irregular gaseous nebulae like the Orion nebula. A large obscuring tract in Taurus is estimated by A. Pannekoek to be at 140 parsecs distance; this may be compared with Kapteyn's value 190 parsecs for the Orion nebula. A catalogue of 182 dark markings in the sky has been given by E. E. Barnard (25).
Nebulae. Whereas the irregular gaseous nebulae are com- paratively near, and within the local star cloud, the spiral neb- ulae are now considered to be exceedingly remote perhaps more remote than the globular clusters. According to one view, they are " island universes " coequal with the great galactic system. Others would consider them rather as outlying dependencies. Unfortunately we have no trustworthy knowledge of their dis- tances; estimates have been made from the apparent magnitudes of the novae which have appeared in them, but these seem to be very speculative. The spirals have been found to possess extraor- dinarily great velocities in the line of sight and in general the motion is directed away from the sun. This seems to argue a lack of dynamical association with the galactic system. The mean speed of 15 spirals measured by Slipher, is about 400 km. per sec. Independent determinations by Slipher, Wright, and Pease agree well on a velocity of 300 km. per sec. for the Andromeda nebula; for some nebulae speeds exceeding 1,000 km. per sec. have been found. The Theory of Relativity suggests an interesting ex- planation of these high speeds, and more particularly the pre- ponderance of receding velocities. De Sitter's form of the theory of curved space-time actually predicts an effect of this kind for very remote objects (26).
The planetary nebulae are presumably much less distant. They have a well-marked galactic concentration; but the solar motion referred to them is apparently not the same as that referred to the stars. They do not show preferential motion along any axis. The average radial velocity is 30 km. per sec. about the same as that of the fastest class of stars (the red dwarfs). When the planetary nebulae are photographed with an objective prism of large dispersion, it is found that the various monochromatic images are of different forms and sizes; so that important information is obtained as to the distribution of the emitting gases through the nebula. Perhaps the most fundamental problem presented by these objects is whether all parts of the disc are independently self-luminous, or whether the light-emission is stimulated by radiation coming from a central star or nucleus.
II. THEORETICAL ASTRONOMY
Gravitation. The epoch-making theory of gravitation, put forward by Einstein in 191 5, is described in the article RELATIV- ITY. We refer to it here because the new law of gravitation, re- quired by his theory, removes the most outstanding divergence between theory and observation in the solar system viz. the progression of the perihelion of Mercury. There is still some discrepancy between theory and observation for the motion of the node of Venus; but this is a much smaller residual, and may perhaps even be attributable to accidental errors. Einstein's predicted deflection of light by the sun's gravitational field was verified by the British eclipse expeditions in 1919. His third crucial test a general displacement of spectral lines to the red in the sun as compared with terrestrial sources was still in 1921 a subject of controversy.
E. W. Brown's lunar theory, developed according to the meth- ods of G. W. Hill, was completed by the publication in 1920 of full Tables of the Moon's Motion. It seems safe to say that no term of appreciable significance has been omitted; nevertheless the moon deviates unmistakably from its theoretical place in an irregular manner. An investigation by H. Glauert (27) seems to show that the irregularities are at least partly due to varia- tions in the rate of our standard timekeeper, viz. the earth's rotation; for the longitudes of the sun, Mercury and Venus exhibit similar irregularities, and the curves closely resemble one another. Besides these irregular changes, there is a general secular acceleration of the moon, which, being cumulative, leads to large changes in the circumstances of ancient eclipses. The historical evidence of all kinds has been rediscussed by J. K. Fotheringham (28) who arrives finally at the values io"-s for the moon's secular acceleration 1 and i"-o for the sun's secular
'The moon goes ahead by the amount to'-sT 2 , where T is the time in centuries. This is the conventional definition of " secular acceleration " in this connexion.
acceleration. These quantities are presumably attributable to tidal friction which causes a direct acceleration of the moon's orbital motion, as well as a spurious acceleration through the increase in the length of the standard of time.
It is now believed that the bodily tides in the earth have little effect and that the most effective retardation is due to tides in land-locked and shallow seas. According to G. I. Taylor the Irish Sea alone contributes fa of the total dissipation of energy.
Evolution of Rotating Masses. The figures of equilibrium and the final disruption of rotating fluid masses have been studied in great detail by J. H. Jeans. In agreement with Liapounoff he has found that the so-called " pear-shaped " figure of equilibrium, which suc- ceeds the Jacobi ellipsoidal form, is unstable. For a full account of his conclusions as to the evolution of double stars, spiral nebulae and clusters reference must be made to his book Problems of Cosmogony and Stellar Dynamics. With regard to the solar system, he finds himself unable to account for the formation of the planets by rotation alone; and he attributes them to a tidal disruption of the sun hav- ing occurred at some distant epoch in the past. If this view is correct the system of the planets is a " freak of nature," owing its existence to a chance encounter of some larger star (which approached within less than the sun's diameter from its surface). Few, if any, other systems of this kind can have been formed; and the common view that the stars in general are attended each by a system of planets may be entirely mistaken.
Mathematical investigations of the possible steady states of a system of stars moving under gravitational forces have been made by Charlier, Jeans and Eddington (29). It appears that the actual con- ditions are such that each star describes an orbit under the averaged attraction of the whole mass, the casual perturbations of a star by its immediate neighbours being negligible. For a spherical distribu- tion, a steady system can be found in which there is preferential motion in a radial direction, illustrating H. H. Turner's explanation of star-streaming. An oblate system can also be in a steady state with radial star-streaming, provided that it is not alone but forms part of a larger system in which the mass as a whole is distributed spherically. It appears fairly certain, however, that an isolated oblate system moving under its own attraction cannot be in a steady state. For this and other reasons we believe that our own oblate stellar system is by no means in dynamical equilibrium, but is collapsing towards some more permanent form.
H. von Zeipel and H. C. Plummer (30) have found that the distri- bution of stars in globular clusters conforms to a definite law, which is in fact the adiabatic law of density of a gravitating sphere of gas for which 7 has the critical value 1-2. Although this appears to have important dynamical significance, no very satisfactory explana- tion can be given.
Radiative Equilibrium of the Stars. The discovery that many of the stars the giant stars are diffuse globes of very low density, gives a stimulus to investigations of their internal conditions of equi- librium; for the material, being practically a perfect gas, will obey comparatively simple laws. In the earlier researches of Lane and Ritter it was supposed that the equilibrium was adiabatic that is to say, the material was continually stirred by convection currents, hot gases ascending to replace the continually cooling material at the surface. But it is now clear that the heat passes to the surface not by material transfer but by radiation ; and the condition of equi- ibrium is that each element will settle down to the temperature at which it radiates an amount of heat equal to that which it absorbs
- rom the radiant heat flowing through it. This was first pointed out
as probable by R. A. Sampson, and the theory of radiative equili- brium was developed by K. Schwarzschild for the external layers of thesun. Eddington (31) has based on this principle a theory of the equilibrium throughout the interior of a star.
At first the principal unknown constant was the molecular weight of the material of the star. It was, however, pointed out by Newall and Jeans that the atoms were probably strongly ionized at the high
- emperatures prevailing; and this led to a simple solution of the
difficulty. The number of electrons surrounding the nucleus of any atom is approximately half the atomic weight ; hence if all the elec- trons break loose, the average molecular weight will in all cases be approximately 2, since each unattached electron counts as a separate molecule. lonization is probably not complete and both theory and >bservation seem to be best satisfied by a value between 3 and 4; )ut any large uncertainty as to the molecular weight is thus removed. The calculation shows that the rate of radiation of energy of a gas- eous (giant) star is given by :
where M is the mass, G the constant of gravitation, c the velocity of ight, k the mass-coefficient of absorption of radiation by the mate-
rial, and a constant depending on the mass and obtained by
solving the quartic equation
i -0 = 0-0026 M 2 m
where M is the mass in terms of the sun, and m the molecular weight n terms of the hydrogen atom. The density does not enter into
