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The two great improvements in this instrument which have been made—the calculus of variations by Euler and La Grange, the method of partial differences by d'Alembert-we have every reason to believe were known, at least in part, to Newton himself. His having solved an isoperimetrical problem (finding the line whose revolution forms the solid of least resistance), shows clearly that he must have made the co-ordinates of the generating curve vary; and his construction agrees exactly with the equation given by that calculus. That he must have tried the process of integrating by parts in attempting to generalize the inverse problem of central forces, before he had recourse to the geometrical approximation which he has given, and also when he sought the means of ascertaining the comet's path, which he has termed by far the most difficult of problems, is eminently probable, when we consider how naturally that method flows from the ordinary process for differentiating compound quantities, by supposing each variable in succession constant; in short, differentiating by parts. As to the calculus of variations having substantially been known to him, no doubt can be entertained. Again, in estimating the ellipticity of the earth, he proceeded upon the assumption of a proposition of which he gave no demonstration (any more than he had done of the isoperimetrical problem) that the ratio of the centrifagal force to gravitation determines the ellipticity. Half a century later, that which no one before knew to be true, which many probably considered to be erroneous, was examined by one of his most distinguished followers, Maclaurin, and demonstrated most satisfactorily to be true. Newton had not failed to perceive the necessary effects of gravitation in producing other phenomena, beside the regular motion of the planets and their satellites in their course round their several centres of attraction. One of these phenonema, wholly unsuspected before the discovery of the general law, is the alternate movement to and fro of the earth's axis, in consequence of the solar (and also of the lunar) attraction combined with the earth's motion. This libration, or nutation, distinctly announced by him as the result of the theory, was not found by actual observation to exist till sixty years and upwards had elapsed, when Bradley proved the fact.
The great discoveries which have been made by La Grange and La Place upon the results of disturbing forces, have established the law of periodical variation of orbits, which secures the stability of the system by prescribing a maximum and a minimum amount of deviation; and this is not a contingent, but a necessary truth, by rigorous demonstration, the inevitable result of undoubted data in point of fact, the eccentricities of the orbits, the directions of the motions, and the movement in one plane of a certain position. That wonderful proposition of Newton, which, with its corollaries, may be said to give the whole doctrine of disturbing forces, has been little more than applied and extended by the labours of succeeding geometricans. Indeed, La Place, struck with wonder at one of his comprehensive general statements on disturbing forces, in another proposition, has not hesitated to assert that it contains the germ of La Grange's celebrated inquiry, 'exactly a century after the Principia was given to the world. The wonderful powers of generalization, combined with the boldness of never shrinking from a conclusion that seemed the legitimate result of his investigations-how new and even startling soever it might appear-was strikingly shown in that memorable inference which he drew from optical phenomena, that the diamond is “an unctuous substance coagulated;" subsequent discoveries having proveil both that such substances are carbonaceous, and that the diamond is crystallized carbon; and the foundations of mechanical chymistry were laid by him
with the boldest invluction and most felicitous anticipations of what has since been effected.
The solution of the inverse problem of disturbing forces has led Le Verrier and Adams to the discovery of a new planet, merely by deductions from the manDer in which the motions of an old one are effected, and its orbit has been so calculated that observers could find it; ray, its disc as measured by them only varies Tooth of a degree from the amount given by the theory. Moreover, when Newton gave his estimate of the earth's density, he wrote tury before Maskelyne, and, by measuring the force of gravitation in the Scotch mountains, gave the proportion to water as 4,716 to 1; and, many years after, by experiments with mechanical apparatus, Cavendish (1798) corrected this to 5.48, and Baily, more recently (1842), to 5.66, Newton having given the proportion as between five and six times. In these instances he only showed the way and anticipated the result of future inquiry by his followers. But the oblate figure of the earth atfords an example of the same kind, with this difference, that here he has himself perfected the discovery, and nearly completed the demonstration. From the mutual gravitation of the particles which form its mass, combined with their motion round its axis, he deduced the proposition that it must be flattened at the poles ; and he calculated the proportion of its polar to its equatorial diameter. By a most refined process, he gave this proportion, upon the supposition of the mass being homogeneous. That the proportion is different in consequence of the mass being heterogeneons, does not in the least affect the soundness of his conclusion. Accurate measurements of a degree of latitude in the equatorial and polar regions, with experiments on the force of gravitation in those regions, by the different lengths of a penduluin vibrating seconds, bave shown that the excess of the equatorial diameter is about eleven miles less than he had there can only once be found a system of the universe to establish.” “Never," says the father of the Institute of France—one filling a high place among the most eminent of its members—“Never,” says M. Biot," was the supremacy of intellect so justly established and so fully confessed. In mathematical and in experimental science, without an equal and without an example, combining the genius for both in its highest degree.” The Principia he terms the greatest work ever produced by the mind of man, adding, in the words of Halley, “that a nearer approach to the Divine nature has not been permitted to mortals.” “In first giving to the world Newton's method of fluxions," says Fontenelle, “Leibnitz did like Prometheus, — he stole fire from Heaven to bestow it upon men.” “Does Newton," L'Hopital asked, "sleep and wake like other men? I figure him to myself as a celestial genius, entirely disengaged from matter."
To so renowned a benefactor of the world, thus exalted w the loftiest place by the common consent of all men,—one whose life, without the intermission of an hour, was passed in the search after truths the most important, and at whose hands the human race has only received good, never evil —no memorial has been raised by those nations which erected statues to the tyrants and conquerors, the scourges of mankind, whose lives were passed, not in the pursuit of truth, but the practice of falsehood; or across whose lips, if truth ever chanced to stray towards some selfish end, it surely failed to obtain belief; who, to slake their insane thirst of power or of pre-eminence, trampled on the rights and squandered the blood of their fellow-creatures ; whose course, like the lightning, blasted while it dazzled; and who, reversing the Roman emperor's noble regret, deemed the day lost that saw the sun go down upon their forbearance,-no victim deceived, or betrayed, or oppressed. That the worshippers of such pestilent genius should consecrate to the memory of the most illustrious of men no outward symbol of the admiration they freely confessed, is not matter of wonder. But that his own countrymen, justly proud of having lived in his time, should have left this duty to their successors, after a century and a half of professed veneration and lip homage, may well be deemed strange. The inscription upon the cathedral, masterpiece of his celebrated friend's architecture, may possibly be applied in defence of this neglect. "If you seek for a monument look around.” “If you seek for a monument, lift up your eyes to the heavens which show forth his fame." Nor when we recollect the Greek orator's exclamation—" The whole earth is the monument of illustrious men,' can we stop short of declaring that the whole universe is Newton's. Yet in raising the statue which preserves his likeness, near the place of his birth, on the spot where his prodigious faculties were unfolded and trained, we at once gratify our honest pride as cti zens of the same state, and humbly testify our grateful sense of the Divine goodness which deigned to bestow upon our race one so marvellously gifted to comprehend the works of Infinite Wisdom, and so piously resolved to make all his study of them the Bource of religious contemplations, both philosophical and sublime.
[FROM THE "TIMES. "]
LINCOLNSHIRE enjoys the proud distinction of having given to the world the illustrious mathematician and philosopher, Sir Isaac Newton,-justly described as "the greatest genius of the human race,"—who was born at the manor house of Woolsthorpe, a hamlet eight miles from this town, on Christmas-day, 1642. Sir Isaac was a posthumous child, his father having died, at a comparatively early age, some three months before the birth of a son whose reputa