nected; and would be connected by the element which they have in common as parts of a really Liberal Education; the element which does not belong either to the mere schoolboy, or the mere jurist, but to the worthy recipient of University Honours.

345 I formerly stated (281) that if such a new Tripos as I there described were instituted, Prizes, analogous to the Medals and other Prizes now given to the greatest Mathematical and Classical proficiency, might be expected to be offered to the University. This has already been verified, so far as Moral Philosophy is concerned; and probably this kind of encouragement will be hereafter given to other subjects. And when persons who have obtained such distinctions as these come before the Electors for Fellowships, the honours thus won will not fail to operate in their favour; and thus the Moral Sciences, (and in like manner the Natural Sciences,) will be established in the University, and the cultivation of them maintained, by the same means as those by which Mathematical and Classical Studies have been so long upheld in prosperity.

SECT. 4. The Natural Sciences Tripos.

346 The Natural Sciences included in this title are the following: Human and Comparative Anatomy, Physiology, Chemistry, Botany, Geology, and Mineralogy excluding the Mathematical part of Crystallography. The Examiners are the Professors of Physic, Anatomy, Chemistry, Botany, Geology, Mineralogy, with an additional Examiner appointed by the Senate, as in the Moral Sciences Tripos. The Examination takes place a little after the Examination for the B.A. Degree.

347 It is evident that to frame such an Examination of four days, including in due proportions all the

above subjects, and to compare the aggregate merits of candidates, taking all the subjects together, must be difficult :—more difficult, perhaps, than in the case of the Moral Sciences. There can be no doubt, however, that the Examiners may, by conference among themselves, make arrangements which may in a great degree overcome this difficulty. And such an attempt to combine the various Natural Sciences into one system will not be without its value for the study of the Sciences themselves.

348 Each Science in this list is capable of being pursued so as to occupy a life, and therefore cannot be exhausted in a few hours of Examination. And in particular, Anatomy is so much a science of detail, that it may at first seem impossible that such a brief Examination in that subject should be of any value. But this objection is greatly removed by considering that the Sciences are here to be taken in connection:that Human and Comparative Anatomy go together, the one being used to illustrate the other:-and that Comparative Anatomy is to be considered mainly in connection with Geology. Such considerations as these may be used to limit and fix the Examinations which would be conducted in these subjects; and probably will be so applied by the Professors in their Examinations and in their Lectures.

349 There is another difficulty belonging to these Sciences as Subjects of Examination; namely, this; that the Examiners, in order to be really decisive of the knowledge of the competitors, must be answered, not by means of words merely, but by a reference to specimens and experiments. A knowledge of Botany is shown, among other ways, by naming species presented, and practically exhibiting their structure; a knowledge of Geology, by referring given specimens to their place in the series of strata, in virtue, for instance, of the organic fossils which they contain, or of other

characters; a knowledge of Chemistry, by determining the elements of a substance by means of actual tests or analysis: and the same in other sciences. This is, no doubt, a difficulty: but it has been overcome, both in the Examinations which form part of a professional (for instance, a medical) education, and in the general educational systems of other places; overcome at least so far, as to make these Natural Sciences important parts of the education so conducted. I presume therefore that among ourselves, the difficulty may be overcome to at least the same extent.

350 It may appear a defect in the above scheme that Zoology does not enter as one of the Natural Sciences, especially as Botany does: the classification of animals, it may be said, is as instructive and as important as the classification of plants. And no doubt this is a defect in the scheme, considered as a systematic combination of sciences: although to a certain extent, the blank is supplied by Comparative Anatomy. But it is to be recollected that the new scheme of studies was constructed by bringing into a new mode of operation the Professorships already existing in the University; and as we have no Professorship of Zoology, or of any branch of it, that science was necessarily not among those which were named. Nor is the defect a fatal imperfection in our system: for Botany is a good representative of the Classificatory Sciences, which is one view of Zoology; while Comparative Anatomy (and Physiology in some degree) gives the results of another aspect of Zoology. Still, if at any future period there should exist in the University a Professor of Zoology, it would naturally follow that he and his subject ought to enter into the arrangements of the Natural Sciences Tripos.

351 It does not appear necessary at present to propose a Board of Natural Studies, as we proposed a Board of Moral Studies; for there does not exist

any Examination holding the same place with reference to the University Honours, which the Examination for Bachelor of Civil Law does. The Examination for the Degree of Bachelor of Medicine is of a kind not general, but professional; although undoubtedly attendance at the Lectures and Examinations of several of the above Professors of the Natural Sciences are introduced as conditions for that Degree. But there does not appear to be, at present, any necessity for any change in the requirement for Medical Degrees. The professional Education now given at Cambridge to medical students, is a sound and extensive one: and the Degrees are not sought except for professional objects. We do not want at present a Board of Natural Studies which shall connect them with the Medical Faculty. But we may observe that for the purposes of the Examination for the Natural Sciences Tripos, the Professors who conduct the Examination, with the additional Examiner, would constitute a Board of Natural Studies, and would be able to act as such for all needful purposes.

SECT. 5. The Mathematical Tripos.

352 I have already stated (286) that the more elementary parts of Mathematics should be defined by means of some standard, and that a satisfactory proficiency in them according to this standard should be made a condition of competition to Higher Mathematical Honours. This arrangement has since been made, and came into operation in January 1848.

The standard of the more Elementary Mathematics, thus established, was in the following terms: "Euclid, Book 1. to vI.; Book xI., Prop. I. to xxi.; Book xii., Prop. 1. and II.

"Arithmetic and the Elementary parts of Algebra; namely, the Rules for the fundamental operations upon

Algebraic 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 at 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 1st, 2nd, and 3rd 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 Elastic Fluid, 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, [treated geometrically,] namely, the laws of Reflection and Refraction of Rays at Plane and Spherical Surfaces, not including Aberrations; the Eye, Telescope, &c.

"The Elementary parts of Astronomy, so far as they are necessary for the explanation of the more simple phenomena, without calculations."

The First Report of the Mathematical Board re

a