tific reputation of the country. The responsibility of introducing the alterations rested with the Moderators and Examiners, no regulations having been provided by the University to which they could refer for authority or guidance: and there is reason to say that the uncertainty as to the subjects the examinations would embrace, and the want of due notice of any extension being given to them, have been felt as a serious inconvenience by the higher class of students. Generally, however, the introduction of each new subject was preceded by the publication of a treatise on the subject by a Cambridge mathematician, in which the Propositions were enunciated and proved in a manner suitable to the established system of examination. It is unnecessary to enumerate here the various treatises that have now come into use: suffice it to say that on the different branches of Pure Mathematics and Natural Philosophy which constitute the present mathematical course, there is a considerable number of English works which are well adapted to convey exact knowledge of the subjects, and at the same time to facilitate the preparation of the students for the examinations.

II. Respecting the Lectures of the Mathematical Professors, it may be sufficient to state the following particulars. The Lectures begun by Professor Airy twenty-three years ago, embraced Mechanics, Hydrostatics and Pneumatics, Geometrical Optics, and the Theory of Light. Lectures on the last four subjects have been continued by the present Plumian Professor, since 1837, at which time the Lowndean Professor also began courses of Lectures alternately on Astronomy and Geometry. In 1843, the Plumian Professor added Practical Astronomy to his other subjects, the Lowndean Professor having discontinued his Astronomical Lectures. The Lectures of the Plumian Professor have had the disadvantage of being given at a time when increasing activity in Astronomical Science demanded extraordinary attention to the duties of the Observatory. They have, however, been attended by a class varying from twenty to thirty, consisting chiefly of the more

advanced students. Since 1838 the Jacksonian Professor has given annually a course of Lectures on Mechanism, and in the present year he has added to these a series of experimental and illustrative Lectures on Mechanics, more immediately bearing on the reading of the students who are preparing for Honours.

It will appear from the foregoing statement that, in order to give increased efficiency to the Lectures of the Mathematical Professors, it is desirable that the subjects should be more equally distributed among the different Professors. These Lectures cannot, however, be expected under any arrangement to supersede other channels of instruction; and it may be doubted whether Professorial Lectures on Pure Mathematics are ever likely to form an effective part of the general system. The case is different with the branches of Natural Philosophy, the importance of experimental and illustrative lectures on which, as supplementary to the other modes of instruction, cannot be too much insisted upon; not only on account of the greater distinctness of conception which is acquired by visible representation of what is read in books, but because such lectures can hardly fail to increase the student's interest in what he reads, and add to his stock of information, and because they afford the opportunity of leading him on to the practical bearings and applications of the subjects of his study. The circumstance of our being able to collect in this University an audience consisting of students who, by previous training, are qualified to understand and appreciate experimental lectures on mathematical subjects, is an advantage by no means to be lost sight of. With respect to any direct means of securing a correspondence between the Lectures of the Professors and the Mathematical Examinations, it is conceived that the publication of a Syllabus, or Outline of the Lectures, accompanied by descriptions of the experimental arrangements, and by mathematical proofs of propositions immediately connected with the facts exemplified, may materially conduce to this end.

III. To the foregoing review of the past and existing state

of the Mathematical Studies of the University, the Board beg leave to add the following recommendations:

(1) Taking into consideration the great number of subjects which now occupy the attention of the candidates, and the doubt which exists as to the range of subjects from which questions may be proposed, the Board recommend that the Mathematical Theories of Electricity, Magnetism, and Heat, be not admitted as subjects of examination.

(2) It has appeared from statements in the former part of this Report, that while the total number of hours of examination has gradually been increased, the time allotted to the solution of Problems has not been altered in the same proportion*. As this arrangement, which could hardly be avoided on account of the large addition to the number of subjects, had the effect of inducing the candidates to neglect examples and problems, it seemed highly desirable to counteract this tendency. Partly with this view and partly to obtain a surer test of the acquaintance of the candidates with the subjects of their reading, examples and deductions have been attached to many of the propositions from books. The Board, however, having had before them an analysis of the answers to the

* The following table exhibits in one view the principal changes in the regulations for conducting the examination which have been mentioned in the course of the Report, together with the average proportion in the successive intervals over which the changes extended, of the number of candidates that obtained Honours, to the whole number of Questionists admitted to the B.A. degree.

questions proposed in 1846, 1847, 1848, and 1849, find that the number of answers to the examples and deductions has fallen below the amount which it is desirable to secure. They are of opinion that such a result may in a great measure be prevented by diminishing the number of questions, and they have agreed to recommend, that the Papers containing the questions from books be shortened, in order to enable the candidates to give more time to Examples and Deductions.

(3) Some uncertainty having been expressed as to the kind of answers the candidates are allowed to give to questions in Optics on the first three days of examination, the Board feel called upon to state, that they understand the term "geometrically" in the Schedule, to mean in a strictly geometrical manner, such, for instance, as that employed in Wood's Optics. At the same time, taking into consideration that the attention of the candidates to geometrical reasoning is sufficiently secured by other subjects of examination on the first three days, they are of opinion, that with reference to Optics, the restriction "geometrically" may with advantage be omitted, and that the questions should be so framed as not necessarily to require any particular kind of demonstration. They, therefore, suggest that it would be desirable to offer to the Senate a Grace for omitting the words "treated geometrically" in the Schedule.

J. CHALLIS, Plumian Professor.

R. WILLIS, Jacksonian Professor.
T. GASKIN.

W. C. MATHISON.

H. GOODWIN, Junior Moderator.

G. G. STOKES.

J. SYKES.

J. C. ADAMS.

W. B. HOPKINS, Senior Moderator.

C. OCTAVUS BUDD.

S. PARKINSON.

May 17, 1849.

A Grace passed the Senate May 23, to omit the words

"treated geometrically" (so far as they relate to Optics) in the Schedule which constitutes the third clause of the Regulations for the Examination of Questionists who are Candidates for Honours, approved by Grace of the Senate, May 13, 1846.

XIII.

SOME REASONS against the expediency of instituting a PUBLIC EXAMINATION OF STUDENTS previous to their Residence in the University.

1 THE duty as well as the privilege of each College is to admit such Students as it considers likely to derive benefit from attending its lectures; that of the University is to see that the Students are duly qualified at the Examinations previous to conferring its degrees. Some Colleges may, by greater attention bestowed on its Students, or by a different style of lectures, or from the smallness of their numbers, or other reasons, be able to prepare a class of young men for the University Examinations, different from that which another College is able or willing to do. I see no necessity for the standard of admission at all Colleges being the same; in fact, the very difference has its advantages. The mode of lecturing is not likely to be the same at all Colleges, neither is it desirable to have entire uniformity. If any one thinks that in consequence of the want of an admission examination by the University "the standard of the College Lecture-rooms is so low, that a young man going from the top of a public school will be nearly losing his time by attending them," he can have very little acquaintance with the Lectures of some of the larger Colleges. Instances not unfrequently occur, of Students, who having been considered unlikely to profit by the Lectures of one College, have gone to another, and by their own steady application, and the pains bestowed upon them, have eventually obtained a degree with credit.

2 It is said that the plan has been tried at Trinity College