Arthur Stanley Eddington

“ The perception of an object by an observer depends on his own situation and circumstances; for example, distance will make it appear smaller and dimmer. We make allowance for this almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude—a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer ”

“ In the case of a star seen behind the sun the added divergence has no time to take effect; but when the light has to travel a stellar distance after the divergence is produced, it becomes weakened by it. ”

“ Actually we know that the intrinsic brightness varies very greatly, so that each increase of telescopic power not only enables us to see stars more remote than before, but also reveals very many smaller stars within the limits previously penetrated. But notwithstanding the great variety of intrinsic brightness of the stars, the ratio of the number of stars of one magnitude to the number of the magnitude next lower (the “star-ratio”) is a guide to the uniformity of their distribution. ”

“ When examined with sufficient telescopic power, a great many of these luminous patches are perceived to be composed of clusters of little stars, which in a smaller telescope are invisible separately, but whose rays of light blend together so as to produce a confused luminous appearance. Others, however, cannot be resolved into individual stars even with the best telescopes, and in many cases the spectroscope gives direct evidence that the nebula has a constitution altogether different from that of a star-cluster. We thus distinguish between the nebulae proper and the star-clusters ”

“ The great majority of the nebulae, including the abundant, small nebulae which shine with a white light (in contrast with the blue-green light of the planetary and irregular nebulae—see below Spectra of nebulae) , are generally classed as spiral nebulae. The spiral structure has been shown to exist in a few of them, but for the remainder it is only inferred. Nebulous stars are true stars surrounded by an atmosphere or aureole of nebulous light. Diffused nebulosities are very faint nebulae of enormous extent, sometimes forming the background of a whole constellation. ”

“ When space and time are relegated to their proper source—the observer—the world of nature which remains appears strangely unfamiliar; but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. ”

“ The comparative nearness of the stars, of the solar type, which we have had occasion to allude to, is confirmed by the fact, that their proper motions are on the average much larger than those of the Sirian stars. Kapteyn finds that magnitude for magnitude, the absolute brightness of the solar stars is only one-fifth of that of the Sirian stars, so that in the mean they must be at less than half the distance. As the numbers of known stars of the two types are nearly equal, it is clear that, at all events in our immediate neighbourhood, the solar stars must greatly outnumber the Sirian. ”

“ The theory of Larmor and Lorentz shows that if any system at rest in the aether is in equilibrium, a similar system in uniform motion through the aether, but with all lengths in the direction of motion diminished in FitzGerald's ratio, will also be in equilibrium so far as the differential equations of the electromagnetic field are concerned. There is thus a general theoretical agreement with the observed contraction, provided the boundary conditions at the surface of an electron behave in the same way. ”

“ The stars selected to be examined for parallax are usually either the brightest stars or those with an especially large proper motion. Neither criterion is a guarantee that the star shall have a measurable parallax. Brightness is particularly deceptive; thus Canopus, the second brightest star in the heavens, has probably a parallax of less than 0·01′′, and so also has Rigel. These two stars must have an intrinsic brilliancy enormously greater than that of the sun for if the sun were removed to such a distance (parallax 0·01′′) it would appear to be of about the tenth magnitude. ”

“ It must, however, be remembered that the identification with polar coordinates is only approximate; and, for example, an equally good approximation is obtained if we write , a substitution often used instead of since it has the advantage of making the coordinate-velocity of light more symmetrical.
We next work out analytically all the mechanical and optical properties of this kind of space-time, and find that they agree observationally with those existing round a particle at rest at the origin with gravitational mass . ”

“ Double nebulae have two principal centres of condensation. The planetary nebulae are nearly uniformly illuminated compact patches of light generally circular or elliptical in shape; they were so called because they appeared to possess disks like planets. Elliptical nebulae are usually nebulae of some flat type (such as annular or spiral) seen rather edgeways, so that the structure is not readily recognizable. The typical spiral nebulae are in the form of a double spiral, the two branches of which proceed from diametrically opposite points of a bright nucleus and wind round it in the same sense ”

“ As we consider a direction such as SQ farther and farther from the pole the boundary of the universe in that direction becomes more and more remote so that more stars are seen, and finally in the directions SR and SR′ in the galactic plane, the boundary is perhaps beyond the limits of our telescopes. That the universe must have a boundary in the directions SR and SR′, we can hardly doubt, but nothing is known of its shape or distance except that in all directions it must be far greater than SP or SP′ ”

“ By realising that an observer in the moving system would measure all velocities in terms of the local space and time of that system, Einstein removed the last discrepancies from Lorentz's transformation.
The relation between the space and time coordinates in two systems in relative motion was now obtained immediately from the principles of space and time-measurement. It must hold for all phenomena provided they do not postulate a medium which can serve as a standard for absolute location and simultaneity. ”

“ A continuous gradation can be traced from the most widely separated visual binaries, whose periods are many thousand years, to spectroscopic binaries, Algol and β Lyrae variables, whose periods are a few hours and whose components may even be in contact, and from these to dumb-bell shaped stars and finally to ordinary single stars. It is a legitimate speculation to suppose that these in the reverse order are the stages in the evolution of a double star. As the simple star radiates heat and contracts, it retains its angular momentum ”

“ But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles so lightly, may fairly be asked to state, not indeed the inscrutable meaning of in nature, but the meaning which conveys to him. ”

“ It is found that the following scheme of potentials rigorously satisfies the equations , according to the values of in Note 5, where and is any constant (see Report, § 28) . Hence these potentials describe a kind of space-time which can occur in nature referred to a possible mesh-system. If , the potentials reduce to those for flat space-time referred to polar coordinates; and, since in the applications required will always be extremely small, our coordinates can scarcely be distinguished from polar coordinates. ”

“ But even such an attempt to systematically plumb the universe can only make us acquainted with the merest inside shell. We should learn perhaps the distribution and luminosities of the stars within a sphere of radius sixty light years (corresponding to a parallax of about 0·05′′) , but of the structure of the million-fold greater system of stars, lying beyond this limit, yet visible in our telescopes, we should learn nothing except by analogy. ”

“ With catalogues containing fainter stars the proportion of large proper motions is somewhat smaller, thus the corresponding percentages for the Groombridge stars are 12 and 31 respectively.
When the parallax of a star is known, we are able to infer from its proper motion its actual linear speed in miles per hour, in so far as the motion is transverse to the line of sight. The velocity in the line of sight can be determined by spectroscopic observation, so that in a few cases the motion of the star is completely known. Several stars appear to have speeds exceeding 100 m. ”

“ The motion of the sun relative to the stars depends on what stars are selected as representative. There is no a priori reason to expect the same result from the different classes of stars, such as the brighter or fainter, northern or southern, nearer or more distant, Solar type or Sirian stars. There is for example some evidence that the declination of the solar apex is really increased when the motion is referred to fainter stars. ”

“ Stars of the different types are therefore not necessarily of different chemical constitution, but rather are in different physical conditions, and it is generally believed that every star in the course of its existence passes through stages corresponding to all (or most of) the different types. The stars are known to be continually losing enormous quantities of energy by radiating their heat into space. ”

“ It was early realized that the proper motions of the stars were changes of position relative to the sun, and that, if the sun had any motion, of its own as compared with the surrounding stars as a whole, this would be shown by a general tendency of the apparent motions of the stars to be directed away from the point to which the sun was moving. ”

“ Stars whose brightness fluctuates are called variable stars. The number of known objects of this class is being added to rapidly, and now amounts to over 4000. The systematic search made at Harvard Observatory is responsible for a large proportion of the recent discoveries. Many of these stars seem to vary quite irregularly; the changes of magnitude do not recur in any orderly way. Others, however, are periodic, that is to say, the sequence of changes is repeated at regular intervals, and it is thus possible to predict when the maximum and minimum brightness will occur. ”

“ The Structure of the Universe.—We now arrive at the greatest of all the problems of sidereal astronomy, the structure and nature of the universe as a whole. It can by no means be taken for granted that the universe has anything that may properly be called a structure. If it is merely the aggregate of the stars, eac.h star or small group of stars may be a practically independent unit, its birth and development taking place without any relation to the evolution of the whole. But it is becoming more and more generally recognized that the stars are not unrelated ”