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15, 1860.] appears as the devoted sister, doing her best to help her brother, whose pursuits happened to be scientific; but that there is nothing remarkable, happily, in that spectacle. This is very true: but now occurs the spectacle which does appear remarkable to all who have heard of it.

Throughout the longest nights of the year,—the astronomer’s summer, or season of fruits,—a light was seen burning in the observatory at Slough as often as the sky was clear, and disappearing only when the dawn was putting out I the stars. Under that light sat Caroline Herschel, noting in silence the observations of her brother, who was at his telescope in the next chamber. If he was silent, she had occupation in working up his calculations; and then nothing was heard but the ticking of the clock, and the moving of his telescope. To be his secretary required no little learning; but to achieve the vast calculations by which his observations were rendered available, required algebraical accomplishments of an order very unusual among women. As “astronomer’s assistant,” she was salaried by the King; and in the discharge of her office, she read her brother’s clocks, and did all the routine part of his work. This might have been thought enough for a good German housekeeper, who sat up till day-light for the greater part of the winter: but she had scientific interests of her own. Her brother had constructed a smaller telescope for her; and when he was away from home she spent many a night alone in the observatory, looking out for unrecorded stars, and for unsuspected comets. She had new nebulæ and clusters of stars to furnish to her brother’s catalogues when he returned: and she discovered seven comets in eleven years,—five of which had certainly never been noted before. Her first work, which supplied omissions in the British catalogue to the extent of 561 stars, observed by Flamsteed, was published by the Royal Society. Eight years after her brother’s death, and her own return to Hanover, and when she was eighty years old, she was presented with the gold medal of the Astronomical Society of England, and elected an honorary member of that body, in consequence of her completion of a catalogue of the clusters of stars and nebulæ observed by her brother, and, though she did not say so, by herself. She lived on till ninety-seven, a perfect exemplification of the best effects of intellectual pursuit of a high order on the whole nature. Her frame was healthy; her mind was serene; her intellect was clear till just the last; her affections were through life genial and faithful; her manners modest and simple; and her old age tranquil and dignified. There is no trace, in her whole career, of any sort of contemptuous usage on account of her scientific tendencies; and the respect with which she was treated at Windsor first, and afterwards by the King and Court at Hanover, till her death in 1848, seems to have been the natural expression of what was felt by everybody who witnessed or heard of the facts and manner of her life.

Next comes the French lady, who was born later and died earlier than Caroline Herschel.

Sophie Germain began her career in a very different way. Hers was a case of such a preponderance of the mathematical faculties that they regulated her whole mind and life. She loved poetry, as many mathematicians have done; and she insisted that the division set up between reason and imagination was arbitrary and false. We now and then hear from superficial persons an expression of wonder that the finest taste is found in those who are conspicuous for judgment; but Mademoiselle Germain would have wondered more if the case had been otherwise; for she saw how the decisions of reason must harmonise with the principles of taste. Goodness was, in her eyes, order; and wisdom was the discernment of fundamental order. As fixed relations exist among all truths and all objects, and the discovery of any one may lead to the discernment of any number, no heights of speculation astonished, and no flights of fancy disconcerted her. She was mathematical if ever human being was so; but this did not mean that she was prosaic, rigid, and narrow. She was qualified for large and philosophical criticism in literature, no less than for inquisition into the theory of numbers; and she applied herself, amidst the tortures of death by cancer, to exhibit the state of, not only the sciences, but of literature at different periods of their culture. This was the subject of her posthumous work.

Her faculty for abstract conception and the pursuit of abstract knowledge did not wait for occasion to show itself. Yet, at the outset, as at the close, it manifested itself in close alliance with the imagination and the moral powers. As a child she read of the serene life of Archimedes amidst the three years’ siege of Syracuse; and the story impressed her so deeply that she longed to make for herself a refuge in mathematical studies from the excitements and terrors of the great revolution then raging, and likely to rage for long. It was in “Montucla’s History of Mathematics” that she had found the account of the life and heroic death of Archimedes which so moved her; and she studied the book, being then thirteen, with a patience and courage altogether consistent with her view of moral order—unable to understand whole portions of it, but first ascertaining how much she could understand, and resolving to master the rest, sooner or later. The more terrible the prophecies she heard in her father’s drawing-room (he being a member of the Constituent Assembly, and therefore living in political society) the more strenuously did little Sophie apply her faculties to this History of Mathematics and the studies it indicated, to the amazement of her family, who could not conceive why she was suddenly engrossed in the study of Euler. They were not only amazed but displeased; and among other modes of opposition they took away all her clothes at night, when the weather was so cold as to freeze the ink in the glass. Sophie quietly rose, when they were all asleep, wrapped herself in the bedclothes, and pursued her studies. The elementary books she could lay hold of were not such as we have to learn from now. They were full of faults and omissions, according to our present view; and they gave her more trouble than her family did. She advanced beyond those books, however; and in time her family let her alone. During the Reign of Terror she made herself