The social and economic preconditions for the modern form of bureaucratic administration are as follows.

(1) There must have developed a money economy to provide for the payment of officials, which nowadays is universally made in money. This is of great importance for the general mode of life of the bureaucracy, although it is not, on the other hand, in any way the decisive factor for its existence. In quantitative terms, the largest historical examples of a bureaucratic system which has achieved some obvious degree of development are: (a) Egypt in the time of the New Kingdom (though there were also marked patrimonial elements present in this case); (b) the later Roman Empire, but especially the Diocletianic monarchy and the Byzantine state which developed from it (though here again there were marked feudal and patrimonial elements present too); (c) the Roman Catholic Church, increasingly from the end of the thirteenth century onwards; (d) China, from the time of Shi Huang Ti to the present day, but with marked patrimonial and prebendal elements; (e) in an increasingly pure form, the modern European state and more and more public corporations, since the evolution of princely absolutism; (f) the modern large capitalist enterprise, which is more bureaucratic the larger and more complex it is.

In the period of the Warring States, the politically determined capitalism which is common in patrimonial states, based on money-lending and contracting for the princes, seems to have been of considerable significance and to have functioned at high rates of profit, as always under such conditions. Mines and trade are also cited as sources of capital accumulation. Under the Han dynasty, there are reputed to have been multi-millionaires, reckoned in terms of copper. But China's political unification into a world-empire, like the unification of the known world by Imperial Rome, had the obvious consequence that this form of capitalism, which was essentially rooted in the state and its competition with other states, went into decline. The development of a purely market capitalism, directed towards free exchange, on the other hand, remained at an embryonic stage. In all sections of industry, of course, even in the cooperative undertakings to be discussed presently, the merchant, here as elsewhere, was conspicuously superior to the technician. This clearly showed itself even in the usual proportions in which profits were distributed within associations. The interlocal industries also, it is plain, often brought in considerable speculative profits. The ancient classical disposition to set a high value on agriculture, as the truly hallowed calling, hence did not prevent a higher valuation being placed, even as early as the first century B.C., on the opportunities for profit from industry than on those from agriculture (just as in the Talmud), nor did it prevent the highest valuation of all being placed on those from trade.

Max Weber has been described as not merely the greatest of sociologists but ‘the sociologist’. Yet for most of his career he would not have described himself as a sociologist at all. His own training was in history, economics and law; he was opposed to the creation of professorships of sociology; and in a letter written at the very end of his life he said that his only reason for being a sociologist was to rid the subject of the influence of the collective – or, as it would now be put, ‘holistic’ – concepts by which it continued to be haunted. It was not until after 1910 that he began to compose the treatise which we now have, still uncompleted, as Economy and Society. It is a work of a markedly different kind from his early writings, whether his historical studies of medieval trading companies and Roman agrarian law or his contemporary investigations of the stock exchange and the condition of agricultural labour in the Junker estates to the East of the Elbe. Yet it would be a mistake to read too much discontinuity into the sequence of his writings. His ideas changed over the course of thirty years, as they were bound to do. But his overriding preoccupations did not.

Weber wrote extensively about politics not only from an academic standpoint but also as a committed participant in the controversies of his own country and period. This is, at first sight, out of keeping with his strictures against those ‘favourably disposed towards the admission of value-judgments into teaching’. But in his own terms, his commitment to nationalist values and his advocacy of the policies which he believed would best serve the interests of Germany as a major power are perfectly consistent with his rigorous separation of academic from political values. He did not claim scientific objectivity for his personal values, and he acknowledged the entitlement of others to support different values provided only that they were consistently held. It is true to say that his insistence on the duty of the scholar to accept the findings of science whether they accord with his preferences or not has an obvious connexion with his insistence on ‘realism’ and ‘facing facts’ in the views which he puts forward about practical politics. His open contempt for those who cherish illusions about peace and progress and his determination to expose hypocrisy and rhetoric among the advocates of Conservatism and Social Democracy alike are both expressions of an underlying commitment to what one of his commentators has called ‘the familiar bourgeois values writ large’.

For all their intrinsic importance, the individual results of the work so far done in experimental psychology on the course of the processes of fatigue and training are not perhaps of much direct assistance to the compilers of this survey for their special purposes for the reasons already mentioned. Nevertheless, it might possibly be of some use to them to acquaint themselves with some of the simpler concepts commonly employed in the more recent studies in this field, even though, unfortunately, the precise meaning of many of them is at present a matter of dispute. However, some of these concepts are sufficiently clear in meaning, represent measurable quantities, are of proven usefulness and can provide the compilers with a convenient summary of certain simple elements in personal qualifications for work, together, if necessary, with a handy terminology: for instance, such concepts as that of ‘fatiguability’ (measured in terms of the rate and degree of onset of fatigue); ‘recuperability’ (measured in terms of the rate of recovery of efficiency after fatigue); ‘capacity for training’ (in terms of the rate of improvement in performance in the course of the work); ‘durability of training’ (in terms of the extent of the residue of training left after breaks and interruptions in the work); ‘stimulability’ (in terms of the extent to which the ‘psychomotor’ influence of working itself improves performance); ‘powers of concentration’ and ‘distractability’ (in terms of the reduction or lack of it in performance caused by an unaccustomed environment or extraneous disturbances, and, in the case of a reduction, in terms of its extent); and, finally, ‘habituation’ (to an unaccustomed environment, extraneous disturbances, and – most important of all in principle – to the combination of different activities).

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 TT1 R 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 T1 D, 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.