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But the daylight that had already arisen on the continent of Europe was soon to visit our island. The next age, in which Galileo, and Kepler, and Descartes, and Torricelli, and Pascal, and Huygens, revolutionized the entire structure and character of the mathematical and mathematico-physical sciences abroad, was ushered in among us by the bold speculations of Bacon and the brilliant inventions of Napier. Of what has been called the Baconian philosophy, and the amount of the effect it may be supposed to have had in impelling and directing the progress of science, we have already spoken. The writings of Bacon probably did more service by exciting and diffusing the spirit of scientific observation and research, than by any new light they afforded for its guidance, which in truth was no more than it must have furnished to itself as soon as it was fairly awakened and engaged in operating. At all events, neither the pure sciences of figure and number, nor even those of the mixed sciences that have been chiefly advanced by the aid of mathematics and calculation, among which are astronomy, mechanics, and all the principal branches of what is commonly called natural philosophy, can well have received either impulse or direction from Bacon, who was not only entirely unacquainted with geometry and algebra, but evidently insensible even of their value or their use. Of those mathematical and analytical investigations which are the chief glory of the science of the seventeenth and eighteenth centuries, there is not the slightest anticipation in Bacon, nor any direction or suggestion by which they could have been at all promoted. Napier's great invention of logarithms, on the contrary, has from his own day to the present hour been one of the most active and efficient servants of all the sciences dependent upon calculation ; nor could those of them in which the most splendid triumphs have been achieved have possibly been carried to the height they have reached without its assist

The Mirifici Logarithmorum Canonis Descriptio was published by Napier at Edinburgh in a small quarto volume in the year 1614; and logarithms received their improved form, or that in which we now possess them, from their inventor and his friend Henry Briggs, in the same or the following year, although they


were partially published in that form only in 1618, after the death of Napier, by Briggs, by whom the calculations had been performed. Many inventions,” says a late distinguished historian of science, “ have been eclipsed or obscured by new discoveries, or they have been so altered by subsequent improvements that their original form can hardly be recognized, and, in some instances, has been entirely forgotten. This has almost always happened to the discoveries made at an early period in the progress of science, and before their principles were fully unfolded. It has been quite otherwise with the invention of logarithms, which came out of the hands of the author so perfect that it has never yet received but one material improvement -- that which it derived, as has just been said, from the ingenuity of his friend in conjunction with his own. Subsequent improvements in science, instead of offering anything that could supplant this invention, have only enlarged the circle to which its utility extended. Logarithms have been applied to numberless purposes which were not thought of at the time of their first construction. Even the sagacity of the author did not see the immense fertility of the principle he had discovered: he calculated his tables merely to facilitate arithmetical, and chiefly trigonometrical computation ; and little imagined that he was at the same time constructing a scale whereon to measure the density of the strata of the atmosphere and the heights of mountains, that he was actually computing the areas and the lengths of innumerable curves, and was preparing for a calculus which was yet to be discovered


of the most refined and most valuable of its resources. Of Napier, therefore, if of any man, it may safely be pronounced, that his name will never be eclipsed by any one more conspicuous, or his invention be superseded by anything more valuable.” 1

In the same volume with his logarithms Napier gave to the world the two very elegant and useful trigonometrical theorems known by his name.

1 Playfair's Dissertation on the Progress of Mechanical and Physical Science (in Encyclopædia Britannica), p. 448.



Of the other English mathematicians of this age, Harriot, Piggs, and Horrocks may be mentioned as the most famous. Thomas Harriot, who died in 1621, is the author of a work on algebra (Artis Analyticæ Praxis), not published till ten years after his death, which makes an epoch in the history of that science, explaining in their full extent certain views first partially propounded by Vieta, and greatly simplifying some of the operations To Harriot we also owe the convenient improvement of the substitution of small for the capital letters which had been used up to this time. It appears, too, from his unpublished papers preserved at Petworth (formerly the seat of his patron the Earl of Northumberland), that he is entitled to a high place among the astronomers of his day, having, among other things, discovered the solar spots before any announcement of them was made by Galileo, and observed the satellites of Jupiter within a very few days after Galileo had first seen them. Henry Briggs, besides the share he had, as mentioned above, in the improvement of logarithms, is entitled to the honor of having made a first step towards what is called the binomial theorem in algebra, finally discovered by Newton. He died in 1630. His Trigonometria Britannica, or tables of the logarithms of sines, &c. (in the preface to which is his distant view of the binomial theorem), was published in 1633, by his friend Henry Gellibrand, who had been for some time associated with him in the calculation of the logarithms. Samuel Horrocks, or Horrox, a native of Toxteth, near Liverpool, was an astronomer of remarkable genius, who died in 1641, at the early age of twenty-two. He was the first person who saw the planet Venus on the body of the sun: his account of this observation (made 24th November, 1639) was printed by Hevelius at the end of his Mercurius in Sole Visus, published at Dantzig in 1662. But Horrocks is principally famous in the history of astronomy as having anticipated, hypothetically, the view of the lunar motions which Newton afterwards showed to be a necessary consequence of the theory of gravitation. This discovery was given to the world by Dr. Wallis, in a collec

1 These facts, ascertained from the examination of Harriot's papers, then in possession of the Earl of Egremont, were first stated by Zach in the Astronomical Epnemeris of the Berlin Royal Society of Sciences for 1788.




tion of Horrocks's posthumous papers which he published at London in 1672. It had been originally communicated by Horrocks in a letter (which has also been preserved, and is to be found in some copies of Wallis's publication) to his friend William Crabtree, whose fate, as well as genius, was singularly similar to his

Crabtree was a clothier at Broughton, near Manchester, and had made many valuable astronomical observations (a portion of which have been preserved and printed) when he was cut off only a few months after his friend Horrocks, and about the same early age. Another member of this remarkable cluster of friends, whom a common devotion to science united at a time when the fiercest political heats were occupying and distracting most of their countrymen, was William Gascoigne, of Middleton, in Yorkshire, who also died very young, having been killed, about two years after the decease of Horrocks and Crabtree, fighting on the royalist side, at the battle of Marston Moor. He appears to have first used two convex glasses in the telescope, and to have been the original inventor of the wire micrometer and of its application to the telescope, and also of the application of the telescope to the quadrant. A fourth of these associated cultivators of science in the north of England was William Milbourne, who was curate of Brancespeth, near Durham, and who is stated to have made his way by himself to certain of the algebraic discoveries first published in Harriot's work, and likewise to have, by his own observations, detected the errors in the astronomical tables of Lansberg, and verified those of Kepler. The names of several other astronomical observers of less eminent merit who existed at this time in England have also been preserved; among which may be particularized that of Jeremiah Shackerly, the author of a work entitled Tabulæ Britannicæ, published at London in 1653, which is stated to have been compiled mostly from papers left by Horrocks that were afterwards destroyed in the great fire of 1666.1

Nor ought we to pass over Edmund Gunter, the inventor of the useful wooden logarithmic scale still known by his name, and also of the sector and of the common surveyor's chain, and the author of several works, one of which, his Canon Triangulorum, first published at London in 1620, is the earliest printed table of logarithmic sines, &c., constructed on the improved or common system of logarithms.

1 See a notice of these English astronomers of the earlier half of the seventeenth century, in an article on Horrocks in the Penny Cyclopædia, xii. 305.

age was

Briggs's tables, as has been stated above, were not printed till 1633. Gunter also appears to have been the author of the convenient terms cosine, cotangent, &c., for sine, tangent, &c., of the complement. “Whatever, in short,” as has been observed, “ could be done - by a well-informed and ready-witted person to make the new theory of logarithms more immediately available in practice to those who were not skilful mathematicians, was done by Gunter.” 1 He has moreover the credit of having been the first observer of the important fact of the variation of the compass itself varying. Another eminent English mathematician of this John Greaves, the author of the first good account of the Pyramids of Egypt, which he visited in 1638, and of various learned · works relating to the Oriental astronomy and geography, and the weights and measures of the ancients. He died in 1652. Briggs, Gunter, Gellibrand, and Greaves were all at one time or other professors in the new establishment of Gresham College, London, which may be regarded as having considerably assisted the promotion of science in England in the early part of the seventeenth century. Its founder, as is well known, was the eminent London merchant Sir Thomas Gresham, who died in 1579, and left his house in Bishopsgate Street for the proposed seminary, although the reserved interest of his widow prevented his intentions from being carried into effect till after her decease in 1596. The seven branches of learning and science for which professorships were instituted were divinity, astronomy, music, geometry, law, physic, and rhetoric; the first four under the patronage of the corporation of the City of London, the three last under that of the Mercers' Company. The chair of geometry, in which Briggs and Greaves had sat, was occupied in a later age by Barrow and Hooke ; and that of astronomy, in which Gellibrand had succeeded Gunter, was afterwards filled by Wren. Another Gresham professorship that has to boast of at least two distinguished names in the seventeenth century is that of music, which was first held by the famous Dr. John Bull, and afterwards by Sir William Petty.

1 Penny Cyclopædia, xi. 497.


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