Agnes Mary Clerke

“ It is impossible to consider without surprise the colossal amount of work accomplished by Kepler under numerous disadvantages. But his iron industry counted no obstacles, and secured for him the highest triumph of genius, that of having given to mankind the best that was in him. ”

“ His emoluments as treasurer at war, together with his wife’s fortune, provided him with ample means, which he lost by rash speculations, a circumstance regarded by his son as the prelude to his own good fortune; for had he been rich, he used to say, he might never have known mathematics.
The genius of Lagrange did not at once take its true bent. His earliest tastes were literary rather than scientific, and he learned the rudiments of geometry during his first year at the college of Turin, without difficulty, but without distinction. ”

“ Huygens never married. He died at the Hague on the 8th of June 1695, bequeathing his manuscripts to the university of Leiden, and his considerable property to the sons of his younger brother. In character he was as estimable as he was brilliant in intellect. Although, like most men of strong originative power, he assimilated with difficulty the ideas of others, his tardiness sprang rather from inability to depart from the track of his own methods than from reluctance to acknowledge the merits of his competitors. ”

“ It is indeed by no means easy to distinguish and apportion the respective merits of the competitors. This is especially the case between Lagrange and Euler on the one side, and between Lagrange and Laplace on the other. The calculus of variations lay undeveloped in Euler’s mode of treating isoperimetrical problems. The fruitful method, again, of the variation of elements was introduced by Euler, but adopted and perfected by Lagrange, who first recognized its supreme importance to the analytical investigation of the planetary movements. ”

“ The pursuit of science needed a more tranquil shelter; and on the raising of the blockade, Kepler obtained permission to transfer his types to Ulm, where, in September 1627, the Rudolphine Tables were at length given to the world. Although by no means free from errors, their value appears from the fact that they ranked for a century as the best aid to astronomy. Appended were tables of logarithms and of refraction, together with Tycho’s catalogue of 777 stars, enlarged by Kepler to 1005. ”

“ The year 1611 was marked by Kepler as the most disastrous of his life. The death by small-pox of his favourite child was followed by that of his wife, who, long a prey to melancholy, was on the 3rd of July carried off by typhus. Public calamity was added to private bereavement. On the 23rd of May 1611 Matthias, brother of the emperor, assumed the Bohemian crown in Prague, compelling Rudolph to take refuge in the citadel, where he died on the 20th of January following. Kepler’s fidelity in remaining with him to the last did not deprive him of the favour of his successor. ”

“ Laplace regarded analytical triumphs as the means of solving the problems of nature. One mind seemed the complement of the other; and both, united in honourable rivalry, formed an instrument of unexampled perfection for the investigation of the celestial machinery. What may be called Lagrange’s first period of research into planetary perturbations extended from 1774 to 1784 (see Astronomy: History) . The notable group of treatises communicated, 1781–1784, to the Berlin Academy was designed, but did not prove to be his final contribution to the theory of the planets. ”

“ From the time of his first introduction to Tycho he had devoted himself to the investigation of the orbit of Mars, which, on account of its relatively large eccentricity, had always been especially recalcitrant to theory, and the results appeared in Astronomia nova αἱτιολογητός, seu Physica coelestis tradita commentariis de motibus stellae Martis (Prague, 1609) . In this, the most memorable of Kepler’s multifarious writings, two of the cardinal principles of modern astronomy—the laws of elliptical orbits and of equal areas—were established (see Astronomy: History) ”

“ It is not often that a man postpones to his seventy-sixth year, and then successfully executes, the crowning task of his life. Yet this was Humboldt’s case. The first two volumes of the Kosmos were published, and in the main composed, between the years 1845 and 1847. The idea of a work which should convey, not only a graphic description, but an imaginative conception of the physical world—which should support generalization by details, and dignify details by generalization, had floated before his mind for upwards of half a century. ”

“ The best recognized function of German astronomers in that day was the construction of prophesying almanacs, greedily bought by a credulous public. Kepler thus found that the first duties required of him were of an astrological nature, and set himself with characteristic alacrity to master the rules of the art as laid down by Ptolemy and Cardan. He, moreover, sought in the events of his own life a verification of the theory of planetary influences ”

“ Euler’s eulogium was enhanced by his desire to quit Berlin, d’Alembert’s by his dread of a royal command to repair thither; and the result was that an invitation, conveying the wish of the “greatest king in Europe” to have the “greatest mathematician” at his court, was sent to Turin. On the 6th of November 1766, Lagrange was installed in his new position, with a salary of 6000 francs, ample leisure for scientific research, and royal favour sufficient to secure him respect without exciting envy. The national jealousy of foreigners, was at first a source of annoyance to him ”

“ The character of Kepler’s genius is especially difficult to estimate. His tendency towards mystical speculation formed a not less fundamental quality of his mind than its strong grasp of positive scientific truth. ”

“ HALLEY, EDMUND (1656–1742) , English astronomer, was born at Haggerston, London, on the 29th of October 1656. His father, a wealthy soapboiler, placed him at St Paul’s school, where he was equally distinguished for classical and mathematical ability. Before leaving it for Queen’s College, Oxford, in 1673, he had observed the change in the variation of the compass, and at the age of nineteen, he supplied a new and improved method of determining the elements of the planetary orbits (Phil. Trans. xi. 683) . ”

“ His early zeal for the improvement of the condition of the miners in Galicia and Franconia, his consistent detestation of slavery, his earnest patronage of rising men of science, bear witness to the large humanity which formed the ground-work of his character. The faults of his old age have been brought into undue prominence by the injudicious publication of his letters to Varnhagen von Ense. ”

“ The first fruits of his labours were contained in two memoirs presented to the Academy, September 16 and October 14, 1839. Pursuing the investigations of Laplace, he demonstrated with greater rigour the stability of the solar system, and calculated the limits within which the eccentricities and inclinations of the planetary orbits vary. This remarkable début excited much attention, and, on the recommendation of François Arago, he took in hand the theory of Mercury, producing, in 1843, vastly improved tables of that planet. ”

“ With the aid of the marquis de Saluces and the anatomist G. F. Cigna, he founded in 1758 a society which became the Turin Academy of Sciences. The first volume of its memoirs, published in the following year, contained a paper by Lagrange entitled Recherches sur la nature et la propagation du son, in which the power of his analysis and his address in its application were equally conspicuous. He made his first appearance in public as the critic of Newton, and the arbiter between d’Alembert and Euler. ”

“ Tycho’s marriage with a peasant-girl in 1573 somewhat strained his family relations. He delivered lectures in Copenhagen by royal command in 1574; and in 1575 travelled through Germany to Venice. The execution of his design to settle at Basel was, however, anticipated by the munificence of Frederick II., king of Denmark, who bestowed upon him for life the island of Hveen in the Sound, together with a pension of 500 thalers, a canonry in the cathedral of Roskilde, and the income of an estate in Norway. ”

“ At the age of nineteen he communicated to Leonhard Euler his idea of a general method of dealing with “isoperimetrical” problems, known later as the Calculus of Variations. It was eagerly welcomed by the Berlin mathematician, who had the generosity to withhold from publication his own further researches on the subject, until his youthful correspondent should have had time to complete and opportunity to claim the invention. This prosperous opening gave the key-note to Lagrange’s career. ”

“ In 1636 he met with a congenial spirit in William Crabtree, a draper of Broughton, near Manchester; and encouraged by his advice he exchanged the guidance of Philipp von Lansberg, a pretentious but inaccurate Belgian astronomer, for that of Kepler. He now set himself to the revision of the Rudolphine Tables (published by Kepler in 1627) , and in the progress of his task became convinced that a transit of Venus overlooked by Kepler would nevertheless occur on the 24th of November (O.S.) 1639. ”

“ He first brought the revolutions of our satellite within the domain of Kepler’s laws, pointing out that her apparent irregularities could be completely accounted for by supposing her to move in an ellipse with a variable eccentricity and directly rotatory major axis, of which the earth occupied one focus. ”

“ John Flamsteed (1835) is the leading authority for his life. It comprises an autobiographical narrative pieced together from various sources, a large collection of Flamsteed’s letters, a revised and enlarged edition of the British Catalogue, besides authoritative and detailed introductory discussions. Some clamour was raised by a publication in which blame for harsh dealings was freely imputed to Newton, but W. Whewell vindicated his character in Flamsteed and Newton (1836) . ”

“ This transit of Venus is remarkable as the first ever observed, that of 1631 predicted by Kepler having been invisible in western Europe. Notwithstanding the rude character of the apparatus at his disposal, Horrocks was enabled by his observation of it to introduce some important corrections into the elements of the planet’s orbit, and to reduce to its exact value the received estimate of its apparent diameter. ”

“ In analytical invention, and mastery over the calculus, the Turin mathematician was admittedly unrivalled. Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way. But Laplace unquestionably surpassed his rival in practical sagacity and the intuition of physical truth. Lagrange saw in the problems of nature so many occasions for analytical triumphs ”

“ HORROCKS, JEREMIAH (1619–1641) , English astronomer, was born in 1619 at Toxteth Park, near Liverpool. His family was poor, and the register of Emmanuel College, Cambridge, testifies to his entry as sizar on the 18th of May 1632. Isolated in his scientific tastes, and painfully straitened in means, he pursued amid innumerable difficulties his purpose of self-education. His university career lasted three years, and on its termination he became a tutor at Toxteth, devoting to astronomical observations his brief intervals of leisure. ”

“ In the appended treatise Sur la Cause de la pesanteur, he rejected gravitation as a universal quality of matter, although admitting the Newtonian theory of the planetary revolutions. From his views on centrifugal force he deduced the oblate figure of the earth, estimating its compression, however, at little more than one-half its actual amount. ”

“ In 1856 he made experimental observations on the Peak of Teneriffe with a view to testing the astronomical advantages of a mountain station. The Admiralty made him a grant of £500 for the purpose, and a yacht—the “Titania”—of 140 tons and a fine 71/2 in. equatorial telescope were placed at his disposal by friends. The upshot of the expedition was to verify Newton’s surmise, that a “most serene and quiet air . . . may perhaps be found on the tops of the highest mountains above the grosser clouds.” ”

“ His father subsequently settled at Bedford and equipped there an observatory, at which Piazzi Smyth received his first lessons in astronomy. At the age of sixteen he went out as assistant to Sir Thomas Maclear at the Cape of Good Hope, where he observed Halley’s comet and the great comet of 1843, and took an active part in the verification and extension of La Caille’s arc of the meridian. In 1845 he was appointed astronomer royal for Scotland and professor of astronomy in the university of Edinburgh. ”

“ Having reached so far as to perceive that the central force of the solar system must decrease inversely as the square of the distance, and applied vainly to Wren and Hooke for further elucidation, he made in August 1684 that journey to Cambridge for the purpose of consulting Newton, which resulted in the publication of the Principia. ”

“ BRAHE, TYCHO (1546–1601) , Danish astronomer, was born on the 14th of December 1546 at the family seat of Knudstrup in Scania, then a Danish province. Of noble family, he was early adopted by his uncle, Jörgen Brahe, who sent him, in April 1559, to study philosophy and rhetoric at Copenhagen. The punctual occurrence at the predicted time, August 21st, 1560, of a total solar eclipse led him to regard astronomy as “something divine” ”

“ He drew the horoscopes of the emperor and Wallenstein, as well as of a host of lesser magnates; but, though keenly alive to the unworthy character of such a trade, he made necessity his excuse for a compromise with superstition. “Nature,” he wrote, “which has conferred upon every animal the means of subsistence, has given astrology as an adjunct and ally to astronomy.” He dedicated to the emperor in 1603 a treatise on the “great conjunction” of that year (Judicium de trigono igneo) ”

“ The unremitting benefits and sincere attachment of two well-meaning princes secured his gratitude, but could not appease his discontent. At first he sought relief from the “nebulous atmosphere” of his new abode by frequent visits to Paris; but as years advanced his excursions were reduced to accompanying the monotonous “oscillations” of the court between Potsdam and Berlin. On the 12th of May 1827 he settled permanently in the Prussian capital, where his first efforts were directed towards the furtherance of the science of terrestrial magnetism. ”

“ Thus that scientific conspiracy of nations which is one of the noblest fruits of modern civilization was by his exertions first successfully organized.
In 1811, and again in 1818, projects of Asiatic exploration were proposed to Humboldt, first by the Russian, and afterwards by the Prussian government; but on each occasion untoward circumstances interposed, and it was not until he had entered upon his sixtieth year that he resumed his early rôle of a traveller in the interests of science. ”

“ The first centenary of his birth was celebrated on the 14th of September 1869, with equal enthusiasm in the New and Old Worlds; and the numerous monuments erected in his honour, and newly explored regions called by his name, bear witness to the universal diffusion of his fame and popularity.
Humboldt never married, and seems to have been at all times more social than domestic in his tastes. ”