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The third of those who helped to bring analytical methods into general use in England was the son of Sir William Hershel (1738-1822), the most illustrious astronomer of the latter half of the eighteenth century and the creator of modern stellar astronomy. Sir John Frederick William Herschel was born on March 7, 1792, educated at St. John's College, Cambridge, and died on May 11, 1871. His earliest original work was a paper on Cotes's theorem, and it was followed by others on mathematical analysis, but his desire to complete his father's work led ultimately to his taking up astronomy. His papers on light and astronomy contain a clear exposition of the principles which underlie the mathematical treatment of those subjects.
In 1813 the Analytical Society published a volume of memoirs, of which the preface and the first paper (on continued products) are due to Babbage; and three years later they issued a translation of Lacroix's Traité élémentaire du calcul différentiel et du calcul intégral. In 1817, and again in 1819, the differential notation was used in the university examinations, and after 1820 its use was well established. The Analytical Society followed up this rapid victory by the issue in 1820 of two volumes of examples illustrative of the new method; one by Peacock on the differential and integral calculus, and the other by Herschel on the calculus of finite differences. Since then English works on the infinitesimal calculus have abandoned the exclusive use of the fluxional notation. It should be noticed in passing that Lagrange and Laplace, like the majority of other modern writers, employ both the fluxional and the differential notation; it was the exclusive adoption of the former that was so hampering.
Amongst those who materially assisted in extending the use of the new analysis were William Whewell (1794-1866) and George Biddell Airy (1801-1892), both Fellows of Trinity College, Cambridge. The former issued in 1819 a work on mechanics, and the latter, who was a pupil of Peacock, published in 1826 his Tracts, in which the new method was applied with great success to various physical problems. The efforts of the society were supplemented by the rapid publication of good text-books in which analysis was freely used. The employment of analytical methods spread from Cambridge over the rest of Britain, and by 1830 these methods had come into general use there.
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