crashing reply, which he published in the 'Philosophical Magazine' in 1827.

It is, however, impossible even to mention the names of the many papers of which he was the author. The few which have been mentioned above prove how soon after his degree he took a leading part in the scientific work of the day. They show also how, from the very beginning, his mind was turned to practical applications, leaving aside any pure theorems of which he did not see the immediate use.

In 1826 Mr. Airy published his mathematical tracts, which almost immediately became the standard text-book for students in the University. In the first edition we find only the lunar theory, the figure of the Earth, precession and the calculus of variations, the tract on the planetary theory and that on the undulatory theory being added in the second edition, 1831. As his object was to give a clear statement of first principles, he put into the book just what was wanted at the time he wrote, making his judgment with admirable skill. The student world has now outgrown the book, but this is in part due to the excellence of the teaching of the book itself. The first tract, that on lunar theory, is interesting to Cambridge students for another reason. The attention of the University had been so long confined to the works of Newton that the analytical mode of treatment had been almost entirely neglected. The methods of Newton are, Mr. Airy remarks, beautiful, but they have all the imperfections which necessarily accompany first attempts; for the explanation of some of the lunar inequalities they are hardly sufficient, and for the calculation of most they are quite inadequate. For other branches of physical astronomy, such as the planetary theory, their inadequacy has never been questioned. In this tract he endeavours to lay before the student an analytical view of the lunar theory, giving references to the 'Principia' to show the connexion between the different systems. The tract on the calculus of variations is the only one which is purely mathematical. Though it does not go very far into the subject, yet the author must have had a deep sense of the power of this calculus, for he has used it in his physical papers, even in places where simpler methods might more naturally have suggested themselves to his mind. In the preface he speaks of this calculus as the most beautiful of all the branches of the differential calculus. The excellence of the tract on the undulatory theory is evident when we remember the length of time in which it was regarded as the standard text-book of the University. When the other tracts, after a long life, became antiquated, this one retained its popularity, and has been reprinted several times by itself, and is even yet in use.

Mr. Airy was elected a Fellow of Trinity College the year after his degree, and later on in life he was chosen one of the three first Honorary Fellows of the College, the others being Thirlwall and

Tennyson. In 1826 he was appointed Lucasian Professor of Mathematics, but this professorship he soon exchanged for the Plumian, to which he was appointed in 1828. According to the Calendar of that date, his predecessor in office merely gave lectures in the first half of the midsummer term, while those of the former Lucasian Professor are only vaguely referred to. But these were greatly enlarged by Mr. Airy, whose syllabus extends over forty-eight pages of print. They comprise statics, dynamics, hydrostatics, and geometrical optics, but their chief character seems to have been the theory of undulations. Many of the experiments on polarised light whose mathematical theory is given in his tract on the undulatory theory were exhibited here. He appears to have been the first to introduce into Cambridge studies the beautiful theories of Fresnel. With these as subjects, treated in his own skilful manner, we need not wonder at the popularity of his lectures. Even after he had become Astronomer Royal, we learn from his first report to the Board of Visitors, that application to the Admiralty had been made by several members of the University and by the Plumian Professor to allow him to give another course of lectures at Cambridge.

Along with the Plumian Professorship Mr. Airy undertook the duties of the Director of the Observatory. He at once entered on these arduous duties with his usual energy. His efforts were well seconded by the University, who at once raised the slender income of the professorship to an amount nearly double its former value. In the first volume of the 'Astronomical Observations' he tells us that he was induced to fix on a plan of publication very different from that of the 'Greenwich Observations.' He remarks that the value of unreduced observations is so small that to most persons they are absolutely useless. Few, who have not made observations, understand how much time and calculation must be employed before they can be applied to any useful purpose. On the average, the preparatory steps and the observation of a transit occupy from five to ten minutes, while the complete reduction and discussion of the observations employ full half an hour. The professor even said that if an offer was made of a mass of regular meridional observations unreduced, he would not think it worth acceptance. In giving, therefore, the results, he was giving the produce of four or five times as much labour, necessarily irksome, as if he gave merely the unreduced observations. The report for the year 1828 covered the interval of five months' residence at the Observatory; he had no assistant, and every step from making the observations to revising the proof-sheets had to be done by himself alone. Yet in April of the following year the report was published with all the necessary reductions. This promptness is maintained in the succeeding years, and excited the admiration of M. Quetelet, the Director of the Obser

1832, et déjà nous possédons les observations de M. Airy, pour toute l'année 1831: et ce qui peut paraître plus étonnant encore, toutes ces observations sont calculées et discutées avec soin."

It is interesting to observe the care with which he chose the objects to which he should turn his attention as an astronomer, and the constancy with which he stuck to his choice when once made. The chief object, he says, must be such that it could be accomplished by a single unassisted observer, and yet be so important as to be of public use. After consideration he decided that the observations of planets had at that time been so neglected, that one who wished to revise the planetary tables would find himself destitute of the necessary data on which to found his investigation. As soon, therefore, as the Cambridge Observatory was placed under his direction, he made the observation of planets the leading object of his labours. He says in one of his reports that "hardly a single observation of a planet has been lost when the transit was at such an hour that in the regular routine of observations it was practicable to observe it." The wisdom of his choice is shown by the fact that his successor followed closely the same objects. Other pressing wants in astronomy were also present in his mind, and others again rose unexpectedly in the course of his work. In reading his yearly volumes of observations, one notices among other things the care which is taken to secure accuracy. No labour is spared, no calculation is allowed to pass without repeated examination. "To observe all night and to calculate all day" is the description of an astronomer's duties given by an astronomer. In the arrangement of his results, we notice, also, how everything is subordinated to increasing their immediate utility as well as securing accuracy in their details.

When Professor Airy first went to the Observatory the only large instrument was a transit, though this was one of the best of its kind. So energetic an astronomer was not likely to be satisfied with this; accordingly in 1834 he obtained a large mural circle. In the report for that year he describes the unexpected and annoying difficulties which arose in connexion with that instrument. In the next report we find that these difficulties have been overcome by considering that the effects of the discordance of zenith points on direct and reflexion observations are equal. Later on the great Northumberland equatoreal was added. The establishment to work these was also necessarily increased, and two assistants were given to him.

Perhaps one of the most remarkable examples of Mr. Airy's insight into astronomical questions is his discovery of a new inequality in the motions of Venus and of the Earth. The attention of the Board of Longitude having been directed to the state of the solar tables used in the construction of the Nautical Almanac,' he was desired to

examine the discrepancies between the computed right ascensions of the Sun and those observed at Greenwich. On making a comparison between the discrepancies in the position of the Sun's perigee as given by late observations with those given by the observations of the last century, he concludes there must be some yet undiscovered inequality which has been omitted from the calculations. He soon discovered that this originated in the fact that thirteen times the periodic time of Venus is so nearly equal to eight years that the term depending on this phase received a multiplier of more than two millions in integrating the differential equations. On the other hand, the coefficient is of the fifth order with regard to the eccentricities and inclinations of the orbits. In the report on this paper drawn up by Whewell and Lubbock for the Royal Society, it is pointed out that no numerical calculation of a perturbation of the fifth order had been executed, except in the case of Jupiter and Saturn, where, as Laplace states, this labour, " pénible par son excessive longueur," had been performed by Burckhardt; and no calculations of a new inequality of a high order, requiring to be placed in the planetary tables, with a new argument, had been published since that of the great inequality by Laplace in 1784. They conclude by remarking that this is the first specific improvement in the solar tables made by an Englishman since the time of Halley. For this brilliant investigation the Astronomical Society in 1833 awarded to its author their gold medal. The whole of Professor Airy's process was afterwards verified, first by Pontécoulant, and secondly by Leverrier, and found to be correct.

In the years 1831-32, Professor Airy, though so fully employed at the Observatory, was yet able to make some important investigations in the theory of light. Thus he communicates to the Cambridge Philosophical Society a paper to show that the two rays produced by the double refraction of quartz are elliptically polarised. This is soon followed by two or three papers on some phenomena connected with Newton's rings. Just as Sir W. Hamilton afterwards predicted internal and external conical refraction after studying the analytical properties of the wave surface, so Professor Airy discovered these phenomena by using Fresnel's general formula for the intensity of reflected light. When Newton's rings are formed by light polarised in a plane perpendicular to that of incidence between two substances of different refractive indices, and the angle of incidence lies between the polarising angles, the rings should appear white centred, instead of having a central dark spot. Here was a recondite phenomenon which could only be seen when several special conditions were satisfied. Would it be confirmed by experiment? He describes the difficulties of the experiment and its final success. As we read the paper, we perceive how he is led on by slight unexpected discrepancies to

improve the theory. He remarks that there must be a gradual, though rapid, change of phase, instead of the sudden one given by Fresnel's formula, thus seeing faintly a result clearly explained five years after by the theoretical investigations of Green.

At this period of his life Professor Airy's labours are evidently divided between astronomy and the theory of light. The first was connected with his work at the Observatory, the second with his lectures as Professor. Thus, in 1833, he writes in the Cambridge Transactions' on Newton's experiments in diffraction; in 1835, on the diffraction of an object glass with a circular aperture; in 1838, on the intensity of light in the neighbourhood of a caustic. In 1840 he chose as the subject of the Bakerian Lecture the theoretical explanation of an apparent new polarity in light.

There is an equally important list of papers on astronomy. In 1832 he communicates to the British Association a report on the progress of astronomy during the present century. This was transJated into German, three years after, by C. L. Littrow, of the Royal Observatory, Vienna. The Viennese astronomer thinks that Professor Airy has treated German astronomy like a step-mother, but, nevertheless, he says there is no other work in which the progress of astronomy is so briefly and so accurately given. In 1834 he writes. for the Nautical Almanac,' on the perturbations of small planets and comets of short period. There is more than one paper on the mass of Jupiter. In 1834 he writes a paper, for the Astronomical Society, on the solar eclipse of July 16, 1833, which was seen extremely well at Cambridge. On this occasion he adopted a new plan of observation; instead of noting the times of the beginning or the end, he so chose the quantities to be measured that any errors in the elements would be observed after they had been largely multiplied. For example, at the beginning of the eclipse, when the discs of the Sun and Moon only slightly overlap, it is obvious that the length of the straight line joining the cusps is much more affected than the versine by any small error in the angular distance of the centres of the discs. To detect such errors, the attention of the observer should be directed to the length of this line. In like manner, the whole duration of the eclipse was divided into periods, for each of which he arranged appropriate measures.

These papers, too numerous to catalogue in this place, did not exhaust the energy of the Professor, for he found time to publish treatises on Trigonometry, the Figure of the Earth, and one on Gravitation. The latter was written for the 'Penny Cyclopædia,' but previously published, in 1834, for the use of students in the University of Cambridge. It was an attempt to explain the perturbations of the solar system without introducing an algebraic symbol. Having thus denied himself the use of the most powerful