In order that my readers may better understand the calculations of Lord Kelvin, and also the general conclusions of astronomers as to the form and dimensions of the stellar universe, I have drawn two diagrams, one showing a plan on the central plane of the Milky Way, the other a section through its poles. Both are on the same scale, and they show the total diameter across the Milky Way as being 3600 light-years, or about half that postulated by Lord Kelvin for his hypothetical universe. I do this because the dimensions given by him are those which are sufficient to lead to motions near the centre such as the stars now possess in a minimum period of twenty-five million years after the initial arrangement he supposes, at which later epoch which we are now supposed to have reached, the whole system would of course be greatly reduced in extent by aggregations towards and near the centre. These dimensions also seem to accord sufficiently with the actual distances of stars as yet measured. The smallest parallax which has been determined with any certainty, according to Professor Newcomb's list, is that of Gamma Cassiopeiæ, which is one-hundredth of a second (0".01), while Lord Kelvin gives none smaller than 0".02, and these will all be included within the solar cluster as I have shown it.
DIAGRAM OF STELLAR UNIVERSE (Section).
Section through Poles of Milky Way.
It must be clearly understood that these two illustrations are merely diagrams to show the main features of the stellar universe according to the best information available, with the proportionate dimensions of these features, so far as the facts of the distribution of the stars and the views of those astronomers who have paid most attention to the subject can be harmonised. Of course it is not suggested that the whole arrangement is so regular as here shown, but an attempt has been made by means of the dotted shading to represent the comparative densities of the different portions of space around us, and a few remarks on this point may be needed.
The solar cluster is shown very dense at the central portion, occupying one-tenth of its diameter, and it is near the outside of this dense centre that our sun is supposed to be situated. Beyond this there seems to be almost a vacuity, beyond which again is the outer portion of the cluster consisting of comparatively thinly scattered stars, thus forming a kind of ring-cluster, resembling in shape the beautiful ring-nebula in Lyra, as has been suggested by several astronomers. There is some direct evidence for this ring-form. Professor Newcomb in his recent book on The Stars gives a list of all stars of which the parallax is fairly well known. These are sixty-nine in number; and on arranging them in the order of the amount of their parallax, I find that no less than thirty-five of them have parallaxes between 0".1 and 0".4 of a second, thus showing that they constitute part of the dense central mass; while three others, from 0".4 to 0".75, indicate those which are our closest companions at the present time, but still at an enormous distance. Those which have parallaxes of less than the tenth and down to one-hundredth of a second are only thirty-one in all; but as they are spread over a sphere ten times the diameter, and therefore a thousand times the cubic content of the sphere containing those above one-tenth of a second, they ought to be immensely more numerous even if very much more thinly scattered. The interesting point, however, is, that till we get down to a parallax of 0".06, there are only three stars as yet measured, whereas those between 0".02 and 0".06, an equal range of parallax, are twenty-six in number, and as these are scattered in all directions they indicate an almost vacant space followed by a moderately dense outer ring.
In the enormous space between our cluster and the Milky Way, and also above and below its plane to the poles of the Galaxy, stars appear to be very thinly scattered, perhaps more densely in the plane of the Milky Way than above and below it where the irresolvable nebulæ are so numerous; and there may not improbably be an almost vacant space beyond our cluster for a considerable distance, as has been supposed, but this cannot be known till some means are discovered of measuring parallaxes of from one-hundredth to one five-hundredth of a second.
These diagrams also serve to indicate another point of considerable importance to the view here advocated. By placing the solar system towards the outer margin of the dense central portion of the solar cluster (which may very possibly include a large proportion of dark stars and thus be much more dense towards the centre than it appears to us), it may very well be supposed to revolve, with the other stars composing it, around the centre of gravity of the cluster, as the force of gravity towards that centre might be perhaps twenty or a hundred times greater than towards the very much less dense and more remote outer portions of the cluster. The sun, as indicated on the diagrams, is about thirty light-years from that centre, corresponding to a parallax of a little more than one-tenth of a second, and an actual distance of 190 millions of millions of miles, equal to about 70,000 times the distance of the sun from Neptune. Yet we see that this position is so little removed from the exact centre of the whole stellar universe, that if any beneficial influences are due to that central position in regard to the Galaxy, it will receive them perhaps to as full an extent as if situated at the actual centre. But if it is situated as here shown, there is no further difficulty as to its proper motion carrying it from one side to the other of the Milky Way in less time than has been required for the development of life upon the earth. And if the solar cluster is really sub-globular, and sufficiently condensed to serve as a centre of gravity for the whole of the stars of the cluster to revolve around, all the component stars which are not situated in the plane of its equator (and that of the Milky Way) must revolve obliquely at various angles up to an angle of 90°. These numerous diverging motions, together with the motions of the nearer stars outside the cluster, some of which may revolve round other centres of gravity made up largely of dark bodies, would perhaps sufficiently account for the apparent random motions of so many of the stars.
Uniform Heat-Supply due to Central Position
We now come to a point of the greatest interest as regards the problem we are investigating. We have seen how great is the difference in the estimates of geologists and those of physicists as to the time that has elapsed during the whole development of life. But the position we have now found for the sun, in the outer portion of the central star-cluster, may afford a clue to this problem. What we require is, some mode of keeping up the sun's heat during the enormous geological periods in which we have evidence of a wonderful uniformity in the earth's temperature, and therefore in the sun's heat-emission. The great central ring-cluster with its condensed central mass, which presumably has been forming for a much longer period than our sun has been giving heat to the earth, must during all this time have been exerting a powerful attraction on the diffused matter in the spaces around it, now apparently almost void as compared with what they may have been. Some scanty remnants of that matter we see in the numerous meteoric swarms which have been drawn into our system. A position towards the outside of this central aggregation of suns would evidently be very favourable for the growth by accretion of any considerable mass. The enormous distance apart of the outer components (the outer ring) of the cluster would allow a large amount of the inflowing meteoritic matter to escape them, and the larger suns situated near the surface of the inner dense cluster would draw to themselves the greater part of this matter.[23] The various planets of our system were no doubt built up from a portion of the matter that flowed in near the plane of the ecliptic, but much of that which came from all other directions would be drawn towards the sun itself or to its neighbouring suns. Some of this would fall directly into it; other masses coming from different directions and colliding with each other would have their motion checked, and thus again fall into the sun; and so long as the matter falling in were not in too large masses, the slow additions to the sun's bulk and increase of its heat would be sufficiently gradual to be in no way prejudicial to a planet at the earth's distance.