nious inventor of the principles of Mercator's Sailing, which was published in 1616, after his death, by his Son, Samuel Wright, with a dedication to the East India Company, and a preface by Mr. Henry Briggs', at that time Professor of Geometry at Gresham College. In 1619, two years after Lord Napier's death, a new edition of his work was published by his Son, Robert Napier, containing the construction of his Canon, and other miscellaneous pieces omitted in the first edition. On the first publication of Lord Napier's invention, Mr. Briggs paid him a visit, and the result of their communication on the subject, was a determination to change the form of the Logarithms for one better adapted to the Decimal scale of Numbers: this alteration we have reason to believe was first suggested by Briggs, as he was the first who published Logarithms on the improved plan, and, it seems, entertained a hope, that a just acknowledgment would be publicly made of the part he had taken in the improvement; in this he was disappointed, ing ingratitude laid claim to the invention. Our author published a work on the Sphere, another on Dialling, and another, very useful to navigators, entitled, The Haven-finding Art: he was the inventor of several instruments useful in their time, for finding the altitude, &c. of celestial objects, and thence the true place of a ship. He was fellow of Gonvil and Caius College, Cambridge; occasionally read lectures on nautical and mathematical subjects; and was Tutor to Prince Henry. After a life spent in the extension of useful knowledge, he died at London in 1615. e Henry Briggs was born at Warleywood in Yorkshire, in 1556: at a proper age he was sent to St. John's College, Cambridge, where after taking the degree of M. A. he was chosen a Fellow in 1588; and, in consequence of his great proficiency in mathematical learning, was appointed Examiner and Lecturer in that faculty. In 1596 he was chosen the first Professor of Geometry at Gresham College in 1619, he was appointed the first Savilian Professor of Geometry at Oxford; in consequence of which, the next year he resigned the Professorship at Gresham College. Besides the works above mentioned, Mr. Briggs was the author of several others equally creditable to his memory. This truly great man terminated a laborious and useful life in January 1631; and was buried in the Choir of the Chapel of Merton College; at which College he had for several years past been a constant resident. for in the second edition of Napier's work, although the alteration is adverted to, no mention is made of any assistance received from Briggs, either by Lord Napier or his Son. If Briggs was really the inventor of the improvement, as it is generally believed he was, the omission was certainly an act of gross injustice. 5. An improved form of Napier's Logarithms, by Mr. John Speidell, came out the same year; and the year following Justus Byrgius published Tables, in which the natural numbers and Logarithms are arranged in a converse order of what they are in our ordinary Tables. Vincent printed a copy of Napier's work at Lyons, as did Ursinus at Cologne; the latter being improved by the addition of Tables of proportional parts. In 1624, the celebrated Kepler published at Marpurg his Chilias Logarithmorum, &c. in which the Logarithms are more conveniently adapted to common numbers than those of Napier; the latter being principally accommodated to the sines of arcs, &c. 6. The Logarithms published by these and some others about the same time, were of the kind which has since been called hyperbolical; a name they received in consequence of their expressing the spaces included between the asymptote, and curve of the hyperbola, 7. To have an adequate idea of the nature of Logarithms, we must consider them as indices, denoting the ratios of numbers to unity. Napier's Logarithm of 10, (that is, the index denoting the ratio of 10 to 1,) is 2.3025851, &c. this Mr. Briggs found deficient in point of simplicity and convenience, and therefore the latter gentleman undertook the laborious task of computing an entire new system, in which he made 1 the Logarithm of 10; whence it follows that 2 will be the Logarithm of 100, 3 of 1000, &c. This has been justly consi dered as an improvement of the greatest value; it introduces a kind of similarity between the series of Logarithms and that of common numbers, simplifies the whole doctrine amazingly, and renders it plain and intelligible to the meanest capacity. 8. The first fruit of Mr. Briggs's labours in this way, was his Logarithmorum Chilias Prima, which appeared in 1617, after Napier's death, containing the first thousand Logarithms to eight places of figures, besides the index. Mr. Edmund Gunter 'adapted Mr. Briggs's Logarithms, first of any, to the sines and tangents; he computed them for every minute to seven places of figures besides the index; this work appeared in 1620, under the title of A Canon of Triangles, which work was reprinted in 1623, with the addition of the Chilias Prima of Briggs. The same year Gunter applied the Logarithms of Numbers, Sines, Tangents, &c. to a straight ruler, whereby computations may be performed by a pair of compasses only: this instrument is still known by the name of Gunter's Scale. Other methods of projecting these numbers on circular, sliding, and spiral instruments, were afterwards invented by Wingate, Oughtred, Milburne, and Partridge. f Edmund Gunter was born in 1581, and received the rudiments of his education at Westminster School, under the famous Dr. Bushy; from thence he went to Christ Church, Oxford, where in 1615 he took the degree of B. D. in 1619 he succeeded Mr. Williams as Professor of Astronomy at Gresham College, where he greatly distinguished himself by his eminent mathematical talents, displayed in his writings and lectures; he died in 1626. Mr. Gunter's inventions and improvements in mixed mathematics were of the greatest value; in 1606, he gave a new projection of the sector, and in 1618, a new portable quadrant for the more easily finding the hour, azimuth, &c. He discovered in 1622 the changeable declination of the magnetic needle, shewing that it had altered 5 degrees in 42 years; which conclusion was verified by his successor, Mr. Gellibrand. He introduced the scale and measuring chain known by his name, and gave ample descriptions of their uses. He introduced the name co-sine, and the use of the arithmetical complements of Logarithms; and the first idea of the logarithmic curve is generally ascribed to him. 9. In 1624, Mr. Briggs published his Arithmetica Logarithmica, containing the Logarithms of Numbers from 1 to 20000, and from 90000 to 100000, with ample directions for their use, and an earnest invitation to Mathematicians to assist in the completion of the work, by computing the intermediate numbers: this was effected soon after by Adrian Vlacq, of Gouda in Holland, who, besides supplying the intermediate chiliads, added Tables of artificial sines, tangents, and secants, for every minute of the quadrant. This ingenious person printed likewise at Gouda, in 1633, a work entitled Trigonometria Artificialis, containing Briggs's Table of the first 20000 Logarithms, with the Logarithmic sines and tangents, and their differences, for every ten seconds of the quadrant, to ten places of figures, with their description and uses. At the same time and place was printed Mr. Briggs's Trigonometria Britannica, under the superintendence of Vlacq; this work contains the Logarithms of 30000 natural numbers, logarithmic sines, and tangents, for the hundredth part of every degree, all to 14 places of figures besides the index, the natural sines for the same parts to 15 places, and the tangents and secants for the same to 10 places, with the construction of the whole but the Author dying in 1630, before the work was complete, his friend, Mr. Henry Gellibrand, Pro This work, which is justly considered as very useful in astronomical calcu lations, has been lately reprinted at Leipsic, by Vega, under the title of Thesaurus Mathematicus. The Reverend Henry Gellibrand was born in London, in 1597; he was sent to Trinity College, Oxford, in 1615; and in 1623, took the degree of M. A. having taken orders, he became curate of Chiddingstone in Kent; but happening to hear a lecture on the mathematics by Sir Henry Saville, he relinquished all prospect of preferment in the Church, and set himself in earnest to study that noble science. He became Professor of Astronomy at Gresham College, upon the death of Mr. Gunter, in 1627; and was the author of several useful pieces, chiefly tending to the improvement of Navigation, a branch to which his atten tion was principally directed: he died in 636. fessor of Astronomy at Gresham College, supplied the preface, and the application to plain and spherical Trigonometry i, &c. Two years after, Mr. Gellibrand published An Institution Trigonometricall, being a smaller work of the same kind, with the addition of other tables, &c. the whole adapted to the use of navigators. 10. Mr. Bonnycastle, Professor of Mathematics at the Royal Military Academy, Woolwich, has lately discovered an ingenious improvement in the Binomial Theorem of the illustrious Newton, whereby he has shewn the method of constructing Logarithms in a new and elegant manner several authors, as Gunter, Huygens, Keill, Newton, Mersenne, James Gregory, Mercator, &c. gave methods of computing Logarithms, derived from their analogy to certain curves; others, as Cotes, Halley, Craig, John Bernoulli, Dr. Brook Taylor, Mr. Jones, &c. employed for that purpose either a flu'xional process, or methods nearly similar to that of Fluxions; but their methods, although ingenious and scientific, are not strictly conformable to the nature of the subject, which is purely arithmetical. The theorems delivered by Mr. Bonnycastle are unexceptionable in this respect, being derived from the principles of pure Algebra, and by means of them the Logarithms, according to Napier, Briggs, or any other system, are readily obtained. 11. As the Logarithms of Napier have obtained the name of hyperbolic, so those of Briggs are usually denominated common Logarithms, from the circumstance of their being better adapted to practice than Napier's, and therefore most in use. The following authors, besides i In the Trigonometria Britannica, Mr. Briggs has shewn the method of generating the coefficients of the terms of any power of a binomial successively from each other, independent of any other power; which is the foundation of Sir Isaac Newton's celebrated Binomial Theorem. Besides the common and hyperbolic Logarithms, there are logistic and pro |