If we examine the beautiful photographs of nebulæ by Dr. Roberts and other observers, we find that they are of many forms. Some are extremely irregular and almost like patches of cirrus clouds, but a large number are either distinctly spiral in form, or show indications of becoming spiral, and this has been found to be the case even with some of the large irregular nebula. Then again we have numerous ring-formed nebulæ, usually with a star involved in dense nebulosity in the centre, separated by a dark space of various widths from the outer ring. All these kinds of nebulæ have stars involved in them, and apparently forming part of their structure, while others which do not differ in appearance from ordinary stars are believed by Dr. Roberts to lie between us and the nebula. In the case of many of the spiral nebulæ, stars are often strung along the coils of the spiral, while other curved lines of stars are seen just outside the nebula, so that it is impossible to avoid the conclusion that both are really connected with it, the outer lines of stars indicating a former greater extension of the nebula whose material has been used up in the growth of these stars. Some of these spiral nebulæ show beautifully regular convolutions, and these usually have a large central star like mass, as in M. 100 Comæ and I. 84 Comæ, in Vol. II. Pl. 14 of Dr. Roberts's photographs. The straight white streaks across the nebula of the Pleiades and some others are believed by Dr. Roberts to be indications of spiral nebulæ seen edgewise. In other cases, clusters of stars are more or less nebulous, and the arrangement of the stars seems to indicate their development from a spiral nebula. It is to be noted that many of the objects classed as planetary nebulæ by Sir John Herschel are shown by the best photographs to be really of the ring-type, though often with a very narrow division between the ring and the central mass. This form may therefore be of frequent occurrence.
But if this annular form with some kind of central nucleus, often very large, is produced under certain conditions by the action of the ordinary laws of motion upon more or less extensive masses of discrete matter, why may not the same laws acting upon similar matter once dispersed over the whole extent of the existing stellar universe, or even beyond what are now its farthest limits, have led to the aggregation of the vast annular formation of the Milky Way, with all the subordinate centres of concentration or dispersal to be found within or around it? And if this is a reasonable conception, may we not hope that by a concentration of attention upon a few of the best marked and most favourably situated annular and spiral systems, sufficient knowledge of their internal motions may be obtained which may serve as a guide to the kind of motion we may expect to find in the great galactic ring and its subordinate stars? We may then perhaps discover which now seem so erratic, are really all parts of a series of orbital movements limited and controlled by the forces of the great system to which they belong, so that, if not mathematically stable, they may yet be sufficiently so to endure for some thousand millions of years.
It is a suggestive fact that the calculated position of the 'solar apex'—the point towards which our sun appears to move—is now found to be much more nearly in the plane of the Milky Way than the position first assigned to it, and Professor Newcomb adopts, as most likely to be accurate, a point near the bright star Vega in the constellation Lyra. Other calculators have placed it still farther east, while Rancken and Otto Stumpe assign it a position actually in the Milky Way; and Mr. G.C. Bompas concludes that the sun's plane of motion nearly coincides with that of the Galaxy. M. Rancken found that 106 stars near the Milky Way showed, in their very small proper motions, a drift along it in a direction from Cassiopeiæ towards Orion, and this, it is supposed, may be partly due to our sun's motion in an opposite direction.
In many other parts of the heavens there are groups of stars which have almost identical proper motions—a phenomenon which the late R.A. Proctor termed 'star-drift'; and he especially pointed out that five of the stars of the Great Bear were all drifting in the same direction; and although this has been denied by later writers, Professor Newcomb, in his recent book on The Stars, declares that Proctor was right, and explains that the error of his critics was due to not making allowance for the divergence of the circles of right ascension. The Pleiades are another group, the stars of which drift in the same direction, and it is a most suggestive fact that photographs now show this cluster to be embedded in a vast nebula, which, therefore, has also a proper motion; but some of the smaller stars do not partake of it. Three stars in Cassiopeiæ also move together, and no doubt many other similarly connected groups remain to be discovered.
These facts have a very important bearing on the question of the motion of our sun in space. For this motion has been determined by comparing the motions of large numbers of stars which are assumed to be wholly independent of each other, and to move, as it were, at random. Miss A.M. Clerke, in her System of the Stars, puts this point very clearly, as follows: 'For the assumption that the absolute movements of the stars have no preference for one direction over another, forms the basis of all investigations hitherto conducted into the translatory advance of the solar system. The little fabric of laboriously acquired knowledge regarding it at once crumbles if that basis has to be removed. In all investigations of the sun's movement, the movements of the stars have been regarded as casual irregularities; should they prove to be in any visible degree systematic, the mode of treatment adopted (and there is no other at present open to us) becomes invalid, and its results null and void. The point is then of singular interest, and the evidence bearing upon it deserves our utmost attention.'
Mr. W.H.S. Monck, a well-known astronomer, takes the same view. He says: 'The proof of this motion rests on the assumption that if we take a sufficient number of stars, their real motions in all directions will be equal, and that therefore the apparent preponderances which we observe in particular directions result from the real motion of the sun. But there is no impossibility in a systematic motion of the majority of the stars used in these researches which might reconcile the observed facts with a motionless sun. And, in the second place, if the sun is not in the exact centre of gravity of the universe, we might expect him to be moving in an orbit around this centre of gravity, and our observations on his actual motion are not sufficiently numerous or accurate to enable us to affirm that he is moving in a right line rather than such an orbit.'
Now this 'systematic motion,' which would render all calculations as to the sun's motion inaccurate or even altogether worthless, is by many astronomers held to be an observed reality. The star-drift, first pointed out by Proctor, has been shown to exist in many other groups of stars, while the curious arrangements of stars all over the heavens in straight lines, or regular curves, or spirals, strongly suggests a wide extension of the same kind of relation. But even more extensive systematic movements have been observed or suggested by astronomers. Sir D. Gill, by an extensive research, believes that he has found indications of a rotation of the brighter fixed stars as a whole in regard to the fainter fixed stars as a whole. Mr. Maxwell Hall has also found indications of a movement of a large group of stars, including our sun, around a common centre, situated in a direction towards Epsilon Andromedæ, and at a distance of about 490 years of light-travel. These last two motions are not yet established; but they seem to prove two important facts—(a) that eminent astronomers believe that some systematic motions must exist among the stars, or they would not devote so much labour to the search for them; and (b) that extensive systematic motions of some kind do exist, or even these results would not have been obtained.
Mr. W.W. Campbell, of the Lick Observatory, thus remarks on the uncertainty of determinations of the sun's motions: 'The motion of the solar system is a purely relative quantity. It refers to specified groups of stars. The results for various groups may differ widely, and all be correct. It would be easy to select a group of stars with reference to which the solar motion would be reversed 180° from the values assigned above' (Astrophysical Journal, vol. xiii. p. 87. 1901).
It must be remembered that, within a uniform cluster of stars, each moving round the common centre of gravity of the whole cluster, Kepler's laws do not prevail, the law being that the angular velocities are all identical, so that the more distant stars move faster than those nearer the centre, subject to modifications, however, due to the varying density of the cluster. But if the cluster is nearly globular, there must be stars moving round the centre in every plane, and this would lead to apparent motions in many directions as viewed by us, although those which were moving in the same plane as ourselves would, when compared with remote stars outside the cluster, appear to be all moving in the same direction and at the same rate, forming, in fact, one of those drifting systems of stars already referred to. Again, if in the process of formation of our cluster, smaller aggregations already having a rotatory motion were drawn into it, this might lead to their revolving in an opposite direction to those which were formed from the original nebula, thus increasing the diversities of apparent motion.
The evidence now briefly set forth fully justifies, I submit, the remarks as to the statements of my astronomical critics at the beginning of this section. They have both given the accepted views as to direction and rate of movement of our sun without any qualification whatever, as if they were astronomical facts of the same certainty and the same degree of accuracy as the sun's distance from the earth; and they will assuredly have been so understood by the great body of non-mathematical readers. It appears, however, if the authorities I have quoted are right, that the whole calculation rests upon certain assumptions, which are certainly to some extent, and may be to a very large extent, erroneous. This is my reply to one part of their criticism.