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Rh It is significant that the line of preferential motion lies exactly in the galactic plane. The phenomenon may be due to two great systems of stars passing through one another; or it may represent some dynamical condition of a single system. The latter view has often been favoured, mainly owing to the very elegant mathe- matical specification of the corresponding velocity distribution given by K. Schwarzschild's ellipsoidal theory (19).

H. H. Turner (20) suggests that if the stars were originally formed as an extended system with little or no initial motion, the system would settle down to a steady state in which the motions were pre- ponderatingly radial; so that, assuming that the sun is placed ex- centrically, the stars in its neighbourhood would be moving prefer- entially in the line towards and away from the centre. An analogy is afforded by the comets in the solar system, which, observed from an outer planet, would appear to move preferentially towards and away from the sun. This explanation seems satisfactory on the whole. It may be objected that, according to statistics of distribu- tion of the stars, the dynamical centre of the stellar system appears to be, not in the direction of the vertex, but 90 away ; and the view favoured by Stromberg and by Jeans is that the star-streaming is due to predominant transverse (circular) motion rather than radial motion. It is difficult to see how such a state of motion could orig- inate. H. Shapley has, however, shown that the " local system " (considered in studies of stellar distribution) is but a small part of a greater galactic system ; we are on the outskirts of the latter, and its centre is in the direction R.A.262, Dec. 30, agreeing reason- ably well with the line of preferential motion.

The more detailed study of the systematic motions of the stars leads to great complexity. After the first approximation outlined above, we have to recognize a third drift, pointed out by J. Halm, which seems to be nearly at rest relative to the mean of the other two. The striking feature is that the type B stars appear to belong to this third drift, and a statistical discussion of their motions shows no indication of the preferential motion, which is always conspicu- ously manifested (though in somewhat different degrees) by the stars of other types. All this complexity is probably a sign that the stellar system is not in any approximate equilibrium, but is progress- ing towards a steadier configuration.

Moving Clusters. Many years ago R. A. Proctor pointed out a group of stars in the neighbourhood of the Hyades with prac- tically equal proper motions; the researches of L. Boss (21) have thrown new light on the nature of this association. He recognized as belonging to the group 39 stars spread over an area 15 square; the motions appear to converge towards a certain point in the sky a perspective effect which would naturally occur if the actual motions in three dimensions are parallel; the direction of the convergent point gives the direction of the common motion of the group relative to the sun.

Knowing the spectroscopic radial velocity of one or more mem- bers, we can by an easy geometrical construction find the whole linear velocity and also locate each star separately in space. We thus obtain exceptionally full and exact information as to the dis- tances and luminosities of this group of stars. The cluster is roughly spherical with a diameter of 10 parsecs; there must be many non- associated stars accidental interlopers in so large a region and perhaps the most significant conclusion is that the casual attractions of these stars have not been able during the lifetime of the cluster to disturb appreciably the parallelism of the motions and so scatter the cluster. Another remarkable " moving cluster " is formed of five stars of the Plough together with stars widely separated in the sky, including Sirius, a Coronae and Eridani. Similar associations are specially frequent among stars of the B type of spectrum, one of the most distinct being a chain of stars crossing the constellation Perseus.

Number and Distribution of Stars. Important statistics of the number of stars down to various limits of magnitude have been obtained by Chapman and Melotte and by P. J. van Rhijn. We give some results of the latter investigation which is the more recent (22).

The total number of stars down to photographic magnitude l6 m -o is 33,000,000 ; by a somewhat risky extrapolation it is estimated that the total number of stars in the system is between three and four thousand millions, and to reach half this number it would be neces- sary to go as far as magnitude 25 ra -5. (Exactly what is meant by the "system" in the foregoing sentence is somewhat difficult to de- fine; there may, of course, be exterior galaxies or extensions which are not reckoned in these counts.) An important point is the well- known flattened distribution of the stars; up to magnitude I6 m , the stars are distributed in the galactic plane 55 times as thickly as at the galactic poles. This is an increase compared with the con- centration of the brighter stars; up to magnitude 5 m, the corre- sponding ratio is 2\. We can easily understand this greater concen- tration of the faint stars, since on the average they carry us to

greater distances, at which the oblate shape of the stellar system has more pronounced effect.

Taking a lower limit of luminosity 1/200 X sun, it is estimated that there are 30 stars within a sphere of five parsecs radius round the sun ; about 20 of these have actually been identified. If this, star density persisted, a sphere of 1,500 parsecs radius would con- tain 800 million stars, besides an unknown but probably rather large number of extinct stars and of stars giving less than i/2ooth of the sun's light. This gives some idea of the possible extent of the star cloud to which we belong; there can be little doubt that the density must fall off very considerably at distances not greater than 1,500 parsecs, more especially in the directions of the galactic poles.

The following table based on an investigation by Kapteyn, van Rhijn and Weersma (23) shows the average parallax of stars of different magnitudes:

Mag.

Mean Parallax.

Mag.

Mean Parallax.

I m -O 2 m -0

3 m ' 4 m -o 5 m - 6 m -o

060"

044" 032" 023" 017" 012"

7 m -o 8 m -o 9 m -o

IC^-O II m -0 I2 m -p

0090" 0065" 0047' 0034' 0025' 0018"

It is an even chance that a particular star has a parallax between 0-23 and 1-13 times the average parallax for its magnitude.

Globular Clusters. About 70 globular clusters are known, distinguishable from the loose irregular star clusters by their symmetrical and condensed appearance. These have been the subject of a remarkable series of researches by H. Shapley (24).

It has already been mentioned that some of them contain many Cepheid variables, whose absolute luminosities are known from their periods. Thus in Messier 3 (Canes Venatici) the mean magnitude of no Cepheid variables is I5 m -so, the individual stars deviating as a rule no more than o-! from this mean. In the cluster a Centauri 76 variables concentrate with similar closeness about a mean magnitude !3 m -57. It is clear that the difference l m -93 must correspond to the greater distance of Messier 3; and we easily deduce that the ratio of the distances is 2-43, this ratio being very accurately determined. We are not quite so certain of the absolute distances of the two clusters ; but the evidence seems to indicate that the absolute magnitude of these variables (with periods less than a day) is o"-2, which gives the following distances o> Centauri, 5,800 parsecs; Messier 3, 14,000 parsecs. When it is recalled that the usual trigonometrical method can scarcely be applied to deter- mining distances greater than 20 parsecs, the extraordinary power of this method of plumbing space will be realized. The method was first used by E. Hertzsprung to determine the distance of the Lesser Magellanic Cloud.

By this method, and by supplementary devices, Shapley has been able to plot the distribution of the globular clusters in space and to form an idea of the extent of the system which they outline. Even in this vaster system the galactic plane is still a plane of symmetry and of flattening though the clusters extend to great distances above and below, the average distance from the plane being eight kilopar- secs. In plan the system is elongated with its axis in galactic longi- tude 325 nearly the direction of star streaming; the greatest diameter is at least 60 kiloparsecs, and the sun is near one end of it so that practically all the globular clusters are found in one hemi- sphere of the sky. The most remote cluster known is distant 67 kiloparsecs or 200,000 light years. We have to recognize that the "stellar system," dealt with in the researches described previously, is but a small star cloud in this greater galactic system. Roughly speaking those researches may be considered to relate to a domain of about 800 parsecs radius; the sun seems to be fairly centrally placed in the local star cloud (about 90 parsecs from the centre, according to Charlier), but this is on the outskirts of a greater sys- tem whose centre is 20,000 parsecs away.

In the foregoing deductions Shapley neglects any possible loss of apparent brightness owing to absorption of light in space. Any- thing of the nature of a fog or scattering medium would cause greater loss of light in the blue than in the red, and would con- sequently betray itself by a general reddening of the light of the more distant stars. Such a reddening has been sought for by King, Kapteyn, H. S. Jones, and others, and provisional estimates of the extinction have been made. Shapley considers that the extinction must be altogether negligible, resting his case on the observation that the colour-indices of stars in clusters range from O^-S to + l m '9 just as those of the nearer stars do. It seems therefore im- possible that their light can have been reddened by a scattering medium. The general absorption in space must be so low that a ray of light proceeding through interstellar space can travel for 3,000 years without meeting obstacles sufficient to deflect I % of its intensity. Nevertheless there are large tracts of obscuring mate- rial in particular regions, which hide more or less completely the stars behind. These are found especially in the Milky Way, and consist of dark or faintly-luminous nebulae often of great extent; perhaps there is no hard and fast division between them and the