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320 mistress of the Differential Calculus of Cousin. Times improved for her when society was so far settled as that the Normal and Polytechnic schools of Paris were opened. By one device or another she obtained the notes of many of the professors’ lessons; and she was presently bewitched by Lagrange’s new and luminous analysis. It was the custom for such students as desired it to offer their observations in writing to the professor, at the close of his course. Sophie took advantage of this custom to get her notes handed in to Lagrange, as coming from a student; and great was the praise awarded to the mysterious student, whose real name was soon betrayed to the great man. He called on her, to praise and encourage her; and from that time she was known as a mathematician, and corresponded with by the most eminent scientific men, so that she had abundant facilities for progress. In correspondence with Gauss of Göttingen, she again wrote under an assumed name; but she was presently recognised, and thenceforward she attempted no concealment.

Her first specific enterprise illustrates her courage and perseverance as thoroughly as her whole life. Napoleon was dissatisfied that there was no scientific expression of the results of the curious experiments of Chladni on the vibrations of elastic metal plates; and he offered an extraordinary prize if the Institute could discover the mathematical laws of those vibrations. Lagrange at once declared the thing impossible; that is, it would require a new species of analysis. Few would have thought of proceeding in the face of such an opinion: but Sophie said, “My dear master, why not try?” After a world of study, she sent in, as the result, an equation of the movement of elastic surfaces. It was faulty; and she saw why. But for the irregularity of her mathematical education the failure could not have happened; and she set to work to remedy the evil. She actually produced the new kind of analysis which Lagrange had declared to be necessary; and he was the first to applaud the feat. Moreover, he obtained the exact equation from her scheme. She herself pursued the application, and obtained honourable mention for this second attempt. She was invited to enter again into the competition; and on this third occasion she succeeded completely. She declared that both Lagrange and Fourier had aided her by their suggestions: but they, and all others, said that a hint or two in the application of her method had nothing to do with the discovery of it, and insisted that the glory was her own without drawback. It does not appear that glory was any object to her in comparison with progress in knowledge. She wrought out the applications of her own methods, and supplied several theorems to Legendre on the theory of numbers, which he published in the supplement to his second edition; and the further she went in mathematics the more widely she extended her studies in other departments, especially chemistry, physics, geography, and the history of philosophy, science, and literature. She employed her analytic faculty in all directions, and manifested her synthetic power on every subject which she touched.

We are told that in her manners and conversation, the utmost grace of accuracy was manifested. Her expression of her ideas and feelings, and her narrative of incidents were so precise, so brief, so perfect, that no improvement was possible, and every alteration must be for the worse. The same fitness, clearness, sincerity, appeared in all she did. Her life was not the less genial for this, nor her conversation the less lively and natural. It had a somewhat poetical cast, or seemed to have to those who were expecting to find “a mathematical prude,” or a dry pedant.

She died in 1831, after long and cruel suffering, heroically borne. She was fifty-five years old—younger by a generation than Caroline Herschel, but dying seventeen years before her.

Meantime, the English, or rather Scotch woman had been reaching middle life, in the pursuit of the studies of both the others, and from the same natural aptitude.

This natural aptitude betrayed itself unexpectedly in Mrs. Somerville’s case, in the midst of an ordinary girl’s education, at the opening of this century. She lived at Musselburgh, near Edinburgh, and was sent to school there, being remarked for nothing except docility, gentleness, and quietness. She learned to sew, as little girls should; and it was natural that, when she was at home, she should sit sewing in the window-seat of the room where her brother took his lessons from his tutor. His sister liked his mathematical lessons best; and she regularly laid hands on his Euclid, and carried it up to her own room, to go over the lesson by herself. One day, her brother was stopped by a difficulty, and, forgetting her secret, little Mary popped out the answer. The tutor started; the family inquired, and very sensibly let her alone. Professor Playfair was an intimate friend of the household; and not very long after the above incident, Mary found an opportunity to put a private question to the professor—Did he think it wrong for a girl to learn Latin? Not necessarily; but much depended on what it was for. Well, she wanted to study Newton’s Principia, and that was the truth. The professor did not see any harm in this, if she liked to try. In a few months she was mastering the Principia.

Her first marriage was favourable to her line of study; or, I should rather say, to this particular one of her various studies. She is a very accomplished woman—understands and speaks several languages; has in her day been an amateur artist of considerable merit, and was considered to play well on the harp. But when she married a naval officer who delighted in her sympathy in his professional studies, she made great progress, and, was becoming qualified for future achievements. Still, we do not hear of the gentle and quiet Mrs. Gregg being pointed out to general notice as a learned lady. The first that was generally heard of her, was when the children of her second marriage, two daughters, were almost grown up, and her son, Mr. Woronzow Gregg, was making his way in the world. She was then the wife of Dr. Somerville, physician of Chelsea Hospital. It was a pleasant house to go to—that airy house at Chelsea, where the host was always delighted to tell the stories of his wife’s early studies, and to show, in the deep drawer full of diplomas, the tokens of her recent fame; and where the hostess