1751, took his B.A. in 1774 as senior wrangler, and died in London on April 1, 1820. He wrote several works on theology. A contemporary says that he had "extensive learning always at his command......great talents for conversation and a dignified simplicity of manner," but he does not seem to have possessed any special qualifications for the Lucasian chair. At an earlier time he had frequently taken part in the examinations in the senate-house, but I believe I am right in saying that after his election to the professorship he never lectured, or taught, or examined in the tripos, or presided in the schools.

The occupants of the Plumian chair during the period treated in this chapter were Robert Smith (see p. 91), Anthony Shepherd, and Samuel Vince.

In 1760 Robert Smith was succeeded by Shepherd. Anthony Shepherd was born in Westmoreland in 1722, took his B.A. from St John's in 1743, was subsequently elected a fellow of Christ's, and died in London on June 15, 1795. Of him I know nothing save that in 1772 he published some refraction and parallax tables, and that in 1776 he printed a list of some experiments on natural philosophy which he had used to illustrate a course of lectures he had given in Trinity College.

Shepherd was followed in 1796 by Vince, a fellow of Caius. Samuel Vince was born in Suffolk about 1754, took his B.A. as senior wrangler in 1775, and died in December, 1821. His original researches consisted chiefly of numerous observations on the laws of friction and the motion of fluids, and he contributed papers on these subjects to the Philosophical transactions for 1785, 1795, and 1798. His results are substantially correct. A list of all his papers sent to various societies is given in Poggendorff. His most important work is an astronomy published in three volumes at Cambridge, 1797-1808; the first volume is descriptive, the second an account of physical astronomy, and the third a collection of tables arranged for

English observers: this was preceded by a work on practical astronomy issued in 1790.

He also wrote text-books on conic sections, algebra, trigonometry, fluxions, the lever, hydrostatics, and gravitation, which form part of a general course of mathematics: these were all published or reissued in 1805 or 1806, and for a short time were recognised as standard text-books for the tripos; but they are badly arranged and were superseded by the works of Wood. His treatise on fluxions first published in 1805 went through numerous editions, and is one of the best expositions of that method. In it, however, as in all the Cambridge works of that time, he used ở to denote, not the fluxion of x, but the increment of x generated in a small time; that is what Newton would have written as xo. He asserts that "this is agreeable to Sir I. Newton's ideas on the subject," and "as the velocities are in proportion to the increments or decrements which would be generated in a given time, if at any instant the velocities were to become uniform, such increments or decrements will represent the fluxions at that instant'." He also used the symbol of integration (see p. 71).

х

A public advertisement of his lectures for 1802 is as follows.

The lectures are experimental, comprising mechanics, hydrostatics, optics, astronomy, magnetism, and electricity; and are adapted to the plan usually followed by the tutors in the university. All the fundamental propositions in the first four branches, are proved by experiments, and accompanied with such explanations as may be useful to the theoretical student. Various machines and philosophical instruments are exhibited in the course of the lectures, and their construction and use explained. And in the two latter branches a set of experiments are instituted to shew all the various phenomena, and such as tend to illustrate the different theories which have been invented to account for them. The lectures are always given in the first half of the midsummer term at 4 o'clock in the afternoon, in the public Lecture-room under the front of the Public Library. Terms are guineas for the first course, 2 guineas for the second, and afterwards gratis.

1 Vince's Fluxions, p. 1.

A "plan" of his lectures with a detailed account of his experiments was published in 1793, and another one was issued in 1797. His lectures are said to have been good, and I believe he was always willing to assist students in their reading. His successors will be mentioned in the next chapter.

In 1749 Thomas Lowndes of Overton founded another professorship' of astronomy and geometry. The first occupant of the chair was Roger Long, a fellow and subsequently master of Pembroke College, and the friend of the poet Gray. Long was born in Norfolk on Feb. 2, 1680, graduated as B.A. in 1701, and died on Dec. 16, 1770. His chief work is one on astronomy in two quarto volumes published in 1742: fresh editions were issued in 1764 and 1784, and it became a standard text-book at Cambridge; the descriptive parts are said to be well written. In 1765, or according to some accounts 1753, he constructed a zodiack or large sphere capable of containing several people and on the inside of which the constellations visible from Cambridge were marked. This famous globe stood in the grounds of Pembroke College, and was only destroyed in 1871.

Long was succeeded in 1771 by John Smith, the master of Caius College, who in his turn was followed in 1795 by William Lax, a fellow of Trinity, who was born in 1751 and held the chair till his death on Oct. 29, 1836. Both of these professors seem to have neither lectured nor taught. Lax wrote a pamphlet on Euclid, 1808: and in 1821 issued some tables for use with the Nautical almanack. He also contributed papers to the Philosophical transactions for 1799 and 1809.

1 The successive professors were as follows. From 1749 to 1771, Roger Long of Pembroke; from 1771 to 1795, John Smith of Caius; from 1795 to 1836, William Lax of Trinity; from 1836 to 1858, George Peacock of Trinity (see p. 124); who in 1858 was succeeded by J. C. Adams of Pembroke, the present professor.

To meet the want of the lectures they should have given Francis John Hyde Wollaston (born about 1761, took his B.A. in 1783, and died in 1823), a fellow of Trinity Hall and Jacksonian professor, lectured on astronomy from 1785 to 1795, and William Farish (born in 1759 and died in 1837), a fellow of Magdalene, who was professor of chemistry from 1794 to 1813 and of natural experimental philosophy from 1813 to 1837, lectured on mechanics. A paper by Farish on isometrical perspective appears in the Cambridge philosophical transactions

for 1822.

Farish was also vicar of St Giles's, Cambridge, and many stories of the complications produced by his extraordinary absence of mind are still current. He is celebrated in the domestic history of the university for having reduced the practice of using Latin as the official language of the schools and the university to a complete farce. On one occasion, when the audience in the schools was unexpectedly increased by the presence of a dog, he stopped the discussion to give the peremptory order Verte canem ex. At another time one of the candidates had forgotten to put on the bands which are still worn on certain ceremonial occasions. Farish, who was presiding, said, Domine opponentium tertie, non habes quod debes. sunt tui...(with a long pause) Anglice bands? To whom with commendable promptness the undergraduate replied, Dignissime domine moderator, sunt in meo (Anglice) pocket. Another piece of scholastic Latin quoted by Wordsworth is, Domine opponens non video vim tuum argumentum'.

Ubi

The only other mathematicians of this time whom I deem it necessary to mention here are George Atwood, Miles Bland, Bewick Bridge, John Brinkley, Daniel Cresswell, William Frend, Francis Maseres, Nevil Maskelyne, John Rowning, Francis Wollaston, and James Wood. I confine myself to a

1 See p. 41 of the Scholae academicae; and Nichol's Literary anecdotes, VIII. 541.

short note on each, and I have arranged these notes roughly in chronological order.

John Rowning, a fellow of Magdalene College, was born in 1701 and died in London in 1771. He wrote A compendious system of natural philosophy, published in two volumes in 1738; a treatise on the method of fluxions, published in 1756; and a description of a machine for solving equations, published in the Philosophical transactions for 1770.

Francis Wollaston, a fellow of Sidney College, who was born on Nov. 23, 1731, and took his B.A. as second wrangler in 1758, wrote several papers and works on practical astronomy; a list of these is given in Poggendorff's Handwörterbuch. He died at Chiselhurst on Oct. 31, 1815.

George Atwood was born in 1746, was educated at Westminster School, took his B.A. as third wrangler and first Smith's prizeman in 1769, and subsequently was elected a fellow and tutor of Trinity College. The inefficiency of the professorial body served as a foil to his lectures, which attracted all the mathematical talent of the university. They were not only accurate and clear, but delivered fluently and illustrated with great ingenuity. The apparatus for calculating the numerical value of the acceleration produced by gravity which is still known by his name was invented by him and used in his Trinity lectures in 1782 and 1783. Analyses of the courses delivered in 1776 and in 1784 were issued by him, and are still extant. Pitt attended Atwood's lectures, and was so much interested in them that he gave him a post in London; and for the last twenty years of his life Atwood was the financial adviser of every successive government. Atwood died in London on July 11, 1807.

His most important work was one on dynamics, published at Cambridge in 1784. He also wrote a treatise on the theory of arches published in 1804. Besides these he contributed several papers to the Philosophical transactions: these include one in 1781 on the theory of the sextant; one in 1794 on the mathematical theory of the watch, especially the times of vibra