The Progress of the Nation page 8

With Baxter and Bunyan the gentle angler, Izaak Walton, claims a place for his – "Lives of Religious Worthies," and not less, for his "Complete Angler," one of the first works, along with "Percy's Reliques of Ancient English Poetry," which awoke the love of nature which now prevails, and where it does not prevail is affected.

Side by side with these worthies stands John Evelyn, a man who mixed with the court and higher circles in Charles II.'s reign without defiling himself by its filth. He was the model of a true English gentleman - pious, honourable, and exerting himself at once to maintain sound morals and to promote science. His memoirs present a lively picture of the dissolute age in which he lived; and he sought to draw men away from the sink of corruption by encouraging them to plant and cultivate their estates. For this he wrote his "Sylva; or, a Discourse of Forest Trees," still a standard and most delightful work. He was one of the first members and promoters of the Royal Society, and wrote "Numismata, a Discourse upon Medals;" a "Parallel of Ancient and Modern Architecture;" a work on Theology, only recently published; and the first "Gardener's Almanac."

As a memoir writer of the same period Samuel Pepys is, however, much more popular than Evelyn. Pepys was secretary to the admiralty in the reigns of Charles IL and James II.; and his inimitably-gossiping volumes of whatever he saw during those times have been of late reprinted and read everywhere with great unction. Pepys, besides this, continued a most invaluable collection of old ballads begun by Seiden, from which Bishop Percy amply helped himself in constructing his "Reliques;" so that to Pepys and John Seiden we really owe much of that great revolution in taste and poetry which we ascribe almost exclusively to Percy. Another memorialist of this period was Sir William Temple, a man who, like Evelyn, maintained a high moral status, and was held in great esteem for his philosophical essays. In Scotland Sir George Mackenzie stood conspicuous for his "Institution of the Laws of Scotland," and not less for various works of taste, as his "Aretina; or, The Serious Romance;" his "Religio Stoici; or, The Virtuoso," &c. Burnet, the author of " The Theory of the Earth," also lived now, but may be mentioned with his namesake the bishop, who belongs more properly to the reign of William and Mary.

The church at this period possessed great and eloquent men - Tillotson, Sherlock, Barrow, South, Stillingfleet, and others. Their sermons' remain as great storehouses of religious argument and enunciation. They were nearly all of the Arminian school. Barrow was, besides, one of the ablest geometricians that have appeared.

Physical Science

During the period now under review a great step in the progress of science was made by the foundation of the Royal Society. The honour of originating this famous society belongs to a Mr. Theodore Haak, a German, but resident in London. Through his suggestions a number, of scientific gentlemen, including Dr. Goddard, a physician in Wood Street, but also a preparer of lenses for telescopes; Dr.. Wallis, the great mathematician; Dr. Wilkins, afterwards bishop of Chester; Drs. Ent, Gisson, and Merrit, and Mr. Samuel Foster, professor of astronomy in Gresham college. They commenced their meetings in 1645, which used to be held at one of their houses, or in Gresham college, or at apartments in Cheapside. Though some of these gentlemen were removed by promotion, others continued to join it, as Boyle, Evelyn, Wren - afterwards Sir Christopher. In 1662 a royal charter was obtained, and in the following year additional privileges were granted under a second charter. The first president was lord Brouncker, and the first council consisted of Mr. - afterwards lord - Brereton, Sir Kenelm Digby, Sir Robert Moray, Sir William Petty, Sir Paul Neile, Messrs. Boyle, Slingsbey, Christopher and Matthew Wren, Balle, Areskine, Aldenburg, Henshaw, and Dudley Palmer, and Drs. Wilkins, Wallis, Timothy Clarke, and Ent. Balle was the first treasurer, and Wilkins and Oldenburg the first secretaries. The society was pledged not to meddle with questions of theology or state, and their chief subjects of notice were the physical sciences, anatomy, medicine, astronomy, mathematics, navigation, statistics, chemistry, magnetism, mechanics, and kindred topics. In the spring of the second year the society numbered a hundred and fifteen members; amongst them, besides many noblemen and gentlemen of distinction, we find the names of Aubrey, Dr. Barrow, Dryden, Cowley, Waller, and Sprayt, afterwards bishop of Rocheste. The society commenced its publication of its transactions in 1665, which became a record of the progress of physical and mathematical science for a long series of years.

During the short period over which the present review ranges - namely, from the restoration in 1660 to the revolution in 1688, that is, only twenty-eight years - some of the greatest discoveries in science were made which have occurred in the history of the world; namely, the discovery of the circulation of the blood by Dr. William Harvey; the improvement of the tables of logarithms constructed by Napier; the invention of fluxions by Newton, and the calculus of fluxions, or the differential calculus, by Leibnitz; the discovery of the perfected theory of gravitation, by Newton; the foundation of modern astronomy, by Flam- stead; and the construction of a steam-engine by the Marquis of Worcester, originally suggested by Solomon de Caus, a Frenchman.

Napier published his tables of logarithms in 1614, under the title of "Mirifici Logarithmorum Canonis Descriptia," and in the same or the following year he and his friend, Henry Briggs, gave them their improved, and, as it proved, perfect form, for from that time to the present they have been found to admit of no further improvement. They came from the hands of their author and his assisting friend perfect. The principle of their construction Napier did not declare; but this important revelation was made by Briggs and Napier's son in a publication in 1619 called "Mirifici Logarithmorum Canonis Constructio; una cum Annotationi- bus aliquot Doctissimi D. Henrici Briggii." By these tables Napier superseded the long and laborious arithmetical operations which all great calculators had previously to undergo, and which the most simple trigonometrical operations demanded. Without this wonderful aid even Newton could not have lived to accomplish the great principles that he drew from and established for ever upon the material accumulated by prior mathematicians. He in fact furnished by these tables a scale by which not only the advantages which he proposed of shortening arithmetical and trigonometrical labour were effected, but which enabled men to go infinitely farther, and enabled his successors to weigh the atmosphere and take the altitudes of mountains, compute the lengths and areas of all curves, and to introduce a calculus by which the most unexpected results should be reached. "By reducing to a few days the labour of many months," says Laplace, "it, doubles, as it were, the life of an astronomer, besides freeing him from the errors and disgust inseparable from long calculations."

We are not, however, to suppose that Napier was the first who had a perception of the nature of logarithms. In almost all grand discoveries the man of genius stands upon the shoulders of preceding geniuses to reach that culminating point which brings out the full discovery. In very early ages it was known that if the terms of an arithmetical and geometrical series were placed in juxtaposition, the multiplication, division, involution, and evolution of the latter would answer to and might actually be affected by a corresponding addition, subtraction, multiplication, and division of the former. Archimedes employed this principle in his "Arenarius," a treatise on the number of the sands. Stifel, in his "Arithmetica Integra," published at Nürnberg in 1644, exhibits a still clearer notion, of the use of this principle; but the merit of Napier was this - that whilst those who preceded him could only apply the principle to certain numbers, he discovered the means of applying it to all, and 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 Logarithmotechnia," 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 envoliente fluxiones invenire, et vice versa" 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 Cyclopaedia, "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.