impact of approximately equal bodies has a far higher probability than complete impact, and also that, cosmically, partial impact has a far higher constructive capacity.

I wish to state that I do not mean, that between unequal bodies partial impact is more frequent than complete. It is certain that the impact of particles of gas upon a body such as our Sun, must practically always be complete. Mr. Beverly has made a calculation of probabilities on the best assumption of the conditions of space attainable, and he finds that in all bodies having a greater ratio of diameter than 6 to 1, complete impact is more likely than partial. That when the equality of diameter is nearer than 6 to 1, partial impact is more likely. Therefore, as an impact of any bodies, whose diameters show a greater ratio than this, is an absolutely insignificant cosmical event, unless one of the bodies had a stupendous proper motion compared to its size, the matter may be thus considered to be placed on a mathematical basis. In calculations relating to the energy of bodies formed from diffused gas, it is impossible to talk of their total energy, as such energy is indefinite if we only consider the body as becoming infinitely small, and it is clearly impossible to say how small a body (such as our Sun, for instance) may become. I have therefore found it much more convenient to treat of the potential energy converted into other forms of energy, which I call “changed potential energy.” I believe it to be a mistake to suppose that very highly-diffused gas, having a definite limit of volume, is necessarily hot. It appears to me, that if the gas be so much diffused that its surface-attraction is very small—that it must be cold, or dissipating into space. There are four different lines of reasoning which point to the conclusion, that as a nebula or gaseous sun gets smaller, it gets hotter. I shall therefore assume that cold, infinitely diffused, disassociated gas, possesses a maximum energy.

Students of kinetics will readily be able to prove that were our Sun twice its present mass and twice its diameter, the energy of attracting a particle from infinity to its surface, without initial motion, would be exactly the same as at present. It can also be shown that such a Sun has lost exactly as much potential energy in forming itself from diffused gas as two such Suns as our own Sun. Therefore, were two such Suns as ours to come into impact, coalesce, and expand, until the whole of the heat of the collision were used in expansion, then the new Sun would have twice the mass, twice the diameter, one-fourth the density, and the same temperature as that of either of the original bodies. Thus it may be seen that two gaseous Suns attracting each other from infinity, without initial motion, were they to produce one Sun at the same temperature, it would only be twice the diameter.

There are reasons to believe that this point of equality of temperature is also a stable condition. Of course, the original suns were in a state of gaseous equilibrium, and as the density of the new Sun is one-fourth of each of the original, and the surface is just four times as great, hence the surface-pressure is one-fourth, and the density one-fourth, the temperature being the same, clearly, according to Marriot's law, this is a stable condition. This would, doubtless, be absolutely true, were the bodies homogeneous, but, as I have shown previously, there is every reason to suppose that “selective escape” would ensue, and would slightly alter the final result. Thus it is proved that the complete impact of equal bodies, without initial motion, will not produce a nebula (disregarding “selective escape”). But a matter of great importance to other parts of the theory is shown here. An impact tends to lessen density, consequently the density of very large masses may reasonably be supposed to be much less than that of smaller bodies. When the available energy of the visible Universe, on the supposition of its formation by partial impact, comes to be considered, this may be an important point.

It is easy to show that in the complete impact of bodies of unequal size the possibility of forming a nebula is still smaller; hence, as it is certain that the complete impact of bodies, without original proper motion, cannot much more than double the diameter of a star, it is clear it cannot produce a nebula, unless the mass were almost nebulous before. Of course, as the final result of an immense number of complete impacts, without loss of energy, a nebula might be produced, and this would be greatly aided by any proper motion any of the bodies might possess. In complete impact, with an original proper motion of a few hundred miles a second, two bodies like our Sun would be converted into a nebula; such an impact, it appears to me, would produce a roughly-spherical nebula without rotation. To produce rotation, it appears that the impact must be either partial, or between unequal bodies. To produce a nebula of definite form, other than spheroidal, appears to demand the same conditions.

In the partial impact of two bodies having a proper motion sufficient to take the two bodies away from each other after impact, nebulæ of various kinds may be produced, as the coalesced part struck off from the two bodies may be of very small mass; yet the velocity at which the two bodies would pass each other would be very great, hence the amount of changed potential energy may be enough, and more than enough, to completely diffuse the coalesced mass into space as gas, and clearly intermediate conditions may make nebulæ of every degree of density. Having shown that partial impact has energy enough to form diffused nebulæ, the kinematic possibilities will be discussed in the origin of special forms of nebulæ.

In my paper on the Visible Universe,^* I have given reasons to show that possibly the whole of the galactic poles consist of more or less diffused nebulous matter. As the reasoning, upon which I based this conclusion, appears to have been too condensed to be readily understood, I will give it a a little more in detail. Suppose the plane of the paper to contain the orbits of the two impacting bodies; when during the impact the centres of the two bodies are at their nearest point, it is probable the gaseous pressure produced by the impact will be near its maximum. It is certain that this pressure can only cause an escape of gas in a plane perpendicular to—and bisecting—the line joining the two centres of the two spheres. But the chief part of the material left by unbalanced momentum will be in the intersection of this plane and the plane of the paper, hence the only direction in which the pressure can act will be in a direction perpendicular to the plane of the paper. But this direction is the same as the axis of the resultant rotation due to the impact, and perpendicular to the plane in which the general mass of the matter will be distributed (which is clearly the plane of the paper). After the central mass has become free from the two bodies, the pressure will act in all directions, but the gas extended during the impact will more or less continue the direction it has taken, and will, doubtless, to a large extent separate itself from the other portions. As its direction will be perpendicular to the general movement, the polarnebular caps, and not unlikely all annular nebulæ which accompany the galaxy, were probably so formed.

Having thus shown that the poles of the milky way were probably at one time covered with diffused nebulous matter, I will discuss the mode in which aggregations may be formed. It appears certain that any very large cosmical bodies would have myriads of bodies travelling around them in all orbits. In the case of the two large bodies which formed the Universe, it would, therefore, probably be so likewise. Many of these bodies would be entrapped by the outrushing gas, and would be carried with it in its journey. The gas would also meet the bodies already existing in the portion of space through which it travelled. At first, the temperature would be so high that the smaller bodies would certainly be heated and volatilized, but would render the mass more or less irregular, and these irregularities, if very considerable, would tend to increase themselves. The larger masses might form permanent nebulæ; in some cases, these would ultimately become stars. As the nebulous mass became colder, a peculiar selective action would not improbably tell upon it. If the temperature of the mass be uniform, the velocity of mean-square of the molecules of the several chemical elements will be inversely as the square-root of these molecules' weight. A body travelling through this mass may have sufficient attractive

powers to collect up the slow heavy molecules, but not the lighter ones, and again the lightest molecules may have velocity enough to gradually escape the mass. Thus, the gas left would only be the intermediate molecular weights.

It is a peculiar coincidence that many nebulæ give only a few spectral lines as though of a single gas, and that gas in some cases nitrogen, an intermediate weight. It is somewhat singular that lithium and rhodium should not be seen in these nebulæ, unless these elements should be cosmically rare. In some cases the temperature may, perhaps, be below that of dissociation of the compounds of these elements, and they may be chemically combined, and their compound molecules may be heavy enough to be picked up by attraction. The star of 1866, before it faded, gave a feeble continuous spectrum with apparently the lines of nitrogen,’ as though selective escape had acted in such a way that the heavy molecules had become dense enough to produce the continuous spectrum, all the hydrogen had escaped, and the nitrogen was forming a nebula. Thus it appears, that in a large diffused nebulous mass we may have aggregation by original irregularities; and also by bodies passing into the mass and being volatilized, then gradually aggregating the denser molecules arround it. Finally, these may become stars, the hydrogen may escape, and the nitrogen may be the only part left in a sufficiently gaseous state to give bright lines.

It does not appear impossible, that a mass of gas may be at too high a temperature for dense aggregation, and may be orbitally connected, and the free molecules may be revolving around the central mass, the nucleus gradually picking it up as its velocity was lessened by loss of heat by radiation, or the velocity diminished by impact, or its direction so changed as to impinge upon the central mass.

Having thus glanced at the various generic modes of the origin of nebulæ, I will shortly discuss their spherical forms and the mode in which they may have originated; but I shall not enter too much into detail, or give any lengthy demonstrations, until I have laid the whole of the broader generalizations before the Institute.

Nebulæ are roughly divided into resolvable and irresolvable nebulæ, according as to whether the telescope can resolve them into stars or not. They are distinguished by their forms into—

• Nebulous stars

• Spherical nebulæ

• Spindle "

• Spiral "

• Cometary "

• Planetary "

• " " with nucleus.

• Annular "

The roughly-spherical nebulæ are by far the most numerous in the heavens, and are chiefly found distributed at the poles of the galactic circle. It is probable that most of these, and also many nebulous stars, may have been formed by volatilization of bodies passing into heated gas, or by aggregation, in the manner already described. Some may have been formed by impact, either complete or partial. But it is in studying the nebulæ of definite forms other than spherical, that the peculiarly striking capacity of partial impact to explain phenomena of the heavens becomes apparent.

The spiral nebulæ have been probably formed by the partial impact of bodies already existing as nebulæ before the impact. The forms of the spiral nebulæ were probably at first spindle-shaped, but as the chief part of the ends of the spindle would belong each to its respective original body, its motion would be directed outward, whilst the inner parts would be in a state of rotation. This would gradually convert the whole into a spiral, or rather a double spiral. Every gradation from a spindle-shape to a spiral are to be found in the heavens; there are spindles showing no signs of spiral, some as in Leo, showing the incipient spiral in the centre, and others in which the spiral is very perfect, and others, again, in which the coils of the spiral appear to have passed into a roughly spherical nebula. In the earlier discussions on the origin of the forms of these bodies considerable difficulty was experienced in understanding how a spiral nebula could have been formed, as it appeared that the extreme pressure of the central mass of the gas must tend to destroy all the spiral structure, especially at the centre of the nebula. When, however, the idea of the impact of previously-existing nebulæ occurred, all the difficulties were removed. But it is evident that if spiral nebulæ were formed by the impact of nebulæ, they would not be found in the galactic circle with the planetary and other nebulæ of regular shape, but at the galactic poles with the general mass of spherical nebulæ. On looking upon a celestial globe this will be found to be the case. I am aware that much discussion has recently taken place as to the existence of these nebulæ, but it seems almost impossible but that some impacts producing them must have taken place, so that not only do I believe that their existence will be clearly demonstrated, but that many of the spherical nebulæ, when carefully examined, will be found to be roughly spiral, as Proctor has demonstrated the Universe to be. Probably some of the double nebulæ are at present in a state of impact; if so, their form ought to alter materially during a single generation.

I do not imagine that the spindle-shaped nebula is confined to the impact of rare bodies. It appears to me that all partial impacts will tend to produce a spindle-shaped body at first; this matter is fully discussed in a paper on the general problem of stellar impact.^* The shape may be re-

tained until a spindle nebula of considerable dimensions is formed. It is not difficult to account for the origin of cometary nebulæ. These have donbtless been formed by an impact in which a want of balance in the momentum left a considerable residual velocity in the nebula, and that as it travels it becomes smaller, both by losing the hotter and more volatile portions, and by its own condensation.

The planetary nebulæ have always been considered the most wonderful objects in the entire heavens. The Herschels devoted much time to their discussion, and in my opinion conclusively proved them to be self-luminous hollow spheres of most stupendous diameter, several of them being many times larger than the most of our most distant planets. Recent spectroscopic observations have proved them to consist of gas; so that the problem before us is—to account for gigantic slightly-luminous hollow spheres of gas many thousand millions of miles in diameter.

Supposing we have an immense crowd collected in one spot, and that each one begins to move on indiscriminately in a straight line, and each if striking against anyone goes on again in the direction the blow has started him, and all continue to move straight on indefinitely: it is certain that in a few days the spot where the crowd was will be clear, and an immense irregular circle of people will exist, and will constantly be extending itself. This I believe to be the condition of a planetary nebula; an impact has taken place; on grounds of probability it was most likely partial; but the physical conditions would be nearly the same were it a complete impact of bodies with a stupendous original proper motion. As I have already stated, such an event appears to me, however, to be of amazing improbability. Either of these two suppositions will supply us with a gaseous body of such a high temperature compared with its mass, that every molecule will have sufficient velocity to escape the gravitating influence of the mass and travel straight on into space. For example: If a particle of gas at the surface of the Sun had a velocity of four hundred miles a second, such a particle would pass out of our system; and it is almost certain that had every particle this velocity—that is to say, the necessary temperature—the Sun would become a planetary nebula or a hollow shell of luminous gas. It is a remarkable confirmation of this theory, that Lord Lindsay has reported that the temporary star of 1877 has become a planetary nebula or a hollow shell of luminous gas. I have already shown how selective escape may have produced a nebula consisting of intermediate, or in fact any group of approximately equal molecular weights; and I need not say such reasoning applies equally to planetary nebulæ; the nucleus being in some cases the aggregated heavy molecules. These bodies are doubtless dynamically in an unstable con-

dition; if not of great age, they are probably increasing their diameter, which may continue until they diffuse themselves into space. If very old, they have probably reached their limit of size, and the molecules may have so far lost their velocity by radiation during molecular impact, and by work done against the gravitating influence of the mass, as to be on their return journey, and in the act of forming themselves into a condensed nebula, and finally an ordinary star. It is singular. It is singular that it is only in the galactic zone that planetary nebulæ occur, and it is clearly in this zone that the great distribution of stars would lead us to expect many impacts.

It appears possible to explain the origin of the annular nebulæ by partial impact in two different ways, and there may be representatives of both in the heavens, which will be found when the observation and classification of nebulæ are more satisfactorily done. In a former paper I have hinted at one of these methods, and the other explanation is the same as that given of the origin of the visible Universe, which would not improbably appear an annular nebula were it possible to see it at a sufficiently distant point in space (but which I have already shown, owing to the probable enormous distribution of small dark bodies in space, is unlikely,—as it is unlikely we see any distant universe). It appears that all annular nebulæ are more or less resolvable. There are many points of interest in connection with the origin of these small stars. Most of these have already been discussed in this paper in connection with the origin of nebulæ by aggregation; but probably almost the entire ring consists of those parts of the original bodies which were not very much affected by the impact as far as regards temperature, and much of this resolvable matter is not unlikely the dense, more infusible, part of the matter which very likely occupied the centre of the original bodies, and which was swept out into a circle, or rather two half-spirals, by the residual motion and attraction immediately after impact.

There is one point in connection with the origin of the very slight eccentricities of all bodies moving in elliptical orbits (which is probably the condition of some of these bodies in annular nebulæ)—such as many double stars, and the members of our Solar System, whose nature has hardly been sufficiently noticed. On first passing away from the central mass, their motion is such that their orbit would be highly eccentric, if there were no agencies at work tending to render them circular. I have already shown that there are many such, and I will attempt to make this point clear. Supposing the body to leave in advance of the general body of the gas, to travel to its extreme distance, return and plunge into the body of the gas, when it has gone some distance into the gas the attraction acting upon it