A glance at the above tables will show that the kind of variability presented by these objects is a very special one, and is remarkable for its great range. The light may be stated in the most general terms to vary about six magnitudes-from the sixth to the twelfth. This, I think, is a fair average; the small number of cases with a smaller variation I shall refer to afterwards. A variation of six magnitudes means roughly that the variable at its maximum is somewhere about 250 times brighter than at its minimum.*

I have already indicated that, with regard to the various origins of the variability of stars which have been suggested, those which have been always most in vogue consider the maximum luminosity of the star as the normal one; and, indeed, with regard to the Algol type of

stars of short period, which obviously are not here in question, there can be no reasonable doubt, that the eclipse explanation is a valid one; but in cases such as we are now considering, when we may say that the ordinary period is a year, this explanation is as much out of place on account of period, as are such suggested causes as stellar rotation and varying amount of spotted area on a stellar surface, on account of range.

We are driven, then, to consider a condition of things in which the minimum represents the constant condition, and the maximum a condition imposed by some cause which produces an excess of light ; so far as I know the only explanation on such a basis as this that has been previously offered is the one we owe to Newton, who suggested such stellar variability as that we are now considering was due to conflagrations brought about at the maximum by the appulse of

comets.

How the Difficulty of Regular Variability on Newton's View is got over in mine.

It will have been noticed that the suggestion put forward by myself is obviously very near akin to the one put forward by Newton, and no doubt his would have been more thoroughly considered than it has been hitherto, if for a moment the true nature of the special class of bodies we are now considering had been en évidence. We know that some of them at their minimum put on a special appearance of their own in that haziness to which I have before referred as having been observed by Mr. Hind. My researches show that they are probably nebulous, if indeed they are not all of them planetary nebule in a further stage of condensation, and such a disturbance as the one I have suggested would be certain to be competent to increase the luminous radiations of such a congeries to the extent indicated.

Some writers have objected to Newton's hypothesis on the ground that such a conflagration as he pictured could not occur periodically; but this objection I imagine chiefly depended upon the idea that the conflagration brought about by one impact of this kind would be quite sufficient to destroy one or both bodies, and thus put an end to any possibilities of rhythmically recurrent action. It was understood that the body conflagrated was solid like our earth. However valid this objection might be as urged against Newton's view, it cannot apply to mine, because in such a swarm as I have suggested, an increase of light to the extent required might easily be produced by the incandescence of a few hundred tons of meteorites.

I have already referred to the fact that the initial species of the stars we are now considering have spectra almost cometary, and this leads us to the view that we may have among them in some cases swarms

with double nuclei -incipient double stars, a smaller swarm revolving round the larger condensation, or rather round their common centre of gravity. In such a condition of things as this, it is obvious that, as before stated, in the swarms having a mean condensation this action is the more likely to take place, for the reason that at first the meteorites are too sparse for many collisions to occur, and that, finally, the outliers of the major swarm are drawn within the orbit of the smaller one, so that it passes clear. The tables show that this view is entirely consistent with the facts observed, for the greater number of instances of variability occur in the case of those stars in which on other grounds mean spacing seems probable.

The Cases of Small Range.

So far, to account for the greatest difference in luminosity at periastron passage, we have supposed the minor swarm to be only involved in the larger one during a part of its revolution, but we can easily conceive a condition of things in which its orbit is so nearly circular that it is almost entirely involved in the larger swarm. Under these conditions, collisions would occur in every part of the orbit, and they would only be more numerous at periastron in the more condensed central part of the swarm, and it is to this that I ascribe the origin of the phenomena in those objects-a very small number-in which the variation of light is very far below the normal range, one or two magnitudes instead of six or seven. Of course, if we imagine two subsidiary swarms, the kind of variability displayed by such objects as ẞ Lyræ is easily explained.

Study of Light Curves,

I owe to the kindness of Mr. Knott the opportunity of studying several light curves of "stars" of this group, and they seem to entirely justify the explanation which I have put forward. It is necessary, however, that the curves should be somewhat carefully considered because in some cases the period of the minimum is extremely small, as if the secondary body scarcely left the atmosphere of the primary one but was always at work. But when we come to examine the shape of the curves more carefully what we find is that the rise to maximum is extremely rapid; in the case of U Geminorum for instance there is a rise of five magnitudes in a day and a half; whereas the fall to minimum is relatively slow. The possible explanation of this is that the rise of the curve gives us the first sudden luminosity due to the collisions of the swarms, while the descent indicates to us the gradual toning down of the disturbance. If it be considered fair to make the descending curve from the maximum exactly symmetrical with the ascending one on the assumption that the immediate effect produced is absolutely instantaneous, then we find in all cases that I

have so far studied that the star would continue for a considerable time at its minimum.

Broadly speaking, then, we may say that the variables in this group are close doubles. The invisibility of the companion being due to the nearness to the primary or to its faintness.

Double Stars.

If, in connexion with this subject, we refer to the various observations which have been made of double nebulæ and stars, we are driven to the conclusion that in many cases a double star has at one time existed as a double nebula, while on the other hand, from what has been stated it seems probable that in many cases the companion is a late addition to the system. It would seem as if we may be able in the future, by observing the spectra of double stars, or possibly even their colours when once each particular colour has been attached to a particular spectrum, to discriminate between these two conditions.

In discussing this matter, however, a difficulty arises on account of the fact that on the new view there will be no constant relation between the mass of a swarm and its brightness. When we see a "star" of a certain magnitude, we cannot tell from its brightness alone whether it is a large faint one or a small bright one, for a large body at a low temperature may be equalled or even excelled in brightness by a smaller "star" at a higher temperature. But when we know the spectra of the bodies, we also know their relative temperatures. In the absence of spectroscopic details, colour helps us to a certain extent.

If a pair of "stars" of unequal masses have condensed from the same nebulosity, the smaller one will be further advanced along the temperature curve than the larger one, and the colours and spectra will be different; but it is not imperative that the magnitudes shall be unequal, for the smaller swarm will for a time be considerably hotter than the larger one.

If the masses be very unequal, the smaller one will have the smaller magnitude for the longest time. Where there is a great difference in magnitude, therefore, it is generally fair to assume that the one with the smaller magnitude has also the smaller mass.

Another difficulty in the discussion, in the absence of spectroscopic details, is due to the similarity in colour of bodies at opposite points of the temperature curve. Thus, bodies in Group III have, as far as we at present know, exactly the same colour, namely, yellow, as those in Group V. Again, many of the members of Group II have the same colour as some in Group VI.

The general conditions with regard to this subject may be thus briefly stated:-If the magnitudes, colours, and spectra of the two

components of a physical double are identical, both had their origin. in the same nebulosity.

If the magnitudes are nearly equal, but the colours and spectra different, it may be that the one with the most advanced spectrum has the smaller mass, and if the advance is in due proportion, we are justified in regarding them as having had a common origin.

If the magnitudes are very unequal, we may take the one with the smaller magnitude as having the smaller mass, and if it is proportionately in advance, as indicated by its spectrum or colour, we may regard both components as having had a common origin. If the smaller one be less advanced than the larger one, as most generally happens, we have to regard it as a late addition to the system.

If the two stars are of equal mass and revolve round their common centre of gravity they have in all probability done so from the nebulous stage, and therefore they will have arrived at the same stage along the evolution road, and their colours and spectra will be identical.

If, however, the masses are very different, then the smaller mass will run through its changes at a much greater rate than the larger one. In this way it is possible that the stars seen so frequently associated with globular nebulæ may be explained; while the nebula with a larger mass remains still in the nebulous condition, the smaller one may be advanced to any point, and may indeed even be totally invisible, while the parent nebula is still a nebula. This condition may be stated most generally by pointing to those double stars in which the companions are small and red, although we know nothing. for certain with regard to their masses. But if we pass to the other category in which the companion is added afterwards, the most extreme form would be a nebula revolving round a completely formed star; a less extreme form would be a bright line star, or a star of the second group, revolving round it. In this case the colour would be blue or greenish-blue or gray; now this is the greatly preponderating condition, as I have gathered from a discussion of the colours of the small companions given in Smyth's Celestial Cycle'; and accepting these colours alone, we should be led to think that most of the small companions of our present stars were not companions originally, but represent later additions to the systems.

It is obvious that there are very many other questions of great interest lying round these considerations, but it is not necessary that I should refer at greater length to them on this occasion, as my present object is only to show that a consideration of the colours of double stars really adds weight to the cause of variability which I have suggested.