[4] Woodhouse was a fellow of the college from 1798 to 1823,[note 1] after which he resigned so as to be able to marry Harriet, the daughter of William Wilkin, a Norwich architect.
[8] In this he explained the differential notation and strongly pressed the employment of it; but he severely criticised the methods used by continental writers, and their constant assumption of non-evident principles.
[1][10] As Plumian Professor he was responsible for installing and adjusting the transit instruments and clocks at the Cambridge Observatory.
[11] Woodhouse did not exercise much influence on the majority of his contemporaries, and the movement might have died away for the time being if it had not been for the advocacy of George Peacock, Charles Babbage, and John Herschel, who formed the Analytical Society, with the object of advocating the general use in the university of analytical methods and of the differential notation.
[12] Woodhouse was the first director of the newly built observatory at Cambridge, a post he held until his death in 1827.