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In the mid-nineteenth century, scientifi c research did not have a prominent place in the British universities. A record of scholarship and of original contributions to the subject was notionally demanded of appointees to chairs; but, in practice, there were many instances of appointment of inferior candidates over better scholars, through political and personal infl uence. In all British universities and colleges apart from Oxford and Cambridge, the number of teaching staff was small, and most professors had heavy teaching loads. In Oxford and Cambridge, however, the professors and most college fellows had light teaching duties and ample time to devote themselves to advancing their subject if they were so inclined. But, as already noted, some professors became absentees, taking on other, usually Church, commitments that absorbed their time; and many fellows sank into a comfortable, and often indolent, life in college.

By the 1830s, the main areas to which mathematics had already been successfully applied were mechanics, planetary astronomy, hydrostatics and hydrodynamics, and optics. All of these were prominently represented in the Tripos; and so it was these topics that mainly attracted the interest of the wranglers. To set the scene (and at great risk of oversimplifi cation), the evolution of the mathematical sciences before 1830 is fi rst summarised; then many of the major advances made during the period 1830–80 are reviewed, with emphasis on the work of our wranglers.

is the study of the equilibrium and motion of bodies under applied forces. (In the mid-twentieth century, this was renamed “classical mechanics” to distinguish it from the new fi elds of statistical, relativistic, and quantum mechanics.) It naturally subdivides into and . Statics is the study of mechanical systems in equilibrium under applied forces, and dynamics concerns the motion of bodies induced by applied forces.

Frequently, a solid body can be regarded as a mass concentrated at a single moving point, to which Newton’s laws are directly applicable. Calculation of the motion of such “point particles”, acted on by a constant gravitational force, adequately describes the paths of solid projectiles (including objects such as cannon-balls). Isaac Newton himself improved on this by incorporating a drag force to model air resistance. Numerical tables of such trajectories were long used in warfare for range-fi nding of artillery. Other early theoretical developments included the laws of impact of colliding bodies, and the motion of pendulums under gravity: the latter crucial to the development of accurate clocks, and for detecting local variations of the force of gravity itself.

We have seen how Cambridge University, at a low intellectual ebb at the start of the early nineteenth century, underwent a revival that by the 1850s established it as the pre-eminent British university for mathematics and its applications. This revival involved several distinct processes. The fi rst was criticism from outside Cambridge, and particularly from Edinburgh, of the oldfashioned mathematical instruction that was offered, and of the poor level of understanding in Britain of recent (and not so recent) continental advances. There were also calls for more general reforms from anxious parents and disaffected former students, who accused the University and colleges of neglecting their duties.

The next advance was the adoption of textbooks on trigonometry and astronomy written by Robert Woodhouse; and the student-driven attempt, by the short-lived Analytical Society, to modernise the mathematical syllabus and to foster analytical research. The subsequent election to college fellowships of two of these students, George Peacock and Richard Gwatkin, enabled them, as Tripos moderators and examiners, to introduce the continental notation of the calculus into the examinations.