values in life, this institution has a field of great usefulness lying before it. In their administration of the generous gift, the trustees, the president and the faculty of the Case School of Applied Science, whether for research, for school instruction or for community education, will have the sympathetic interest of astronomers, of all lovers of the truth. This observatory may assist in the solution of important problems concerning the universe of which we form a part. The universities, the colleges, and the technical schools of our country, and of other countries, are graduating every year many hundreds of young men, ready to start upon the more serious phases of their lives, who can tell us all about the lights in our houses, but not one word about the lights in our sky. This institution will do its quota in approximating to a liberal education. The casual visitor who enters its portals in search of knowledge, yea, the passerby in the street who merely sees a dignified and purposeful observatory set upon a hill, will have his thoughts directed to higher levels.

COSMOGONY AND STELLAR EVOLUTION.1

By J. H. JEANS, F. R. S.

I. THE EVOLUTION OF GASEOUS MASSES.

The progress of observational astronomy has made it abundantly clear that astronomical formations fall into well-defined classes: they are almost "manufactured articles" in the sense in which Clerk Maxwell applied the phrase to atoms. Just as atoms of hydrogen or calcium are believed to be of similar structure no matter where they are found, so star-clusters, spiral nebulæ, binary stars are seen to be similar, although in a less degree, no matter in what part of the sky they appear. The problem of cosmogony is to investigate the origins of these comparatively uniform formations and the process of transition from one class to another.

In attacking this problem the cosmogonist of to-day stands upon the shoulders not only of previous cosmogonists, but also, what is of even greater importance, upon the shoulders of the brilliant and industrious astronomical observers of the past century. We shall find it convenient to take as our starting point the most famous theory of cosmogony ever propounded-the nebular hypothesis of Laplaceand we shall examine to what extent it remains tenable in the light of modern observational and theoretical research.

Laplace's hypothesis referred primarily to the genesis of the solar system, which he believed to have originated out of a hot nebulous mass that shrank as it cooled. The nebula was supposed to be in rotation, so that the principle of conservation of angular momentum required that as the mass cooled its speed of rotation should increase. It is well known that a mass either of gas or of liquid in rotation can not rest in equilibrium in the spherical shape which would be assumed in the absence of rotation. If the rotation is very slow the equilibrium shape will be an oblate spheriod of small eccentricity. As the rotation increases, the ellipticity will increase, but it is found that the spheroidal shape is soon departed from. Laplace believed, as a matter of conjecture rather than of reasoned proof, that with con

1 Lectures delivered at King's College, London, on May 3 and 10, 1921. Reprinted by permission from Nature, June 30 and July 7, 1921.

tinually increasing rotation a mass of gas would in time reach a stage at which it could no longer exist as a single continuous mass. When this stage was reached he believed that a ring of particles would be discharged from the equator through the centrifugal force of rotation outweighing the centripetal force of gravitation. The mathematical researches of Roche (1873) provided some support for this general conjecture, and more recent investigations put its general accuracy beyond doubt.

It is found that the changes of shape which accompany increase of rotation are, in their general features, the same for all masses, whether gaseous or fluid, provided only that there is sufficient central condensation of mass. When the rotation becomes so great that the spheroidal figure is departed from, the equator of the mass is found to pull out into a pronounced edge, which ultimately becomes perfectly sharp (see fig. 1). The mass has now assumed a lenticular shape, and any further increase of rotation results in matter being discharged from this sharp edge. The lenticular shape is retained from now on, the sharp edge acting like a safety valve and emitting just so much matter as is necessary to carry off the excess of angular momentum beyond the maximum which can be carried by the central mass. Figure 1 shows the configurations of the lenticular figures

FIG. 1.-Figures of equilibrium for rotating masses of gas.

for masses of gas in adiabatic equilibrium,in which y (ratio of specific heats) has the extreme values 1.2 and 2.2, respectively. Other calculated lenticular figures show generally similar shapes. With a further increase of rotation beyond that for which these curves are drawn, the figures would remain unaltered save for the addition of a distribution of matter in the equatorial plane-the matter already thrown off from the sharp edge of the lens.

If gaseous stars assume these forms our telescopes refuse to reveal them. Even in the most powerful telescopes the stars remain infinitesimal points of light; the only bodies which show any observable shape are the nebulæ. It is highly significant that a number of these exhibit precisely the lenticular shape just described. This is in most cases accompanied by a distribution of matter in the plane through the sharp edge of the lens. A number of such nebulæ have been found by direct spectroscopic observation to be in rotation about an axis perpendicular to this plane. Thus there is very strong justification for supposing that these nebulæ are masses of gas or other mat

ter with high central condensation behaving precisely as imagined by Laplace-rotating and throwing off their excess of angular momentum as they cool by the ejection of matter in their equatorial planes.

There is, however, almost incontrovertible evidence that the nebulæ which have just been described are nothing but ordinary spiral nebulæ seen edgewise, for observation discloses a continuous sequence of nebulæ the shapes of which bridge completely the gap between the lenticular nebula, in which we are looking at right angles to the axis of rotation, and the familiar spiral nebula in which we look approximately along this axis. The characteristic nebula shows a nucleus which we can now identify with the lenticular figure demanded by theory, having two arms emerging symmetrically from opposite points of the nucleus. If our identification is correct these arms must be formed out of the matter already discharged from the nucleus. It has in point of fact been found by van Maanen and Kostinsky that the matter in the arms appears to be in motion approximately along the arms and in the outward direction.

Any external gravitational field, whether of the universe as a whole or of neighboring stars or nebulæ, would produce a tidal field similar to that produced by the sun and moon on the surface of our earth, a field specified mathematically by a second harmonic. This field, no matter how small in amount, would suffice to destroy the exact circular shape of the "equator" of the nucleus and so would concentrate the emission of matter at two opposite points on this equator. Thus it is easy to understand why the nebulæ, as a rule, exhibit two symmetrical arms emerging from antipodal points. It is very much less easy to understand why these arms should be of the universal spiral form the absence of any explanation of this form must be regarded as a serious drawback to our interpretation of the spiral nebulæ. It is readily proved that the ejected filaments of matter, whatever the shape they assume, could not remain of uniform line-density. Such a distribution of density would be unstable, and it can be proved that nuclei would form at approximately equal distances, around which the matter of the arms would condense. In this way it is possible to explain the nuclei and condensations which are observed in the arms of the spiral nebulæ. It is also found possible to calculate the amount of matter which will condense around each nucleus; the mass of each is found to be of the order of magnitude of the known masses of the stars.

In this way I have been led to conjecture that the spiral nebulæ are whirling masses of gas which, owing to their rapidity of rotation, throw off gaseous stars much as a "Catherine-wheel " firework throws off sparks. If so, the condensations in the arms of these nebulæ are stars in the process of birth. Dynamically the mechanism is almost

identical with that imagined by Laplace as resulting in the birth of systems of planets and satellites, but on a far more stupendous scale. The final product of the chain of events we have been considering must be some type of star cluster-perhaps a globular star cluster, or possibly an "island universe" similar to our galactic system. The difficulties in the way of an exact mathematical investigation into the history of the ejected gas, as the filaments condense around nuclei and as these form stars and begin to move as detached bodies, are enormous. On the other hand, the determination of the final steady states possible for a system of stars created in this way is quite simple. There is found to be only one type of final steady state possible for a system of stars created out of a rotating mass of gas, and this shows exactly the features presented by the system of stars of which our sun is a member. The system of stars will be of a flattened shape, symmetrical about the plane of greatest crosssection (the galactic plane in our system); the velocities in any small region of space will not be distributed at random, but will show a preference for two opposite directions ("star streaming "); these directions will be parallel to the plane of symmetry and perpendicular to the radius to the center of the system. This last direction is that given by Charlier for the direction of "star streaming " in our system. Our system passes all tests for having been born out of a spiral nebula the plane of which was what is now the plane of the Milky Way; indeed, Easton and others have claimed to find traces of the two spiral arms still surviving in the distribution of stars in this plane, as though the final steady state had not yet been reached.

one.

[Added February, 1922.-The test, however, is not a very stringent For if a number of stellar systems, each one of which had been born out of a rotating nebula in the way we have imagined, were to fall together as the result of gravitational action and unite into a single giant system of stars, it can be shown that this giant system, if or when it attained a steady state, would show precisely these same properties. Thus our test leaves it an open question whether our universe has been born out of a single nebula or out of a great number of smaller nebulæ. It probably accords best with present observational knowledge to suppose that our universe has been formed by the intermingling of a large number of separate star groups each of which is the product of a single spiral nubula. The globular clusters may well be groups of this type which have not yet mingled with the main mass of stars, while the moving star clusters, such as the Taurus cluster, the Ursa-major cluster, and possibly also the whole system of the B-type stars, may be groups, or the remains of groups, which have fallen into the main mass and become inter