thus was enabled to construct and bring to perfection at once his admirable tables. There was an attempt to show that he had stolen the idea from Longomontanus, but that great mathematician settles this matter by himself attributing the whole invention to Napier.
Besides the Logarithms, Napier is also noted for his elegant theorems, called his "Analogies," and his theorem of "the five circular parts," which furnishes a ready solution of all the cases of right-angled spherical triangles. He also invented what are called "Napier's Bones," to facilitate the performance of multiplication and division; instruments of such value, that had he not discovered the logarithms, they would have, to a certain extent, supplied their place.
The discoveries of Sir Isaac Newton, however, put the crown to the glories of this period. The extent of these discoveries can only be learnt by a perusal of his "Principia; or, Mathematical Principles of Natural Philosophy," containing his complete theory of the laws of the universe, based on the grand doctrine of gravitation, of which he published afterwards a popular view under the title of "De Mundi Systemate," enunciating the truths contained in the third book of the "Principia." His "Optics," containing his theories of light and colours, founded on a host of curious experiments; his "De Quadratura Curvarum," containing an exposition of his method of fluxions; his "Method of Fluxions and Analysis by Infinite Series;" or, in the Latin, "Analysis per Equationes Numero Terminorum Infinitas." A great many of those discoveries were communicated to the public through his communications to the Royal Society. The announcement of his binomial theory, by which he was able to determine the area and rectification of curves, the surface and contact of the solids formed by their revolution, and the position of their centre of gravity—a theory of infinite avail in his determination of the laws of the planetary bodies—is dated 1664, that of his "Method of Fluxions," 1665; but he did not claim this till 1669. He professed to have written a tract on the subject in 1664, but he did not produce this tract till he had seen some of the same results published in "Mercator's Logarithimotechnia," four years afterwards. In 1666 he demonstrated the great law of gravitation, and applied it to the planets, but was baffled in his attempts to apply it to the moon through a false estimate of the earth's diameter. This was corrected by Picard's measurement of an arc of the meridian, with which he became acquainted in 1682, and then after sixteen years' delay he completed his system. But his "Principia" was not published collectively till 1687; his "Optics" till 1704, together with his "De Quadratura Curvarum," containing his method of fluxions.
Unparalleled as were the achievements of Newton, these were not accomplished, any more than any other great performances, without substantial hints and assistance from previous or contemporary genius. The very principle of gravitation had been pointed out by Robert Hooke, and Newton was compelled to admit, and offered to publish a scolium admitting the fact, that Hooke, Wren, and Halley had already deduced this law—that the gravitation of the planets was as the curvic square of the distance from Kepler's second law of analogy, between the periodic times and the mean distances of the planets. Newton's defenders say that he probably made this concession for the sake of peace; but was Newton likely to surrender a great truth, vitally affecting his fame, for science and discovery, if there were not solid grounds for it?
Still less to the credit of Newton was his conduct towards Leibnitz in the dispute regarding the differential calculus. Leibnitz having heard through Oldenburg that Newton had made discoveries as to the measurement of tangents, in fact, as to his binomial theorem, and as to fluxions, desired to have some account of them, and Newton, through Oldenburg, communicated to Leibnitz his binomial theorem, but concealed his knowledge of fluxions under a most abstruse anagram, which was formed from the words, "Data Equatione quotcunque fluentes quantitates envolente fluxiones invenire, et vice versâ." It has been well observed that if Leibnitz could draw any light from that anagram, he must have possessed superhuman sagacity. Leibnitz, however, having himself made most important discoveries in fluxions, at once and candidly communicated the theory of what he called, and what is still called, the differential calculus, to Newton. This, Newton, in a scolium included in his "Principia," admitted to be a method hardly differing from his own except in his form of words and symbols. Yet in the third edition of the "Principia" he totally omitted this confession, claimed the exclusive invention of the differential calculus for himself, and branded Leibnitz as a plagiarist. The fact was, that Leibnitz had gone a step beyond Newton. Newton had discovered fluxions, but Leibnitz had discovered the fluxionary calculus, or, as he termed it, the differential calculus.
Still more disgraceful was the conduct of Newton to the astronomer Flamstead. Flamstead was the first astronomer royal. Charles II. established an observatory at Greenwich, one of the very best things he ever did. The observatory was, in fact, the queen's house in Greenwich Park, and Flamstead was appointed astronomical observator, with the magnificent salary of a hundred pounds a year, and not a single instrument, not even a telescope. It was in vain that he applied for instruments; and his appointment might have been a sinecure had he not procured instruments at his own expense, and taught pupils to maintain himself. But through all these difficulties he went on making his observations, and in time not only made a mass of the most valuable lunar observations, but had made a map and catalogue of the stars, such as there had never been before for completeness and accuracy. His catalogue included three thousand three hundred stars, "whose places," says the Penny Cyclopædia, "were more accurate than any determined in the next fifty years, and whose selection and nomenclature has served as a basis to every catalogue since that time." Mr. Bailey, Flamstead's biographer, claims, and, as it seems to us, very justly, that the commencement of modern astronomy dates from his observations, for no one would care to go beyond them to compare any made in our day.
Newton was very intimate with Flamstead, and with good cause, for he depended on his supplying him with the necessary observations, to enable him to establish his lunar
