Statical reasoning, as it has generally been made. And I much fear that students who see the property of the Lever proved in the complex and indirect way in which Mr Goodwin proves it, will never see what a simple and cardinal truth it is. It is true that Mr Goodwin has given in a note the independent proof of the property of the Lever; but this is far, I fear, from being likely to remove the confusion which is likely to arise from giving to a Science so old, a new form in an Elementary Course. Many of the questions which have usually been discussed in books of Mechanics become unintelligible in this way of treating the subject*.

357 I should be disposed to object, although in a less degree, to the mode in which the subject of Cycloidal Motion is treated. Mr Goodwin has, in a note in the second edition, introduced a method of proving the properties of Cycloidal Oscillations which is conformable to the University Regulation; the method introduced in the text being certainly one which the University could not have contemplated in passing the Grace. I have every temptation to be pleased with Mr Goodwin's adoption of this mode of proof, for it is, in substance, one which I invented, and inserted in my Mechanics several years ago. It was invented for the sake of introducing ratios, instead of an arbitrary radius;-the ground, as I have already said, on which our Cambridge Mathematicians made the innovations

* I may remark that my objection to this mode of dealing with the subject of Statics arises from no want of interest in the proofs of the composition of forces at a point. Several such proofs have been devised in recent times, one of which is that which Mr Goodwin gives. I have myself invented one such proof, which was published in a book entitled Analytical Statics, in 1833; and which coincides with a proof published about the same time by M. Poisson, though invented quite independently. And I believe I was the first person who published; for the use of Cambridge Students, a Treatise on Mechanics in which the Composition of Forces at a Point was statically demonstrated.

in Trigonometry, of which I have spoken. But I confess I still prefer the older method invented by Cotes, and adopted by Wood; and I think the student would derive from it a clearer notion of the proof; as certainly it has a far better claim to be considered as a classical proposition than mine has.

358 I do not think that I entertain any other objections to Mr Goodwin's book which are so important that I need mention them here. Some parts of his work are well suited to their purpose.

The Conic Sections, as treated by Mr Goodwin, though brief, are sufficiently rigorous. The Newton will not give a very exact notion of Newton's reasoning to those who do not consult the original text: but it is to be hoped that all the more active minded students will do so. The Optics would, I think, have been clearer for elementary students if it had been more Geometrical; but the propositions are very properly illustrated by several good figures, which in a great measure remedy the defect. The Astronomy is such as meets the occasion; and if there be introduced more concerning astronomical instruments than is absolutely needed, this part may serve to turn the attention of the better students to an interesting subject. And the same may be said of the mode of constructing Solar Eclipses, which makes an acceptable addition to the Astronomical part of the Course. I cannot but rejoice that we have the whole of the Elementary Course of Mathematics to which we direct the candidates for Mathematical Honours thus collected in a single moderate octavo volume.

359 The separation of the higher Mathematics from the elementary in the Examination of our candidates for Mathematical Honours was in operation in the Examinations of January 1848, and January 1849; and so far as can yet be judged, has tended much to produce, or to ascertain, the state of things which was

aimed at ; namely, that those who sought Honours as students of the higher Mathematics should also be well grounded in elementary knowledge. This would seem to be now the case; since, as we are told, it was found that those who, in the later part of the Examination, distinguished themselves most in the higher Mathematical subjects, had, for the most part, previously acquitted themselves best in the introductory Examination in the elementary subjects; and that in no case did persons who had been decidedly defective in elementary knowledge reach high Honours by any lucky speculations in the more elevated and difficult part of the Examination.

360 In the Report of the Board of Mathematical Studies notice is taken of a gradual change which has occurred in the Mathematical Examinations, and which I also had noticed (229). They remark that the time allotted to Questions from Books had increased in a much greater proportion than the time allotted to Examples and Problems*. And they state that having examined a considerable series of answers, they find that the number of answers to the examples and deductions has fallen below the amount which it is desirable to secure. They recommend, on this ground, that the papers containing questions from books be shortened, in order to enable the candidates to give more time to Examples and Deductions.

or

I am of opinion that this recommendation, if acted on, will tend to make our students have a better understanding of their Mathematical principles than they, at least, many of them, have generally had. For as I have already said, (230) "A person may answer by rote a Question from a Book, but in order to solve a

66

* By a note to their paper it appears that the time allotted to Questions diminished in the years 1827-1848, from 39-100ths to 27-100ths of the whole time.

Problem by means of a Principle, he must see the Principle with some degree of clearness."

I have spoken so much of the Mathematical part of the University System in the previous part of the work, that I need not now dwell longer upon that subject. But I must still say a few words on the means of promoting the study both of Mathematics and of the Natural Sciences as a part of the general education of the country.

SECT. 6. The Great Classical Schools.

361 Any one who has thought at all on the subject of the education of the middle and higher classes in England, must be aware that the Great Classical Schools exercise a very powerful influence upon such education. The flower of our English youth spend at these Schools the years during which the greater part is acquired of all that youths do acquire in the way of learning. It is there that their mental habits in a great measure receive the form which they retain in after life. The tastes there generated, the estimate of different kinds of knowledge there communicated by the contagion of society, are not easily afterwards changed. Even if at the University they are introduced to new subjects of thought, new modes of study, new associates, new motives, still the influence of the School continues to be extremely powerful, and though it may be modified, is never obliterated by subsequent agencies.

362 But the views which have been presented in the preceding pages show us this influence operating still more powerfully in another way. If the scholars who come from the Great Schools to the University are not in any great degree afterwards moulded by the University system :-if they are not engaged upon new subjects and modes of study;-if they obtain University Honours, and College emoluments, merely by con

tinuing the pursuit of their schoolboy labours;—if, having done this, they become so numerous in the governing body of the University as to be able to control and direct its measures;-if they exercise this power so as to protect the next generation of schoolboys from being constrained to any studies except those of the Schools; then the University is no longer a place of higher education, supplying the deficiencies of the Schools, balancing their partial system, liberalizing their necessarily narrow plan, converting the education of the Grammar School into a University education: the University then is merely an appendage to the Great Schools: rewarding their best scholars, but teaching them nothing; giving prizes, but giving these to proficiency acquired at School; exercising little influence to modify or correct, but much to confirm the impressions made by the mere classical education of boyhood.

363 I will not say that Cambridge has reached this condition; but I conceive that she is in no small danger of it, if she proceeds in the direction of the measure of October last. And there is at least peril enough of this kind in view, to make it worth while for us to consider whether there ought not to be some modification of system in the Great Schools themselves. This, indeed, is a question which it would be well worth while to consider, independently of any danger which we may apprehend to the system hitherto prevailing in our University. For without referring to any such consideration, it is not, I conceive, too much to say that the Great Schools exercise a greater influence than the Universities upon the higher education in England: and that no measures for the improvement of that education will be efficacious if they do not extend their effects to the Schools as well as the Universities. Indeed it appears to me clear, that, so far as Cambridge is concerned, if anything more in the way of