we can calculate that a globe of gas having the mass and density of 5 Cephei will vibrate in a period between 4 and 10 days (varying between these limits according to the adiabatic constant of the material of which it is composed); the observed period is 5-37 days. The most serious objection urged against the pulsation theory of Cepheids is that it requires a broadening of the spectral lines at minimum and maximum, because all parts of the disc would not be moving with the same speed in the line of sight; this has not yet been observed. It is to be hoped that this crucial but rather difficult effect will be thoroughly sought for in the near future. It may be remarked that some variation of light will arise directly from the dilatation and contraction of the surface; but this is not the leading variation since the actual maxima and minima occur when the star is passing through its mean volume. The indirect effect of the compression, changing the rate of flow of radiation, is much more important; and although the detailed mathematical discussion of the problem has not proved tractable, there is a general accordance of theory and observation.
The name "Cepheid" was at first restricted to stars with periods usually between three and eight days; but longer and shorter periods' have been found, and it is now recognized that the "cluster variables" with periods less than a day are of the same nature. These occur abundantly in several of the globular clusters. In examining a globular cluster we have the great advantage that all the stars under review are at practically the same distance from us, so that apparent differences of brightness are real differences of brightness, and are not confused by effects of distance. Now it is found that in a globular cluster Cepheids of the same period have all the same brightness; so that a Cepheid of definite period is a standard object, whose absolute brightness will presumably be the same under all circumstances. This remarkable uniformity was first noticed by Miss Leavitt for the variables in the Lesser Magellanic Cloud; the results have since been extended by Shapley who has calculated the curve connecting luminosity with period. It appears that the Cepheids are among the brightest and probably the most massive stars, ranging in absolute magnitude from I M ~5 for periods of three days to 4 M -o for 18 days, and so on. Most are of spectral type F G, becoming redder as the period lengthens; those with periods under a day are of type A. The range of the variation in magnitude is generally between o"-5 and oP'-q, but doubtless many with smaller variations escape notice. The Pole Star is a Cepheid with a light range of only o m -l and a period of 3-97 days.
Novae. Two "new stars" of unusual brilliance have appeared in recent years. Nova Aquilae III. was discovered independently by a great many observers on June 8 1918, when it was already a first-magnitude star. Its earlier history has been supplied from an examination of photographic records of the sky. From 1888 onwards it remained steady at io m -s and a photograph taken by Max Wolf three days before discovery showed that it was still normal. Incidentally we may note that it cannot have been a red star (types K or M) or it would have appeared in visual catalogues. On June 7 it had reached 6 m according to a Harvard photograph. The next day (when it was discovered) it had brightened to o m -8; and on June 9 it was only slightly inferior to Sirius. Then followed the usual slow decline with occasional fluctuations; and it had faded to s m -s by the end of October. W. F. Denning discovered a Nova in Cygnus on August 20 1920, which reached the second magnitude. Its earlier history is unknown, but it must have been fainter than is m in 1908.
Broadly speaking each Nova reproduces the same sequence of phenomena with remarkable faithfulness (15). At the brightest the spectrum is that of a star of type A$. A few days later broad emission lines appear by the side of corresponding absorption lines which are strongly displaced to the violet. The absorption lines become doubled and tripled, as though there were several layers of uprushing gas travelling at different speeds in the line of sight. About a fortnight after maximum bright nebula lines appear; the continuous spectrum weakens and the star's light now comes mainly from emission lines. After some months the spectrum approximates to that of a planetary nebula. The great speed of upward rush of the absorbing gases is very remarkable, velocities of the order 2,000 km. per sec. being observed; there is no reason to doubt that these velocities are genuine, for the star expands and in the later stages shows a visible disc in large telescopes. The observed rate of spreading seems to agree with the speeds indicated by the spectroscope. Many theories have been suggested to account for the outbreak. A collision of two stars seems unlikely on account of its statistical improbability; and, moreover, the regular sequence of changes could scarcely be started by a haphazard impact. An eruption from within, whether occurring spontaneously at a certain stage of evolution or precipitated by the entry of the star into a nebula, may be more likely; but this theory also presents difficulties. J. H. Moore has recently obtained evidence that the extended nebulous disc, which is ultimately formed, shows differential motions of rotation in different parts. In any case it seems likely from the very rapid sequence of changes that the main outbreak is only skin-deep.
Novae always occur within the limits of the Milky Way (or in spiral nebulae) ; but this may perhaps be due to the greater depth of the stellar universe in this direction. So far as can be judged the Nova before the outbreak is a dwarf star; and at least in the case of Nova Aquilae it cannot have been a very red star. (The long-period vari- ables, whose violent outbreaks are rather suggestive of the explosion of a Nova, are giant red stars.) We may meditate on the fact that the stars subject to these catastrophes are probably in about the same stage of evolution as that through which the sun is now passing. Stellar Velocities. In 1910 J. C. Kapteyn and W. W. Campbell announced independently that (after allowing for the solar motion) the average speeds of the stars increase continuously as we pass through the spectral series from type B to type M. Kapteyn deduced the result from the proper motions, and Camp- bell from the spectroscopic radial velocities. At that time the older view, that the progression from B to M was the order of evolution, held the field; and it seemed as though the motion of a star must increase as it grows older. But the giant and dwarf theory shows that it is not a question of stage of evolution. Take for example Campbell's figures: the average radial speeds are type B, 6-5; A, 10-9; F, 14-4; G, 15-0; K, 16-8; M, 17-1 km. per second. In this investigation the K and M stars were almost all giants, so that so far as this analysis goes the youngest stars have the highest speeds; but Eddington found that the dwarf K and M stars at the other extreme in the sequence of evolution have still higher speeds. Of the 19 nearest stars, the nine brightest have a mean transverse speed of 29 km. per sec. (corresponding to a mean radial speed of 18-5 km. per sec.) whereas the 10 faintest, with luminosities less than X sun, have a mean transverse speed of 68 km. per sec. ( = radial speed 43 km. per sec.). W. S. Adams confirmed this by determination of the radial velocities; of 16 stars whose luminosity is less than j^ X sun, the mean radial velocity is 36 km. per sec. or more than twice that of the giant stars of the same type.
Similar results were found in a more extensive statistical investigation by Eddington and Hartley. Finally Kapteyn and Adams (16) announced a general progressive dependence of velocity on absolute brightness, the faintest stars having the greatest average speed. We see then that there is a correlation of speed both with spectral type and with luminosity. It seems likely that the primary association is between speed and mass, the dependence on luminosity and spectral type being due to the correlation of these with mass; as already mentioned, only the most massive stars can reach the hottest spectral types. If this view is correct we must regard the quick-moving dwarf stars of types K and M as having particularly low masses either because the smallest stars run their course of evolution more quickly, or because mass has been lost along with the energy radiated during their past history. The last suggestion may seem extravagant, but it must be pointed out that all energy has mass; so that a radiating star is continually losing mass; the only question is whether the life of the star is long enough for this loss of mass to amount to anything appreciable; and as to the length of life the most widely divergent views are current. With regard to the explanation of this association of speed and mass, J. Halm (17) has advocated the tempting hypothesis that it is an example of the equipartition of energy brought about by the laws of statistical dynamics exactly as in a gas where molecules of different masses are mixed. But starting with an arbitrary mixture of stellar velocities, it would take about lo 15 years to approach this equipartition by mutual perturbations of the stars; and most astronomers shrink from attributing such an age to the stellar universe. A simpler suggestion is that the small stars were formed in the outer parts of the stellar system, where star-forming material was more 'rarefied; and they have acquired greater velocities by the longer fall towards the central region where we now observe them.
The Star Streams. Many researches have confirmed Kapteyn's discovery that the stars (or at least those near enough for investigation) move preferentially in two favoured directions. Since the article STAR (see 25.784) was written, the spectroscopic radial velocities have become available for testing the theory and they confirm it decisively. Relatively to the sun the favoured directions are inclined at about 120 (the apices being at R.A.96 Dec.+8, and R.A.2QO , Dec. -54); but referred to the mean of the stars they are necessarily two opposite directions along a straight line. The extremities of this axis of preferential motion are called the vertices. The following appear to be the most accurate determinations of the vertex by the two independent methods (18):
From proper motions (Boss's catalogue) R.A.94-2, Dec. + 1 1 -9- From radial velocities (Lick catalogues) R.A.94-6, Dec. + i2 -5-