# Once a Week (magazine)/Series 1/Volume 3/Representative women: The scientific students - Caroline L. Herschel, Sophie Germain, Mrs. Somerville

The people discussed in this article are Caroline Herschel (1750–1848), Sophie Germain (1776–1831), and Mary Somerville (1780–1872).
REPRESENTATIVE WOMEN. Scientific Students. caroline l. herschel; sophie germain; and mrs. somerville.
I am not aware whether others have made the observation, but it appears to me that the repugnance of our sex to “learned ladies” does not affect female mathematicians. Our jests are levelled at the literary women; and yet more, at the “philosophers,” or those who study psychology, in a German, French, or English form. I should say “jests were levelled,” but that there are still publications and men antiquated enough to attempt to keep up the old insolence and the old joke, after society in general has arrived at better taste; for the reason, possibly, that there are still women (a few in England, and not a few in America,) who are antiquated enough to make themselves foolish and disagreeable, instead of wise and companionable, through their pursuit of knowledge. I need not enlarge on this; for there is no pleasure, and at this time of day no profit in contemplating pedantry on the one hand, or scoffing on the other. I have referred to the old and worn-out topic only because it appears to me that if female mathematicians and physical discoverers have escaped the insults, and almost the criticism, bestowed on literary women half a century ago, it must be because their pursuits carry their own test with them. The attainments of such women are not a matter of opinion, but of fact. Man or woman may be mistaken about his or her comprehension of Kant’s apparatus of Conditions, or accuracy in the reading of dead languages; but there can be no deception of self or others as to the reality of knowledge in the science of Space and Numbers; or the detection of new agencies in Nature which can be brought to the test. Even where this is questioned, on account of the many false starts in discovery that have been made, up to this time, the doubt is, not about the reality of the knowledge, but the correctness of the inferences of the discoverer. On the whole, we may, I think, fairly say, that in the scientific departments of human knowledge women rank equally with men in respect of society. Whether they have equal access to that field of knowledge is another affair.
Let us look at two or three recently dead or still living, and see what aspects they present.
The senior of the three (German, French, and English), whom our own generation may have seen, was both a mathematician and a physical discoverer. Caroline Lucretia Herschel, the sister of Sir William Herschel, was the German. She was born at Hanover (March 16th, 1750), and lived there till she was one-and-twenty. She was sixteen, and her brother eight-and-twenty when he, in England, began to attend to astronomy; the whole family being supposed to be engrossed by music, as they were certainly devoted to it professionally. It is not, therefore, likely that Caroline was prepared by education for scientific pursuit in any other direction; and her taking it up at last, in order to assist her brother, seems to show that she had no original overmastering genius for science, such as must have taken her out of the ordinary conditions of female life, but that the labours of her life from that time forward were a merely natural exercise of perfectly natural powers. She came over to England as soon as she was old enough (one-and-twenty) to keep her brother’s house at Bath, where he was organist to a chapel. She was his helper and sympathiser in the astronomical pursuits which were his delight, as his best recreation from his professional business. She worked out his calculations when he had provided the elements: she watched with an anxiety like his own the production of the telescope he made because he could not afford to buy one; and when he discovered a planet, ten years after she had joined him, she enjoyed the triumph and its results very keenly. The King gave Brother William 300l. a year, and called him Astronomer to the Court; and the (then) bachelor brother and his staid sister removed to Slough, to do as they liked for the rest of their lives.
Thus far, it may be said that Caroline Herschel ​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 ​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 ​was the model of a hostess, well dressed, genial and hospitable, apparently with the constant blessings of a good cook, a neat house, and a perfect knowledge on her own part how to keep it. Her harp was in the corner, and her pictures on the walls; and there was the best society in London in her drawing-room.
This was when the impression of her first great work was fresh. Some experiments that she had made, showing the magnetic influence of the violet rays of the solar spectrum, had before directed the attention of some philosophical inquirers to her capabilities; and when the Society for the Diffusion of Useful Knowledge was set up, she was invited to prepare for it a popular version of Laplace’s “Mécanique Céleste.” She accomplished the task, but not in a form suitable for the Society; and her work was published independently under the title of “The Mechanism of the Heavens.” It was a radical mistake to set Mrs. Somerville to work on popular versions of scientific works. A different quality and character of mind is required for discovering abstract truths, and for putting them into a form which unscientific minds may comprehend. From her gentleness and simplicity, Mrs. Somerville was tractable, and undertook what she was told would be most useful; but the work was perplexing to her. When her first and second editions were sold in a wonderfully short time, her publisher asked her, with all due deference, whether she could not simplify some parts of the book, so as to bring them down to the comprehension of ordinary readers. She tried, and declared it the most difficult thing she had ever attempted. What the publisher and others called simplifying, seemed to her to be obscuring and perplexing her sense. When she quitted the precision and brevity of scientific terms, she could never tell what the matter would spread out to. This should have put an end to all interference with her course, as it proved the error of expecting the same mind to supply the two methods of exposition—the scientific and the popular.
If her first great work indicated her mathematical powers, her next exhibited the course of her philosophical tastes. She had given a brief account of her view of the Connexion of the Physical Sciences in the introduction to the “Mechanism of the Heavens:” and this view formed the groundwork of her second book. It is very interesting in its disclosures to unlearned persons, and as indicating the direction and variety of her studies; but it is defective in the masterly closeness, directness, and precision which her mind was capable of when dealing with mathematical truths. Its popularity amazed her, and delighted her friends; who, for the most part were unaware of the extent to which the country could furnish a reading public for scientific works, and who had mistaken the reasons for the failure of the publications of the Diffusion Society. One edition after another had to be prepared; and most conscientiously did Mrs. Somerville apply herself to improve each one as it was demanded. She was not the sort of author to write more books than she otherwise would, because she was sure of a favourable reception for anything she would publish. As far as I know, there is only one more book of hers; and that was issued many years later, when she had long resided abroad. This work, “Physical Geography,” appeared in 1848.
A characteristic feature of Mrs. Somerville’s taste appears in the dedications of her books, and indeed in their being dedicated at all. Not only recoiling from innovation in almost all ways, but somewhat old-fashioned in her habits of mind, she has through life taken pains to do what was proper, and in that anxiety has made such few and superficial mistakes as she has made. They are not worth a reference except for the light they cast on the force of her abstract faculties. She who dedicated her works (one to the Queen, and another to Sir J. Herschel), in the fashion of a former age, when author and readers had not been brought face to face; she who, because she was advised, not only went to Court, but took her daughters there; she who allowed her portrait to be prefixed to one of her own works; she who has always carefully kept abreast of a cautious conventionalism, and dreaded manifesting any originality except in one direction, has been so inspired in that direction as to be unconscious of the peculiarity which all the world was admiring. Hence her security from being spoiled. In 1835, she was chosen an honorary member of the Royal Astronomical Society; and the learned Societies of every civilised country followed this lead, till, as I said, she had a deep drawer full of diplomas; but neither this nor any other form of homage ever made the slightest difference in her manners, or seemed to occupy any part of her thoughts. Sitting beside old Dr. Dalton, on the sofa, talking of the atomic theory, or what not, she never perceived that the eyes of many strangers were upon her, and that the great men of the scientific world were trying to catch the tones of her voice. Her partial absence of mind is another evidence of the character and action of her intellect. No one can be further from what is called “absent” in society. No one can be more awake and alive to the conversation and the interests of others; yet her husband used to amuse himself, and astonish an occasional guest by proving how long it took to stir her up from her studies. She did not need an elaborate privacy for her pursuits. She used the family sitting room, when studying or writing; and, as soon as she was fairly engaged, her husband would begin libelling her in extravagant terms, and in a loud voice, without making her look up, till, at last, when he shouted her name, she would ask if he was speaking to her, and be surprised to see everybody laughing. Hers is the strongest and clearest case possible of a special intellectual organisation, compelling its own exercise in simplicity and honour.
Mrs. Somerville has been lost sight of, though never forgotten, for many years. About twenty years since, the health of Dr. Somerville caused the removal of the family to Italy, whence they have never returned, Dr. Somerville having died at the age of 93, a few weeks ago.
Their friends felt a sort of indignation at an incident which occurred soon after their departure. Of all people in Europe, Mrs. Somerville was the one who could by no means obtain a proper view of the comet of 1843. The only accessible ​telescope of value was in the observatory of a Jesuit convent, in Tuscany, where no woman was allowed to cross the threshold. This indignation in England looks like evidence that the world has advanced in its intellectual and moral liberties.
Whatever the Tuscan Jesuits might think of her case, I believe that Mrs. Somerville and all her many friends would say, if asked, that they never heard of a disrespectful word being spoken of her, in connection with her powers and her pursuits. Her work is over, for she is almost seventy years of age; and it is not a case in which death is required to silence levity or sarcasm; for there is none of either to put to shame. Under such circumstances, we may reasonably hope that these female mathematicians may be, indeed, Representative Women,—leaders of an honoured and increasing class.
Ingleby Scott.