The following letter has reference to Airy's proposal to introduce certain Physico-Mathematical subjects into the Senate-House Examination for B.A. Honors at Cambridge. On various occasions he sharply criticized the Papers set for the Senate-House Examination and the Smith's Prize Examination, and greatly lamented the growing importance of pure mathematics and the comparative exclusion of physical questions in those examinations. His proposal as finally submitted in the letter that follows was somewhat modified (as regards the mode of introducing the subjects) from his original draft, in deference to the opinions of Whewell, Adams, Routh, and other friends to whom he had submitted it. His proposal was favourably received by the Mathematical Board, and recommendations were made in the direction, though not to the extent, that he desired, and he subsequently submitted a Memorandum on those recommendations:

ROYAL OBSERVATORY, GREENWICH, _1866, May 11_.

MY DEAR SIR,

You will perceive, from perusal of the enclosed paper, that I have acted on the permission which you kindly gave me, to transmit to you my proposal for extension of the mathematical education of the University in the Physical direction.

It is an unavoidable consequence of the structure of the University that studies there will have a tendency to take an unpractical form depending much on the personal tastes of special examiners. I trust that, as a person whose long separation from the daily business of the University has enabled him to see in some measure the wants of the external scientific and practical world, I may be forgiven this attempt to bring to the notice of the University my ideas on the points towards which their attention might perhaps be advantageously turned.

I am, my dear Sir, Very faithfully yours, G.B. AIRY.

_The Rev. Dr Cartmell, Master of Christ's College and Vice-Chancellor._

ROYAL OBSERVATORY, GREENWICH, _1866, May 11_.

MY DEAR MR VICE-CHANCELLOR,

About two years ago, by the kindness of the University, an opportunity was presented to me of orally stating what I conceived to be deficiencies in the educational course of the University as regards mathematical physics. Since that time, the consideration of those deficiencies, which had long been present to me, has urged itself on my attention with greater force: and finally I have entertained the idea that I might without impropriety communicate to you my opinion, in a less fugitive form than on the occasion to which I have alluded: with the request that, if you should deem such a course appropriate, you would bring it before the Board of Mathematical Studies, and perhaps ultimately make it known to the Resident Members of the Senate.

I will first give the list of subjects, which I should wish to see introduced, and to the prosecution of which the generally admirable course of the University is remarkably well adapted: and I will then, without entering into every detail, advert to the process by which I think it probable the introduction of these subjects could be effected.

In the following list, the first head is purely algebraical, and the second nearly so: but they are closely related to observational science, and to the physical subjects which follow. Some of the subjects which I exhibit on my list are partially, but in my opinion imperfectly, taught at present. I entirely omit from my list Physical Optics, Geometrical Astronomy, and Gravitational Astronomy of Points: because, to the extent to which Academical Education ought to go, I believe that there is no teaching on these sciences comparable to that in the University of Cambridge. (It is, of course, still possible that improvements may be made in the books commonly used.) It might, however, be a question, whether, as regards the time and manner of teaching them, some parts of these subjects might ultimately be a.s.sociated with the other subjects included in my list.

I. _List of subjects proposed for consideration_.

(1) Partial Differential Equations to the second order, with their arbitrary functions: selected princ.i.p.ally with reference to the physical subjects.

(2) The Theory of Probabilities as applied to the combination of Observations.

(3) Mechanics (including Hydraulic Powers) in the state which verges upon practical application, and especially including that part in which the abstract ideas of _power_ and _duty_ occur.

(4) Attractions. This subject is recognized in the existing course of the University: but, so far as I can infer from examination-papers, it appears to be very lightly pa.s.sed over.

(5) The Figure of the Earth, and its consequences, Precession, &c. I believe that the proposal is sanctioned, of adopting some part of this theory in the ordinary course; but perhaps hardly so far as is desirable.

(6) The Tides.

(7) Waves of Water.

(8) Sound (beginning with Newton's investigation); Echoes; Pipes and Vibrating Strings; Acoustics; the Mathematical part of Music.

(9) Magnetism, terrestrial and experimental, and their connection.

(I omit for the present Mineralogy and Mathematical Electricity.)

This list of subjects appears formidable: but they are in reality easy, and would be mastered in a short time by the higher Wranglers.

II. _Mode of introducing these subjects into the University_.

After much consideration, and after learning the opinions of several persons whose judgment claims my deepest respect, I propose the gradual introduction of these subjects into the Examination for Honors at admission to the B.A. Degree, as soon as the preparation of Books and the readiness of Examiners shall enable the University to take that step. I conceive that, by a judicious pruning of the somewhat luxuriant growth of Pure Algebra, a.n.a.lytical Geometry, and Mere Problems, sufficient leisure may be gained for the studies of the undergraduates, and sufficient time for the questions of the examiners. I do not contemplate that the students could advance very far into the subjects; but I know the importance of beginning them; and, judging from the train of thoughts, of reading, and of conversation, among the Bachelors with whom I a.s.sociated many years ago, I believe that there is quite a sufficient number who will be anxious to go deep into the subjects if they have once entered into them. If six Wranglers annually would take them up, my point would be gained. The part which these gentlemen might be expected, in a short time, to take in the government of the University, would enable them soon to act steadily upon the University course: the efficiency of the University instruction would be increased; and the external character of the University would be raised.

The real difficulties, and they are not light ones, would probably be found in providing Examiners and Books. At present, both are wanting within the University. Where there is a great and well-founded objection to intrusting examinations to persons foreign to the University, and where the books have to be created with labour and with absolute outlay of money (for their sale could never be remunerative), the progress must be slow. Still progress would be certain, if the authorities of the University should think the matter deserving of their hearty encouragement.

Requesting that you and the Members of the University will accept this proposal as an indication of my deep attachment to my University,

I am, My dear Mr Vice-Chancellor, Your very faithful servant, G.B. AIRY.

_The Rev. Dr Cartmell, &c. &c.

Vice-Chancellor of the University of Cambridge_.

1867

"In this year it was arranged that my Treasury accounts were to be transferred to the Admiralty, making the simplification which I had so long desired.--From the Report to the Visitors it appears that a relic of the Geodetic operations commenced in 1787 for connecting the Observatories of Greenwich and Paris, in the shape of an observing cabin on the roof of the Octagon Room, was shifted and supported in such a manner that the pressure on the flat roof was entirely avoided.--With regard to the Transit Circle, the new Collimators with telescopes of seven inches aperture had been mounted. When the Transit Telescope directed vertically is interposed, the interruptions in the central cube impair the sharpness of definition, still leaving it abundantly good for general use. It had been regarded as probable that the astronomical flexure of the telescope, after cutting away small portions of the central cube, would be found sensibly changed: and this proved to be the case. The difference of flexures of the two ends has been altered more than a second of arc.--Referring to a new Portable Altazimuth which had lately been tested, the Report states as follows: 'I may mention that a study of defects in the vertical circle of a small Altazimuth formerly used by me, and an inspection of the operations in the instrument-maker's work-shop, have convinced me that the princ.i.p.al error to be feared in instruments of this cla.s.s is ovality of the graduated limb; this cannot be eliminated by two microscopes, and such an instrument should never be fitted with two only. Our instrument has four.'--'In Osler's Anemometer, a surface of 2 square feet is now exposed to the wind instead of one foot as formerly; and the plate is supported by weak vertical springs instead of rods running on rollers. Its indications are much more delicate than formerly.'--'The Meteors on Nov. 14th were well observed. Eight thousand and three hundred were registered. The variations of frequency at different times were very well noted. The points of divergence were carefully determined.'--Referring to the gradual improvement in the steadiness of chronometers from 1851 to 1866, it appears that from 1851 to 1854 the 'trial number' (which is a combination of changes of weekly rate representing the fault of the chronometer) varied from 34.8s to 52.5s, while from 1862 to 1866 it varied from 21.2s to 25.8s.--The following statement will shew the usual steadiness of the Great Clock on the Westminster Palace: On 38 per cent. of days of observation, the clock's error was below 1s. On 38 per cent, the error was between 1s and 2s. On 21 per cent. it was between 2s and 3s. On 2 per cent. between 3s and 4s. On 1 per cent.

between 4s and 5s.--The Report contains an account of the determination of the longitude of Cambridge U.S. by Dr B. A. Gould, by means of galvanic currents through the Atlantic Cable, in the spring of 1867: and advantage was taken of this opportunity for re-determining the longitude of Feagh Main near Valencia in Ireland. The longitude of Feagh Main, found by different methods is as follows: By chronometers in 1844, 41m 23.23s; by galvanic communication with Knight's Town in 1862, 41m 23.37s; by galvanic communication with Foilhommerum in 1866, 41m 23.19s. The collected results for longitude of Cambridge U.S. from different sources are: By moon-culminators (Walker in 1851, and Newcomb in 1862-3), 4h 44m 28.42s and 4h 44m 29.56s respectively; by Eclipses (Walker in 1851), 4h 44m 29.64s; by occultations of Pleiades (Peirce 1838-1842, and 1856-1861), 4h 44m 29.91s and 4h 44m 30.90s respectively; by chronometers (W. C. Bond in 1851, and G. P. Bond in 1855), 4h 44m 30.66s and 4h 44m 31.89s respectively; by Atlantic Cable 1866, 4h 44m 30.99s.--After noticing that many meteorological observatories had suddenly sprung up and had commenced printing their observations in detail, the Report continues thus: 'Whether the effect of this movement will be that millions of useless observations will be added to the millions that already exist, or whether something may be expected to result which will lead to a meteorological theory, I cannot hazard a conjecture. This only I believe, that it will be useless, at present, to attempt a process of mechanical theory; and that all that can be done must be, to connect phenomena by laws of induction. But the induction must be carried out by numerous and troublesome trials in different directions, the greater part of which would probably be failures.'--There was this year an annular eclipse; I made large preparations at the limits of the annularity; failed entirely from very bad weather."--In this year Airy contributed a Paper to the Inst.i.tution of Civil Engineers 'On the use of the Suspension Bridge with stiffened roadway for Railway and other Bridges of Great Span,' for which a Telford Medal was awarded to him by the Council of the Inst.i.tution. And he communicated several Papers to the Royal Society and the Royal Astronomical Society.

Of private history: There was the usual visit to Playford in January.--In April there was a short run to Alnwick and the neighbourhood, in company with Mr and Mrs Routh.--From June 27th to July 4th he was in Wales with his two eldest sons, visiting Uriconium, &c. on his return.--From August 8th to Sept. 7th he spent a holiday in Scotland and the Lake District of c.u.mberland with his daughter Christabel, visiting the Langtons at Barrow House, near Keswick, and Isaac Fletcher at Tarn Bank.

In June of this year (1867) Airy was elected an Honorary Fellow of his old College of Trinity in company with Connop Thirlwall, the Bishop of St David's. They were the first Honorary Fellows elected by the College. The announcement was made in a letter from the Master of Trinity (W.H. Thompson), and Airy's reply was as follows:

ROYAL OBSERVATORY, GREENWICH, LONDON, S.E.

_1867, June 12th_.

MY DEAR MASTER,

I am very much gratified by your kind note received this morning, conveying to me the notice that the Master and Sixteen Senior Fellows had elected me, under their new powers, as Honorary Fellow of the College.

It has always been my wish to maintain a friendly connection with my College, and I am delighted to receive this response from the College. The peculiar form in which the reference to the Statute enables them to put it renders it doubly pleasing.

As the Statute is new, I should be obliged by a copy of it. And, at any convenient time, I should be glad to know the name of the person with whom I am so honorably a.s.sociated.

I am, My dear Master, Very faithfully yours, G.B. AIRY.

Consequent on Airy's proposals in 1866 for the introduction of new physical subjects into the Senate-House Examination and his desire that the large number of questions set in Pure Mathematics, or as he termed it "Useless Algebra," should be curtailed, there was a smart and interesting correspondence between him and Prof. Cayley, who was the great exponent and advocate of Pure Mathematics at Cambridge. Both of them were men of the highest mathematical powers, but diametrically opposed in their views of the use of Mathematics. Airy regarded mathematics as simply a useful machine for the solution of practical problems and arriving at practical results. He had a great respect for Pure Mathematics and all the processes of algebra, so far as they aided him to solve his problems and to arrive at useful results; but he had a positive aversion to mathematical investigations, however skilful and elaborate, for which no immediate practical value could be claimed. Cayley on the contrary regarded mathematics as a useful exercise for the mind, apart from any immediate practical object, and he considered that the general command of mathematics gained by handling abstruse mathematical investigations (though barren in themselves) would be valuable for whatever purpose mathematics might be required: he also thought it likely that his researches and advances in the field of Pure Mathematics might facilitate the solution of physical problems and tend to the progress of the practical sciences. Their different views on this subject will be seen from the letters that follow:

ROYAL OBSERVATORY, GREENWICH, LONDON, S.E.

_1867, Nov. 8_.

MY DEAR SIR,

I think it best to put in writing the purport of what I have said, or have intended to say, in reference to the Mathematical Studies in the University.