Chapter VIII: At Greenwich Observatory--1866 to 1876 (1)

1866

In this year the cube of the Transit Circle was pierced, to permit reciprocal observations of the Collimators without raising the instrument. This involved the construction of improved Collimators, which formed the subject of a special Address to the Members of the Board of Visitors on Oct. 21st 1865.--From the Report to the Visitors it appears that "On May 23rd 1865, a thunderstorm of great violence passed very close to the Observatory. After one flash of lightning, I was convinced that the principal building was struck. Several galvanometers in the Magnetic Basement were destroyed. Lately it has been remarked that one of the old chimneys of the principal building had been dislocated and slightly twisted, at a place where it was surrounded by an iron stay-band led from the Telegraph Pole which was planted upon the leads of the Octagon Room."--"On consideration of the serious interruptions to which we have several times been exposed from the destruction of our open-air Park-wires (through snow-storms and gales), I have made an arrangement for leading the whole of our wires in underground pipes as far as the Greenwich Railway Station."--"The Committee of the House of Commons, to whom the Greenwich and Woolwich Line of the South Eastern Railway was referred, finally assented to the adoption of a line which I indicated, passing between the buildings of the Hospital Schools and the public road to Woolwich."--"The Galvanic Chronometer attached to the S. E. Equatoreal often gave us a great deal of trouble. At last I determined, on the proposal of Mr Ellis, to attempt an extension of Mr R. L. Jones's regulating principle. It is well known that Mr Jones has with great success introduced the system of applying galvanic currents originating in the vibrations of a normal pendulum, not to drive the wheelwork of other clocks, but to regulate to exact agreement the rates of their pendulums which were, independently, nearly in agreement; each clock being driven by weight-power as before. The same principle is now applied to the chronometer.... The construction is perfectly successful; the chronometer remains in coincidence with the Transit Clock through any length of time, with a small constant error as is required by mechanical theory."--"The printed volume of Observations for 1864 has two Appendixes; one containing the calculations of the value of the Moon's Semi-diameter deduced from 295 Occultations observed at Cambridge and Greenwich from 1832 to 1860, and shewing that the Occultation Semi-diameter is less than the Telescopic Semi-diameter by 2"; the other containing the reduction of the Planetary Observations made at the Royal Observatory in the years 1831-1835; filling up the gap, between the Planetary Reductions 1750-1830 made several years ago under my superintendence, and the Reductions contained in the Greenwich Volumes 1836 to the present time: and conducted on the same general principles."--"Some trouble had been found in regulating the temperature of the Magnetic Basement, but it was anticipated that in future there would be no difficulty in keeping down the annual variation within about 5° and the diurnal variation within 3°.--Longitudes in America were determined in this year by way of Valencia and Newfoundland: finished by Nov. 14th."

Of private history: In April he made a short visit to Ventnor in the Isle of Wight.--From June 15th to July 23rd he was on an expedition in Norway with his son Osmund and his nephew Gorell Barnes.--There was probably a short stay at Playford in the winter.

In this and in the previous year (1865) the free-thinking investigations of Colenso, the Bishop of Natal, had attracted much notice, and had procured him the virulent hostility of a numerous section. His income was withheld from him, and in consequence a subscription fund was raised for his support by his admirers. Airy, who always took the liberal side in such questions, was a subscriber to the fund, and wrote the following letter to the Bishop:

ROYAL OBSERVATORY, GREENWICH, S.E.,
_1865, July 24_.

MY LORD,

With many thanks I have to acknowledge your kind recollection of me in sending as a presentation copy the work on Joshua, Judges, and especially on the divided authorship of Genesis; a work whose investigations, founded in great measure on severe and extensive verbal criticism, will apparently bear comparison with your Lordship's most remarkable examination of Deuteronomy. I should however not do justice to my own appreciation if I did not remark that there are other points considered which have long been matters of interest to me.

On several matters, some of them important, my present conclusions do not absolutely agree with your Lordship's. But I am not the less grateful for the amount of erudition and thought carefully directed to definite points, and above all for the noble example of unwearied research and freedom in stating its consequences, in reference to subjects which scarcely ever occupy the attention of the clergy in our country.

I am, My Lord,
Yours very faithfully,
G.B. AIRY.

_The Lord Bishop of Natal_.

* * * * *

Here also is a letter on the same subject, written to Professor Selwyn, Professor of Divinity at Cambridge:--

ROYAL OBSERVATORY, GREENWICH,
LONDON, S.E.,
_1866, May 5_.

MY DEAR SIR,

The MS. concerning Colenso duly arrived.

I note your remarks on the merits of Colenso. I do not write to tell you that I differ from you, but to tell you why I differ.

I think that you do not make the proper distinction between a person who invents or introduces a tool, and the person who uses it.

The most resolute antigravitationist that ever lived might yet acknowledge his debt to Newton for the Method of Prime and Ultimate Ratios and the Principles of Fluxions by which Newton sought to establish gravitation.

So let it be with Colenso. He has given me a power of tracing out truth to a certain extent which I never could have obtained without him. And for this I am very grateful.

As to the further employment of this power, you know that he and I use it to totally different purposes. But not the less do I say that I owe to him a new intellectual power.

I quite agree with you, that the sudden disruption of the old traditional view seems to have unhinged his mind, and to have sent him too far on the other side. I would not give a pin for his judgment.

Nevertheless, I wish he would go over the three remaining books of the Tetrateuch.

I know something of Myers, but I should not have thought him likely to produce anything sound on such things as the Hebrew Scriptures. I never saw his "Thoughts."

I am, my dear Sir,
Yours very truly,
G.B. AIRY.

_Professor Selwyn_.

* * * * *

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 associated 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 principally 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 passed 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, Analytical 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 associated 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 principal error to be feared in instruments of this class 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 Institution 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 Institution. 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 Cumberland 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 associated.

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.

First, I will remark on the study of Partial Differential Equations. I do not know that one branch of Pure Mathematics can be considered higher than another, except in the utility of the power which it gives. Measured thus, the Partial Differential Equations are very useful and therefore stand very high, as far as the Second Order. They apply, to that point, in the most important way, to the great problems of nature concerning _time_, and _infinite division of matter_, and _space_: and are worthy of the most careful study. Beyond that Order they apply to nothing. It was for the purpose of limiting the study to the Second Order, and at the same time working it carefully, philosophically, and practically, up to that point, that I drew up my little work.

On the general question of Mathematical Studies, I will first give my leading ideas on what I may call the moral part. I think that a heavy responsibility rests on the persons who influence most strongly the course of education in the University, to direct that course in the way in which it will be most useful to the students--in the two ways, of disciplining their powers and habits, and of giving them scientific knowledge of the highest and most accurate order (applying to the phenomena of nature) such as will be useful to them through life. I do not think that the mere personal taste of a teacher is sufficient justification for a special course, unless it has been adopted under a consideration of that responsibility. Now I can say for myself that I have, for some years, inspected the examination papers, and have considered the bearing of the course which they imply upon the education of the student, and am firmly convinced that as regards men below the very few first--say below the ten first--there is a prodigious loss of time without any permanent good whatever. For the great majority of men, such subjects as abstract Analytical Geometry perish at once. With men like Adams and Stokes they remain, and are advantageous; but probably there is not a single man (beside them) of their respective years who remembers a bit, or who if he remembers them has the leisure and other opportunities of applying them.

I believe on the other hand that a careful selection of physical subjects would enable the University to communicate to its students a vast amount of information; of accurate kind and requiring the most logical treatment; but so bearing upon the natural phenomena which are constantly before us that it would be felt by every student to possess a real value, that (from that circumstance) it would dwell in his mind, and that it would enable him to correct a great amount of flimsy education in the country, and, so far, to raise the national character.

The consideration of the education of the reasoning habits suggests ideas far from favourable to the existing course. I am old enough to remember the time of mere geometrical processes, and I do not hesitate to say that for the cultivation of accurate mental discipline they were far superior to the operations in vogue at the present day. There is no subject in the world more favourable to logical habit than the Differential Calculus in all its branches _if logically worked in its elements_: and I think that its applications to various physical subjects, compelling from time to time an attention to the elementary grounds of the Calculus, would be far more advantageous to that logical habit than the simple applications to Pure Equations and Pure Algebraical Geometry now occupying so much attention.

I am, my dear Sir,
Yours very truly,
G.B. AIRY.

_Professor Cayley_.

* * * * *

DEAR SIR,

I have been intending to answer your letter of the 8th November. So far as it is (if at all) personal to myself, I would remark that the statutory duty of the Sadlerian Professor is that he shall explain and teach the principles of Pure Mathematics and apply himself to the advancement of the Science.

As to Partial Differential Equations, they are "high" as being an inverse problem, and perhaps the most difficult inverse problem that has been dealt with. In regard to the limitation of them to the second order, whatever other reasons exist for it, there is also the reason that the theory to this order is as yet so incomplete that there is no inducement to go beyond it; there could hardly be a more valuable step than anything which would give a notion of the form of the general integral of a Partial Differential Equation of the second order.

I cannot but differ from you _in toto_ as to the educational value of Analytical Geometry, or I would rather say of Modern Geometry generally. It appears to me that in the Physical Sciences depending on Partial Differential Equations, there is scarcely anything that a student can do for himself:--he finds the integral of the ordinary equation for Sound--if he wishes to go a step further and integrate the non-linear equation (dy/dx)²(d²y/dt²) = a²(d²y/dx²) he is simply unable to do so; and so in other cases there is nothing that he can add to what he finds in his books. Whereas Geometry (of course to an intelligent student) is a real inductive and deductive science of inexhaustible extent, in which he can experiment for himself--the very tracing of a curve from its equation (and still more the consideration of the cases belonging to different values of the parameters) is the construction of a theory to bind together the facts--and the selection of a curve or surface proper for the verification of any general theorem is the selection of an experiment in proof or disproof of a theory.

I do not quite understand your reference to Stokes and Adams, as types of the men who alone retain their abstract Analytical Geometry. If a man when he takes his degree drops mathematics, he drops geometry--but if not I think for the above reasons that he is more likely to go on with it than with almost any other subject--and any mathematical journal will shew that a very great amount of attention is in fact given to geometry. And the subject is in a very high degree a progressive one; quite as much as to Physics, one may apply to it the lines, Yet I doubt not thro' the ages one increasing purpose runs, and the thoughts of men are widened with the progress of the suns.

I remain, dear Sir,
Yours very sincerely,
A. CAYLEY.

CAMBRIDGE,
_6 Dec., 1867_.

* * * * *

ROYAL OBSERVATORY, GREENWICH,
LONDON, S.E.
_1867, December 9_.

MY DEAR SIR,

I have received with much pleasure your letter of December 6. In this University discussion, I have acted only in public, and have not made private communication to any person whatever till required to do so by private letter addressed to me. Your few words in Queens' Hall seemed to expect a little reply.

Now as to the Modern Geometry. With your praises of this science--as to the room for extension in induction and deduction, &c.; and with your facts--as to the amount of space which it occupies in Mathematical Journals; I entirely agree. And if men, after leaving Cambridge, were designed to shut themselves up in a cavern, they could have nothing better for their subjective amusement. They might have other things as good; enormous complication and probably beautiful investigation might be found in varying the game of billiards with novel islands on a newly shaped billiard table. But the persons who devote themselves to these subjects do thereby separate themselves from the world. They make no step towards natural science or utilitarian science, the two subjects which the world specially desires. The world could go on as well without these separatists.

Now if these persons lived only for themselves, no other person would have any title to question or remark on their devotion to this barren subject. But a Cambridge Examiner is not in that position. The University is a national body, for education of young men: and the power of a Cambridge Examiner is omnipotent in directing the education of the young men; and his responsibility to the cause of education is very distinct and very strong. And the question for him to consider is--in the sense in which mathematical education is desired by the best authorities in the nation, is the course taken by this national institution satisfactory to the nation?

I express my belief that it is _not_ satisfactory. I believe that many of the best men of the nation consider that a great deal of time is lost on subjects which they esteem as puerile, and that much of that time might be employed on noble and useful science.

You may remember that the Commissions which have visited Cambridge originated in a Memorial addressed to the Government by men of respected scientific character: Sabine was one, and I may take him as the representative. He is a man of extensive knowledge of the application of mathematics as it has been employed for many years in the science of the world; but he has no profundity of science. He, as I believe, desired to find persons who could enter accurately into mathematical science, and naturally looked to the Great Mathematical University; but he must have been much disappointed. So much time is swallowed up by the forced study of the Pure Mathematics that it is not easy to find anybody who can really enter on these subjects in which men of science want assistance. And so Sabine thought that the Government ought to interfere, probably without any clear idea of what they could do.

I am, my dear Sir,
Yours very truly,
G.B. AIRY.

_Professor Cayley_.

* * * * *

DEAR SIR,

I have to thank you for your last letter. I do not think everything should be subordinated to the educational element: my idea of a University is that of a place for the cultivation of all science. Therefore among other sciences Pure Mathematics; including whatever is interesting as part of this science. I am bound therefore to admit that your proposed extension of the problem of billiards, _if it_ were found susceptible of interesting mathematical developments, would be a fit subject of study. But in this case I do not think the problem could fairly be objected to as puerile--a more legitimate objection would I conceive be its extreme speciality. But this is not an objection that can be brought against Modern Geometry as a whole: in regard to any particular parts of it which may appear open to such an objection, the question is whether they are or are not, for their own sakes, or their bearing upon other parts of the science to which they belong, worthy of being entered upon and pursued.

But admitting (as I do not) that Pure Mathematics are only to be studied with a view to Natural and Physical Science, the question still arises how are they best to be studied in that view. I assume and admit that as to a large part of Modern Geometry and of the Theory of Numbers, there is no present probability that these will find any physical applications. But among the remaining parts of Pure Mathematics we have the theory of Elliptic Functions and of the Jacobian and Abelian Functions, and the theory of Differential Equations, including of course Partial Differential Equations. Now taking for instance the problem of three bodies--unless this is to be gone on with by the mere improvement in detail of the present approximate methods--it is at least conceivable that the future treatment of it will be in the direction of the problem of two fixed centres, by means of elliptic functions, &c.; and that the discovery will be made not by searching for it directly with the mathematical resources now at our command, but by "prospecting" for it in the field of these functions. Even improvements in the existing methods are more likely to arise from a study of differential equations in general than from a special one of the equations of the particular problem: the materials for such improvements which exist in the writings of Hamilton, Jacobi, Bertrand, and Bour, have certainly so arisen. And the like remarks would apply to the physical problems which depend on Partial Differential Equations.

I think that the course of mathematical study at the University is likely to be a better one if regulated with a view to the cultivation of Science, as if for its own sake, rather than directly upon considerations of what is educationally best (I mean that the best educational course will be so obtained), and that we have thus a justification for a thorough study of Pure Mathematics. In my own limited experience of examinations, the fault which I find with the men is a want of analytical power, and that whatever else may have been in defect Pure Mathematics has certainly not been in excess.

I remain, dear Sir,
Yours sincerely,
A. CAYLEY.

CAMBRIDGE,
_10th Dec., 1867_.

* * * * *

_1867, December 17_.

MY DEAR SIR,

Since receiving your letter of 9th I positively have not had time to express the single remark which I proposed to make on it.

You state your idea that the educational element ought not to be the predominating element in the University. "I do not think that every thing should be subordinated to the educational element." I cannot conceal my surprise at this sentiment. Assuredly the founders of the Colleges intended them for education (so far as they apply to persons in statu pupillari), the statutes of the University and the Colleges are framed for education, and fathers send their sons to the University for education. If I had not had your words before me, I should have said that it is impossible to doubt this.

It is much to be desired that Professors and others who exercise no control by force should take every method, not only of promoting science in themselves, but also of placing the promoted science before students: and it is much to be desired that students who have passed the compulsory curriculum should be encouraged to proceed into the novelties which will be most agreeable to them. But this is a totally different thing from using the Compulsory Force of Examination to drive students in paths traced only by the taste of the examiner. For them, I conceive the obligation to the nation and the duty to follow the national sense on education (as far as it can be gathered from its best representatives) to be undoubted; and to be, in the intensity of the obligation and duty, most serious.

I am, my dear Sir,
Yours very truly,
G.B. AIRY.

_Professor Cayley_.

* * * * *

1868

"In the South-East Dome, the alteration proposed last year for rendering the building fire-proof had been completely carried out. The middle room, which was to be appropriated to Chronometers, was being fitted up accordingly.--From the Report it appears that 'our subterranean telegraph wires were all broken by one blow, from an accident in the Metropolitan Drainage Works on Groom's Hill, but were speedily repaired.'--In my office as Chairman of successive Commissions on Standards, I had collected a number of Standards, some of great historical value (as Ramsden's and Roy's Standards of Length, Kater's Scale-beam for weighing great weights, and others), &c. These have been transferred to the newly-created Standards Department of the Board of Trade."--In the Report is given a detailed account of the system of preserving and arranging the manuscripts and correspondence of the Observatory, which was always regarded by Airy as a matter of the first importance.--From a careful discussion of the results of observation Mr Stone had concluded that the refractions ought to be diminished. 'Relying on this, we have now computed our mean refractions by diminishing those of Bessel's Fundamenta in the proportion of 1 to 0.99797.'--The Magnetometer-Indications for the period 1858-1863 had been reduced and discussed, with remarkable results. It is inferred that magnetic disturbances, both solar and lunar, are produced mediately by the Earth, and that the Earth in periods of several years undergoes changes which fit it and unfit it for exercising a powerful mediate action.--The Earth-current records had been reduced, and the magnetic effect which the currents would produce had been computed. The result was, that the agreement between the magnetic effects so computed and the magnetic disturbances really recorded by the magnetometers was such as to leave no doubt on the general validity of the explanation of the great storm-disturbances of the magnets as consequences of the galvanic currents through the earth.--Referring to the difficulty experienced in making the meteorological observations practically available the Report states thus: 'The want of Meteorology, at the present time, is principally in suggestive theory.'--In this year Airy communicated to the Royal Astronomical Society a Paper 'On the Preparatory Arrangements for the Observation of the Transits of Venus 1874 and 1882': this subject was now well in hand.--The First Report of the Commissioners (of whom he was Chairman) appointed to enquire into the condition of the Exchequer Standards was printed: this business took up much time.--He was in this year much engaged on the Coinage Commission.

Of private history: There was the usual winter visit to Playford, and a short visit to Cambridge in June.--From about Aug. 1st to Sept. 3rd he was travelling in Switzerland with his youngest son and his two youngest daughters. In the course of this journey they visited Zermatt. There had been much rain, the rivers were greatly flooded, and much mischief was done to the roads. During the journey from Visp to Zermatt, near St Nicholas, in a steep part of the gorge, a large stone rolled from the cliffs and knocked their baggage horse over the lower precipice, a fall of several hundred feet. The packages were all burst, and many things were lost, but a good deal was recovered by men suspended by ropes.

In this year also Airy was busy with the subject of University Examination, which in previous years had occupied so much of his attention, as will be seen from the following letters:

ROYAL OBSERVATORY, GREENWICH,
LONDON, S.E.
_1868, March 12_.

MY DEAR MASTER,

I have had the pleasure of corresponding with you on matters of University Examination so frequently that I at once turn to you as the proper person to whom I may address any remarks on that important subject.

Circumstances have enabled me lately to obtain private information of a most accurate kind on the late Mathematical Tripos: and among other things, I have received a statement of every individual question answered or partly answered by five honour-men. I have collected the numbers of these in a small table which I enclose.

I am struck with the _almost_ nugatory character of the five days' honour examination as applied to Senior Optimes, and I do not doubt that it is _totally_ nugatory as applied to Junior Optimes. It appears to me that, for all that depends on these days, the rank of the Optimes is mere matter of chance.

In the examinations of the Civil Service, the whole number of marks is published, and also the number of marks gained by each candidate. I have none of their papers at hand, but my impression is that the lowest candidates make about 1 in 3; and the fair candidates about 2 in 3, instead of 1 in 10 or 1 in 13 as our good Senior Optimes.

I am, my dear Master,
Very truly yours,
G.B. AIRY.

_The Rev. Dr Cookson,
Master of St Peters College,
&c. &c._

The Table referred to in the above letter is as follows:

Number of Questions, and numbers of Answers to Questions as given by several Wranglers and Senior Optimes, in the Examination of Mathematical Tripos for Honours, 1868, January 13, 14, 15, 16, 17.

Number of Questions and Riders in the Printed Papers.

Questions. Riders. Aggregate.
In the 10 Papers of the 5 days 123 101 224

NUMBER OF QUESTIONS AND RIDERS ANSWERED.

Questions. Riders. Aggregate.
By a Wrangler, between the
1st and 7th 69-1/2 25-1/2 95 1 in 2.36
By a Wrangler, between the
12th and 22nd 48-1/2 12-1/2 61 1 in 3.68
By a Wrangler, between the
22nd and 32nd 36 12-1/2 48-1/2 1 in 4.62
By a Sen. Opt. between the
1st and 10th 17-1/2 5 22-1/2 1 in 9.95
By a Sen. Opt. between the
10th and 20th 14-1/2 2 16-1/2 1 in 3.60

G.B. AIRY.

_1868, March 12_.

* * * * *

ST PETER'S COLLEGE LODGE, CAMBRIDGE,
_March 13th, 1868_.

MY DEAR SIR,

I am much obliged by your letter and enclosed paper.

Anything done in the last five days by a Junior Optime only shews (generally) that he has been employing some of his time _mischievously_, for he must have been working at subjects which he is quite unable to master or cramming them by heart on the chance of meeting with a stray question which he may answer.

The chief part of the Senior Optimes are in something of the same situation.

I think that the proposed addition of a day to the first part of the Examination, in which "easy questions in physical subjects" may be set, is, on this account, a great improvement.

Our new Scheme comes on for discussion on Friday next, March 20, at 2 p.m. in the Arts School. It is much opposed by private tutors, examiners and others, and may possibly be thrown out in the Senate this year, though I hope that with a little patience it may be carried, in an unmutilated form, eventually.

The enclosed Report on the Smith's Prize Examination will be discussed at the same time.

I will consider what is best to be done on the subject to which your note refers, without delay. With many thanks,

I am,
Very faithfully yours,
H.W. COOKSON,

_The Astronomer Royal._

* * * * *

In this year certain Members of the Senate of the University of Cambridge petitioned Parliament against the abolition of religious declarations required of persons admitted to Fellowships or proceeding to the degree of M.A. The document was sent to Airy for his signature, and his reply was as follows:

ROYAL OBSERVATORY, GREENWICH,
LONDON, S.E.
_1868, March 18_.

MY DEAR SIR,

Though I sympathize to a great extent with the prayer of the petition to Parliament which you sent to me yesterday, and assent to most of the reasons, I do not attach my signature to it, for the following considerations:

1. I understand, from the introductory clause, and from the unqualified character of the phrase "any such measures" in the second clause, that the petition objects to granting the M.A. degree without religious declaration. I do not see any adequate necessity for this objection, and I cannot join in it.

2. It appears to me that the Colleges were intended for two collateral objects:--instruction by part of the Fellows, on a religious basis; and support of certain Fellows for scientific purposes, without the same ostentatious connection with religion. I like this spirit well, and should be glad to maintain it.

3. I therefore think (as I have publicly stated before) that the Master of the College ought to be in holy orders; and so ought those of the Fellows who may be expected to be usually resident and to take continuous part in the instruction. But there are many who, upon taking a fellowship, at once lay aside all thoughts of this: and I think that such persons ought not to be trammelled with declarations.

4. My modification of existing regulations, if it once got into shape, would I dare say be but a small fraction of that proposed by the "measures in contemplation." Still I do not like to join in unqualified resistance to interference in the affairs of the Established Colleges, with that generality of opposition to interference which the petition seems to intimate.

I agree with articles 3, 4, and 5; and I am pleased with the graceful allusion in article 4 to the assistance which has been rendered by the Colleges, and by none perhaps so honourably as Trinity, to the parishes connected with it. And I could much wish that the spirit of 3 and 5 could be carried out, with some concession to my ideas in _my_ paragraph 3, above.

I am, my dear Sir,
Yours very truly,
G.B. AIRY.

_Rev. Dr Lightfoot._

* * * * *

1869

From the Report to the Board of Visitors it appears that application had been made for an extension of the grounds of the Observatory to a distance of 100 feet south of the Magnetic Ground, and that a Warrant for the annexation of this space was signed on 1868, Dec. 8. The new Depôt for the Printed Productions of the Observatory had been transferred to its position in the new ground, and the foundations for the Great Shed were completed.--"The courses of our wires for the registration of spontaneous terrestrial galvanic currents have been entirely changed. The lines to Croydon and Deptford are abandoned; and for these are substituted, a line from Angerstein Wharf to Lady Well Station, and a line from North Kent Junction to Morden College Tunnel. At each of these points the communication with Earth is made by a copper plate 2 feet square. The straight line connecting the extreme points of the first station intersects that connecting the two points of the second station, nearly at right angles, and at little distance from the Observatory.--The question of dependence of the measurable amount of sidereal aberration upon the thickness of glass or other transparent material in the telescope (a question which involves, theoretically, one of the most delicate points in the Undulatory Theory of Light) has lately been agitated on the Continent with much earnestness. I have calculated the curvatures of the lenses of crown and flint glass (the flint being exterior) for correcting spherical and chromatic aberration in a telescope whose tube is filled with water, and have instructed Mr Simms to proceed with the preparation of an instrument carrying such a telescope. I have not finally decided whether to rely on Zenith-distances of gamma Draconis or on right-ascensions of Polaris. In any form the experiment will probably be troublesome.--The transit of Mercury on 1868, Nov. 4th, was observed by six observers. The atmospheric conditions were favourable; and the singular appearances usually presented in a planetary transit were well seen.--Mr Stone has attached to the South-East Equatoreal a thermo-multiplier, with the view of examining whether heat radiating from the principal stars can be made sensible in our instruments. The results hitherto obtained are encouraging, but they shew clearly that it is vain to attempt this enquiry except in the most superb weather; and there has not been a night deserving that epithet for some months past.--The preparations for observing the Transits of Venus were now begun in earnest. I had come to the conclusion, that after every reliance was placed on foreign and colonial observatories, it would be necessary for the British Government to undertake the equipment of five or six temporary stations. On Feb. 15th I sent a pamphlet on the subject to Mr Childers (First Lord of Admiralty), and in April I wrote to the Secretary, asking authority for the purchase of instruments. On June 22nd authority is given to me for the instruments: the Treasury assent to _£10,500_. On August 9th I had purchased 3 equatoreals.--I have given a short course of Lectures in the University of Cambridge on the subject of Magnetism, with the view of introducing that important physical science into the studies of the University. The want of books available to Students, and the novelty of the subject, made the preparation more laborious than the duration of the lectures would seem to imply."--In this year there was much work on the Standards Commission, chiefly regarding the suggested abolition of Troy Weight, and several Papers on the subject were prepared by Airy.--He also wrote a long and careful description of the Great Equatoreal at Greenwich.

Of private history: There was the usual visit to Playford in the winter. Mrs Airy was now becoming feebler, and did not now leave Greenwich: since April of this year her letters were written in pencil, and with difficulty, but she still made great efforts to keep up the accustomed correspondence.--In April Airy went to Cambridge to deliver his lectures on magnetism to the undergraduates: the following passage occurs in one of his letters at this time: "I have a mighty attendance (there were 147 names on my board yesterday), and, though the room is large with plenty of benches, I have been obliged to bring in some chairs. The men are exceedingly attentive, and when I look up I am quite struck to see the number of faces staring into mine. I go at 12, and find men at the room copying from my big papers: I lecture from 1 to 2, and stop till after 3, and through the last hour some men are talking to me and others are copying from the papers; and I usually leave some men still at work. The men applaud and shew their respect very gracefully. There are present some two or three persons who attended my former lectures, and they say that I lecture exactly as I did formerly. One of my attendants is a man that they say cannot, from years and infirmity and habit, be induced to go anywhere else: Dr Archdall, the Master of Emmanuel. I find that some of my old lecturing habits come again on me. I drink a great deal of cold water, and am very glad to go to bed early."--From June 10th-30th he was travelling in Scotland, and staying at Barrow House near Keswick (the residence of Mr Langton), with his son Hubert.--Subsequently, from Aug. 17th to 31st, he was again in the Lake District, with his daughter Christabel, and was joined there by his son Hubert on the 24th. The first part of the time was spent at Tarn Bank, near Carlisle, the residence of Mr Isaac Fletcher, M.P. From thence he made several expeditions, especially to Barrow in Furness and Seascale, where he witnessed with great interest the Bessemer process of making steel. From Barrow House he made continual excursions among the Cumberland mountains, which he knew so well.

1870