mission to them, if they have been prevented by illness, or other reasonable cause, from entering the Honour Examination at the usual time, to defer it for one year.

The examination for honours in Mathematics is divided into two parts: the first part is concluded in three days, and the second part is extended to five days; and both are conducted entirely by means of printed papers.

The first three days are assigned to an examination in the more elementary parts of Mathematics and Natural Philosophy. The design of this regulation is more completely to secure in all candidates for mathematical honours a knowledge of the more elementary parts of Mathematics and Natural Philosophy, and to determine with a greater degree of certainty the amount of mathematical knowledge required of such candidates.

tested by the results, and the practical as well as the discriminative faculty is called into action. Hence a larger scope and a wider discipline, and one more adapted to the future exigencies of life. To secure to the student of the Mixed Mathematics all the advantages which their pursuit, so considered, can afford, it is quite necessary that the natural or elementary relations of the subject should throughout be kept steadily in view, and pointedly and fixedly dwelt upon-that all unnecessary exuberance of an analytical calculation be repressed, and that, among methods of connecting assumed principles with their remote consequences, the more lucid should be preferred to the more powerful, and the subject matter pressed on the attention, and not suffered to become overlaid and lost in symbolic detail. There can be no mental discipline where there is no clearness of conception, and there can be no clearness of conception where there is no apprehension of the mode and sequence of action by which the acting powers and the conditions under which they act bring about the result; none in which explanation does not march pari passu with calculation.

"It is by the application of mathematical principles and processes to such branches of Natural Philosophy as admit of this exact mode of treatment, that the noblest triumphs and most useful improvements of modern science have been achieved in Mechanics, in Optics, in Astronomy, in the Exposition of the System of the World. While mathematical knowledge is thus of the highest value, considered as an acquirement, the study of it is equally valuable as a discipline of the intellect. It may be regarded as the best and most effectual exercise of the reasoning powers, habituating the mind to clearness of ideas, precision of statements, and coherence of argument. In this manner it has a wholesome influence beyond the bounds of its own immediate province, and serves to check vague and extravagant speculations even in such popular branches of Natural or Moral Science, as are not reducible to the rigour of mathematical demonstration."

The following is the scheme of subjects of examination for the first three days :

Euclid, Books I. to VI. Book XI., Props. 1 to 21. Book XII., Props. 1, 2.

Arithmetic, and the elementary parts of Algebra; namely, the rules for the fundamental operations upon Algebraical symbols, with their proofs; the solution of simple and quadratic equations; arithmetical and geometrical progression, permutations and combinations, the Binomial Theorem, and the principles of Logarithms.

The elementary parts of Plane Trigonometry, so far as to include the solution of triangles.

The elementary parts of Conic Sections, treated geometrically, together with the values of the Radius of Curvature, and of the Chords of Curvature passing through the focus and

centre.

The elementary parts of Statics, treated without the Differential Calculus; namely, the Composition and Resolution of Forces acting in one plane on a point, the mechanical powers, and the properties of the centre of gravity.

The elementary parts of Dynamics, treated without the Differential Calculus; namely, the doctrine of uniform and uniformly accelerated motion, of falling bodies, projectiles, collision, and cycloidal oscillations.

The first, second, and third sections of Newton's Principia ; the propositions to be proved in Newton's manner.

The elementary parts of Hydrostatics, treated without the Differential Calculus; namely, the pressure of non-elastic fluids, specific gravities, floating bodies, the pressure of the air, and the construction and use of the more simple instruments and machines.

The elementary parts of Optics; namely the laws of reflection and refraction of rays at plane and spherical surfaces, not including aberrations; the eye, telescopes.

The elementary parts of Astronomy; so far as they are necessary for the explanation of the more simple phenomena without calculation.

In all these subjects, examples, and questions, arising

directly out of the propositions, shall be introduced into the examination, in addition to the propositions themselves.

The moderators and examiners determine, from the answers to the questions and problems they have proposed, and declare what students have so acquitted themselves as to deserve, at least, a place in the third class of mathematical honours. Those who are declared to have so acquitted themselves, and no others, are allowed to proceed to the examination in the higher parts of Mathematics and Natural Philosophy, which is continued for five days.

After the completion of the five days' examination, the moderators and examiners, taking into account the examination of the eight days, arrange the successful students into three classes: the first class, Wranglers; the second, Senior Optimes; the third, Junior Optimes; each individual being placed in order of merit in each class. These classes are published in the Senate House on the morning preceding the general admission of students to the degree of B.A.

THE CLASSICAL TRIPOS.

The Classical Tripos was instituted, by Grace of the Senate, on May 28, 1822, to commence in 1824, for all students whose names should appear in one of the three classes of mathematical honours.

In the year 1849, some new regulations were framed, whereby it was determined that the following students only should be admitted to the Classical Tripos Examination:

1. Those who shall have obtained honours at the mathematical examination of the preceding January.

2. Those who, having been declared by the moderators and examiners for mathematical honours in the preceding January to have deserved to pass (according to the present standard) for an ordinary degree, so far as the mathematical part of the examination for such degree is concerned, shall have afterwards passed in the other subjects of that examination.

3. Those whose names shall have been placed (according to

the present standard) in the first class in the examination for an ordinary degree in the preceding January.

4. Those persons entitled to noblemen's degrees, who shall have entered into their eighth term at least, having previously kept six terms, exclusive of the term in which they were admitted, and shall have passed the examination for an ordinary degree in the preceding January; provided, however, that not more than eight terms shall have passed in the case of any such student after his first term of residence.

It was also determined that the names in the first and second classes should be arranged in order of merit, and the third alphabetically. This mode of arrangement of the third class was continued from 1851 to 1859, when the former mode of arrangement by order of merit was resumed.

On May 3, 1854, it was determined, by Grace of the Senate, that in the year 1857, and in every subsequent year, the examination of candidates for honours in the Classical Tripos bo epen to all students who are of the proper standing to be candidates for the Mathematical Tripos in that year; and that students who obtain honours in the Classical Tripos be entitled to the degree of Bachelor of Arts.

On October 28, 1858, the permission was granted, by Grace of the Senate, that a Bachelor designate in Arts may be a candidate for honours in the Classical Tripos of any year, if at the end of the examination, he shall have entered upon his ninth term at least, having previously kept eight terms; provided that not more than ten terms shall have passed after the first of the said eight terms; and that, excepting candidates for degrees jure natalium, no student of a different standing be allowed to be a candidate for classical honours, unless he shall have obtained permission from the Syndicate appointed to consider the cases of students who have degraded.

Also, that a student who has been admitted to the degree of B.A. jure natalium, or who is a candidate for such degree, may, without passing the Previous Examination, be a candidate for honours in the Classical Tripos of any year, if at the end of the examination he shall have entered on his seventh term at least, having previously kept six terms;

provided that not more than eight terms shall have passed after the first of the said eight terms.

The subjects of examination for classical honours consist of-(1) Passages selected from the best Greek and Latin authors, to be translated into English, with such questions to be answered as arise immediately out of such passages; (2) Passages selected from English writers in prose and verse, to be translated into Greek and Latin prose and verse; (3) Questions on Ancient History.

The examination is conducted entirely by printed papers, and it is provided that there shall not be contained in any paper longer passages for translation, normore questions than students well prepared have generally been found able to translate and answer in the time allowed for the paper; also, that the paper set by each examiner shall be submitted to his colleagues for their approval; and that in the paper on History, the questions shall be fixed upon by the four examiners in common. The examination continues for five days, and the morning of the sixth day; the hours of attendance being from nine till twelve in the morning, and from one till four in the afternoon. On the mornings of the first four days translations from English into Greek and Latin are required; on the afternoons of the first four days, and on the fifth day, translations from Greek and Latin into English; and questions of Ancient History on the morning of the sixth day.

On October 28, 1858, it was ordered, by Grace of the Senate that the exercises in Composition be examined by three, at least, of the examiners; and the translations and the answers to the questions on History by two at least.

The names of those students who pass the examination with credit are arranged in three classes, in order of merit, and published by the examiners in the Senate House.

THE MORAL SCIENCES TRIPOS.

The Moral Sciences Tripos was first instituted, by Grace of the Senate, on October 31, 1848; and was designed for such students as had been admitted to their first degree.