Great Astronomers by R. S. Ball - HTML preview

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The Earl Of Rosse

The subject of our present sketch occupies quite a distinct position in scientific history. Unlike many others who have risen by their scientific discoveries from obscurity to fame, the great Earl of Rosse was himself born in the purple. His father, who, under the title of Sir Lawrence Parsons, had occupied a distinguished position in the Irish Parliament, succeeded on the death of his father to the Earldom which had been recently created. The subject of our present memoir was, therefore, the third of the Earls of Rosse, and he was born in York on June 17, 1800. Prior to his father's death in 1841, he was known as Lord Oxmantown.

The University education of the illustrious astronomer was begun in Dublin and completed at Oxford. We do not hear in his case of any very remarkable University career. Lord Rosse was, however, a diligent student, and obtained a first-class in mathematics. He always took a great deal of interest in social questions, and was a profound student of political economy. He had a seat in the House of Commons, as member for King's County, from 1821 to 1834, his ancestral estate being situated in this part of Ireland.

[PLATE: THE EARL OF ROSSE.]

Lord Rosse was endowed by nature with a special taste for mechanical pursuits. Not only had he the qualifications of a scientific engineer, but he had the manual dexterity which qualified him personally to carry out many practical arts. Lord Rosse was, in fact, a skilful mechanic, an experienced founder, and an ingenious optician. His acquaintances were largely among those who were interested in mechanical pursuits, and it was his delight to visit the works or engineering establishments where refined processes in the arts were being carried on. It has often been stated--and as I have been told by members of his family, truly stated--that on one occasion, after he had been shown over some large works in the north of England, the proprietor bluntly said that he was greatly in want of a foreman, and would indeed be pleased if his visitor, who had evinced such extraordinary capacity for mechanical operations, would accept the post. Lord Rosse produced his card, and gently explained that he was not exactly the right man, but he appreciated the compliment, and this led to a pleasant dinner, and was the basis of a long friendship.

I remember on one occasion hearing Lord Rosse explain how it was that he came to devote his attention to astronomy. It appears that when he found himself in the possession of leisure and of means, he deliberately cast around to think how that means and that leisure could be most usefully employed. Nor was it surprising that he should search for a direction which would offer special scope for his mechanical tastes. He came to the conclusion that the building of great telescopes was an art which had received no substantial advance since the great days of William Herschel. He saw that to construct mighty instruments for studying the heavens required at once the command of time and the command of wealth, while he also felt that this was a subject the inherent difficulties of which would tax to the uttermost whatever mechanical skill he might possess. Thus it was he decided that the construction of great telescopes should become the business of his life.

[PLATE: BIRR CASTLE.

 

PLATE: THE MALL, PARSONSTOWN.]

In the centre of Ireland, seventy miles from Dublin, on the border between King's County and Tipperary, is a little town whereof we must be cautious before writing the name. The inhabitants of that town frequently insist that its name is Birr,* while the official designation is Parsonstown, and to this day for every six people who apply one name to the town, there will be half a dozen who use the other. But whichever it may be, Birr or Parsonstown--and I shall generally call it by the latter name--it is a favourable specimen of an Irish county town. The widest street is called the Oxmantown Mall. It is bordered by the dwelling-houses of the chief residents, and adorned with rows of stately trees. At one end of this distinctly good feature in the town is the Parish Church, while at the opposite end are the gates leading into Birr Castle, the ancestral home of the house of Parsons. Passing through the gates the visitor enters a spacious demesne, possessing much beauty of wood and water, one of the most pleasing features being the junction of the two rivers, which unite at a spot ornamented by beautiful timber. At various points illustrations of the engineering skill of the great Earl will be observed. The beauty of the park has been greatly enhanced by the construction of an ample lake, designed with the consummate art by which art is concealed. Even in mid-summer it is enlivened by troops of wild ducks preening themselves in that confidence which they enjoy in those happy localities where the sound of a gun is seldom heard. The water is led into the lake by a tube which passes under one of the two rivers just mentioned, while the overflow from the lake turns a water-wheel, which works a pair of elevators ingeniously constructed for draining the low-lying parts of the estate.

*Considering the fame acquired by Parsonstown from Lord Rosse's mirrors, it may be interesting to note the following extract from "The Natural History of Ireland," by Dr. Gerard Boate, Thomas Molyneux M.D., F.R.S., and others, which shows that 150 years ago Parsonstown was famous for its glass:--

"We shall conclude this chapter with the glass, there having been several glasshouses set up by the English in Ireland, none in Dublin or other cities, but all of them in the country; amongst which the principal was that of Birre, a market town, otherwise called Parsonstown, after one Sir Lawrence Parsons, who, having purchased that lordship, built a goodly house upon it; his son William Parsons having succeeded him in the possession of it; which town is situate in Queen's County, about fifty miles (Irish) to the southwest of Dublin, upon the borders of the two provinces of Leinster and Munster; from this place Dublin was furnished with all sorts of window and drinking glasses, and such other as commonly are in use. One part of the materials, viz., the sand, they had out of England; the other, to wit the ashes, they made in the place of ash-tree, and used no other. The chiefest difficulty was to get the clay for the pots to melt the materials in; this they had out of the north."--Chap. XXI., Sect. VIII. "Of the Glass made in Ireland." Birr Castle itself is a noble mansion with reminiscences from the time of Cromwell. It is surrounded by a moat and a drawbridge of modern construction, and from its windows beautiful views can be had over the varied features of the park. But while the visitors to Parsonstown will look with great interest on this residence of an Irish landlord, whose delight it was to dwell in his own country, and among his own people, yet the feature which they have specially come to observe is not to be found in the castle itself. On an extensive lawn, sweeping down from the moat towards the lake, stand two noble masonry walls. They are turreted and clad with ivy, and considerably loftier than any ordinary house. As the visitor approaches, he will see between those walls what may at first sight appear to him to be the funnel of a steamer lying down horizontally. On closer approach he will find that it is an immense wooden tube, sixty feet long, and upwards of six feet in diameter. It is in fact large enough to admit of a tall man entering into it and walking erect right through from one end to the other. This is indeed the most gigantic instrument which has ever been constructed for the purpose of exploring the heavens. Closely adjoining the walls between which the great tube swings, is a little building called "The Observatory." In this the smaller instruments are contained, and there are kept the books which are necessary for reference. The observatory also offers shelter to the observers, and provides the bright fire and the cup of warm tea, which are so acceptable in the occasional intervals of a night's observation passed on the top of the walls with no canopy but the winter sky.

Almost the first point which would strike the visitor to Lord Rosse's telescope is that the instrument at which he is looking is not only enormously greater than anything of the kind that he has ever seen before, but also that it is something of a totally different nature. In an ordinary telescope he is accustomed to find a tube with lenses of glass at either end, while the large telescopes that we see in our observatories are also in general constructed on the same principle. At one end there is the object-glass, and at the other end the eyepiece, and of course it is obvious that with an instrument of this construction it is to the lower end of the tube that the eye of the observer must be placed when the telescope is pointed to the skies. But in Lord Rosse's telescope you would look in vain for these glasses, and it is not at the lower end of the instrument that you are to take your station when you are going to make your observations. The astronomer at Parsonstown has rather to avail himself of the ingenious system of staircases and galleries, by which he is enabled to obtain access to the mouth of the great tube. The colossal telescope which swings between the great walls, like Herschel's great telescope already mentioned, is a reflector, the original invention of which is due of course to Newton. The optical work which is accomplished by the lenses in the ordinary telescope is effected in the type of instrument constructed by Lord Rosse by a reflecting mirror which is placed at the lower end of the vast tube. The mirror in this instrument is made of a metal consisting of two parts of copper to one of tin. As we have already seen, this mixture forms an alloy of a very peculiar nature. The copper and the tin both surrender their distinctive qualities, and unite to form a material of a very different physical character. The copper is tough and brown, the tin is no doubt silvery in hue, but soft and almost fibrous in texture. When the two metals are mixed together in the proportions I have stated, the alloy obtained is intensely hard and quite brittle being in both these respects utterly unlike either of the two ingredients of which it is composed. It does, however, resemble the tin in its whiteness, but it acquires a lustre far brighter than tin; in fact, this alloy hardly falls short of silver itself in its brilliance when polished.

[PLATE: LORD ROSSE'S TELESCOPE. From a photograph by W. Lawrence, Upper Sackville Street, Dublin.]

The first duty that Lord Rosse had to undertake was the construction of this tremendous mirror, six feet across, and about four or five inches thick. The dimensions were far in excess of those which had been contemplated in any previous attempt of the same kind. Herschel had no doubt fashioned one mirror of four feet in diameter, and many others of smaller dimensions, but the processes which he employed had never been fully published, and it was obvious that, with a large increase in dimensions, great additional difficulties had to be encountered. Difficulties began at the very commencement of the process, and were experienced in one form or another at every subsequent stage. In the first place, the mere casting of a great disc of this mixture of tin and copper, weighing something like three or four tons, involved very troublesome problems. No doubt a casting of this size, if the material had been, for example, iron, would have offered no difficulties beyond those with which every practical founder is well acquainted, and which he has to encounter daily in the course of his ordinary work. But speculum metal is a material of a very intractable description. There is, of course, no practical difficulty in melting the copper, nor in adding the proper proportion of tin when the copper has been melted. There may be no great difficulty in arranging an organization by which several crucibles, filled with the molten material, shall be poured simultaneously so as to obtain the requisite mass of metal, but from this point the difficulties begin. For speculum metal when cold is excessively brittle, and were the casting permitted to cool like an ordinary copper or iron casting, the mirror would inevitably fly into pieces. Lord Rosse, therefore, found it necessary to anneal the casting with extreme care by allowing it to cool very slowly. This was accomplished by drawing the disc of metal as soon as it had entered into the solid state, though still glowing red, into an annealing oven. There the temperature was allowed to subside so gradually, that six weeks elapsed before the mirror had reached the temperature of the external air. The necessity for extreme precaution in the operation of annealing will be manifest if we reflect on one of the accidents which happened. On a certain occasion, after the cooling of a great casting had been completed, it was found, on withdrawing the speculum, that it was cracked into two pieces. This mishap was eventually traced to the fact that one of the walls of the oven had only a single brick in its thickness, and that therefore the heat had escaped more easily through that side than through the other sides which were built of double thickness. The speculum had, consequently, not cooled uniformly, and hence the fracture had resulted. Undeterred, however, by this failure, as well as by not a few other difficulties, into a description of which we cannot now enter, Lord Rosse steadily adhered to his self-imposed task, and at last succeeded in casting two perfect discs on which to commence the tedious processes of grinding and polishing. The magnitude of the operations involved may perhaps be appreciated if I mention that the value of the mere copper and tin entering into the composition of each of the mirrors was about 500 pounds.
In no part of his undertaking was Lord Rosse's mechanical ingenuity more taxed than in the devising of the mechanism for carrying out the delicate operations of grinding and polishing the mirrors, whose casting we have just mentioned. In the ordinary operations of the telescope-maker, such processes had hitherto been generally effected by hand, but, of course, such methods became impossible when dealing with mirrors which were as large as a good-sized dinner table, and whose weight was measured by tons. The rough grinding was effected by means of a tool of cast iron about the same size as the mirror, which was moved by suitable machinery both backwards and forwards, and round and round, plenty of sand and water being supplied between the mirror and the tool to produce the necessary attrition. As the process proceeded and as the surface became smooth, emery was used instead of sand; and when this stage was complete, the grinding tool was removed and the polishing tool was substituted. The essential part of this was a surface of pitch, which, having been temporarily softened by heat, was then placed on the mirror, and accepted from the mirror the proper form. Rouge was then introduced as the polishing powder, and the operation was continued about nine hours, by which time the great mirror had acquired the appearance of highly polished silver. When completed, the disc of speculum metal was about six feet across and four inches thick. The depression in the centre was about half an inch. Mounted on a little truck, the great speculum was then conveyed to the instrument, to be placed in its receptacle at the bottom of the tube, the length of which was sixty feet, this being the focal distance of the mirror. Another small reflector was inserted in the great tube sideways, so as to direct the gaze of the observer down upon the great reflector. Thus was completed the most colossal instrument for the exploration of the heavens which the art of man has ever constructed.

[PLATE: ROMAN CATHOLIC CHURCH AT PARSONSTOWN.]

It was once my privilege to be one of those to whom the illustrious builder of the great telescope entrusted its use. For two seasons in 1865 and 1866 I had the honour of being Lord Rosse's astronomer. During that time I passed many a fine night in the observer's gallery, examining different objects in the heavens with the aid of this remarkable instrument. At the time I was there, the objects principally studied were the nebulae, those faint stains of light which lie on the background of the sky. Lord Rosse's telescope was specially suited for the scrutiny of these objects, inasmuch as their delicacy required all the light-grasping power which could be provided.

One of the greatest discoveries made by Lord Rosse, when his huge instrument was first turned towards the heavens, consisted in the detection of the spiral character of some of the nebulous forms. When the extraordinary structure of these objects was first announced, the discovery was received with some degree of incredulity. Other astronomers looked at the same objects, and when they failed to discern--and they frequently did fail to discern--the spiral structure which Lord Rosse had indicated, they drew the conclusion that this spiral structure did not exist. They thought it must be due possibly to some instrumental defect or to the imagination of the observer. It was, however, hardly possible for any one who was both willing and competent to examine into the evidence, to doubt the reality of Lord Rosse's discoveries. It happens, however, that they have been recently placed beyond all doubt by testimony which it is impossible to gainsay. A witness never influenced by imagination has now come forward, and the infallible photographic plate has justified Lord Rosse. Among the remarkable discoveries which Dr. Isaac Roberts has recently made in the application of his photographic apparatus to the heavens, there is none more striking than that which declares, not only that the nebulae which Lord Rosse described as spirals, actually do possess the character so indicated, but that there are many others of the same description. He has even brought to light the astonishingly interesting fact that there are invisible objects of this class which have never been seen by human eye, but whose spiral character is visible to the peculiar delicacy of the photographic telescope.

In his earlier years, Lord Rosse himself used to be a diligent observer of the heavenly bodies with the great telescope which was completed in the year 1845. But I think that those who knew Lord Rosse well, will agree that it was more the mechanical processes incidental to the making of the telescope which engaged his interest than the actual observations with the telescope when it was completed. Indeed one who was well acquainted with him believed Lord Rosse's special interest in the great telescope ceased when the last nail had been driven into it. But the telescope was never allowed to lie idle, for Lord Rosse always had associated with him some ardent young astronomer, whose delight it was to employ to the uttermost the advantages of his position in exploring the wonders of the sky. Among those who were in this capacity in the early days of the great telescope, I may mention my esteemed friend Dr. Johnston Stoney.

Such was the renown of Lord Rosse himself, brought about by his consummate mechanical genius and his astronomical discoveries, and such the interest which gathered around the marvellous workshops at Birr castle, wherein his monumental exhibitions of optical skill were constructed, that visitors thronged to see him from all parts of the world. His home at Parsonstown became one of the most remarkable scientific centres in Great Britain; thither assembled from time to time all the leading men of science in the country, as well as many illustrious foreigners. For many years Lord Rosse filled with marked distinction the exalted position of President of the Royal Society, and his advice and experience in practical mechanical matters were always at the disposal of those who sought his assistance. Personally and socially Lord Rosse endeared himself to all with whom he came in contact. I remember one of the attendants telling me that on one occasion he had the misfortune to let fall and break one of the small mirrors on which Lord Rosse had himself expended many hours of hard personal labour. The only remark of his lordship was that "accidents will happen."

The latter years of his life Lord Rosse passed in comparative seclusion; he occasionally went to London for a brief sojourn during the season, and he occasionally went for a cruise in his yacht; but the greater part of the year he spent at Birr Castle, devoting himself largely to the study of political and social questions, and rarely going outside the walls of his demesne, except to church on Sunday mornings. He died on October 31, 1867.

He was succeeded by his eldest son, the present Earl of Rosse, who has inherited his father's scientific abilities, and done much notable work with the great telescope.

Airy

In our sketch of the life of Flamsteed, we have referred to the circumstances under which the famous Observatory that crowns Greenwich Hill was founded. We have also had occasion to mention that among the illustrious successors of Flamsteed both Halley and Bradley are to be included. But a remarkable development of Greenwich Observatory from the modest establishment of early days took place under the direction of the distinguished astronomer whose name is at the head of this chapter. By his labours this temple of science was organised to such a degree of perfection that it has served in many respects as a model for other astronomical establishments in various parts of the world. An excellent account of Airy's career has been given by Professor H. H. Turner, in the obituary notice published by the Royal Astronomical Society. To this I am indebted for many of the particulars here to be set down concerning the life of the illustrious Astronomer Royal.

The family from which Airy took his origin came from Kentmere, in Westmoreland. His father, William Airy, belonged to a Lincolnshire branch of the same stock. His mother's maiden name was Ann Biddell, and her family resided at Playford, near Ipswich. William Airy held some small government post which necessitated an occasional change of residence to different parts of the country, and thus it was that his son, George Biddell, came to be born at Alnwick, on 27th July, 1801. The boy's education, so far as his school life was concerned was partly conducted at Hereford and partly at Colchester. He does not, however, seem to have derived much benefit from the hours which he passed in the schoolroom. But it was delightful to him to spend his holidays on the farm at Playford, where his uncle, Arthur Biddell, showed him much kindness. The scenes of his early youth remained dear to Airy throughout his life, and in subsequent years he himself owned a house at Playford, to which it was his special delight to resort for relaxation during the course of his arduous career. In spite of the defects of his school training he seems to have manifested such remarkable abilities that his uncle decided to enter him in Cambridge University. He accordingly joined Trinity College as a sizar in 1819, and after a brilliant career in mathematical and physical science he graduated as Senior Wrangler in 1823. It may be noted as an exceptional circumstance that, notwithstanding the demands on his time in studying for his tripos, he was able, after his second term of residence, to support himself entirely by taking private pupils. In the year after he had taken his degree he was elected to a Fellowship at Trinity College.

Having thus gained an independent position, Airy immediately entered upon that career of scientific work which he prosecuted without intermission almost to the very close of his life. One of his most interesting researches in these early days is on the subject of Astigmatism, which defect he had discovered in his own eyes. His investigations led him to suggest a means of correcting this defect by using a pair of spectacles with lenses so shaped as to counteract the derangement which the astigmatic eye impressed upon the rays of light. His researches on this subject were of a very complete character, and the principles he laid down are to the present day practically employed by oculists in the treatment of this malformation.
On the 7th of December, 1826, Airy was elected to the Lucasian Professorship of Mathematics in the University of Cambridge, the chair which Newton's occupancy had rendered so illustrious. His tenure of this office only lasted for two years, when he exchanged it for the Plumian Professorship. The attraction which led him to desire this change is doubtless to be found in the circumstance that the Plumian Professorship of Astronomy carried with it at that time the appointment of director of the new astronomical observatory, the origin of which must now be described.

Those most interested in the scientific side of University life decided in 1820 that it would be proper to found an astronomical observatory at Cambridge. Donations were accordingly sought for this purpose, and upwards of 6,000 pounds were contributed by members of the University and the public. To this sum 5,000 pounds were added by a grant from the University chest, and in 1824 further sums amounting altogether to 7,115 pounds were given by the University for the same object. The regulations as to the administration of the new observatory placed it under the management of the Plumian Professor, who was to be provided with two assistants. Their duties were to consist in making meridian observations of the sun, moon, and the stars, and the observations made each year were to be printed and published. The observatory was also to be used in the educational work of the University, for it was arranged that smaller instruments were to be provided by which students could be instructed in the practical art of making astronomical observations.

The building of the Cambridge Astronomical Observatory was completed in 1824, but in 1828, when Airy entered on the discharge of his duties as Director, the establishment was still far from completion, in so far as its organisation was concerned. Airy commenced his work so energetically that in the next year after his appointment he was able to publish the first volume of "Cambridge Astronomical Observations," notwithstanding that every part of the work, from the making of observations to the revising of the proofsheets, had to be done by himself.

It may here be remarked that these early volumes of the publications of the Cambridge Observatory contained the first exposition of those systematic methods of astronomical work which Airy afterwards developed to such a great extent at Greenwich, and which have been subsequently adopted in many other places. No more profitable instruction for the astronomical beginner can be found than that which can be had by the study of these volumes, in which the Plumian Professor has laid down with admirable clearness the true principles on which meridian work should be conducted.

[PLATE: SIR GEORGE AIRY. From a Photograph by Mr. E.P. Adams, Greenwich.]

Airy gradually added to the instruments with which the observatory was originally equipped. A mural circle was mounted in 1832, and in the same year a small equatorial was erected by Jones. This was made use of by Airy in a well-known series of observations of Jupiter's fourth satellite for the determination of the mass of the great planet. His memoir on this subject fully ex pounds the method of finding the weight of a planet from observations of the movements of a satellite by which the planet is attended. This is, indeed, a valuable investigation which no student of astronomy can afford to neglect. The ardour with which Airy devoted himself to astronomical studies may be gathered from a remarkable report on the progress of astronomy during the present century, which he communicated to the British Association at its second meeting in 1832. In the early years of his life at Cambridge his most famous achievement was connected with a research in theoretical astronomy for which consummate mathematical power was required. We can only give a brief account of the Subject, for to enter into any full detail with regard to it would be quite out of the question.

Venus is a planet of about the same size and the same weight as the earth, revolving in an orbit which lies within that described by our globe. Venus, consequently, takes less time than the earth to accomplish one revolution round the sun, and it happens that the relative movements of Venus and the earth are so proportioned that in the time in which our earth accomplishes eight of her revolutions the other planet will have accomplished almost exactly thirteen. It, therefore, follows that if the earth and Venus are in line with the sun at one date, then in eight years later both planets will again be found at the same points in their orbits. In those eight years the earth has gone round eight times, and has, therefore, regained its original position, while in the same period Venus has accomplished thirteen complete revolutions, and, therefore, this planet also has reached the same spot where it was at first. Venus and the earth, of course, attract each other, and in consequence of these mutual attractions the earth is swayed from the elliptic track which it would otherwise pursue. In like manner Venus is also forced by the attraction of the earth to revolve in a track which deviates from that which it would otherwise follow. Owing to the fact that the sun is of such preponderating magnitude (being, in fact, upwards of 300,000 times as heavy as either Venus or the earth), the disturbances induced in the motion of either planet, in consequence of the attraction of the other, are relatively insignificant to the main controlling agency by which each of the movements is governed. It is, however, possible under certain circumstances that the disturbing effects produced upon one planet by the other can become so multiplied as to produce peculiar effects which attain measurable dimensions. Suppose that the periodic times in which the earth and Venus revolved had no simple relation to each other, then the points of their tracks in which the two planets came into line with the sun would be found at different parts of the orbits, and consequently the disturbances would to a great extent neutralise each other, and produce but little appreciable effect. As, however, Venus and the earth come back every eight years to nearly the same positions at the same points of their track, an accumulative effect is produced. For the disturbance of one planet upon the other will, of course, be greatest when those two planets are nearest, that is, when they lie in line with the sun and on the same side of it. Every eight years a certain part of the orbit of the earth is, therefore, disturbed by the attraction of Venus with peculiar vigour. The consequence is that, owing to the numerical relation between the movements of the planets to which I have referred, disturbing effects become appreciable which would otherwise be too small to permit of recognition. Airy proposed to himself to compute the effects which Venus would have on the movement of the earth in consequence of the circumstance that eight revolutions of the one planet required almost the same time as thirteen revolutions of the other. This is a mathematical inquiry of the most arduous description, but the Plumian Professor succeeded in working it out, and he had, accordingly, the gratification of announcing to the Royal Society that he had detected the influence which Venus was thus able to assert on the movement of our earth around the sun. This remarkable investigation gained for its author the gold medal of the Royal Astronomical Society in the year 1832.

In consequence Of his numerous discoveries, Airy's scientific fame had become so well recognised that the Government awarded him a special pension, and in 1835, when Pond, who was then Astronomer Royal, resigned, Airy was offered the post at Greenwich. There was in truth, no scientific inducement to the Plumian Professor to leave the comparatively easy post he held at Cambridge, in which he had ample leisure to devote himself to those researches which specially interested him, and accept that of the much more arduous observatory at Greenwich. There were not even pecuniary inducements to make the change; however, he felt it to be his duty to accede to the request which the Government had made that he would take up the position which Pond had vacated, and accordingly Airy went to Greenwich as Astronomer Royal on October 1st, 1835.

He immediately began with his usual energy to organise the systematic conduct of the business of the National Observatory. To realise one of the main characteristics of Airy's great work at Greenwich, it is necessary to explain a point that might not perhaps be understood without a little explanation by those who have no practical experience in an observatory. In the work of an establishment such as Greenwich, an observation almost always consists of a measurement of some kind. The observer may, for instance, be making a measurement of the time at which a star passes across a spider line stretched through the field of view; on another occasion his object may be the measurement of an angle which is read off by examining through a microscope the lines of division on a graduated circle when the telescope is so pointed that the star is placed on a certain mark in the field of view. In either case the immediate result of the astronomical observation is a purely numerical one, but it rarely happens, indeed we may say it never happens, that the immediate numerical result which the observation gives expresses directly the quantity which we are really seeking for. No doubt the observation has been so designed that the quantity we want to find can be obtained from the figures which the measurement gives, but the object sought is not those figures, for there are always a multitude of other influences by which those figures are affected. For example, if an observation were to be perfect, then the telescope with which the observation is made should be perfectly placed in the exact position which it ought to occupy; this is, however, never the case, for no mechanic can ever construct or adjust a telescope so perfectly as the wants of the astronomer demand. The clock also by which we determine the time of the observation should be correct, but this is rarely if ever the case. We have to correct our observations for such errors, that is to say, we have to determine the errors in the positions of our telescopes and the errors in the going of our clocks, and then we have to determine what the observations would have been had our telescopes been absolutely perfect, and had our clocks been absolutely correct. There are also many other matters which have to be attended to in order to reduce our observations so as to obtain from the figures as yielded to the observer at the telescope the actual quantities which it is his object to determine. The work of effecting these reductions is generally a very intricate and laborious matter, so that it has not unfrequently happened that while observations have accumulated in an observatory, yet the tedious duty of reducing these observations has been allowed to fall into arrear. When Airy entered on his duties at Greenwich he found there an enormous mass of observations which, though implicitly containing materials of the greatest value to astronomers, were, in their unreduced form, entirely unavailable for any useful purpose. He, therefore, devoted himself to coping with the reduction of the observations of his predecessors. He framed systematic methods by which the reductions were to be effected, and he so arranged the work that little more than careful attention to numerical accuracy would be required for the conduct of the operations. Encouraged by the Admiralty, for it is under this department that Greenwich Observatory is placed, the Astronomer Royal employed a large force of computers to deal with the work. BY his energy and admirable organisation he managed to reduce an extremely valuable series of planetary observations, and to publish the results, which have been of the greatest importance to astronomical investigation.

The Astronomer Royal was a capable, practical engineer as well as an optician, and he presently occupied himself by designing astronomical instruments of improved pattern, which should replace the antiquated instruments he found in the observatory. In the course of years the entire equipment underwent a total transformation. He ordered a great meridian circle, every part of which may be said to have been formed from his own designs. He also designed the mounting for a fine equatorial telescope worked by a driving clock, which he had himself invented. Gradually the establishment at Greenwich waxed great under his incessant care. It was the custom for the observatory to be inspected every year by a board of visitors, whose chairman was the President of the Royal Society. At each annual visitation, held on the first Saturday in June, the visitors received a report from the Astronomer Royal, in which he set forth the business which had been accomplished during the past year. It was on these occasions that applications were made to the Admiralty, either for new instruments or for developing the work of the observatory in some other way. After the more official business of the inspection was over, the observatory was thrown open to visitors, and hundreds of people enjoyed on that day the privilege of seeing the national observatory. These annual gatherings are happily still continued, and the first Saturday in June is known to be the occasion of one of the most interesting reunions of scientific men which takes place in the course of the year.

Airy's scientific work was, however, by no means confined to the observatory. He interested himself largely in expeditions for the observation of eclipses and in projects for the measurement of arcs on the earth. He devoted much attention to the collection of magnetic observations from various parts of the world. Especially will it be remembered that the circumstances of the transits of Venus, which occurred in 1874 and in 1882, were investigated by him, and under his guidance expeditions were sent forth to observe the transits from those localities in remote parts of the earth where observations most suitable for the determination of the sun's distance from the earth could be obtained. The Astronomer Royal also studied tidal phenomena, and he rendered great service to the country in the restoration of the standards of length and weight which had been destroyed in the great fire at the House of Parliament in October, 1834. In the most practical scientific matters his advice was often sought, and was as cheerfully rendered. Now we find him engaged in an investigation of the irregularities of the compass in iron ships, with a view to remedying its defects; now we find him reporting on the best gauge for railways. Among the most generally useful developments of the observatory must be mentioned the telegraphic method for the distribution of exact time. By arrangement with the Post Office, the astronomers at Greenwich despatch each morning a signal from the observatory to London at ten o'clock precisely. By special apparatus, this signal is thence distributed automatically over the country, so as to enable the time to be known everywhere accurately to a single second. It was part of the same system that a time ball should be dropped daily at one o'clock at Deal, as well as at other places, for the purpose of enabling ship's chronometers to be regulated.

Airy's writings were most voluminous, and no fewer than forty- eight memoirs by him are mentioned in the "Catalogue of Scientific Memoirs," published by the Royal Society up to the year 1873, and this only included ten years out of an entire life of most extraordinary activity. Many other subjects besides those of a purely scientific character from time to time engaged his attention. He wrote, for instance, a very interesting treatise on the Roman invasion of Britain, especially with a view of determining the port from which Caesar set forth from Gaul, and the point at which he landed on the British coast. Airy was doubtless led to this investigation by his study of the tidal phenomena in the Straits of Dover. Perhaps the Astronomer Royal is best known to the general reading public by his excellent lectures on astronomy, delivered at the Ipswich Museum in 1848. This book has passed through many editions, and it gives a most admirable account of the manner in which the fundamental problems in astronomy have to be attacked.

As years rolled by almost every honour and distinction that could be conferred upon a scientific man was awarded to Sir George Airy. He was, indeed, the recipient of other honours not often awarded for scientific distinction. Among these we may mention that in 1875 he received the freedom of the City of London, "as a recognition of his indefatigable labours in astronomy, and of his eminent services in the advancement of practical science, whereby he has so materially benefited the cause of commerce and civilisation."

Until his eightieth year Airy continued to discharge his labours at Greenwich with unflagging energy. At last, on August 15th, 1881, he resigned the office which he had held so long with such distinction to himself and such benefit to his country. He had married in 1830 the daughter of the Rev. Richard Smith, of Edensor. Lady Airy died in 1875, and three sons and three daughters survived him. One daughter is the wife of Dr. Routh, of Cambridge, and his other daughters were the constant companions of their father during the declining years of his life. Up to the age of ninety he enjoyed perfect physical health, but an accidental fall which then occurred was attended with serious results. He died on Saturday, January 2nd, 1892, and was buried in the churchyard at Playford.

Hamilton

William Rowan Hamilton was born at midnight between the 3rd and 4th of August, 1805, at Dublin, in the house which was then 29, but subsequently 36, Dominick Street. His father, Archibald Hamilton, was a solicitor, and William was the fourth of a family of nine. With reference to his descent, it may be sufficient to notice that his ancestors appear to have been chiefly of gentle Irish families, but that his maternal grandmother was of Scottish birth. When he was about a year old, his father and mother decided to hand over the education of the child to his uncle, James Hamilton, a clergyman of Trim, in County Meath. James Hamilton's sister, Sydney, resided with him, and it was in their home that the days of William's childhood were passed.

In Mr. Graves' "Life of Sir William Rowan Hamilton" a series of letters will be found, in which Aunt Sydney details the progress of the boy to his mother in Dublin. Probably there is no record of an infant prodigy more extraordinary than that which these letters contain. At three years old his aunt assured the mother that William is "a hopeful blade," but at that time it was his physical vigour to which she apparently referred; for the proofs of his capacity, which she adduces, related to his prowess in making boys older than himself fly before him. In the second letter, a month later, we hear that William is brought in to read the Bible for the purpose of putting to shame other boys double his age who could not read nearly so well. Uncle James appears to have taken much pains with William's schooling, but his aunt said that "how he picks up everything is astonishing, for he never stops playing and jumping about." When he was four years and three months old, we hear that he went out to dine at the vicar's, and amused the company by reading for them equally well whether the book was turned upside down or held in any other fashion. His aunt assures the mother that " Willie is a most sensible little creature, but at the same time has a great deal of roguery." At four years and five months old he came up to pay his mother a visit in town, and she writes to her sister a description of the boy;-

"His reciting is astonishing, and his clear and accurate knowledge of geography is beyond belief; he even draws the countries with a pencil on paper, and will cut them out, though not perfectly accurate, yet so well that a anybody knowing the countries could not mistake them; but, you will think this nothing when I tell you that he reads Latin, Greek, and Hebrew."

Aunt Sydney recorded that the moment Willie got back to Trim he was desirous of at once resuming his former pursuits. He would not eat his breakfast till his uncle had heard him his Hebrew, and he comments on the importance of proper pronunciation. At five he was taken to see a friend, to whom he repeated long passages from Dryden. A gentleman present, who was not unnaturally sceptical about Willie's attainments, desired to test him in Greek, and took down a copy of Homer which happened to have the contracted type, and to his amazement Willie went on with the greatest ease. At six years and nine months he was translating Homer and Virgil; a year later his uncle tells us that William finds so little difficulty in learning French and Italian, that he wishes to read Homer in French. He is enraptured with the Iliad, and carries it about with him, repeating from it whatever particularly pleases him. At eight years and one month the boy was one of a party who visited the Scalp in the Dublin mountains, and he was so delighted with the scenery that he forthwith delivered an oration in Latin. At nine years and six months he is not satisfied until he learns Sanscrit; three months later his thirst for the Oriental languages is unabated, and at ten years and four months he is studying Arabic and Persian. When nearly twelve he prepared a manuscript ready for publication. It was a "Syriac Grammar," in Syriac letters and characters compiled from that of Buxtorf, by William Hamilton, Esq., of Dublin and Trim. When he was fourteen, the Persian ambassador, Mirza Abul Hassan Khan, paid a visit to Dublin, and, as a practical exercise in his Oriental languages, the young scholar addressed to his Excellency a letter in Persian; a translation of which production is given by Mr. Graves. When William was fourteen he had the misfortune to lose his father; and he had lost his mother two years previously. The boy and his three sisters were kindly provided for by different members of the family on both sides.

It was when William was about fifteen that his attention began to be turned towards scientific subjects. These were at first regarded rather as a relaxation from the linguistic studies with which he had been so largely occupied. On November 22nd, 1820, he notes in his journal that he had begun Newton's "Principia": he commenced also the study of astronomy by observing eclipses, occultations, and similar phenomena. When he was sixteen we learn that he had read conic sections, and that he was engaged in the study of pendulums. After an attack of illness, he was moved for change to Dublin, and in May, 1822, we find him reading the differential calculus and Laplace's "Mecanique Celeste." He criticises an important part of Laplace's work relative to the demonstration of the parallelogram of forces. In this same year appeared the first gushes of those poems which afterwards flowed in torrents.

His somewhat discursive studies had, however, now to give place to a more definite course of reading in preparation for entrance to the University of Dublin. The tutor under whom he entered, Charles Boyton, was himself a distinguished man, but he frankly told the young William that he could be of little use to him as a tutor, for his pupil was quite as fit to be his tutor. Eliza Hamilton, by whom this is recorded, adds, "But there is one thing which Boyton would promise to be to him, and that was a FRIEND; and that one proof he would give of this should be that, if ever he saw William beginning to be UPSET by the sensation he would excite, and the notice he would attract, he would tell him of it." At the beginning of his college career he distanced all his competitors in every intellectual pursuit. At his first term examination in the University he was first in Classics and first in Mathematics, while he received the Chancellor's prize for a poem on the Ionian Islands, and another for his poem on Eustace de St. Pierre.

There is abundant testimony that Hamilton had "a heart for friendship formed." Among the warmest of the friends whom he made in these early days was the gifted Maria Edgeworth, who writes to her sister about "young Mr. Hamilton, an admirable Crichton of eighteen, a real prodigy of talents, who Dr. Brinkley says may be a second Newton, quiet, gentle, and simple." His sister Eliza, to whom he was affectionately attached, writes to him in 1824:--
"I had been drawing pictures of you in my mind in your study at Cumberland Street with 'Xenophon,' &c., on the table, and you, with your most awfully sublime face of thought, now sitting down, and now walking about, at times rubbing your hands with an air of satisfaction, and at times bursting forth into some very heroical strain of poetry in an unknown language, and in your own internal solemn ventriloquist-like voice, when you address yourself to the silence and solitude of your o

This letter is quoted because it refers to a circumstance which all who ever met with Hamilton, even in his latest years, will remember. He was endowed with two distinct voices, one a high treble, the other a deep bass, and he alternately employed these voices not only in ordinary conversation, but when he was delivering an address on the profundities of Quaternions to the Royal Irish Academy, or on similar occasions. His friends had long grown so familiar with this peculiarity that they were sometimes rather surprised to find how ludicrous it appeared to strangers.

Hamilton was fortunate in finding, while still at a very early age, a career open before him which was worthy of his talents. He had not ceased to be an undergraduate before he was called to fill an illustrious chair in his university. The circumstances are briefly as follows.

We have already mentioned that, in 1826, Brinkley was appointed Bishop of Cloyne, and the professorship of astronomy thereupon became vacant. Such was Hamilton's conspicuous eminence that, notwithstanding he was still an undergraduate, and had only just completed his twenty-first year, he was immediately thought of as a suitable successor to the chair. Indeed, so remarkable were his talents in almost every direction that had the vacancy been in the professorship of classics or of mathematics, of English literature or of metaphysics, of modern or of Oriental languages, it seems difficult to suppose that he would not have occurred to every one as a possible successor. The chief ground, however, on which the friends of Hamilton urged his appointment was the earnest of original power which he had already shown in a research on the theory of Systems of Rays. This profound work created a new branch of optics, and led a few years later to a superb discovery, by which the fame of its author became world-wide.

At first Hamilton thought it would be presumption for him to apply for so exalted a position; he accordingly retired to the country, and resumed his studies for his degree. Other eminent candidates came forward, among them some from Cambridge, and a few of the Fellows from Trinity College, Dublin, also sent in their claims. It was not until Hamilton received an urgent letter from his tutor Boyton, in which he was assured of the favourable disposition of the Board towards his candidature, that he consented to come forward, and on June 16th, 1827, he was unanimously chosen to succeed the Bishop of Cloyne as Professor of Astronomy in the University. The appointment met with almost universal approval. It should, however, be noted that Brinkley, whom Hamilton succeeded, did not concur in the general sentiment. No one could have formed a higher opinion than he had done of Hamilton's transcendent powers; indeed, it was on that very ground that he seemed to view the appointment with disapprobation. He considered that it would have been wiser for Hamilton to have obtained a Fellowship, in which capacity he would have been able to exercise a greater freedom in his choice of intellectual pursuits. The bishop seems to have thought, and not without reason, that Hamilton's genius would rather recoil from much of the routine work of an astronomical establishment. Now that Hamilton's whole life is before us, it is easy to see that the bishop was entirely wrong. It is quite true that Hamilton never became a skilled astronomical observer; but the seclusion of the observatory was eminently favourable to those gigantic labours to which his life was devoted, and which have shed so much lustre, not only on Hamilton himself, but also on his University and his country.

In his early years at Dunsink, Hamilton did make some attempts at a practical use of the telescopes, but he possessed no natural aptitude for such work, while exposure which it involved seems to have acted injuriously on his health. He, therefore, gradually allowed his attention to be devoted to those mathematical researches in which he had already given such promise of distinction. Although it was in pure mathematics that he ultimately won his greatest fame, yet he always maintained and maintained with justice, that he had ample claims to the title of an astronomer. In his later years he set forth this position himself in a rather striking manner. De Morgan had written commending to Hamilton's notice Grant's "History of Physical Astronomy." After becoming acquainted with the book, Hamilton writes to his friend as follows:--

"The book is very valuable, and very creditable to its composer. But your humble servant may be pardoned if he finds himself somewhat amused at the title, `History of Physical Astronomy from the Earliest Ages to the Middle of the Nineteenth Century,' when he fails to observe any notice of the discoveries of Sir W. R. Hamilton in the theory of the 'Dynamics of the Heavens.'"

The intimacy between the two correspondents will account for the tone of this letter; and, indeed, Hamilton supplies in the lines which follow ample grounds for his complaint. He tells how Jacobi spoke of him in Manchester in 1842 as "le Lagrange de votre pays," and how Donkin had said that, "The Analytical Theory of Dynamics as it exists at present is due mainly to the labours of La Grange Poisson, Sir W. R. Hamilton, and Jacobi, whose researches on this subject present a series of discoveries hardly paralleled for their elegance and importance in any other branch of mathematics." In the same letter Hamilton also alludes to the success which had attended the applications of his methods in other hands than his own to the elucidation of the difficult subject of Planetary Perturbations. Even had his contributions to science amounted to no more than these discoveries, his tenure of the chair would have been an illustrious one. It happens, however, that in the gigantic mass of his intellectual work these researches, though intrinsically of such importance, assume what might almost be described as a relative insignificance.

The most famous achievement of Hamilton's earlier years at the observatory was the discovery of conical refraction. This was one of those rare events in the history of science, in which a sagacious calculation has predicted a result of an almost startling character, subsequently confirmed by observation. At once this conferred on the young professor a world-wide renown. Indeed, though he was still only twenty-seven, he had already lived through an amount of intellectual activity which would have been remarkable for a man of threescore and ten.

Simultaneously with his growth in fame came the growth of his several friendships. There were, in the first place, his scientific friendships with Herschel, Robinson, and many others with whom he had copious correspondence. In the excellent biography to which I have referred, Hamilton's correspondence with Coleridge may be read, as can also the letters to his lady correspondents, among them being Maria Edgeworth, Lady Dunraven, and Lady Campbell. Many of these sheets relate to literary matters, but they are largely intermingled With genial pleasantry, and serve at all events to show the affection and esteem with which he was regarded by all who had the privilege of knowing him. There are also the letters to the sisters whom he adored, letters brimming over with such exalted sentiment, that most ordinary sisters would be tempted to receive them with a smile in the excessively improbable event of their still more ordinary brothers attempting to pen such effusions. There are also indications of letters to and from other young ladies who from time to time were the objects of Hamilton's tender admiration. We use the plural advisedly, for, as Mr. Graves has set forth, Hamilton's love affairs pursued a rather troubled course. The attention which he lavished on one or two fair ones was not reciprocated, and even the intense charms of mathematical discovery could not assuage the pangs which the disappointed lover experienced. At last he reached the haven of matrimony in 1833, when he was married to Miss Bayly. Of his married life Hamilton said, many years later to De Morgan, that it was as happy as he expected, and happier than he deserved. He had two sons, William and Archibald, and one daughter, Helen, who became the wife of Archdeacon O'Regan.

[PLATE: SIR W. ROWAN HAMILTON.]

The most remarkable of Hamilton's friendships in his early years was unquestionably that with Wordsworth. It commenced with Hamilton's visit to Keswick; and on the first evening, when the poet met the young mathematician, an incident occurred which showed the mutual interest that was aroused. Hamilton thus describes it in a letter to his sister Eliza:--

"He (Wordsworth) walked back with our party as far as their lodge, and then, on our bidding Mrs. Harrison good-night, I offered to walk back with him while my party proceeded to the hotel. This offer he accepted, and our conversation had become so interesting that when we had arrived at his home, a distance of about a mile, he proposed to walk back with me on my way to Ambleside, a proposal which you may be sure I did not reject; so far from it that when he came to turn once more towards his home I also turned once more along with him. It was very late when I reached the hotel after all this walking."

Hamilton also submitted to Wordsworth an original poem, entitled "It Haunts me Yet." The reply of Wordsworth is worth repeating:--
"With a safe conscience I can assure you that, in my judgment, your verses are animated with the poetic spirit, as they are evidently the product of strong feeling. The sixth and seventh stanzas affected me much, even to the dimming of my eyes and faltering of my voice while I was reading them aloud. Having said this, I have said enough. Now for the per contra. You will not, I am sure, be hurt when I tell you that the workmanship (what else could be expected from so young a writer?) is not what it ought to be. . .

"My household desire to be remembered to you in no formal way. Seldom have I parted-never, I was going to say--with one whom after so short an acquaintance I lost sight of with more regret. I trust we shall meet again."

The further affectionate intercourse between Hamilton and Wordsworth is fully set forth, and to Hamilton's latest years a recollection of his "Rydal hours" was carefully treasured and frequently referred to. Wordsworth visited Hamilton at the observatory, where a beautiful shady path in the garden is to the present day spoken of as "Wordsworth's Walk."

It was the practice of Hamilton to produce a sonnet on almost every occasion which admitted of poetical treatment, and it was his delight to communicate his verses to his friends all round. When Whewell was producing his "Bridgewater Treatises," he writes to Hamilton in 1833:--

"Your sonnet which you showed me expressed much better than I could express it the feeling with which I tried to write this book, and I once intended to ask your permission to prefix the sonnet to my book, but my friends persuaded me that I ought to tell my story in my own prose, however much better your verse might be."

The first epoch-marking contribution to Theoretical Dynamics after the time of Newton was undoubtedly made by Lagrange, in his discovery of the general equations of Motion. The next great step in the same direction was that taken by Hamilton in his discovery of a still more comprehensive method. Of this contribution Hamilton writes to Whewell, March 31st, 1834:--

"As to my late paper, a day or two ago sent off to London, it is merely mathematical and deductive. I ventured, indeed, to call it the 'Mecanique Analytique' of Lagrange, 'a scientific poem'; and spoke of Dynamics, or the Science of Force, as treating of 'Power acting by Law in Space and Time.' In other respects it is as unpoetical and unmetaphysical as my gravest friends could desire."

It may well be doubted whether there is a more beautiful chapter in the whole of mathematical philosophy than that which contains Hamilton's dynamical theory. It is disfigured by no tedious complexity of symbols; it condescends not to any particular problems; it is an all embracing theory, which gives an intellectual grasp of the most appropriate method for discovering the result of the application of force to matter. It is the very generality of this doctrine which has somewhat impeded the applications of which it is susceptible. The exigencies of examinations are partly responsible for the fact that the method has not become more familiar to students of the higher mathematics. An eminent professor has complained that Hamilton's essay on dynamics was of such an extremely abstract character, that he found himself unable to extract from it problems suitable for his examination papers.

The following extract is from a letter of Professor Sylvester to Hamilton, dated 20th of September, 1841. It will show how his works were appreciated by so consummate a mathematician as the writer:--

"Believe me, sir, it is not the least of my regrets in quitting this empire to feel that I forego the casual occasion of meeting those masters of my art, yourself chief amongst the number, whose acquaintance, whose conversation, or even notice, have in themselves the power to inspire, and almost to impart fresh vigour to the understanding, and the courage and faith without which the efforts of invention are in vain. The golden moments I enjoyed under your hospitable roof at Dunsink, or moments such as they were, may probably never again fall to my lot.

At a vast distance, and in an humble eminence, I still promise myself the calm satisfaction of observing your blazing course in the elevated regions of discovery. Such national honour as you are able to confer on your country is, perhaps, the only species of that luxury for the rich (I mean what is termed one's glory) which is not bought at the expense of the comforts of the million."

The study of metaphysics was always a favourite recreation when Hamilton sought for a change from the pursuit of mathematics. In the year 1834 we find him a diligent student of Kant; and, to show the views of the author of Quaternions and of Algebra as the Science of Pure Time on the "Critique of the Pure Reason," we quote the following letter, dated 18th of July, 1834, from Hamilton to Viscount Adare:--

"I have read a large part of the 'Critique of the Pure Reason,' and find it wonderfully clear, and generally quite convincing. Notwithstanding some previous preparation from Berkeley, and from my own thoughts, I seem to have learned much from Kant's own statement of his views of 'Space and Time.' Yet, on the whole, a large part of my pleasure consists in recognising through Kant's works, opinions, or rather views, which have been long familiar to myself, although far more clearly and systematically expressed and combined by him.. . . Kant is, I think, much more indebted than he owns, or, perhaps knows, to Berkeley, whom he calls by a sneer, `GUTEM Berkeley'. . . as it were, `good soul, well meaning man,' who was able for all that to shake to its centre the world of human thought, and to effect a revolution among the early consequences of which was the growth of Kant himself."

At several meetings of the British Association Hamilton was a very conspicuous figure. Especially was this the case in 1835, when the Association met in Dublin, and when Hamilton, though then but thirty years old, had attained such celebrity that even among a very brilliant gathering his name was perhaps the most renowned. A banquet was given at Trinity College in honour of the meeting. The distinguished visitors assembled in the Library of the University. The Earl of Mulgrave, then Lord Lieutenant of Ireland, made this the opportunity of conferring on Hamilton the honour of knighthood, gracefully adding, as he did so: "I but set the royal, and therefore the national mark, on a distinction already acquired by your genius and labours."

The banquet followed, writes Mr. Graves. "It was no little addition to the honour Hamilton had already received that, when Professor Whewell returned thanks for the toast of the University of Cambridge, he thought it appropriate to add the words, 'There was one point which strongly pressed upon him at that moment: it was now one hundred and thirty years since a great man in another Trinity College knelt down before his sovereign, and rose up Sir Isaac Newton.' The compliment was welcomed by immense applause."

A more substantial recognition of the labours of Hamilton took place subsequently. He thus describes it in a letter to Mr. Graves of 14th of November, 1843:--

"The Queen has been pleased--and you will not doubt that it was entirely unsolicited, and even unexpected, on my part--'to express her entire approbation of the grant of a pension of two hundred pounds per annum from the Civil List' to me for scientific services. The letters from Sir Robert Peel and from the Lord Lieutenant of Ireland in which this grant has been communicated or referred to have been really more gratifying to my feelings than the addition to my income, however useful, and almost necessary, that may have been."

The circumstances we have mentioned might lead to the supposition that Hamilton was then at the zenith of his fame but this was not so. It might more truly be said, that his achievements up to this point were rather the preliminary exercises which fitted him for the gigantic task of his life. The name of Hamilton is now chiefly associated with his memorable invention of the calculus of Quaternions. It was to the creation of this branch of mathematics that the maturer powers of his life were devoted; in fact he gives us himself an illustration of how completely habituated he became to the new modes of thought which Quaternions originated. In one of his later years he happened to take up a copy of his famous paper on Dynamics, a paper which at the time created such a sensation among mathematicians, and which is at this moment regarded as one of the classics of dynamical literature. He read, he tells us, his paper with considerable interest, and expressed his feelings of gratification that he found himself still able to follow its reasoning without undue effort. But it seemed to him all the time as a work belonging to an age of analysis now entirely superseded.

In order to realise the magnitude of the revolution which Hamilton has wrought in the application of symbols to mathematical investigation, it is necessary to think of what Hamilton did beside the mighty advance made by Descartes. To describe the character of the quaternion calculus would be unsuited to the pages of this work, but we may quote an interesting letter, written by Hamilton from his deathbed, twenty-two years later, to his son Archibald, in which he has recorded the circumstances of the discovery:-- Indeed, I happen to be able to put the finger of memory upon the year and month-October, 1843--when having recently returned from visits to Cork and Parsonstown, connected with a meeting of the British Association, the desire to discover the laws of multiplication referred to, regained with me a certain strength and earnestness which had for years been dormant, but was then on the point of being gratified, and was occasionally talked of with you. Every morning in the early part of the above- cited month, on my coming down to breakfast, your (then) little brother William Edwin, and yourself, used to ask me, 'Well papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: 'No, I can only ADD and subtract them,'

But on the 16th day of the same month--which happened to be Monday, and a Council day of the Royal Irish Academy--I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an UNDERCURRENT of thought was going on in my mind which gave at last a RESULT, whereof it is not too much to say that I felt AT ONCE the importance. An ELECTRIC circuit seemed to CLOSE; and a spark flashed forth the herald (as I FORESAW IMMEDIATELY) of many long years to come of definitely directed thought and work by MYSELF, if spared, and, at all events, on the part of OTHERS if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse--unphilosophical as it may have been--to cut with a knife on a stone of Brougham Bridge as we passed it, the fundamental formula which contains the SOLUTION of the PROBLEM, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on 'Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following."

Writing to Professor Tait, Hamilton gives further particulars of the same event. And again in a letter to the Rev. J. W. Stubbs:--

"To-morrow will be the fifteenth birthday of the Quaternions. They started into life fullgrown on the 16th October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge--which my boys have since called Quaternion Bridge. I pulled out a pocketbook which still exists, and made entry, on which at the very moment I felt that it might be worth my while to expend the labour of at least ten or fifteen years to come. But then it is fair to say that this was because I felt a problem to have been at that moment solved, an intellectual want relieved which had haunted me for at least fifteen years before.

But did the thought of establishing such a system, in which geometrically opposite facts-namely, two lines (or areas) which are opposite IN SPACE give ALWAYS a positive product--ever come into anybody's head till I was led to it in October, 1843, by trying to extend my old theory of algebraic couples, and of algebra as the science of pure time? As to my regarding geometrical addition of lines as equivalent to composition of motions (and as performed by the same rules), that is indeed essential in my theory but not peculiar to it; on the contrary, I am only one of many who have been led to this view of addition."

Pilgrims in future ages will doubtless visit the spot commemorated by the invention of Quaternions. Perhaps as they look at that by no means graceful structure Quaternion Bridge, they will regret that the hand of some Old Mortality had not been occasionally employed in cutting the memorable inscription afresh. It is now irrecoverably lost.

It was ten years after the discovery that the great volume appeared under the title of "Lectures on Quaternions," Dublin, 1853. The reception of this work by the scientific world was such as might have been expected from the extraordinary reputation of its author, and the novelty and importance of the new calculus. His valued friend, Sir John Herschel, writes to him in that style of which he was a master:--

"Now, most heartily let me congratulate you on getting out your book--on having found utterance, ore rotundo, for all that labouring and seething mass of thought which has been from time to time sending out sparks, and gleams, and smokes, and shaking the soil about you; but now breaks into a good honest eruption, with a lava stream and a shower of fertilizing ashes.

Metaphor and simile apart, there is work for a twelve-month to any man to read such a book, and for half a lifetime to digest it, and I am glad to see it brought to a conclusion."

 

We may also record Hamilton's own opinion expressed to Humphrey Lloyd:--

"In general, although in one sense I hope that I am actually growing modest about the quaternions, from my seeing so many peeps and vistas into future expansions of their principles, I still must assert that this discovery appears to me to be as important for the middle of the nineteenth century as the discovery of fluxions was for the close of the seventeenth."

Bartholomew Lloyd died in 1837. He had been the Provost of Trinity College, and the President of the Royal Irish Academy. Three candidates were put forward by their respective friends for the vacant Presidency. One was Humphrey Lloyd, the son of the late Provost, and the two others were Hamilton and Archbishop Whately. Lloyd from the first urged strongly the claims of Hamilton, and deprecated the putting forward of his own name. Hamilton in like manner desired to withdraw in favour of Lloyd. The wish was strongly felt by many of the Fellows of the College that Lloyd should be elected, in consequence of his having a more intimate association with collegiate life than Hamilton; while his scientific eminence was world-wide. The election ultimately gave Hamilton a considerable majority over Lloyd, behind whom the Archbishop followed at a considerable distance. All concluded happily, for both Lloyd and the Archbishop expressed, and no doubt felt, the pre-eminent claims of Hamilton, and both of them cordially accepted the office of a Vice-President, to which, according to the constitution of the Academy, it is the privilege of the incoming President to nominate. In another chapter I have mentioned as a memorable episode in astronomical history, that Sir J. Herschel went for a prolonged sojourn to the Cape of Good Hope, for the purpose of submitting the southern skies to the same scrutiny with the great telescope that his father had given to the northern skies. The occasion of Herschel's return after the brilliant success of his enterprise, was celebrated by a banquet. On June 15th, 1838, Hamilton was assigned the high honour of proposing the health of Herschel. This banquet is otherwise memorable in Hamilton's career as being one of the two occasions in which he was in the company of his intimate friend De Morgan.

In the year 1838 a scheme was adopted by the Royal Irish Academy for the award of medals to the authors of papers which appeared to possess exceptionally high merit. At the institution of the medal two papers were named in competition for the prize. One was Hamilton's "Memoir on Algebra, as the Science of Pure Time." The other was Macullagh's paper on the "Laws of Crystalline Reflection and Refraction." Hamilton expresses his gratification that, mainly in consequence of his own exertions, he succeeded in having the medal awarded to Macullagh rather than to himself. Indeed, it would almost appear as if Hamilton had procured a letter from Sir J. Herschel, which indicated the importance of Macullagh's memoir in such a way as to decide the issue. It then became Hamilton's duty to award the medal from the chair, and to deliver an address in which he expressed his own sense of the excellence of Macullagh's scientific work. It is the more necessary to allude to these points, because in the whole of his scientific career it would seem that Macullagh was the only man with whom Hamilton had ever even an approach to a dispute about priority. The incident referred to took place in connection with the discovery of conical refraction, the fame of which Macullagh made a preposterous attempt to wrest from Hamilton. This is evidently alluded to in Hamilton's letter to the Marquis of Northampton, dated June 28th, 1838, in which we read:--

And though some former circumstances prevented me from applying to the person thus distinguished the sacred name of FRIEND, I had the pleasure of doing justice...to his high intellectual merits...I believe he was not only gratified but touched, and may, perhaps, regard me in future with feelings more like those which I long to entertain towards him."

Hamilton was in the habit, from time to time, of commencing the keeping of a journal, but it does not appear to have been systematically conducted. Whatever difficulties the biographer may have experienced from its imperfections and irregularities, seem to be amply compensated for by the practice which Hamilton had of preserving copies of his letters, and even of comparatively insignificant memoranda. In fact, the minuteness with which apparently trivial matters were often noted down appears almost whimsical. He frequently made a memorandum of the name of the person who carried a letter to the post, and of the hour in which it was despatched. On the other hand, the letters which he received were also carefully preserved in a mighty mass of manuscripts, with which his study was encumbered, and with which many other parts of the house were not unfrequently invaded. If a letter was laid aside for a few hours, it would become lost to view amid the seething mass of papers, though occasionally, to use his own expression, it might be seen "eddying" to the surface in some later disturbance.
The great volume of "Lectures on Quaternions" had been issued, and the author had received the honours which the completion of such a task would rightfully bring him. The publication of an immortal work does not, however, necessarily provide the means for paying the printer's bill. The printing of so robust a volume was necessarily costly; and even if all the copies could be sold, which at the time did not seem very likely, they would hardly have met the inevitable expenses. The provision of the necessary funds was, therefore, a matter for consideration. The Board of Trinity College had already contributed 200 pounds to the printing, but yet another hundred was required. Even the discoverer of Quaternions found this a source of much anxiety. However, the board, urged by the representation of Humphrey Lloyd, now one of its members, and, as we have already seen, one of Hamilton's staunchest friends, relieved him of all liability. We may here note that, notwithstanding the pension which Hamilton enjoyed in addition to the salary of his chair, he seems always to have been in some what straitened circumstances, or, to use his own words in one of his letters to De Morgan, "Though not an embarrassed man, I am anything rather than a rich one." It appears that, notwithstanding the world-wide fame of Hamilton's discoveries, the only profit in a pecuniary sense that he ever obtained from any of his works was by the sale of what he called his Icosian Game. Some enterprising publisher, on the urgent representations of one of Hamilton's friends in London, bought the copyright of the Icosian Game for 25 pounds. Even this little speculation proved unfortunate for the purchaser, as the public could not be induced to take the necessary interest in the matter.

After the completion of his great book, Hamilton appeared for awhile to permit himself a greater indulgence than usual in literary relaxations. He had copious correspondence with his intimate friend, Aubrey de Vere, and there were multitudes of letters from those troops of friends whom it was Hamilton's privilege to possess. He had been greatly affected by the death of his beloved sister Eliza, a poetess of much taste and feeling. She left to him her many papers to preserve or to destroy, but he said it was only after the expiration of four years of mourning that he took courage to open her pet box of letters.

The religious side of Hamilton's character is frequently illustrated in these letters; especially is this brought out in the correspondence with De Vere, who had seceded to the Church of Rome. Hamilton writes, August 4, 1855:--

"If, then, it be painfully evident to both, that under such circumstances there CANNOT (whatever we may both DESIRE) be NOW in the nature of things, or of minds, the same degree of INTIMACY between us as of old; since we could no longer TALK with the same degree of unreserve on every subject which happened to present itself, but MUST, from the simplest instincts of courtesy, be each on his guard not to say what might be offensive, or, at least, painful to the other; yet WE were ONCE so intimate, an retain still, and, as I trust, shall always retain, so much of regard and esteem and appreciation for each other, made tender by so many associations of my early youth and your boyhood, which can never be forgotten by either of us, that (as times go) TWO OR THREE VERY RESPECTABLE FRIENDSHIPS might easily be carved out from the fragments of our former and ever-to-be-remembered INTIMACY. It would be no exaggeration to quote the words: 'Heu! quanto minus est cum reliquis versari, quam tui meminisse!'" In 1858 a correspondence on the subject of Quaternions; commenced between Professor Tait and Sir William Hamilton. It was particularly gratifying to the discoverer that so competent a mathematician as Professor Tait should have made himself acquainted with the new calculus. It is, of course, well known that Professor Tait subsequently brought out a most valuable elementary treatise on Quaternions, to which those who are anxious to become acquainted with the subject will often turn in preference to the tremendous work of Hamilton.

In the year 1861 gratifying information came to hand of the progress which the study of Quaternions was making abroad. Especially did the subject attract the attention of that accomplished mathematician, Moebius, who had already in his "Barycentrische Calculus" been led to conceptions which bore more affinity to Quaternions than could be found in the writings of any other mathematician. Such notices of his work were always pleasing to Hamilton, and they served, perhaps, as incentives to that still closer and more engrossing labour by which he became more and more absorbed. During the last few years of his life he was observed to be even more of a recluse than he had hitherto been. His powers of long and continuous study seemed to grow with advancing years, and his intervals of relaxation, such as they were, became more brief and more infrequent.

It was not unusual for him to work for twelve hours at a stretch. The dawn would frequently surprise him as he looked up to snuff his candles after a night of fascinating labour at original research. Regularity in habits was impossible to a student who had prolonged fits of what he called his mathematical trances. Hours for rest and hours for meals could only be snatched in the occasional the lucid intervals between one attack of Quaternions and the next. When hungry, he would go to see whether any thing could be found on the sideboard; when thirsty, he would visit the locker, and the one blemish in the man's personal character is that these latter visits were sometimes paid too often.

As an example of one of Hamilton's rare diversions from the all- absorbing pursuit of Quaternions, we find that he was seized with curiosity to calculate back to the date of the Hegira, which he found on the 15th July, 622. He speaks of the satisfaction with which he ascertained subsequently that Herschel had assigned precisely the same date. Metaphysics remained also, as it had ever been, a favourite subject of Hamilton's readings and meditations and of correspondence with his friends. He wrote a very long letter to Dr. Ingleby on the subject of his "Introduction to Metaphysics." In it Hamilton alludes, as he has done also in other places, to a peculiarity of his own vision. It was habitual to him, by some defect in the correlation of his eyes, to see always a distinct image with each; in fact, he speaks of the remarkable effect which the use of a good stereoscope had on his sensations of vision. It was then, for the first time, that he realised how the two images which he had always seen hitherto would, under normal circumstances, be blended into one. He cites this fact as bearing on the phenomena of binocular vision, and he draws from it the inference that the necessity of binocular vision for the correct appreciation of distance is unfounded. "I am quite sure," he says, "that I SEE DISTANCE with EACH EYE SEPARATELY."
The commencement of 1865, the last year of his life saw Hamilton as diligent as ever, and corresponding with Salmon and Cayley. On April 26th he writes to a friend to say, that his health has not been good for years past, and that so much work has injured his constitution; and he adds, that it is not conducive to good spirits to find that he is accumulating another heavy bill with the printer for the publication of the "Elements." This was, indeed, up to the day of his death, a cause for serious anxiety. It may, however, be mentioned that the whole cost, which amounted to nearly 500 pounds, was, like that of the previous volume, ultimately borne by the College. Contrary to anticipation, the enterprise, even in a pecuniary sense, cannot have been a very unprofitable one. The whole edition has long been out of print, and as much as 5 pounds has since been paid for a single copy.

It was on the 9th of May, 1865, that Hamilton was in Dublin for the last time. A few days later he had a violent attack of gout, and on the 4th of June he became alarmingly ill, and on the next day had an attack of epileptic convulsions. However, he slightly rallied, so that before the end of the month he was again at work at the "Elements." A gratifying incident brightened some of the last days of his life. The National Academy of Science in America had then been just formed. A list of foreign Associates had to be chosen from the whole world, and a discussion took place as to what name should be placed first on the list. Hamilton was informed by private communication that this great distinction was awarded to him by a majority of two-thirds.

In August he was still at work on the table of contents of the "Elements," and one of his very latest efforts was his letter to Mr. Gould, in America, communicating his acknowledgements of the honour which had been just conferred upon him by the National Academy. On the 2nd of September Mr. Graves went to the observatory, in response to a summons, and the great mathematician at once admitted to his friend that he felt the end was approaching. He mentioned that he had found in the 145th Psalm a wonderfully suitable expression of his thoughts and feelings, and he wished to testify his faith and thankfulness as a Christian by partaking of the Lord's Supper. He died at halfpast two on the afternoon of the 2nd of September, 1865, aged sixty years and one month. He was buried in Mount Jerome Cemetery on the 7th of September.

Many were the letters and other more public manifestations of the feelings awakened by Hamilton's death. Sir John Herschel wrote to the widow:--

"Permit me only to add that among the many scientific friends whom time has deprived me of, there has been none whom I more deeply lament, not only for his splendid talents, but for the excellence of his disposition and the perfect simplicity of his manners--so great, and yet devoid of pretensions."

De Morgan, his old mathematical crony, as Hamilton affectionately styled him, also wrote to Lady Hamilton:--

"I have called him one of my dearest friends, and most truly; for I know not how much longer than twenty-five years we have been in intimate correspondence, of most friendly agreement or disagreement, of most cordial interest in each other. And yet we did not know each other's faces. I met him about 1830 at Babbage's breakfast table, and there for the only time in our lives we conversed. I saw him, a long way off, at the dinner given to Herschel (about 1838) on his return from the Cape and there we were not near enough, nor on that crowded day could we get near enough, to exchange a word. And this is all I ever saw, and, so it has pleased God, all I shall see in this world of a man whose friendly communications were among my greatest social enjoyments, and greatest intellectual treats."

There is a very interesting memoir of Hamilton written by De Morgan, in the "Gentleman's Magazine" for 1866, in which he produces an excellent sketch of his friend, illustrated by personal reminiscences and anecdotes. He alludes, among other things, to the picturesque confusion of the papers in his study. There was some sort of order in the mass, discernible however, by Hamilton alone, and any invasion of the domestics, with a view to tidying up, would throw the mathematician as we are informed, into "a good honest thundering passion."

Hardly any two men, who were both powerful mathematicians, could have been more dissimilar in every other respect than were Hamilton and De Morgan. The highly poetical temperament of Hamilton was remarkably contrasted with the practical realism of De Morgan. Hamilton sends sonnets to his friend, who replies by giving the poet advice about making his will. The metaphysical subtleties, with which Hamilton often filled his sheets, did not seem to have the same attraction for De Morgan that he found in battles about the quantification of the Predicate. De Morgan was exquisitely witty, and though his jokes were always appreciated by his correspondent, yet Hamilton seldom ventured on anything of the same kind in reply; indeed his rare attempts at humour only produced results of the most ponderous description. But never were two scientific correspondents more perfectly in sympathy with each other. Hamilton's work on Quaternions, his labours in Dynamics, his literary tastes, his metaphysics, and his poetry, were all heartily welcomed by his friend, whose letters in reply invariably evince the kindliest interest in all Hamilton's concerns. In a similar way De Morgan's letters to Hamilton always met with a heartfelt response.

Alike for the memory of Hamilton, for the credit of his University, and for the benefit of science, let us hope that a collected edition of his works will ere long appear--a collection which shall show those early achievements in splendid optical theory, those achievements of his more mature powers which made him the Lagrange of his country, and finally those creations of the Quaternion Calculus by which new capabilities have been bestowed on the human intellect.

Le Verrier

The name of Le Verrier is one that goes down to fame on account of very different discoveries from those which have given renown to several of the other astronomers whom we have mentioned. We are sometimes apt to identify the idea of an astronomer with that of a man who looks through a telescope at the stars; but the word astronomer has really much wider significance. No man who ever lived has been more entitled to be designated an astronomer than Le Verrier, and yet it is certain that he never made a telescopic discovery of any kind. Indeed, so far as his scientific achievements have been concerned, he might never have looked through a telescope at all.

For the full interpretation of the movements of the heavenly bodies, mathematical knowledge of the most advanced character is demanded. The mathematician at the outset calls upon the astronomer who uses the instruments in the observatory, to ascertain for him at various times the exact positions occupied by the sun, the moon, and the planets. These observations, obtained with the greatest care, and purified as far as possible from the errors by which they may be affected form, as it were, the raw material on which the mathematician exercises his skill. It is for him to elicit from the observed places the true laws which govern the movements of the heavenly bodies. Here is indeed a task in which the highest powers of the human intellect may be worthily employed.

Among those who have laboured with the greatest success in the interpretation of the observations made with instruments of precision, Le Verrier holds a highly honoured place. To him it has been given to provide a superb illustration of the success with which the mind of man can penetrate the deep things of Nature.

The illustrious Frenchman, Urban Jean Joseph Le Verrier, was born on the 11th March, 1811, at St. Lo, in the department of Manche. He received his education in that famous school for education in the higher branches of science, the Ecole Polytechnique, and acquired there considerable fame as a mathematician. On leaving the school Le Verrier at first purposed to devote himself to the public service, in the department of civil engineering; and it is worthy of note that his earliest scientific work was not in those mathematical researches in which he was ultimately to become so famous. His duties in the engineering department involved practical chemical research in the laboratory. In this he seems to have become very expert, and probably fame as a chemist would have been thus attained, had not destiny led him into another direction. As it was, he did engage in some original chemical research. His first contributions to science were the fruits of his laboratory work; one of his papers was on the combination of phosphorus and hydrogen, and another on the combination of phosphorus and oxygen.

His mathematical labours at the Ecole Polytechnique had, however, revealed to Le Verrier that he was endowed with the powers requisite for dealing with the subtlest instruments of mathematical analysis. When he was twenty-eight years old, his first great astronomical investigation was brought forth. It will be necessary to enter into some explanation as to the nature of this, inasmuch as it was the commencement of the life- work which he was to pursue.

If but a single planet revolved around the sun, then the orbit of that planet would be an ellipse, and the shape and size, as well as the position of the ellipse, would never alter. One revolution after another would be traced out, exactly in the same manner, in compliance with the force continuously exerted by the sun. Suppose, however, that a second planet be introduced into the system. The sun will exert its attraction on this second planet also, and it will likewise describe an orbit round the central globe. We can, however, no longer assert that the orbit in which either of the planets moves remains exactly an ellipse. We may, indeed, assume that the mass of the sun is enormously greater than that of either of the planets. In this case the attraction of the sun is a force of such preponderating magnitude, that the actual path of each planet remains nearly the same as if the other planet were absent. But it is impossible for the orbit of each planet not to be affected in some degree by the attraction of the other planet. The general law of nature asserts that every body in space attracts every other body. So long as there is only a single planet, it is the single attraction between the sun and that planet which is the sole controlling principle of the movement, and in consequence of it the ellipse is described. But when a second planet is introduced, each of the two bodies is not only subject to the attraction of the sun, but each one of the planets attracts the other. It is true that this mutual attraction is but small, but, nevertheless, it produces some effect. It "disturbs," as the astronomer says, the elliptic orbit which would otherwise have been pursued. Hence it follows that in the actual planetary system where there are several planets disturbing each other, it is not true to say that the orbits are absolutely elliptic.

At the same time in any single revolution a planet may for most practical purposes be said to be actually moving in an ellipse. As, however, time goes on, the ellipse gradually varies. It alters its shape, it alters its plane, and it alters its position in that plane. If, therefore, we want to study the movements of the planets, when great intervals of time are concerned, it is necessary to have the means of learning the nature of the movement of the orbit in consequence of the disturbances it has experienced.

We may illustrate the matter by supposing the planet to be running like a railway engine on a track which has been laid in a long elliptic path. We may suppose that while the planet is coursing along, the shape of the track is gradually altering. But this alteration may be so slow, that it does not appreciably affect the movement of the engine in a single revolution. We can also suppose that the plane in which the rails have been laid has a slow oscillation in level, and that the whole orbit is with more or less uniformity moved slowly about in the plane.

In short periods of time the changes in the shapes and positions of the planetary orbits, in consequence of their mutual attractions, are of no great consequence. When, however, we bring thousands of years into consideration, then the displacements of the planetary orbits attain considerable dimensions, and have, in fact, produced a profound effect on the system.
It is of the utmost interest to investigate the extent to which one planet can affect another in virtue of their mutual attractions. Such investigations demand the exercise of the highest mathematical gifts. But not alone is intellectual ability necessary for success in such inquiries. It must be united with a patient capacity for calculations of an arduous type, protracted, as they frequently have to be, through many years of labour. Le Verrier soon found in these profound inquiries adequate scope for the exercise of his peculiar gifts. His first important astronomical publication contained an investigation of the changes which the orbits of several of the planets, including the earth, have undergone in times past, and which they will undergo in times to come.

As an illustration of these researches, we may take the case of the planet in which we are, of course, especially interested, namely, the earth, and we can investigate the changes which, in the lapse of time, the earth's orbit has undergone, in consequence of the disturbance to which it has been subjected by the other planets. In a century, or even in a thousand years, there is but little recognisable difference in the shape of the track pursued by the earth. Vast periods of time are required for the development of the large consequences of planetary perturbation. Le Verrier has, however, given us the particulars of what the earth's journey through space has been at intervals of 20,000 years back from the present date. His furthest calculation throws our glance back to the state of the earth's track 100,000 years ago, while, with a bound forward, he shows us what the earth's orbit is to be in the future, at successive intervals of 20,000 years, till a date is reached which is 100,000 years in advance Of A.D. 1800.

The talent which these researches displayed brought Le Verrier into notice. At that time the Paris Observatory was presided over by Arago, a SAVANT who occupies a distinguished position in French scientific annals. Arago at once perceived that Le Verrier was just the man who possessed the qualifications suitable for undertaking a problem of great importance and difficulty that had begun to force itself on the attention of astronomers. What this great problem was, and how astonishing was the solution it received, must now be considered.

Ever since Herschel brought himself into fame by his superb discovery of the great planet Uranus, the movements of this new addition to the solar system were scrutinized with care and attention. The position of Uranus was thus accurately determined from time to time. At length, when sufficient observations of this remote planet had been brought together, the route which the newly-discovered body pursued through the heavens was ascertained by those calculations with which astronomers are familiar. It happens, however, that Uranus possesses a superficial resemblance to a star. Indeed the resemblance is so often deceptive that long ere its detection as a planet by Herschel, it had been observed time after time by skilful astronomers, who little thought that the starlike point at which they looked was anything but a star. From these early observations it was possible to determine the track of Uranus, and it was found that the great planet takes a period of no less than eighty-four years to accomplish a circuit. Calculations were made of the shape of the orbit in which it revolved before its discovery by Herschel, and these were compared with the orbit which observations showed the same body to pursue in those later years when its planetary character was known. It could not, of course, be expected that the orbit should remain unaltered; the fact that the great planets Jupiter and Saturn revolve in the vicinity of Uranus must necessarily imply that the orbit of the latter undergoes considerable changes. When, however, due allowance has been made for whatever influence the attraction of Jupiter and Saturn, and we may add of the earth and all the other Planets, could possibly produce, the movements of Uranus were still inexplicable. It was perfectly obvious that there must be some other influence at work besides that which could be attributed to the planets already known.

Astronomers could only recognise one solution of such a difficulty. It was impossible to doubt that there must be some other planet in addition to the bodies at that time known, and that the perturbations of Uranus hitherto unaccounted for, were due to the disturbances caused by the action of this unknown planet. Arago urged Le Verrier to undertake the great problem of searching for this body, whose theoretical existence seemed demonstrated. But the conditions of the search were such that it must needs be conducted on principles wholly different from any search which had ever before been undertaken for a celestial object. For this was not a case in which mere survey with a telescope might be expected to lead to the discovery.

Certain facts might be immediately presumed with reference to the unknown object. There could be no doubt that the unknown disturber of Uranus must be a large body with a mass far exceeding that of the earth. It was certain, however, that it must be so distant that it could only appear from our point of view as a very small object. Uranus itself lay beyond the range, or almost beyond the range, of unassisted vision. It could be shown that the planet by which the disturbance was produced revolved in an orbit which must lie outside that of Uranus. It seemed thus certain that the planet could not be a body visible to the unaided eye. Indeed, had it been at all conspicuous its planetary character would doubtless have been detected ages ago. The unknown body must therefore be a planet which would have to be sought for by telescopic aid.

There is, of course, a profound physical difference between a planet and a star, for the star is a luminous sun, and the planet is merely a dark body, rendered visible by the sunlight which falls upon it. Notwithstanding that a star is a sun thousands of times larger than the planet and millions of times more remote, yet it is a singular fact that telescopic planets possess an illusory resemblance to the stars among which their course happens to lie. So far as actual appearance goes, there is indeed only one criterion by which a planet of this kind can be discriminated from a star. If the planet be large enough the telescope will show that it possesses a disc, and has a visible and measurable circular outline. This feature a star does not exhibit. The stars are indeed so remote that no matter how large they may be intrinsically, they only exhibit radiant points of light, which the utmost powers of the telescope fail to magnify into objects with an appreciable diameter. The older and well-known planets, such as Jupiter and Mars, possess discs, which, though not visible to the unaided eye, were clearly enough discernible with the slightest telescopic power. But a very remote planet like Uranus, though it possessed a disc large enough to be quickly appreciated by the consummate observing skill of Herschel, was nevertheless so stellar in its appearance, that it had been observed no fewer than seventeen times by experienced astronomers prior to Herschel. In each case the planetary nature of the object had been overlooked, and it had been taken for granted that it was a star. It presented no difference which was sufficient to arrest attention.

As the unknown body by which Uranus was disturbed was certainly much more remote than Uranus, it seemed to be certain that though it might show a disc perceptible to very close inspection, yet that the disc must be so minute as not to be detected except with extreme care. In other words, it seemed probable that the body which was to be sought for could not readily be discriminated from a small star, to which class of object it bore a superficial resemblance, though, as a matter of fact, there was the profoundest difference between the two bodies.

There are on the heavens many hundreds of thousands of stars, and the problem of identifying the planet, if indeed it should lie among these stars, seemed a very complex matter. Of course it is the abundant presence of the stars which causes the difficulty. If the stars could have been got rid of, a sweep over the heavens would at once disclose all the planets which are bright enough to be visible with the telescopic power employed. It is the fortuitous resemblance of the planet to the stars which enables it to escape detection. To discriminate the planet among stars everywhere in the sky would be almost impossible. If, however, some method could be devised for localizing that precise region in which the planet's existence might be presumed, then the search could be undertaken with some prospect of success.

To a certain extent the problem of localizing the region on the sky in which the planet might be expected admitted of an immediate limitation. It is known that all the planets, or perhaps I ought rather to say, all the great planets, confine their movements to a certain zone around the heavens. This zone extends some way on either side of that line called the ecliptic in which the earth pursues its journey around the sun. It was therefore to be inferred that the new planet need not be sought for outside this zone. It is obvious that this consideration at once reduces the area to be scrutinized to a small fraction of the entire heavens. But even within the zone thus defined there are many thousands of stars. It would seem a hopeless task to detect the new planet unless some further limitation to its position could be assigned.

It was accordingly suggested to Le Verrier that he should endeavour to discover in what particular part of the strip of the celestial sphere which we have indicated the search for the unknown planet should be instituted. The materials available to the mathematician for the solution of this problem were to be derived solely from the discrepancies between the calculated places in which Uranus should be found, taking into account the known causes of disturbance, and the actual places in which observation had shown the planet to exist. Here was indeed an unprecedented problem, and one of extraordinary difficulty. Le Verrier, however, faced it, and, to the astonishment of the world, succeeded in carrying it through to a brilliant solution. We cannot here attempt to enter into any account of the mathematical investigations that were necessary. All that we can do is to give a general indication of the method which had to be adopted.
Let us suppose that a planet is revolving outside Uranus, at a distance which is suggested by the several distances at which the other planets are dispersed around the sun. Let us assume that this outer planet has started on its course, in a prescribed path, and that it has a certain mass. It will, of course, disturb the motion of Uranus, and in consequence of that disturbance Uranus will follow a path the nature of which can be determined by calculation. It will, however, generally be found that the path so ascertained does not tally with the actual path which observations have indicated for Uranus. This demonstrates that the assumed circumstances of the unknown planet must be in some respects erroneous, and the astronomer commences afresh with an amended orbit. At last after many trials, Le Verrier ascertained that, by assuming a certain size, shape, and position for the unknown Planet's orbit, and a certain value for the mass of the hypothetical body, it would be possible to account for the observed disturbances of Uranus. Gradually it became clear to the perception of this consummate mathematician, not only that the difficulties in the movements of Uranus could be thus explained, but that no other explanation need be sought for. It accordingly appeared that a planet possessing the mass which he had assigned, and moving in the orbit which his calculations had indicated, must indeed exist, though no eye had ever beheld any such body. Here was, indeed, an astonishing result. The mathematician sitting at his desk, by studying the observations which had been supplied to him of one planet, is able to discover the existence of another planet, and even to assign the very position which it must occupy, ere ever the telescope is invoked for its discovery.

Thus it was that the calculations of Le Verrier narrowed greatly the area to be scrutinised in the telescopic search which was presently to be instituted. It was already known, as we have just pointed out, that the planet must lie somewhere on the ecliptic. The French mathematician had now further indicated the spot on the ecliptic at which, according to his calculations, the planet must actually be found. And now for an episode in this history which will be celebrated so long as science shall endure. It is nothing less than the telescopic confirmation of the existence of this new planet, which had previously been indicated only by mathematical calculation. Le Verrier had not himself the instruments necessary for studying the heavens, nor did he possess the skill of the practical astronomer. He, therefore, wrote to Dr. Galle, of the Observatory at Berlin, requesting him to undertake a telescopic search for the new planet in the vicinity which the mathematical calculation had indicated for the whereabouts of the planet at that particular time. Le Verrier added that he thought the planet ought to admit of being recognised by the possession of a disc sufficiently definite to mark the distinction between it and the surrounding stars.

It was the 23rd September, 1846, when the request from Le Verrier reached the Berlin Observatory, and the night was clear, so that the memorable search was made on the same evening. The investigation was facilitated by the circumstance that a diligent observer had recently compiled elaborate star maps for certain tracts of the heavens lying in a sufficiently wide zone on both sides of the equator. These maps were as yet only partially complete, but it happened that Hora. XXI., which included the very spot which Le Verrier's results referred to, had been just issued. Dr. Galle had thus before his, eyes a chart of all the stars which were visible in that part of the heavens at the time when the map was made. The advantage of such an assistance to the search could hardly be overestimated. It at once gave the astronomer another method of recognising the planet besides that afforded by its possible possession of a disc. For as the planet was a moving body, it would not have been in the same place relatively to the stars at the time when the map was constructed, as it occupied some years later when the search was being made. If the body should be situated in the spot which Le Verrier's calculations indicated in the autumn of 1846, then it might be regarded as certain that it would not be found in that same place on a map drawn some years previously.

The search to be undertaken consisted in a comparison made point by point between the bodies shown on the map, and those stars in the sky which Dr. Galle's telescope revealed. In the course of this comparison it presently appeared that a star-like object of the eighth magnitude, which was quite a conspicuous body in the telescope, was not represented in the map. This at once attracted the earnest attention of the astronomer, and raised his hopes that here was indeed the planet. Nor were these hopes destined to be disappointed. It could not be supposed that a star of the eighth magnitude would have been overlooked in the preparation of a chart whereon stars of many lower degrees of brightness were set down. One other supposition was of course conceivable. It might have been that this suspicious object belonged to the class of variables, for there are many such stars whose brightness fluctuates, and if it had happened that the map was constructed at a time when the star in question had but feeble brilliance, it might have escaped notice. It is also well known that sometimes new stars suddenly develop, so that the possibility that what Dr. Galle saw should have been a variable star or should have been a totally new star had to be provided against.

Fortunately a test was immediately available to decide whether the new object was indeed the long sought for planet, or whether it was a star of one of the two classes to which I have just referred. A star remains fixed, but a planet is in motion. No doubt when a planet lies at the distance at which this new planet was believed to be situated, its apparent motion would be so slow that it would not be easy to detect any change in the course of a single night's observation. Dr. Galle, however, addressed himself with much skill to the examination of the place of the new body. Even in the course of the night he thought he detected slight movements, and he awaited with much anxiety the renewal of his observations on the subsequent evenings. His suspicions as to the movement of the body were then amply confirmed, and the planetary nature of the new object was thus unmistakably detected.

Great indeed was the admiration of the scientific world at this superb triumph. Here was a mighty planet whose very existence was revealed by the indications afforded by refined mathematical calculation. At once the name of Le Verrier, already known to those conversant with the more profound branches of astronomy, became everywhere celebrated. It soon, however, appeared, that the fame belonging to this great achievement had to be shared between Le Verrier and another astronomer, J. C. Adams, of Cambridge. In our chapter on this great English mathematician we shall describe the manner in which he was independently led to the same discovery.
Directly the planetary nature of the newly-discovered body had been established, the great observatories naturally included this additional member of the solar system in their working lists, so that day after day its place was carefully determined. When sufficient time had elapsed the shape and position of the orbit of the body became known. Of course, it need hardly be said that observations applied to the planet itself must necessarily provide a far more accurate method of determining the path which it follows, than would be possible to Le Verrier, when all he had to base his calculations upon was the influence of the planet reflected, so to speak, from Uranus. It may be noted that the true elements of the planet, when revealed by direct observation, showed that there was a considerable discrepancy between the track of the planet which Le Verrier had announced, and that which the planet was actually found to pursue.

The name of the newly-discovered body had next to be considered. As the older members of the system were already known by the same names as great heathen divinities, it was obvious that some similar source should be invoked for a suggestion as to a name for the most recent planet. The fact that this body was so remote in the depths of space, not unnaturally suggested the name "Neptune." Such is accordingly the accepted designation of that mighty globe which revolves in the track that at present seems to trace out the frontiers of our system.

Le Verrier attained so much fame by this discovery, that when, in 1854, Arago's place had to be filled at the head of the great Paris Observatory, it was universally felt that the discoverer of Neptune was the suitable man to assume the office which corresponds in France to that of the Astronomer Royal in England. It was true that the work of the astronomical mathematician had hitherto been of an abstract character. His discoveries had been made at his desk and not in the observatory, and he had no practical acquaintance with the use of astronomical instruments. However, he threw himself into the technical duties of the observatory with vigour and determination. He endeavoured to inspire the officers of the establishment with enthusiasm for that systematic work which is so necessary for the accomplishment of useful astronomical research. It must, however, be admitted that Le Verrier was not gifted with those natural qualities which would make him adapted for the successful administration of such an establishment. Unfortunately disputes arose between the Director and his staff. At last the difficulties of the situation became so great that the only possible solution was to supersede Le Verrier, and he was accordingly obliged to retire. He was succeeded in his high office by another eminent mathematician, M. Delaunay, only less distinguished than Le Verrier himself.

Relieved of his official duties, Le Verrier returned to the mathematics he loved. In his non-official capacity he continued to work with the greatest ardour at his researches on the movements of the planets. After the death of M. Delaunay, who was accidentally drowned in 1873, Le Verrier was restored to the directorship of the observatory, and he continued to hold the office until his death.

The nature of the researches to which the life of Le Verrier was subsequently devoted are not such as admit of description in a general sketch like this, where the language, and still less the symbols, of mathematics could not be suitably introduced. It may, however, be said in general that he was particularly engaged with the study of the effects produced on the movements of the planets by their mutual attractions. The importance of this work to astronomy consists, to a considerable extent, in the fact that by such calculations we are enabled to prepare tables by which the places of the different heavenly bodies can be predicted for our almanacs. To this task Le Verrier devoted himself, and the amount of work he has accomplished would perhaps have been deemed impossible had it not been actually done.

The superb success which had attended Le Verrier's efforts to explain the cause of the perturbations of Uranus, naturally led this wonderful computer to look for a similar explanation of certain other irregularities in planetary movements. To a large extent he succeeded in showing how the movements of each of the great planets could be satisfactorily accounted for by the influence of the attractions of the other bodies of the same class. One circumstance in connection with these investigations is sufficiently noteworthy to require a few words here. Just as at the opening of his career, Le Verrier had discovered that Uranus, the outermost planet of the then known system, exhibited the influence of an unknown external body, so now it appeared to him that Mercury, the innermost body of our system, was also subjected to some disturbances, which could not be satisfactorily accounted for as consequences of any known agents of attraction. The ellipse in which Mercury revolved was animated by a slow movement, which caused it to revolve in its plane. It appeared to Le Verrier that this displacement was incapable of explanation by the action of any of the known bodies of our system. He was, therefore, induced to try whether he could not determine from the disturbances of Mercury the existence of some other planet, at present unknown, which revolved inside the orbit of the known planet. Theory seemed to indicate that the observed alteration in the track of the planet could be thus accounted for. He naturally desired to obtain telescopic confirmation which might verify the existence of such a body in the same way as Dr. Galle verified the existence of Neptune. If there were, indeed, an intramercurial planet, then it must occasionally cross between the earth and the sun, and might now and then be expected to be witnessed in the actual act of transit. So confident did Le Verrier feel in the existence of such a body that an observation of a dark object in transit, by Lescarbault on 26th March, 1859, was believed by the mathematician to be the object which his theory indicated. Le Verrier also thought it likely that another transit of the same object would be seen in March, 1877. Nothing of the kind was, however, witnessed, notwithstanding that an assiduous watch was kept, and the explanation of the change in Mercury's orbit must, therefore, be regarded as still to be sought for.

Le Verrier naturally received every honour that could be bestowed upon a man of science. The latter part of his life was passed during the most troubled period of modern French history. He was a supporter of the Imperial Dynasty, and during the Commune he experienced much anxiety; indeed, at one time grave fears were entertained for his personal safety.

Early in 1877 his health, which had been gradually failing for some years, began to give way. He appeared to rally somewhat in the summer, but in September he sank rapidly, and died on Sunday, the 23rd of that month.
His remains were borne to the cemetery on Mont Parnasse in a public funeral. Among his pallbearers were leading men of science, from other countries as well as France, and the memorial discourses pronounced at the grave expressed their admiration of his talents and of the greatness of the services he had rendered to science.

Adams

The illustrious mathematician who, among Englishmen, at all events, was second only to Newton by his discoveries in theoretical astronomy, was born on June the 5th, 1819, at the farmhouse of Lidcot, seven miles from Launceston, in Cornwall. His early education was imparted under the guidance of the Rev. John Couch Grylls, a first cousin of his mother. He appears to have received an education of the ordinary school type in classics and mathematics, but his leisure hours were largely devoted to studying what astronomical books he could find in the library of the Mechanics' Institute at Devonport. He was twenty years old when he entered St. John's College, Cambridge. His career in the University was one of almost unparalleled distinction, and it is recorded that his answering at the Wranglership examination, where he came out at the head of the list in 1843, was so high that he received more than double the marks awarded to the Second Wrangler.

Among the papers found after his death was the following memorandum, dated July the 3rd, 1841: "Formed a design at the beginning of this week of investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus, Which are as yet unaccounted for, in order to find whether they may be attributed to the action of an undiscovered planet beyond it; and, if possible, thence to determine the elements of its orbit approximately, which would lead probably to its discovery."

After he had taken his degree, and had thus obtained a little relaxation from the lines within which his studies had previously been necessarily confined, Adams devoted himself to the study of the perturbations of Uranus, in accordance with the resolve which we have just seen that he formed while he was still an undergraduate. As a first attempt he made the supposition that there might be a planet exterior to Uranus, at a distance which was double that of Uranus from the sun. Having completed his calculation as to the effect which such a hypothetical planet might exercise upon the movement of Uranus, he came to the conclusion that it would be quite possible to account completely for the unexplained difficulties by the action of an exterior planet, if only that planet were of adequate size and had its orbit properly placed. It was necessary, however, to follow up the problem more precisely, and accordingly an application was made through Professor Challis, the Director of the Cambridge Observatory, to the Astronomer Royal, with the object of obtaining from the observations made at Greenwich Observatory more accurate values for the disturbances suffered by Uranus. Basing his work on the more precise materials thus available, Adams undertook his calculations anew, and at last, with his completed results, he called at Greenwich Observatory on October the 21st, 1845. He there left for the Astronomer Royal a paper which contained the results at which he had arrived for the mass and the mean distance of the hypothetical planet as well as the other elements necessary for calculating its exact position.

[PLATE: JOHN COUCH ADAMS.] As we have seen in the preceding chapter, Le Verrier had been also investigating the same problem. The place which Le Verrier assigned to the hypothetical disturbing planet for the beginning of the year 1847, was within a degree of that to which Adams's computations pointed, and which he had communicated to the Astronomer Royal seven months before Le Verrier's work appeared. On July the 29th, 1846, Professor Challis commenced to search for the unknown object with the Northumberland telescope belonging to the Cambridge Observatory. He confined his attention to a limited region in the heavens, extending around that point to which Mr. Adams' calculations pointed. The relative places of all the stars, or rather star-like objects within this area, were to be carefully measured. When the same observations were repeated a week or two later, then the distances of the several pairs of stars from each other would be found unaltered, but any planet which happened to lie among the objects measured would disclose its existence by the alterations in distance due to its motion in the interval. This method of search, though no doubt it must ultimately have proved successful, was necessarily a very tedious one, but to Professor Challis, unfortunately, no other method was available. Thus it happened that, though Challis commenced his search at Cambridge two months earlier than Galle at Berlin, yet, as we have already explained, the possession of accurate starmaps by Dr. Galle enabled him to discover the planet on the very first night that he looked for it.

The rival claims of Adams and Le Verrier to the discovery of Neptune, or rather, we should say, the claims put forward by their respective champions, for neither of the illustrious investigators themselves condescended to enter into the personal aspect of the question, need not be further discussed here. The main points of the controversy have been long since settled, and we cannot do better than quote the words of Sir John Herschel when he addressed the Royal Astronomical Society in 1848:--

"As genius and destiny have joined the names of Le Verrier and Adams, I shall by no means put them asunder; nor will they ever be pronounced apart so long as language shall celebrate the triumphs Of science in her sublimest walks. On the great discovery of Neptune, which may be said to have surpassed, by intelligible and legitimate means, the wildest pretensions of clairvoyance, it Would now be quite superfluous for me to dilate. That glorious event and the steps which led to it, and the various lights in which it has been placed, are already familiar to every one having the least tincture of science. I will only add that as there is not, nor henceforth ever can be, the slightest rivalry on the subject between these two illustrious men--as they have met as brothers, and as such will, I trust, ever regard each other--we have made, we could make, no distinction between then, on this occasion. May they both long adorn and augment our science, and add to their own fame already so high and pure, by fresh achievements."

Adams was elected a Fellow of St. John's College, Cambridge, in 1843; but as he did not take holy orders, his Fellowship, in accordance with the rules then existing came to an end in 1852. In the following year he was, however, elected to a Fellowship at Pembroke College, which he retained until the end of his life. In 1858 he was appointed Professor of Mathematics in the University of St. Andrews, but his residence in the north was only a brief one, for in the same year he was recalled to Cambridge as Lowndean Professor of Astronomy and Geometry, in succession to Peacock. In 1861 Challis retired from the Directorship of the Cambridge Observatory, and Adams was appointed to succeed him.

The discovery of Neptune was a brilliant inauguration of the astronomical career of Adams. He worked at, and wrote upon, the theory of the motions of Biela's comet; he made important corrections to the theory of Saturn; he investigated the mass of Uranus, a subject in which he was naturally interested from its importance in the theory of Neptune; he also improved the methods of computing the orbits of double stars. But all these must be regarded as his minor labours, for next to the discovery of Neptune the fame of Adams mainly rests on his researches upon certain movements of the moon, and upon the November meteors.

The periodic time of the moon is the interval required for one circuit of its orbit. This interval is known with accuracy at the present day, and by means of the ancient eclipses the period of the moon's revolution two thousand years ago can be also ascertained. It had been discovered by Halley that the period which the moon requires to accomplish each of its revolutions around the earth has been steadily, though no doubt slowly, diminishing. The change thus produced is not appreciable when only small intervals of time are considered, but it becomes appreciable when we have to deal with intervals of thousands of years. The actual effect which is produced by the lunar acceleration, for so this phenomenon is called, may be thus estimated. If we suppose that the moon had, throughout the ages, revolved around the earth in precisely the same periodic time which it has at present, and if from this assumption we calculate back to find where the moon must have been about two thousand years ago, we obtain a position which the ancient eclipses show to be different from that in which the moon was actually situated. The interval between the position in which the moon would have been found two thousand years ago if there had been no acceleration, and the position in which the moon was actually placed, amounts to about a degree, that is to say, to an arc on the heavens which is twice the moon's apparent diameter.

If no other bodies save the earth and the moon were present in the universe, it seems certain that the motion of the moon would never have exhibited this acceleration. In such a simple case as that which I have supposed the orbit of the moon would have remained for ever absolutely unchanged. It is, however, well known that the presence of the sun exerts a disturbing influence upon the movements of the moon. In each revolution our satellite is continually drawn aside by the action of the sun from the place which it would otherwise have occupied. These irregularities are known as the perturbations of the lunar orbit, they have long been studied, and the majority of them have been satisfactorily accounted for. It seems, however, to those who first investigated the question that the phenomenon of the lunar acceleration could not be explained as a consequence of solar perturbation, and, as no other agent competent to produce such effects was recognised by astronomers, the lunar acceleration presented an unsolved enigma.

At the end of the last century the illustrious French mathematician Laplace undertook a new investigation of the famous problem, and was rewarded with a success which for a long time appeared to be quite complete. Let us suppose that the moon lies directly between the earth and the sun, then both earth and moon are pulled towards the sun by the solar attraction; as, however, the moon is the nearer of the two bodies to the attracting centre it is pulled the more energetically, and consequently there is an increase in the distance between the earth and the moon. Similarly when the moon happens to lie on the other side of the earth, so that the earth is interposed directly between the moon and the sun, the solar attraction exerted upon the earth is more powerful than the same influence upon the moon. Consequently in this case, also, the distance of the moon from the earth is increased by the solar disturbance. These instances will illustrate the general truth, that, as one of the consequences of the disturbing influence exerted by the sun upon the earthmoon system, there is an increase in the dimensions of the average orbit which the moon describes around the earth. As the time required by the moon to accomplish a journey round the earth depends upon its distance from the earth, it follows that among the influences of the sun upon the moon there must be an enlargement of the periodic time, from what it would have been had there been no solar disturbing action.

This was known long before the time of Laplace, but it did not directly convey any explanation of the lunar acceleration. It no doubt amounted to the assertion that the moon's periodic time was slightly augmented by the disturbance, but it did not give any grounds for suspecting that there was a continuous change in progress. It was, however, apparent that the periodic time was connected with the solar disturbance, so that, if there were any alteration in the amount of the sun's disturbing effect, there must be a corresponding alteration in the moon's periodic time. Laplace, therefore, perceived that, if he could discover any continuous change in the ability of the sun for disturbing the moon, he would then have accounted for a continuous change in the moon's periodic time, and that thus an explanation of the long-vexed question of the lunar acceleration might be forthcoming.

The capability of the sun for disturbing the earth-moon system is obviously connected with the distance of the earth from the sun. If the earth moved in an orbit which underwent no change whatever, then the efficiency of the sun as a disturbing agent would not undergo any change of the kind which was sought for. But if there were any alteration in the shape or size of the earth's orbit, then that might involve such changes in the distance between the earth and the sun as would possibly afford the desired agent for producing the observed lunar effect. It is known that the earth revolves in an orbit which, though nearly circular, is strictly an ellipse. If the earth were the only planet revolving around the sun then that ellipse would remain unaltered from age to age. The earth is, however, only one of a large number of planets which circulate around the great luminary, and are guided and controlled by his supreme attracting power. These planets mutually attract each other, and in consequence of their mutual attractions the orbits of the planets are disturbed from the simple elliptic form which they would otherwise possess. The movement of the earth, for instance, is not, strictly speaking, performed in an elliptical orbit. We may, however, regard it as revolving in an ellipse provided we admit that the ellipse is itself in slow motion.

It is a remarkable characteristic of the disturbing effects of the planets that the ellipse in which the earth is at any moment moving always retains the same length; that is to say, its longest diameter is invariable. In all other respects the ellipse is continually changing. It alters its position, it changes its plane, and, most important of all, it changes its eccentricity. Thus, from age to age the shape of the track which the earth describes may at one time be growing more nearly a circle, or at another time may be departing more widely from a circle. These alterations are very small in amount, and they take place with extreme slowness, but they are in incessant progress, and their amount admits of being accurately calculated. At the present time, and for thousands of years past, as well as for thousands of years to come, the eccentricity of the earth's orbit is diminishing, and consequently the orbit described by the earth each year is becoming more nearly circular. We must, however, remember that under all circumstances the length of the longest axis of the ellipse is unaltered, and consequently the size of the track which the earth describes around the sun is gradually increasing. In other words, it may be said that during the present ages the average distance between the earth and the sun is waxing greater in consequence of the perturbations which the earth experiences from the attraction of the other planets. We have, however, already seen that the efficiency of the solar attraction for disturbing the moon's movement depends on the distance between the earth and the sun. As therefore the average distance between the earth and the sun is increasing, at all events during the thousands of years over which our observations extend, it follows that the ability of the sun for disturbing the moon must be gradually diminishing.

[PLATE: CAMBRIDGE OBSERVATORY.]

It has been pointed out that, in consequence of the solar disturbance, the orbit of the moon must be some what enlarged. As it now appears that the solar disturbance is on the whole declining, it follows that the orbit of the moon, which has to be adjusted relatively to the average value of the solar disturbance, must also be gradually declining. In other words, the moon must be approaching nearer to the earth in consequence of the alterations in the eccentricity of the earth's orbit produced by the attraction of the other planets. It is true that the change in the moon's position thus arising is an extremely small one, and the consequent effect in accelerating the moon's motion is but very slight. It is in fact almost imperceptible, except when great periods of time are involved. Laplace undertook a calculation on this subject. He knew what the efficiency of the planets in altering the dimensions of the earth's orbit amounted to; from this he was able to determine the changes that would be propagated into the motion of the moon. Thus he ascertained, or at all events thought he had ascertained, that the acceleration of the moon's motion, as it had been inferred from the observations of the ancient eclipses which have been handed down to us, could be completely accounted for as a consequence of planetary perturbation. This was regarded as a great scientific triumph. Our belief in the universality of the law of gravitation would, in fact, have been seriously challenged unless some explanation of the lunar acceleration had been forthcoming. For about fifty years no one questioned the truth of Laplace's investigation. When a mathematician of his eminence had rendered an explanation of the remarkable facts of observation which seemed so complete, it is not surprising that there should have been but little temptation to doubt it. On undertaking a new calculation of the same question, Professor Adams found that Laplace had not pursued this approximation sufficiently far, and that consequently there was a considerable error in the result of his analysis. Adams, it must be observed, did not impugn the value of the lunar acceleration which Halley had deduced from the observations, but what he did show was, that the calculation by which Laplace thought he had provided an explanation of this acceleration was erroneous. Adams, in fact, proved that the planetary influence which Laplace had detected only possessed about half the efficiency which the great French mathematician had attributed to it. There were not wanting illustrious mathematicians who came forward to defend the calculations of Laplace. They computed the question anew and arrived at results practically coincident with those he had given. On the other hand certain distinguished mathematicians at home and abroad verified the results of Adams. The issue was merely a mathematical one. It had only one correct solution. Gradually it appeared that those who opposed Adams presented a number of different solutions, all of them discordant with his, and, usually, discordant with each other. Adams showed distinctly where each of these investigators had fallen into error, and at last it became universally admitted that the Cambridge Professor had corrected Laplace in a very fundamental point of astronomical theory.

Though it was desirable to have learned the truth, yet the breach between observation and calculation which Laplace was believed to have closed thus became reopened. Laplace's investigation, had it been correct, would have exactly explained the observed facts. It was, however, now shown that his solution was not correct, and that the lunar acceleration, when strictly calculated as a consequence of solar perturbations, only produced about half the effect which was wanted to explain the ancient eclipses completely. It now seems certain that there is no means of accounting for the lunar acceleration as a direct consequence of the laws of gravitation, if we suppose, as we have been in the habit of supposing, that the members of the solar system concerned may be regarded as rigid particles. It has, however, been suggested that another explanation of a very interesting kind may be forthcoming, and this we must endeavour to set forth.

It will be remembered that we have to explain why the period of revolution of the moon is now shorter than it used to be. If we imagine the length of the period to be expressed in terms of days and fractions of a day, that is to say, in terms of the rotations of the earth around its axis, then the difficulty encountered is, that the moon now requires for each of its revolutions around the earth rather a smaller number of rotations of the earth around its axis than used formerly to be the case. Of course this may be explained by the fact that the moon is now moving more swiftly than of yore, but it is obvious that an explanation of quite a different kind might be conceivable. The moon may be moving just at the same pace as ever, but the length of the day may be increasing. If the length of the day is increasing, then, of course, a smaller number of days will be required for the moon to perform each revolution even though the moon's period was itself really unchanged. It would, therefore, seem as if the phenomenon known as the lunar acceleration is the result of the two causes. The first of these is that discovered by Laplace, though its value was overestimated by him, in which the perturbations of the earth by the planets indirectly affect the motion of the moon. The remaining part of the acceleration of our satellite is apparent rather than real, it is not that the moon is moving more quickly, but that our time-piece, the earth, is revolving more slowly, and is thus actually losing time. It is interesting to note that we can detect a physical explanation for the apparent checking of the earth's motion which is thus manifested. The tides which ebb and flow on the earth exert a brake-like action on the revolving globe, and there can be no doubt that they are gradually reducing its speed, and thus lengthening the day. It has accordingly been suggested that it is this action of the tides which produces the supplementary effect necessary to complete the physical explanation of the lunar acceleration, though it would perhaps be a little premature to assert that this has been fully demonstrated.

The third of Professor Adams' most notable achievements was connected with the great shower of November meteors which astonished the world in 1866. This splendid display concentrated the attention of astronomers on the theory of the movements of the little objects by which the display was produced. For the definite discovery of the track in which these bodies revolve, we are indebted to the labours of Professor Adams, who, by a brilliant piece of mathematical work, completed the edifice whose foundations had been laid by Professor Newton, of Yale, and other astronomers.

Meteors revolve around the sun in a vast swarm, every individual member of which pursues an orbit in accordance with the well-known laws of Kepler. In order to understand the movements of these objects, to account satisfactorily for their periodic recurrence, and to predict the times of their appearance, it became necessary to learn the size and the shape of the track which the swarm followed, as well as the position which it occupied. Certain features of the track could no doubt be readily assigned. The fact that the shower recurs on one particular day of the year, viz., November 13th, defines one point through which the orbit must pass. The position on the heavens of the radiant point from which the meteors appear to diverge, gives another element in the track. The sun must of course be situated at the focus, so that only one further piece of information, namely, the periodic time, will be necessary to complete our knowledge of the movements of the system. Professor H. Newton, of Yale, had shown that the choice of possible orbits for the meteoric swarm is limited to five. There is, first, the great ellipse in which we now know the meteors revolve once every thirty three and one quarter years. There is next an orbit of a nearly circular kind in which the periodic time would be a little more than a year. There is a similar track in which the periodic time would be a few days short of a year, while two other smaller orbits would also be conceivable. Professor Newton had pointed out a test by which it would be possible to select the true orbit, which we know must be one or other of these five. The mathematical difficulties which attended the application of this test were no doubt great, but they did not baffle Professor Adams.

There is a continuous advance in the date of this meteoric shower. The meteors now cross our track at the point occupied by the earth on November 13th, but this point is gradually altering. The only influence known to us which could account for the continuous change in the plane of the meteor's orbit arises from the attraction of the various planets. The problem to be solved may therefore be attacked in this manner. A specified amount of change in the plane of the orbit of the meteors is known to arise, and the changes which ought to result from the attraction of the planets can be computed for each of the five possible orbits, in one of which it is certain that the meteors must revolve. Professor Adams undertook the work. Its difficulty principally arises from the high eccentricity of the largest of the orbits, which renders the more ordinary methods of calculation inapplicable. After some months of arduous labour the work was completed, and in April, 1867, Adams announced his solution of the problem. He showed that if the meteors revolved in the largest of the five orbits, with the periodic time of thirty three and one quarter years, the perturbations of Jupiter would account for a change to the extent of twenty minutes of arc in the point in which the orbit crosses the earth's track. The attraction of Saturn would augment this by seven minutes, and Uranus would add one minute more, while the influence of the Earth and of the other planets would be inappreciable. The accumulated effect is thus twenty-eight minutes, which is practically coincident with the observed value as determined by Professor Newton from an examination of all the showers of which there is any historical record. Having thus showed that the great orbit was a possible path for the meteors, Adams next proved that no one of the other four orbits would be disturbed in the same manner. Indeed, it appeared that not half the observed amount of change could arise in any orbit except in that one with the long period. Thus was brought to completion the interesting research which demonstrated the true relation of the meteor swarm to the solar system.

Besides those memorable scientific labours with which his attention was so largely engaged, Professor Adams found time for much other study. He occasionally allowed himself to undertake as a relaxation some pieces of numerical calculation, so tremendously long that we can only look on them with astonishment. He has calculated certain important mathematical constants accurately to more than two hundred places of decimals. He was a diligent reader of works on history, geology, and botany, and his arduous labours were often beguiled by novels, of which, like many other great men, he was very fond. He had also the taste of a collector, and he brought together about eight hundred volumes of early printed works, many of considerable rarity and value. As to his personal character, I may quote the words of Dr. Glaisher when he says, "Strangers who first met him were invariably struck by his simple and unaffected manner. He was a delightful companion, always cheerful and genial, showing in society but few traces of his really shy and retiring disposition. His nature was sympathetic and generous, and in few men have the moral and intellectual qualities been more perfectly balanced.

In 1863 he married the daughter of Haliday Bruce, Esq., of Dublin and up to the close of his life he lived at the Cambridge Observatory, pursuing his mathematical work and enjoying the society of his friends.

He died, after a long illness, on 21st January, 1892, and was interred in St. Giles's Cemetery, on the Huntingdon Road, Cambridge.

 

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