of these would save many minds the trouble of travelling the same, or nearly the same, road.

William Herschel was born in Hanover, on the 15th of November, 1738. We know but little about the ancestors of this great man.* We learn that his great-grandfather, Abraham Herschel, lived at Mähren, from which place he was expelled on account of his strong attachment to the Protestant faith; that Isaac, his son, was a farmer in the vicinity of Leipzig; and that Isaac's oldest son, Jacob Herschel, disappointed his fathers's earnest desire that he should become an agriculturist; but he had a natural aptitude and fondness for music, which induced him to embrace the profession of a musician, and to establish himself in Hanover.

Jacob Herschel was the father of the astronomer, William Herschel. He is said to have been an eminent musician, and as much distinguished for the good qualities of his heart as for the great talent which he possessed. He was in humble circumstances, and he could not, therefore, give his children (six boys and four girls) a very complete education. It would seem, however, that they inherited their father's musical talents, for they all became, by his care and instruction, excellent musicians. Jacob, the oldest, even acquired an unusual skill as a practical musician, and this procured for him the appointment of master of the band in a Hanoverian regiment, with which he passed over to England. William, the third son, remained, during this time, under the paternal roof. Here he

M. Arago has collected all the accessible information respecting them, in his Analysis of Herschel's Life and Works, published in the Annuaire for 1842.

turned his attention to the fine arts, studied diligently the French language, and devoted, also, a part of his time to the study of metaphysics, for which he preserved a decided taste up to the end of his days.

In 1759, William Herschel, then twenty-one years of age, went to England with his oldest brother, Jacob, and not, says Arago, with his father, as is generally stated. Since Jacob had previously been in England, and had become somewhat acquainted with the manners and customs of the people, William's prospects for making a beginning there seemed to be favorable. Notwithstanding these apparently advantageous circumstances, young Herschel did not find either London or the country towns to afford him any resources, and the first two or three years following his expatriation were marked by many privations; but they were manfully borne. A mind like Herschel's, however, is not to be turned aside from the object of its pursuit till every available means has been tried. Honorable exertion seldom fails in an enlightened country to bring its just reward. Through some means Lord Durham had become acquainted with his musical talents and acquirements, and he engaged the young Hanoverian to instruct the musicians of an English regiment stationed on the frontiers of Scotland. Herschel's reputation now spread rapidly, and in the course of the year 1765, through the influence of a gentleman to whom his merits had become known, he was appointed organist at Halifax, in Yorkshire. The emoluments of this place, together with what he obtained by giving lessons in the town and country, secured to Herschel a respectable income, which enabled him to gratify, to a certain extent, the desire which he had for knowledge. His early education having been somewhat neglected from necessity, he now undertook to retrieve it. While he was in this place he applied himself to the study of Latin and Italian, and gained a knowledge of these languages with no other help than a grainmar and a dictionary. He also found time to gain a smattering of Greek. But his efforts did not stop here. His desire for more extensive knowledge connected with his profession induced him to undertake the study of Dr. Robert Smith's

learned, though rather obscure, work on the mathematical theory of music. The author of this work supposed the reader acquainted with both algebra and geometry,- sciences with which young Herschel was but little, if at all, familiar. To remedy this defect in his education, he applied himself to the study of these branches of mathematics, and it is said that he very soon mastered them, so far, at least, as to answer his purpose at that time.

Let us pause here for a moment to say that Herschel followed the method of nature; that is, the method which nature points out for the study of pure mathematics. Abstract mathematics is but an instrument with which the mind discovers the truths of nature, after we have first observed her phenomena so as to arrive at her general laws, which serve as a basis for our reasoning; and certainly it would generally be a slow and tedious process to learn how to use any instrument that we do not expect to employ for any practical purpose, or at least do not know when and where we shall so employ it. But when we feel the need of anything to help us forward in whatever we have undertaken, we can soon, and with comparative ease, make ourselves masters of it. We believe, and we could quote the opinions and experiences of several excellent mathematical scholars, if this were a suitable place, to sustain us, that, in general, mathematics (above arithmetic) is given as a task to students, and for which they have but little relish, when, in reality, such an instrument should be placed in their hands only when it is asked for, to enable them to carry on their studies in those departments of inquiry which require such aid. First teach a knowledge of the phenomena of the natural world so far as it can be taught without the principle of mathematical science, and not leave the student in doubt in regard to the conclusions.

In the year 1766, Herschel was appointed organist to the Octagon Chapel at Bath. This was a more lucrative position than the one which he held at Halifax, but new obligations were connected with it. He was required to play almost constantly either at the oratorios, in the rooms at the baths, at the theatre, or in the public concerts. Besides this, his reputation

as a musician brought him through his patrons in the most fashionable circles in England numerous pupils, whom he could not refuse, to be instructed in his art. We might here pause to ask how it was possible, amid such incessant employment, and so many things to distract his attention, for him to continue his studies, which at Halifax seemed to demand an uncommon degree of resolution and perseverance, combined with extraordinary talent. But a mind which thirsts for knowledge will find time to acquire it, where one less desirous would see no opportunity.

We have already seen that music led Herschel to mathematics, and this, in its turn, led him to the science of optics, a department of natural philosophy which was the source of his illustrious career and the great reputation which he subsequently acquired. "The time finally arrived when his theoretic knowledge was to guide the young musician into a laborious application of principles quite foreign to his habits, and of which the brilliant success, as well as the excessive temerity, must excite reasonable astonishment."

While Herschel was residing at Bath, a reflecting telescope, two feet in length, fell into his hands. This little instrument showed him, as a different one, years before, had shown Galileo, numerous stars which the naked eye cannot discern: it showed him, also, terrestrial objects, well known to him, apparently much enlarged; and it revealed to him other things which the uninstructed imagination could never conceive of. The new field of knowledge, thus opened to him, interested him so much that he resolved to purchase for himself a similar telescope, though of larger size. To accomplish this he commissioned a friend in London to procure one for him, probably specifying what he could afford to pay for it. The answer from London was delayed some days, and Herschel's extreme anxiety caused those days to seem almost like years to him. When the answer did arrive, however, he found the price fixed by the optician too high for the means which he, a mere organist, could command. Herschel, like any other person under like circumstances, doubtless felt much disappointed, but he was not disheartened. The obsta

cle thus unexpectedly thrown between him and the immediate gratification of his laudable desire would have been, to most minds, insurmountable, but not so to him. Indeed, one of the principal marks of a great mind is its ability to surmount great difficulties. We may suppose, with some probability of its truth, that Herschel's inability to purchase that telescope was the direct means of developing those qualities of his mental powers which enabled him to transcend in so great a degree what had previously been done in the construction of reflecting telescopes, and in thus opening up to us, by their great power, the means of acquiring a much more complete knowledge of the distant regions of the universe. However this may be, we know that the reply of the London optician stimulated Herschel to undertake the construction of a telescope with his own hands. "The musician of the Octagon Chapel rushes immediately into a multitude of experiments on metallic alloys that reflect light with the greatest intensity, on the means of giving the parabolic figure to the mirrors, on the causes that in the operation of polishing affect the regularity of the reflection, etc."* These labors, so perseveringly followed, brought their reward. In 1774, Herschel had the satisfaction of being able to examine the heavens with a five-foot Newtonian telescope, entirely the work of his own hands. The success which attended the experiment of constructing a telescope not only gave him confidence in his powers, but it attached him so strongly to the science of the stars that he willingly sacrificed a part of the emolument which his musical profession brought him, by limiting his professional engagements and the number of his pupils. His leisure was employed in constructing more powerful instruments, and he produced in succession reflecting telescopes of seven, eight, ten, and even twenty feet focus. We are informed, by good authority,t that Herschel constructed no fewer than two hundred seven-foot Newtonian reflectors, one hundred and fifty ten-foot, and eighty twenty-foot in focal length.

* See Annuaire pour 1842, p. 253.

+ Brewster's Optics, p. 296.