The Junior Assistant to lecture on Arithmetic and Algebra to Biquadratic Equations, including Newton’s Method of approximation to roots of Equations, also on the application of Algebra to Geometry as given by Newton. The Senior Assistant to lecture on Logarithms, Analytical Trigonometry, with its application to Terrestrial Measurement, application of Algebra to Geometry managed by the equations of figures. The Professor to lecture on the more advanced parts of Mathematics, including the Method of Indeterminate Coefficients, with its application to the management of Series, and other matters not contained in the Course of the Assistant, also Differential and Integral Calculus and the Method of Variations. The programme of the subjects of these lectures shows that there was a large advance in the mathematical education of the students made at this time. Analytical Geometry and Trigonometry were taught to the Honour men among the undergraduates, and the Differential and Integral Calculus and the higher branches of Mathematics were expounded by the Professor of Mathematics to the candidates for Fellowship. Hitherto the mathematical studies of the members of the College were mainly geometrical. The great start in analytical science, which has developed itself so largely in the University, seems to date from this time, and is due very much to the influence of Dr. Bartholomew Lloyd, who had in 1813 been appointed to the Chair of Mathematics. It was not until 1830 that a similar progress was made in the study of Mixed Mathematics. We find that in November of that year a committee, consisting of the Professors of Mathematics and Natural Philosophy, with Dr. Wall, was appointed to recommend to the Board a proper course of Mixed Mathematics, and they were instrumental in introducing the Mechanics of Poisson into the subjects for examination for the higher mathematical honours. A small but important improvement in the existing method of conducting the Term Examinations of ordinary students was made at the same time. Hitherto some of the classes were submitted to be tested by the same Junior Fellow in Science and in Classics. In 1831 it was decided that these branches of studies should be judged by separate examiners in every case. At this time there was no special examination for the degree of Bachelor of Arts. Senior Sophister students who answered in an unsatisfactory manner at the Michaelmas Term Examination were “sent to the Regent House” to be examined. In 1807 it was decreed that every student who is “cautioned to the Regent House” shall be examined in every part of the Undergraduate Course for which he has got a _mediocriter_ at his last examination. It was not until October, 1838, that this examination in the Regent House was formally discontinued, although it had fallen into disuse. It was then arranged that one _vix mediocriter_ for the B.A. degree should subject the candidate to another examination.