William Lax

In 1785 Lax was appointed curate of Tideswell in the Peak District of Derbyshire with an annual stipend of £35.[9] In 1786, as was essentially the due of Senior Wranglers, he was elected a fellow of Trinity College.[10] According to Peter Linehan, fellows at this time, "were becoming richer, living and behaving more like gentlemen".[3] He was ordained as a minister in 1787 at Peterborough and received his Master of Arts (M.A.) in 1788.[11] He was a moderator from 1789 to 1791 which entailed him presiding over oral examinations which were then necessary for the B.A. to be awarded. As a moderator Lax was responsible for the introduction of "very high flown compliments, and at the same time extending the disputations to double the usual length, which was around one hour and ten minutes" which "sent a ripple through tradition" according to Greg Dening.[12][13] Dening argues that this was, "Lax's way of getting into the act and making Acts flourish".[13] In 1791 he was appointed as a taxor by the University.[14] Lax was an assistant tutor from 1797 until 1801, but resigned when he married Margaret Cradock, as College fellows were not permitted to marry.[7][15]

Wren Library, Trinity College, Cambridge.

In 1795 Lax was appointed Lowndean Professor of Astronomy and Geometry in succession to John Smith. The position was a sinecure with an annual salary initially of around £300, later rising to around £500 per annum by 1821.[16][17] Cambridge had two astronomical chairs, and the Lowndean was seen as the more theoretical and less experimental of the two. During Lax's tenure a mathematical chair was seen as "a prize or a means of securing leisure, and at best, merely as offering a position where a man could pursue his own researches undisturbed by other duties".[18] In 1816 Lax was described as holding the professorship with "great reputation".[19] The sole duty of Lax's professorship was that he was required to examine students annually for the Smith's Prize, including John Herschel, Adam Sedgwick, George Biddell Airy and William Cavendish, 7th Duke of Devonshire.[20][21]

During Lax's time at Cambridge: "the mathematicians were in the saddle, and it would be difficult to dispute the judgement that they controlled Cambridge studies almost as completely as the logicians had done in the Middle Ages."[22] In early nineteenth century Cambridge "the discipline of mathematics was at the very heart".[23] Newtonian mathematics teaching as exemplified by "Cambridge traditionalists" such as Lax and his generation began to wane as the Georgian era drew to a close.[24] In 1817 George Peacock successfully introduced the new French mathematics (such as Pierre-Simon Laplace and Joseph Louis Lagrange) into the Senate House Examinations. Peacock reported to Herschel, "The introduction of d's into the papers excited much remark. Wood, Vince, Lax & Milner were very angry & threatened to protest against [the infiltration of] French mathematics."[25] For the traditionalists the struggle was more than one of intellectual difference as for them, "Newton's rational mechanics, fluxions, and experimental philosophy were an excellent antidote against materialism and atheism."[26] However, from 1816 to 1824 Lax continued to sit on the Peacock-led board that established Cambridge Observatory.[27]

Lax did encounter some criticism during his tenure. Whilst at the university he "never, as far as is known, delivered a single lecture", despite his chair's bequest that the holder deliver forty lectures each year, although his predecessor had not given any lectures either.[28][29] The excuse was made that there was already an astronomical chair at Cambridge established before the Lowndean that already gave lectures.[16] By the 1820s it was no longer acceptable to consider chairs as sinecures, and Lax received criticism from a living descendant of the original benefactor, Thomas Lowndes, for being remiss in his duties.[16] His successor to the Lowndean chair George Peacock promised "to do his duty in a less lax manner than his predecessor", and although he struggled to get anyone to attend his lectures on pure mathematics, his lectures on practical astronomy were well attended.[24] However, Peacock's translation as Dean of Ely three years later meant that he was largely absent from his chair, which he was severely criticised for retaining.[30][31]

Somerset House in 1836, where the Royal Society met in Lax's time.

Lax was admitted a Fellow of the Royal Society on 5 April 1796. He was nominated by the Astronomer Royal Nevil Maskelyne, Anthony Shepherd, Richard Farmer and William Wales.[32] However, due to an enmity of the President Joseph Banks, friends of Charles Hutton and Maskelyne, such as Lax, Samuel Vince and Thomas Mudge, frequently saw their submissions for publications overlooked.[33] If any of them submitted papers to the Society:

they had the honour of having them carefully lodged in the archives of the Society, where the world in general, or even the members of the Society, would derive no more benefit from them than if they were deposited at the centre of the earth.[34]

Lax delivered two papers to the Royal Society which were published in Philosophical Transactions. In 1799 he delivered A Method of finding the Latitude of a place, by Means of two Altitudes of the Sun and the Time elapsed betwixt the Observations. It was described as "a very valuable paper" by Abraham Rees, and apparently contained "several valuable remarks", but it was criticised as "a subject of no great importance" by the Philosophical Magazine.[35][36][37] In his 1809 work On A Method of Examining the Divisions of Astronomical Instruments Lax wrote that no instrument was to be trusted without "previous examination".[38] This argument had an influence on scientists such as Henry Cavendish and was described as an "ingenious...examination" in the Edinburgh Encyclopedia.[39][40] However the method described by Lax "though very ingenious, requires great labour and time, and is inferior in accuracy and efficiency to that which was adopted by Mr. Troughton for tabulating the errors of the primary divisions of circular instruments."[37] It was also criticised for "greatly resembl[ing]" a method first explicated by the Duke of Chaulnes.[41] In 1807 Lax delivered Remarks on a Supposed Error in the Elements of Euclid to the Royal Society, however it was not published in Philosophical Transactions, but was eventually published independently. In it Lax defended the Greek mathematician against a charge levied at him by Georges-Louis Le Sage in 1756. Lax's defence was applauded by the British Critic as 'perfectly sound'.[42] Lax also espoused the worth of Euclid's Elements in the work, which he considered to reflect "the highest honour upon the human intellect".[43]

Lax was elected to the Board of Longitude after he was nominated to the Lowndean chair in 1795, and remained on the board until it was dissolved in 1828.[44][45] The Board was a governmental body charged with administering a scheme of prizes intended to encourage innovators to solve the problem of finding longitude at sea, which was vital for accurate navigation. Lax published a set of tables for use with the Nautical Almanac for finding latitude and longitude; these were published by the Board of Longitude in 1821, and whilst they were not considered to be of much practical use for seamen, they were described by The Nautical Magazine as a "very meritorious attempt to solve the problems of nautical astronomy by one uniform system."[46][47] In 1821, the Board awarded Lax £1050 for his tables, which were intended to replace Nevil Maskelyne's Requisite Tables.[48] However, the extraordinarily accurate chronometers of John Harrison were generally available from the 1820s onwards, rendering the lunar distance method, which Lax had used to create the tables, immaterial. Meanwhile, Edward Sabine criticised errors in Lax's work.[49]

As a scientific member of the Board, Lax was one of eighteen men who were, according to Edmund Dews, "ultimately responsible for the form and contents of the Nautical Almanac. It would have been difficult in these years to select another group equally eminent in their field."[50] Lax was notable for his strong attendance record at the quarterly meetings, not missing a single meeting between 1822 – 25, a record equalled by only three other members, although non-attendance of meetings would have resulted in his not being paid his annual salary of £100.[50] In 1828 Lax appended An easy method of correcting the lunar distance, on account of the spheroidal figure of the earth to the Nautical Almanac. After the Board was dissolved in 1828 Lax unsuccessfully attempted to convince George Biddell Airy to aid in a campaign for its restoration.[51] In 1834 a new edition of his nautical tables was published posthumously.[1] Eva Germaine Rimington Taylor later concluded that all of Lax's works were "of value to the art of navigation".[52]