penetrating views; whose enactments nevertheless impress upon it a spirit in perpetuum, for good or for evil.

Some notice of the Mathematical Examination must now be added. It is only since 1825 that separate Examiners have been appointed for this department; at which era Mathematics appeared to become de facto a separate Faculty which had branched off from the Stock of "Arts.". It includes all those Physical Sciences which are brought under the domain of the modern analytical Calculus ; so that, previously to 1825, Arts was in theory a jumble quite worthy of the Middle Ages. We may regard 1825 as the era which decided the triumph of the New, as opposed to the Old, Mathematics at Oxford; but as it has been effected by thrusting the study itself into the Faculties, a common starvation is possibly the only result. Indeed the Public Mathematical Professors are (against their will) more inefficient than ever; since, through the exertions of the Colleges to provide Mathematical Tutors among their own Fellows, the little which needs to be done in this way is done without the help of the Professors. Yet an Oxford First Class in Mathematics is in itself at a very respectable elevation. The Examination lasts four days and a half; and the questions are directed to try the knowledge of the candidates in the following subjects :

Pure Mathematics, as high as the Integral Calculus.

Mechanics, Hydrostatics and Pneumatics, treated analytically. Opening of Newton's Principia, with the Elements of Physical Astronomy, treated analytically.

Geometrical Optics (analytically).

Elements of Plane Astronomy.

A small part of the Examination is conducted by word of mouth, but by far the most important part is in writing; and the chief stress is laid on the application of the principles of the books to solve problems set before the candidate. To answer the questions under all the heads set down above, is not absolutely requisite for a first class: thus, of the four Sciences,-Optics, Plane Astronomy,

It is

Hydrostatics and Pneumatics,-the two first might be sufficient, or the first, third and fourth, or the second, third and fourth. difficult to describe the limit up to which the skill of the candidates must reach; but we may say generally, that in spite of tendencies and lapses into an opposite system, the prevailing rule is to aim at processes of analysis elevated in principle, rather than tangled and wearisome in detail. Their Integral Calculus barely reaches to Elliptic Functions and Linear Differential Equations; and their progress in Analytical Geometry and the annexed Physical Sciences is bounded by this line. Practical minutiæ are of course little sought after in any of the applications, as professional skill is not the object. In the actual management of the examination, there is not the racing of one against another in mere rapidity, which (as reported by Cambridge men) appears to strangers so unpleasing a feature of the Cambridge regulations.

The changes made in the year 1830, though doubtless on the whole for the benefit of the Classical Studies, affected the Mathematics more slightly, and perhaps not for the better. A fourth Class in Mathematics (as in Classics) was introduced; whether with any sensible advantage, I am unable to say: but, beside this, a step backwards was taken in the arrangements concerning Examiners. In 1825, as was noticed above, separate Examiners for Mathematics were appointed: but in 1830,-in order to relieve the Classical Examiners from a part of the drudgery which fell upon them, - instead of granting them assistance from other quarters where it might be had in abundance, the Mathematical Examiners were required to take part in examining the candidates for common degrees. The consequence is, that precisely those men, who, by their single devotion to Mathematics, are most competent to serve as Mathematical Examiners, are found sometimes to decline the office; because it would force them to spend time and thoughts on details long since forgotten and not valued by them.

About the year 1830, (I believe,) there was also founded a University Mathematical Scholarship; but it has not uniformly elicited candidates at all to the satisfaction of the Oxford Mathematicians. Indeed the annual average number has been only

three; while the Ireland Scholarships (for Classics) have an average of about thirty. The following Questions however, which were given last year, will show at what sort of standard they expect their candidates to aim. I am enabled to present them, by the kindness of the Rev. Professor Powell; and as they are fewer than those given for the First Class, I have preferred them to the Examination Papers of the Public Schools.

Questions given at the Oxford Mathematical Scholarship, 1841.

I.

1. Every equation has as many roots as it has dimensions, and

2. What is meant by a discontinuous function?

tracing a locus of such a function.

Illustrate by

3. Three planes at right angles to each other are tangents to an ellipsoid: it is required to determine the locus of their intersection.

4. A vessel filled with wine has an orifice opened in the base; and as the wine runs out, the loss is continually supplied with water which mixes instantly with the wine. Find the proportions of wine and water after a given time.

6. What is meant by general differentiation? Obtain a general

expression for the nth differential coefficient of u=-.

7. A homogeneous prismatic beam rests with one end on a semicircular plate whose diameter is horizontal; find the nature of a curve supporting the other extremity, that it may be at rest at all inclinations.

8. It is required to determine the curve along which a body descending by the force of gravity exerts a pressure at any point reciprocally proportional to the radius of curvature.

9. State and prove the principle of least action, and apply it to the law of ordinary refraction of a ray of light.

10. The moon's motion may be represented by supposing it to move in an ellipse, the elements of which are continually changing. It is required to show this.

11. Determine the effect upon the elliptic orbits of the planets, if they are supposed to move in a medium in which the resistance varies as the square of the velocity.

12. What is meant by polarized light? Explain the separation of common light by doubly refracting crystals, and show that both rays are polarized.

tions in which shall be the independent whole.

2. The parallax and latitude of the moon being respectively P = (1+e cos (c0 — a) +m3 cos [ (2 — 2m)0—28]

to explain the effect of the different terms.

3. To investigate the variation in the eccentricity of a disturbed orbit.

4. It is required to give a physical explanation of the phenomena of precession and nutation.

5. To deduce the laws of the reflexion and refraction of light from the undulatory hypothesis.

6. Of all plane curves of a given length drawn between two given points, to determine that which by its revolution produces the solid of the greatest surface.

7. It is required to determine the color, origin, and intensity of a ray that results from the interference of two others having different origins and intensities.

8. To investigate a method of determining the longitude of a place by observing the distance of the moon from a star.