On The Uses Of Harmonic Analysis.

Submitted—The following memorandum by Professor Stokes :

Meteorological elements may be considered and discussed from two points of view. We may either contemplate the progress of the changes at any particular time, as, for example, in tracing the history of a particular storm, or in endeavouring to make out general laws connecting the changes of the various elements, such as Buys Ballot's Law; or we may seek to deduce from large masses of observations regular fluctuations which underlie the total fluctuations presented as the immediate result of observation, of which last a more or less considerable part have no immediate relation to the time, but in contemplating the regular periodic fluctuations are to be regarded as casual.

For the first object great accuracy is not required; what we want is to get a general comprehensive view; and this is afforded in a very available form by the published diagrams. Moreover, for this object means are useless, or very nearly so.

It is for the second object that the publication of hourly results is chiefly, if not exclusively, demanded. Besides the more obvious regular changes which have long been known, investigators may wish to examine whether there may not be other regular periodic changes which may be discovered by discussing a great number of observations.

Suppose now the results for each day were subjected to harmonic analysis, and the numbers read off on the cylinders of the machine alone published, we should have five or seven numbers (according as the analysis was carried to the second or third order) to publish, instead of 24.

S. Kensington,

3rd Nov., 1890.

Dear Sir George,

In the summer you asked me to let you have some quartz fibre. I now leave a box containing one long one wound 18 times up and down the frame. The front and back of the box are of glass so that the fibre may be examined without risk, and black paper is placed at one end in case a dark background may be required.

The glass may be taken out after first removing a screw at the end, and then the frame can be removed.

The fibre is good, in that under the prism test it shows both perfectly uniform pieces and places where the variation in diameter gives rise to small [i.e. short but pronounced and jagged] bends in the dark bands of the spectrum.

To see these spectra to perfection the following is the best way to hold the box and a prism: first see the colours with the naked eye [with light from a slit, the box intervening] and then hold a low-angle prism in front of the eye, not in the natural position of minimum deviation, but inclined so that incident light falls at about the polarising angle. It is only thus that the dark bands appear really dark.

On then moving the box along its own length so as to make successive parts of the fibres occupy the same position, you will see some of the fibres giving a constant spectrum which is the test of uniformity, while some show the irregularities described.

LETTERS TO DR ROMNEY ROBINSON, 1875–1879 AND 1880–1881.

The first group of the following letters have been selected from a series belonging to the period 1875-9, carefully arranged in years evidently by Dr Robinson himself. The remaining part is printed from duplicate typewritten copies preserved among Prof. Stokes’ manuscripts.

A long correspondence on anemometers of the year 1877 is omitted: reference may be made to Dr Robinson's memoir, Phil. Trans. 1878, also to Math, and Phys. Papers, Vol. v. pp. 73–99.

Cambridge, 4th Jan. 1875.

…I heard to-day from Mrs Harcourt. The instrument she referred to is a finely graduated circle, with telescopes for measuring refractive indices, which she gave to me for my life time, leaving the ultimate destination yet to be settled. I was not aware this had been sent to you, and I am not sure that it was. When I was at Nuneham shortly after Mr Harcourt's death, she expressed a wish to give us each some instrument of his. She may have mentioned the refractometer as for you (I cannot now recollect), and I may have suggested that you had an equivalent instrument already, and that it might be very valuable to me as I did not possess one. If she had thought of giving it to you she may have recollected the intention and supposed it had been actually sent. I could not suppose that she meant to offer to me an instrument she had already given to you.

I am not sure whether I mentioned that the Chances have made an experiment on a silico-titanic glass. Hopkinson, Senior Wrangler in 1871, who is their scientific adviser, had the superintendence of it. He sent me a specimen of the glass.

UNIVERSITÉ DE PARIS.

L'Université de Paris est heureuse de vous apporter aujourd'hui ses félicitations et de saluer en vous un Maître éminent de la Physique mathématique et de la Philosophie expérimentale.

Dans votre longue et féconde carrière, si dignement parcourue, vous avez hardiment abordé les questions les plus difficiles de l'Optique, de l'Hydrodynamique, de la Physique solaire et terrestre, et vous les avez résolues avec un égal succès, donnant ainsi l'exemple si rare de la puissance mathématique alliée à l'habileté expérimentale.

L'Optique vous a très souvent attiré. Vous avez suivi dans leur marche les rayons lumineux réfractés dans les corps cristallisés ou réfléchis par les métaux.

Vous avez traité le problème fondamental de la Spectroscopie. Avant vous, les effets mystérieux de la fluorescence semblaient échapper à toute loi; vous nous avez appris la relation qui existe entre les vitesses des vibrations de la lumière émise et de la lumière génératrice. Vous avez appliqué votre analyse pénétrante au calcul de l'aberration de la lumière. Vous avez étudié les causes de la rotation du radiométre. Vous avez heureusement contribué à l'exploration du Soleil par la photographie de la couronne solaire et par la mesure du rayonnement solaire.

Les phénomènes compliquès de l'Hydrodynamique ont attiré votre attention: vous avez su définir l'effet retardateur du gaz ambiant sur le mouvement du pendule, et calculer le coefficient de correction dû à la résistance de l'air.

Récemment encore vous avez contribué à élucider les singulières propriétés des rayons de Rœntgen, en les assimilant à des séries d'impulsions isolées, bien différentes des vibrations périodiques qui constituent la lumière ordinaire.

4, Windsor Terrace, Malahide, Co. Dublin. 4 August, 1881.

Dear Sir John Lubbock,

I got your proof here, which was forwarded from Armagh. I expect to be going there tomorrow. I saw Miss Stokes the day before yesterday, and gave her your message.

I have read your proof, and have made some reference marks, in the margin, numbers enclosed in circles. I also corrected a few misprints which I happened to see. It is no trouble to correct them, and they might be overlooked, especially by the author, who is apt to read a proof as it was meant to be.

In what follows, the numbers refer to the reference marks.

1. A few of the more conspicuous of the fixed lines were discovered by Wollaston near the beginning of the century, by viewing a slit through a prism applied to the naked eye. This observation however remained but little noticed.

2. Long ago, but I have not got the date, and have not reference books here, Fox Talbot showed that the red given to a flame by strontium and the red due to a salt of lithium might be at once distinguished by the prism. I think too, but I am not sure, that he dwelt on the delicacy of this test for the detection of lithium. I do not recollect whether this was before or after 1835 [Wheatstone's experiments]. It is to Kirchhoff and Bunsen that we owe the great impetus that has been given to spectrum analysis, and perhaps it would be proper to mention their names in this connexion; it rather looks as if they had merely applied what had been done by their predecessors.

Trinity College,Oct. 3rd, 1853.

Dear Sir,

What I said about chlorophyll was merely a vague remembrance of one out of a number of facts in Chemistry which Professor Gregory mentioned to me last Winter during a visit to his laboratory. I am very sure that he told me of its isolation but less sure about its colour. He gave me no reference to any source of information and at that time I had no intention of asking for any.

I have written to him on the subject, but I have not yet received an answer.

With respect to my conjecture about Haidinger's brushes, your statement of it is quite accurate and expresses all that deserves the name even of conjecture†. In August 1850 I noted down some experiments and deductions from them, some of which are the same with those which I have since seen described in the fourth part of Moigno's Répertoire d'Optique, particularly the experiment with a plate of quartz.

I have published nothing on the subject. In fact I have had no opportunity of obtaining sufficient foundation for a theory, and a conjecture is best corroborated by the existence of identical or similar conjectures springing up independently.

It has been thought that but slight advantage would arise from attempting any connected description of Sir George Stokes’ scientific work. The published collection of his Mathematical and Physical Papers in five volumes, taken in connexion with the historical analyses by Lord Rayleigh, Lord Kelvin, and others, forms ample material for the mathematician or physicist; while an account, to be interesting to the general reader, would have to be too long. Moreover in his Burnett Lectures on Light, and the other scientific addresses mentioned in the Preface to Vol. v. of his Papers, he has himself gone over much of the ground of his researches, in a manner which forms a model for popular and at the same time accurate exposition.

His scientific relation to the times in which he lived comes out most clearly in his correspondence. It has been felt to be inadvisable to break up the longer series of scientific letters; but some of the shorter groups, and those illustrating the events of his life, are here set forth in order of time, without any attempt at making up a continuous narrative.

A main impression derived from a general survey of his public activity, as revealed by the many thousands of letters that exist, is the state of dependence upon him which was the normal condition, as regards scientific investigations, of most of the numerous Committees of which he was a member.

Vienna, 14 Nov. 1852.

Dear Sir,

I beg leave to introduce myself, and to address you directly. I have read a notice on the interesting crystals with a, metallic surface, you described at the Belfast meeting. I enclose a small portion of crystals I examined some years ago, which I trust will be very interesting to you, as they almost exactly agree with those you examined, except in the point of transparency. The crystals I send are also allied to chinine. They were discovered by Prof. Wöhler, and named Grünes Hydrochinon. To him I have been indebted also for the small portion wrapt up here. The present crystals have evidently the same metallic aspect as those which you described, but they have a deep and beautiful violet blue colour by transmitted light. They are, however, but very faintly translucent, and in no direction they appear colourless or transparent, as it is said in the notice contained in Abbé Moigno's Cosmos 24 Octobre 1852, page 574.—There is also a mode of chemical preparation given there, but I failed in succeeding. Then I believe I can do nothing better, than asking you the favour yourself, in exchange for the small portion of hydrochinon, to send me also a very little quantity of the crystals you examined. Beside the one here included, I have examined a number of other crystals and substances shewing similar phenomena, and I lately drew up a catalogue of them, and presented it to our Academy. I sent a separate copy, inscribed to you, together with a number of others, to our mutual friend, Professor Miller, begging him to forward them to you.

I made acquaintance with Stokes in 1850 at the meetings of the Ray Club. That was a society at Cambridge for the cultivation of Natural Science by friendly intercourse, which had been formed in 1837 in order to fill, so far as that could be done without Henslow's inspiration, the gap left by the cessation of Henslow's weekly receptions of members of the University interested in Natural History. Natural History was still, when I joined the Club, most frequently the subject of conversation at its gatherings, and it may seem surprising that Stokes, who at that time (1850) was best known as a great mathematician, and had just been elected Lucasian professor, should have been a very regular attendant at the weekly meetings of such a Club. Really, however, his bent was to Natural Philosophy, as his work showed, where his great mathematical ability was employed in handling the problems of Nature. His elder brother, William, a fellow of Caius, had been one of the original promoters of the Club, and was a mineralogist and a chemist with whom I fraternised at once; but I very soon found that George Stokes was equally interested in the same subjects, and quite as ready to discuss, with a beginner, questions connected with them on which probably his own conclusions had been reached by a much shorter induction.

The following statement was made by General Sabine, President of the Royal Society, at the Anniversary Meeting, Nov. 30, 1866, in transmitting the Copley Medal to Professor Plücker.

To an audience not exclusively mathematical it is obviously impossible to enter into details of researches which deal with geometrical questions of no ordinary difficulty. Amongst these, however, may be indicated, as especially appreciated by those who are interested in the progress of analytical geometry, his theory of the singularities of plane curves as developed in the “Algebräische Curven,” with its six equations connecting them with the order of the curves: the papers on point and line coordinates, and on the general use of symbols, may also be noticed as establishing his claim to a position in the department of abstract science which is attained by few even of those who give to it their undivided attention. But Professor Plücker has high merits in two other widely different fields of research, viz. in Magnetism and Spectrology: and to these I may more freely invite your attention.

Shortly after Faraday's discovery of the sensibility of bodies generally to the action of a magnet, and of diamagnetism, Professor Plücker, in repeating some of Faraday's experiments, was led to the discovery of magnecrystallic action,—that is, that a crystallized body behaves differently in the magnetic field according to the orientation of certain directions in the crystal.