In measuring proper motion, or radial velocity, our standard of reference is the sun ; and the foregoing result shows that the stars in the mean are travelling past the sun in the direction towards Columba. This however is rather an egocentric way of expressing the facts. It is more natural to say that the sun is travelling relatively to the mean of the stars in the opposite direction—towards a point in Hercules or Lyra not far from the bright star Vega. This point is called the solar apex, and the relative velocity that is found is the solar motion. Attempts to determine an accurate position of the solar apex are not very closely accordant, and it does not seem possible to fix it to within 5°. In particular, radial velocity determinations seem to give systematically a lower declination than the proper motions, and bright stars give a lower declination than faint stars. We could scarcely expect the apex to be definite, because the "mean of the stars" is an indefinite conception. The stellar background appears to consist of interpenetrating clusters with different motions, and the relative solar motion will depend on what part of this back ground is sampled by our observational data. In round figures the general result is: Solar apex, R.A. 270°, dec.--F3o° ; speed 20 km. per sec.
In measuring .the parallaxes of stars we use the diameter of the earth's orbit as base line—a length of two astronomical units. The solar motion of 20 km. per sec. transports the observer through 4.2 astronomical units per year, so that observations taken now and 5o years ago give us a base line of 210 astronomical units. With the longer base line it should be possible to survey the stellar system to a distance far exceeding that attainable by parallax measurement. The method cannot be applied to in dividual stars because the parallactic displacement cannot be discriminated from the star's own motion; but when we are dealing with a class of stars (e.g., stars of 9th magnitude, bright stars of type K, long-period variables, etc.) which are not likely to have any important common tendency of motion as compared with the general mean of the stars, the method will give the average parallax of the class. Fortunately, results obtained in this way can be checked by an independent determination based on similar principles. The cross proper motion, or component at right angles to the line towards the solar apex, is a component of the individual motion of the star; the radial velocity (after correcting for the known solar motion) is also a component of individual velocity. Hence, for a class of stars we can find the average value of a component of individual velocity both in arc and in linear measure ; comparing the two results we deduce the mean distance. These methods have proved extremely useful in supplementing the meagre knowledge of the distances and absolute luminosities of the stars furnished by direct parallax determinations. For still greater distances the method described under Cepheid Variables and analogous methods are employed.
common origin, i.e., are evolved from the same nebulous con densation. Apparently, having started to move together, they continue to move together simply because encounters which might deflect them are extremely rare. One of the arguments against the existence of great numbers of dark stars in space, is that their passage between the stars of the moving cluster would break it up too rapidly. There is a typical moving cluster in Taurus, studied by L. Boss, which includes many of the stars in the Hyades. The true motions of these stars must be very nearly equal and parallel, otherwise the cluster would rapidly disperse, but as projected on the sky they appear to converge towards one point. As the cluster covers a reasonably large area the convergent point can be found with considerable accuracy. By geometrical construction it becomes possible (without parallax measurement) to determine the distance of each star of the group and to find the precise arrangement of the stars in three dimen sions. Another cluster consists of five stars of the Plough together with Sirius and some other bright stars; the sun is in the midst of this moving cluster, so that its members appear in different parts of the sky. The stars of type B seem to have a special tendency to form associations of this kind ; one of the best marked groups consists of about 16 stars in Perseus and neighbouring constella tions. Perhaps the most important conclusion to be drawn from these clusters is that the stars are not born individually and independently, e.g., by accidental collisions of extinct stars, but that the evolutionary process of star formation is capable of generating a number of stars simultaneously.