Such was the mathematical tripos and its history. Whatever its demerits, it dominated the situation, and Cambridge mathematics and mathematicians of the nineteenth century were the direct product of the system it embodied. Judged by the output, I do not think it can be said to have resulted in failure; and perhaps Cayley, Sylvester, Adams, Green, Stokes, Kelvin, and Maxwell—to mention no others—were none the worse for having been compelled to go through the course.

The reconstitution in 1907 of the tripos, and the destruction of many of its distinctive features must profoundly modify the future history of mathematics at Cambridge, but forecasts on such a theme would be useless.

The curious origin of the term tripos has been repeatedly told, and an account of it may fitly close this chapter. Formerly there were three principal occasions on which questionists were admitted to the title or degree of bachelor. The first of these was at the comitia priora, held on Ash-Wednesday, for the best men in the year. The next was at the comitia posteriora, which was held a few weeks later, and at which any student who had distinguished himself in the quadragesimal exercises subsequent to Ash-Wednesday had his seniority reserved to him. [312] ]Lastly, there was the comitia minora, for students who had in no special way distinguished themselves.

In the fifteenth century an important part in the ceremony on each of these occasions was taken by a certain “ould bachilour,” who sat upon a three-legged stool or tripos before the proctors and tested the abilities of the would-be graduates by arguing some question with the “eldest son,” who was selected from them as their representative. To assist the latter in what might be an unequal contest his “father,” that is, the officer of his college who was to present him for his degree, was allowed to come to his assistance.

The discussion took place in Great St Mary’s Church, and marked the admission of the student to a position with new responsibilities, while the season of Lent was chosen with a view to bring this into prominence. The puritan party objected to the semi-ecclesiastical character of the proceedings, and in the course of the sixteenth century set themselves to bring the ceremony into disrepute. The part played by the questionist now became purely formal, though a serious debate still sometimes took place between the father of the senior questionist and a regent master who represented the University: this, however, came to be prefaced by a speech by the bachelor, who was now called Mr Tripos, just as we speak of a judge as the bench, or of a rower [313] ]as an oar. Ultimately public opinion permitted Mr Tripos to say pretty much what he pleased, so long as it was not dull and was scandalous. The speeches he delivered or the verses he recited were generally printed and preserved by the registrary, and were known as the tripos verses: originally they referred to the subjects of the disputations then propounded. The earliest copies now extant are those for 1575.

The university officials, to whom the personal criticisms in which Mr Tripos indulged were by no means pleasing, repeatedly exhorted him to remember “while exercising his privilege of humour, to be modest withal.” In 1710, says Mullinger[81], “the authorities after condemning the excessive license of the tripos announced that the comitia at Lent would in future be conducted in the Senate-House; and all members of the University, of whatever order or degree, were forbidden to assail or mock the disputants with scurrilous jokes or unseemly witticisms. About the year 1747–8, the moderators initiated the practice of printing the honour lists on the back of the sheets containing the tripos verses, and after the year 1755 this became the invariable practice. By virtue of this purely arbitrary connection these lists [314] ]themselves became known as the tripos; and eventually the examination itself, of which they represented the results, also became known by the same designation.”

Mr Tripos ceased to deliver his speech about 1750, but the issue of tripos verses continued for nearly 150 years longer. During the latter part of this time they consisted of four sets of verses, usually in Latin, but occasionally in Greek, in which current topics in the University were treated lightly or seriously as the writer thought fit. They were written for the proctors and moderators by undergraduates or commencing bachelors, each of whom was supposed to receive a pair of white kid gloves in recognition of his labours. Thus gradually the word tripos changed its meaning “from a thing of wood to a man, from a man to a speech, from a speech to sets of verses, from verses to a sheet of coarse foolscap paper, from a paper to a list of names, and from a list of names to a system of examination[82].”

In 1895 the proctors and moderators, without consulting the senate, sent in no verses, and thus, in spite of widespread regret, an interesting custom of many centuries standing was destroyed. In defence of this action, it was said that the custom had never been embodied in statute or ordinance, [315] ]and thus was not obligatory, and further that its continuance was not of material benefit to anybody. Such arguments are not conclusive, and we may well regret the disappearance of historic ties unless it can be shown that they cause inconvenience, which of course in this case could not be asserted.

By way of supplement to the foregoing account, I append a list of those who have held or hold the various university mathematical chairs and lectureships.

The Lucasian Professorship of Mathematics was founded in 1663 by Henry Lucas. The successive occupants of the chair have been: Isaac Barrow, 1664–1669; Isaac Newton, 1669–1702; William Whiston, 1702–1711; Nicholas Saunderson (Sanderson), 1711–1739; John Colson, 1739–1760; Edward Waring, 1760–1798; Isaac Milner, 1798–1820; Robert Woodhouse, 1820–1822; Thomas Turton, 1822–1826; George Biddell Airy, 1826–1828; Charles Babbage, 1828–1839; Joshua King, 1839–1849; George Gabriel Stokes, 1849–1903; Joseph Larmor, 1903 et seq.

The Plumian Professorship of Astronomy and Experimental Philosophy was founded in 1704 by Thomas Plume. The successive occupants of the chair have been: Roger Cotes, 1707–1716; Robert Smith, 1716–1760; Anthony Shepherd, 1760–1796; Samuel Vince, 1796–1822; Robert Woodhouse, 1822–1828; George Biddell Airy, 1828–1836; James Challis, 1836–1883; George Howard Darwin, 1883–1912; Arthur Stanley Eddington, 1913 et seq.

The Lowndean Professorship of Astronomy and Geometry was founded in 1749 by Thomas Lowndes. The successive occupants of the chair have been: Roger Long, 1750–1771; John Smith, 1771–1795; William Lax, 1795–1836; George Peacock, 1836–1858; John Couch Adams, 1858–1892; Robert Stawell Ball, 1892–1913; Henry Frederick Baker, 1914 et seq.

The Sadleirian Professorship of Pure Mathematics was founded, in 1863 from a benefaction given in 1710 by Lady Sadleir. The successive occupants of the chair have been: Arthur Cayley, 1863–1895; Andrew Russell Forsyth, 1895–1910; Ernest William Hobson, 1910 et seq.

[316]
]The Cavendish Professorship of Experimental Physics was founded in 1871 by the University; the laboratory attached being built at the expense of the then Chancellor, the Duke of Devonshire. The successive occupants of the chair have been: James Clerk Maxwell, 1871–1879; John William, Baron Rayleigh, 1879–1884; Joseph John Thomson, 1884 et seq.

The Professorship of Mechanism and Applied Mechanics, with laboratories and shops attached, was founded by the University in 1875. The successive occupants of the chair have been: James Stuart, 1875–1890; James Alfred Ewing, 1890–1903; Bertram Hopkinson, 1903 et seq.

Five Lectureships in Mathematics were created in 1882 under the directions of Royal Commissioners, and subsequently two others (now reduced to one other) tenable, if desired, with one of the above, were founded. The successive holders have been: Joseph John Thomson, 1884; Andrew Russell Forsyth, 1884–1895; William Herrick Macaulay, 1884–1887; Richard Tetley Glazebrook, 1884–1898; Ernest William Hobson, 1884–1910; Joseph Larmor, 1885–1903; Richard Pendlebury, 1888–1901; Henry Frederick Baker, 1895–1914; Augustus Edward Hough Love, 1898–1899; Hector Munro Macdonald, 1899–1904; Herbert William Richmond, 1901 et seq.; George Ballard Mathews, 1903–1905; James Hopwood Jeans, 1904–1906, 1910–1912; John Gaston Leathem, 1905–1909; Robert Alfred Herman, 1906 et seq.; Edmund Taylor Whittaker, 1905–1906; Thomas James I’Anson Bromwich, 1909 et seq.; John Hilton Grace, 1901 et seq.; Godfrey Harold Hardy, 1914 et seq.; Arthur Berry, 1914 et seq.