My last lecture was devoted mostly to Eddington's contributions to theoretical astrophysics and to justifying Russell's assessment of him as the most distinguished representative of astrophysics of his time. In this lecture, I shall turn to Eddington as an expositor and an exponent of the general theory of relativity, to the part he played in the Greenwich-Cambridge expeditions to observe the solar eclipse of May 29, 1919 with the express purpose of verifying Einstein's prediction of the deflection of light by a gravitational field, and to his efforts, extending over sixteen years, in cosmology and – quoting his own description – in ‘unifying quantum theory and relativity theory’. But in contrast to my last lecture, I am afraid that this lecture will not altogether be a happy one.

I shall begin with the happier side.

After founding the principles of the special theory of relativity in 1905, Einstein's principal preoccupation in the ten following years was to bring the Newtonian theory of gravitation into conformity with those same principles and, in particular, with the requirement that no signal be propagated with a velocity exceeding that of light. After many false starts, Einstein achieved his goal in a spectacular series of short communications to the Berlin Academy of Sciences during the summer and the autumn of 1915. Because of the war, the news of Einstein's success would not have crossed the English Channel (not to mention the Atlantic Ocean) had it not been for the neutrality of the Netherlands and Einstein's personal friendship with Lorentz, Ehrenfest, and deSitter.

May I begin by expressing my gratitude to the Master of Trinity and his Council for their trust in assigning to me the privilege of giving the Centenary Lectures in memory of one of the most distinguished members of the College and of the University. I knew Eddington as a member of the Fellowship of Trinity during the early and the middle thirties when, besides Eddington, it included J. J. Thomson, Ernest Rutherford, George Trevelyan, Douglas Adrian, Donald Robertson, G. H. Hardy, J. E. Littlewood, and a host of others. It is hardly necessary for me to say how much it means to me to have been a member of that society during those years and to be asked now, almost fifty years later, to give these lectures in honour of one whose personal friendship I was fortunate to enjoy.

When Eddington died in November 1944 at the age of sixtytwo, Henry Norris Russell, his great contemporary across the Atlantic, wrote: ‘The death of Sir Arthur Eddington deprives astrophysics of its most distinguished representative.’ I have taken my cue from Russell for the substance of this, the first of my two lectures.

Before I turn to an assessment of Eddington's contributions to astronomy and to astrophysics, I should like to start with a few biographical notes which may give some impression of the manner of man he was.

THIS BOOK is based on lectures given annually in the University of Cambridge and on a parallel course of instruction in Practical Astronomy at the Observatory. The recent changes in the almanacs have, in many respects, affected the position of the older textbooks as channels of information on current practice, and the present work is intended to fill the gap caused by modern developments. In addition to the time-honoured problems of Spherical Astronomy, the book contains the essential discussion of such important subjects as helio-graphic co-ordinates, proper motions, determination of position at sea, the use of photography in precise astronomical measurements and the orbits of binary stars, all or most of which have received little attention in works of this kind. In order to make certain subjects as complete as possible, I have not hesitated to cross the traditional frontiers of Spherical Astronomy. This is specially the case as regards the spectroscopic determination of radial velocity which is considered, the physical principles being assumed, in relation to such problems as solar parallax, the solar motion and the orbits of spectroscopic binary stars.

Throughout, only the simplest mathematical tools have been used and considerable attention has been paid to the diagrams illustrating the text. I have devoted the first chapter to the proofs and numerical applications of the formulae of spherical trigonometry which form the mathematical foundation of the subsequent chapters. Although other formulae have been given for reference, I have limited myself to the use of the basic formulae only.

A writer of a textbook on Spherical Astronomy cannot avoid a certain measure of detailed reference to the principal astronomical instruments and, accordingly, general descriptions of instruments have been given in the appropriate places, usually with a simple discussion of the chief errors which must be taken into account in actual observational work.

In numerical applications, the almanac for 1931 has been used.

Introduction.

When we look at the stars on a clear night we have the familiar impression that they are all sparkling points of light, apparently situated on the surface of a vast sphere of which the individual observer is the centre. The eye, of course, fails to give any indication of the distances of the stars from us; however, it allows us to make some estimate of the angles subtended at the observer by any pairs of stars and, with suitable instruments, these angles can be measured with great precision. Spherical Astronomy is concerned essentially with the directions in which the stars are viewed, and it is convenient to define these directions in terms of the positions on the surface of a sphere— the celestial sphere—in which the straight lines, joining the observer to the stars, intersect this surface. It is in this sense that the usual expression “the position of a star on the celestial sphere” is to be interpreted. The radius of the sphere is entirely arbitrary. The foundation of Spherical Astronomy is the geometry of the sphere.

The spherical triangle.

Any plane passing through the centre of a sphere cuts the surface in a circle which is called a great circle. Any other plane intersecting the sphere but not passing through the centre will also cut the surface in a circle which, in this case, is called a small circle. In Fig. 1, EAB is a great circle, for its plane passes through O, the centre of the sphere. Let QOP be the diameter of the sphere perpendicular to the plane of the great circle EAB. Let R be any point in OP and suppose a plane drawn through R parallel to the plane of EAB; the surface of the sphere is then intersected in the small circle FCD. It follows from the construction that OP is also perpendicular to the plane of FCD. The extremities P and Q of the common perpendicular diameter QOP are called the poles of the great circle and of the parallel small circle.

Introductory

The phenomenon of precession was discovered by Hipparchus in the second century B.C. By comparing contemporary observations with observations made about a century and a half earlier, he was led to the conclusion that the longitudes of the stars appeared to be increasing at the rate of 36″ per annum (the modern value is about 50″) while, as far as he could detect, their latitudes showed no definite changes. There are two possible explanations; either all the stars examined had real and identical motions in longitude—an improbable hypothesis—or the funda- mental reference point, the vernal equinox T from which longitudes are measured along the ecliptic, could no longer be regarded as a fixed point on the ecliptic. Now T is defined to be one of the two points of intersection of the ecliptic and the equator on the celestial sphere; the observations showed no changes in the latitudes of the stars and therefore it was legiti- mate to conclude that the ecliptic was a fixed plane. According to the second hypothesis (which was adopted by Hipparchus), it was necessary to assume that the equator and, in consequence, the vernal equinox moved in such a way that the longitudes of the stars increased uniformly by an amount in accordance with the observations.

In Fig. 92 let LTM denote the fixed ecliptic, TTR the celestial equator at time t and TT1R the celestial equator one year later. In one year the vernal equinox has moved from T to T1 and thus the longitude of a star S has increased from TD to T1D, that is, by about 50″. The uniform backward movement of T along the ecliptic is called the precession of the equinox. Now Hipparchus satisfied himself that the obliquity € of the ecliptic had suffered no appreciable change and it therefore followed that the motion of the equator must be such that the pole P moved from P to P1 around K in a small circle, KP or KP1 being the obliquity ε.

SINCE this book was first published there have been considerable changes in the terminology and the quantities tabulated in the Astronomical Ephemeris and other almanacs. In making this revision I have felt that it is important to recognise these changes and to ensure compatibility of the book with the Astronomical Ephemeris. While I hope that this has been generally achieved, slight differences do remain in the treatment of solar eclipses and in the definition of the Besselian Day Numbers for annual aberration.

Without doubt the most important change in the almanacs has been the introduction of Ephemeris Time. As it is this time that is used as the argument in almost all tabulation in the almanacs, it clearly requires an important place and adequate description in an introductory text such as this. Accordingly I have made substantial revision to the chapter on Time in stressing the distinction between Ephemeris and Universal Time. A difficulty arose, however, in connection with the exposition of this distinction. Professor Smart had used the term, mean sun, to define Universal Time. The mean sun is a wholly fictitious body that was introduced to define solar time long before the distinction, that we are concerned with, was recognised. Newcomb called it the fictitious mean sun and gave it a very precise and formal definition. Newcomb's work naturally related to the subsequent definition of Ephemeris Time and so I have retained, his term, the fictitious mean sun, as a reference point for Ephemeris Time. For continuity, I have also retained Smart's use of the term, mean sun, as a reference point for Universal Time. I hope that this dichotomy, which is not standard usage, will not lead to confusion in practice. It is not intended to imply that only one of the reference points is fictitious; both are.

I have taken the opportunity of adding a number of exercises at the end of several chapters. Some of these are taken, by permission from recent examination papers of Glasgow University. It is hoped that some of these examples will be helpful in illustrating new material that has been added to the text.

The rotation of the earth is a basis for time-measurement and as regards Universal Time (U.T.) this rate of rotation is assumed to be uniform. Recently, first crystal and then atomic clocks-now accurate to 1 part in 1013-have shown that the earth's rotation is at times irregular, the deviations from uniformity being minute—of the order of 1 or 2 milliseconds per day—and unpredictable. In the gravitational theories of the bodies of the solar system, the passage of time is postulated to be uniform', this time is defined as Ephemeris Time (E.T.) and it is in terms of E.T. that astronomical quantities are now tabulated in the almanacs. The epoch from which E.T. is measured is

1900 January 0.5 [E.T.],

more elaborately defined in 1958 as “the instant near the beginning of the calendar year A.D. 1900 when the mean longitude of the sun was 279° 41' 48".04, at which instant the measure of E.T. was 1900 January 0, 12 h. precisely.” The epoch for U.T. is 1900 January 0, 12 h. [U.T.]. Although the two epochs are apparently denoted by the same expression, they do not correspond to the same instant of time, the epoch of E.T. being 4 s. later than that of U.T.

The E.T. for any instant is then defined by the following formula for the geometric mean longitude of the sun:

L = 279° 41' 48".04+129602768".13T+ 1".089T2.

Here T is the ephemeris time measured in Julian centuries of 36525 ephemeris days from the fundamental epoch. The R.A. of the fictitious mean sun is given by the same expression with the effect of aberration added. The R.A. of the fiducial point for U.T., which we are calling simply the mean sun, has the same expression as that of the fictitious mean sun with universal time replacing ephemeris time as the argument.

It may be added that the fundamental unit of time is 1 second (E.T.) derived as 1/31556925.9747 of the length of the tropical year for 1900.0.