Agnes Mary Clerke

“ Discarding these obscure and misleading notions, Galileo taught that gravity and levity are relative terms, and that all bodies are heavy, even those which, like the air, are invisible; that motion is the result of force, instantaneous or continuous; that weight is a continuous force, attracting towards the centre of the earth; that, in a vacuum, all bodies would fall with equal velocities ”

“ Hearne wrote in 1723 of his ‘very strange unaccountable genius,’ by which he became ‘a prodigy for his skill in astronomy, and had he lived in all probability would have proved the greatest man in the whole world in his profession’ (MS. Diary in Bodleian Library, No. 102, p. 62) . His genius was akin, and certainly not inferior, to that of Kepler. He had the same patient fervour in the pursuit of knowledge, the same instinct for generalisation, the same fidelity to truth, and without Kepler's touch of extravagance. ”

“ From the time of Archimedes there had existed a science of equilibrium, but the science of motion began with Galileo. It is not too much to say that the final triumph of the Copernican system was due in larger measure to his labours in this department than to his direct arguments in its favour. The problem of the heavens is essentially a mechanical one; and without the mechanical conceptions of the dependence of motion upon force which Galileo familiarized to men’s minds, that problem might have remained a sealed book even to the intelligence of Newton. ”

“ To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems. ”

“ Laplace nowhere displayed the massiveness of his genius more conspicuously than in the theory of probabilities. The science which B. Pascal and P. de Fermat had initiated he brought very nearly to perfection; but the demonstrations are so involved, and the omissions in the chain of reasoning so frequent, that the Théorie analytique (1812) is to the best mathematicians a work requiring most arduous study. The theory of probabilities, which Laplace described as common sense expressed in mathematical language, engaged his attention from its importance in physics and astronomy ”

“ Horrocks had extraordinary intuitions of truth. He first ascribed to the moon an elliptic orbit of which the earth occupied one focus, adding a variation of the eccentricity, and a revolution of the line of apsides. ”

“ But the fantastic relations imagined by him of planetary movements and distances to musical intervals and geometrical constructions seemed to himself discoveries no less admirable than the achievements which have secured his lasting fame. Outside the boundaries of the solar system, the metaphysical side of his genius, no longer held in check by experience, fully asserted itself. ”

“ He received every mark of private favour. The pope admitted him to six long audiences in the course of two months, wrote an enthusiastic letter to the grand-duke praising the great astronomer, not only for his distinguished learning, but also for his exemplary piety, and granted a pension to his son Vincenzio, which was afterwards transferred to himself, and paid, with some irregularities, to the end of his life. But on the subject of the decree of 1616, the revocation of which Galileo had hoped to obtain through his personal influence, he found him inexorable. ”

“ Of these the most conspicuous was offered by the opposite inequalities of Jupiter and Saturn, which the emulous efforts of L. Euler and J. L. Lagrange had failed to bring within the bounds of theory. The discordance of their results incited Laplace to a searching examination of the whole subject of planetary perturbations, and his maiden effort was rewarded with a discovery which constituted, when developed and completely demonstrated by his own further labours and those of his illustrious rival Lagrange, the most important advance made in physical astronomy since the time of Newton. ”

“ He was at the time president of the Royal Astronomical Society.
The abilities of Francis Baily were not of the highest order. As a mathematician his range was a limited one. He never mastered the refinements of modern analysis, and was frequently indebted to the aid of Professors Airy and De Morgan in working out his investigations. Nor was his mind visited by any of the luminous inspirations of genius. Yet his life presents an almost unique example of laborious usefulness to science. ”

“ 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. ”

“ The establishment of the principle of the composition of motions formed a conclusive answer to the most formidable of the arguments used against the rotation of the earth, and we find it accordingly triumphantly brought forward by Galileo in the second of his dialogues on the systems of the world. It was urged by anti-Copernicans that a body flung upward or cast downward would, if the earth were in motion, be left behind by the rapid translation of the point from which it started ”

“ In the morning, till eleven or twelve, she is dull and weary, but as the day advances she gains life, and is quite “fresh and funny” at ten o'clock p.m., and sings old rhymes, nay, even dances! to the great delight of all who see her.’ Her ninety-sixth birthday was marked by Humboldt's transmission to her, in the name of the king of Prussia, of the gold medal for science. On the succeeding anniversary she entertained the crown prince and princess with great animation for two hours, even singing to them a composition of her brother William. ”

“ To this lofty quality of intellect he added a rare sagacity in perceiving analogies, and in detecting the new truths that lay concealed in his formulae, and a tenacity of mental grip, by which problems, once seized, were held fast, year after year, until they yielded up their solutions. In every branch of physical astronomy, accordingly, deep traces of his work are visible. ”

“ 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. ”

“ With these brilliant performances the first period of Laplace’s scientific career may be said to have closed. If he ceased to make striking discoveries in celestial mechanics, it was rather their subject-matter than his powers that failed. The general working of the great machine was now laid bare, and it needed a further advance of knowledge to bring a fresh set of problems within reach of investigation. ”

“ For above forty years he was one of the calculators for the ‘Nautical Almanack,’ and on his retirement received the thanks of the Board of Longitude, with a handsome present in recognition of his services. Dr. Hutton employed him similarly for Moore's and other almanacks, and Dr. Maskelyne corresponded with him during nearly fifty years. By him and others he was esteemed no less for the modesty and integrity of his character than for the singular abilities by which he had raised himself from a humble station to a position of honour amongst men of science. ”

“ The recognition of the second—that of the independence of different motions—must be added to form the true theory of projectiles. This was due to Galileo. Up to his time it was universally held in the schools that the motion of a body should cease with the impulse communicated to it, but for the “reaction of the medium” helping it forward. Galileo showed, on the contrary, that the nature of motion once impressed is to continue indefinitely in a uniform direction, and that the effect of the medium is a retarding, not an impelling one. ”

“ 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 investigation of the figure of equilibrium of a rotating fluid mass engaged the persistent attention of Laplace. His first memoir was communicated to the Academy in 1773, when he was only twenty-four, his last in 1817, when he was sixty-eight. The results of his many papers on this subject—characterized by him as “un des points les plus intéressans du système du monde”—are embodied in the Mécanique céleste, and furnish one of the most remarkable proofs of his analytical genius. ”

“ Newton's resumption of his toil upon the lunar theory brought him into constant intercourse with the astronomer royal. ‘Sir Isaac,’ Flamsteed said afterwards, ‘worked with the ore he had dug.’ ‘If he dug the ore,’ Sir Isaac replied, ‘I made the gold ring’ (Brewster, Memoirs of Newton, ii. 178) .
On 1 Sept. 1694 Newton visited the Royal Observatory, and Flamsteed, ‘esteeming him to be an obliged friend,’ explained the progress of his work, and gave him a hundred and fifty observed places of the moon with their tabular errors, for his private use in correcting the theory of her motions. ”

“ Another commonly received axiom was that no body could be affected by more than one movement at one time, and it was thus supposed that a cannon ball, or other projectile, moves forward in a right line until its first impulse is exhausted, when it falls vertically to the ground. In the fourth of Galileo’s dialogues on mechanics, he demonstrated that the path described by a projectile, being the result of the combination of a uniform transverse motion with a uniformly accelerated vertical motion, must, apart from the resistance of the air, be a parabola. ”

“ 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. ”

“ By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism. The expressions designated by Dr Whewell, Laplace’s coefficients (see Spherical Harmonics) were definitely introduced in the memoir of 1785 on attractions above referred to. In the figure of the earth, the theory of attractions, and the sciences of electricity and magnetism this powerful calculus occupies a prominent place. ”

“ The interdependence of motion and force was not indeed formulated into definite laws by Galileo, but his writings on dynamics are everywhere suggestive of those laws, and his solutions of dynamical problems involve their recognition. The extraordinary advances made by him in this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries ”