It is not only small stars that are variable, nor only what are called "temporary stars" that have made quick transition from great splendour to feeble luminosity. Thus a star in Argo (n) which stood, next to Sirius in brightness, has experienced what M. Guillemin terms "astounding transformations." "Towards the end of the seventeenth century Eta in Argo was only a fourth magnitude star, but in less than a century afterwards it had reached the second magnitude. Sixty years still later, it had declined to its first intensity, to enlarge again up to 1826. Since that epoch it has passed through the most astonishing phases, oscillating between the first and second magnitudes, now equal to Alpha Crucis, then to Alpha Centauris, now surpassing Canopus, and finally approaching Sirius." In a note he adds that Mr. F. Abbott found that it reached the brightness of Sirius in 1843, and then passed through diminishing magnitudes, until in 1863 it was no longer visible to the naked eye.

Changes of magnitude or apparent lustre may or may not, according to circumstances, be connected with alteration in hue. Recent attention has been strongly called to these colour changes, some of which appear to take the form of periodical alternations, while others follow laws of which we have no idea.* Thus the ancients saw Sirius as a red star. He is now white, and does not present any indications of reverting to his former condition. Regular periodical changes in colour or brightness may result from the approach and recession of planets attending on stars, and which may excite them as Mr. Balfour Stewart conceives, but other colour changes may result from internal conditions, and it is possible that no star would be found invariable in this respect if watched for periods sufficiently long. Thus among the future contingences that may await our earth may be that of some day receiving coloured light instead of white, a modification that would have a considerable effect upon animal and vegetable life.

The heavens become the more deeply interesting as they lose the attribute of unchangeableness formerly ascribed to them, and when we gaze upon constellations that impress us with their magnificence, and serve as boundary marks in space, tones of wonder and awe vibrate through the mind, as we reflect that some at least of these combinations are breaking up, that, if humanity endures long enough, some future members of our race will not only find that our present pole-star has forsaken the pole, but that the Cross has ceased to be the glory

* M. Guillemin's plate of coloured stars has not been prepared with sufficient care. Leonis is a complete failure, and no telescope in existence can show the close couple in y Andromedæ as represented. The colours of Albireo 8 Cygni are badly given.

of the southern hemisphere through its components wandering, as Humboldt tells us, in different ways.*

M. Guillemin gives a table of the computed velocity with which certain stars move. Arcturus is put down as traversing fifty-four miles in a second, 61 Cygni forty miles in the same time, Capella thirty-nine, Sirius fourteen, Vega thirteen, and the Pole Star one and a half miles. Our sun and his attendant planets appears to be moving towards some point in Hercules with a velocity of about four miles a second.

All the testimonies of science concur in pointing to the oneness of the universe. We cannot, therefore, regard the grouping of stars as otherwise than resulting from some general law, and to that same, or to some other great law, must be ascribed the singular and frequently fantastic forms in which nebulous matter is arranged. M. Guillemin gives, from various authorities, a considerable number of woodcuts and plates illustrating clusters and nebula, and the contemplation of such delineations is well calculated to impel his readers towards the contemplation of the objects themselves.†

Mr. Huggins's discoveries have demonstrated the existence of real nebula as contradistinguished from star clusters appearing nebulous simply through their remoteness from our earth. It was a very illogical proceeding on the part of many astronomers to imagine that because some so-called nebulæ were resolved by large telescopes, all could be resolved if sufficiently powerful instruments were provided; and the evidence to the contrary afforded by spectrum analysis not only restores to the heavens one portion of their rich variety of objects, but once more opens wide the doors of rational speculation which were too summarily closed.

It is not excusable that M. Guillemin, in his third edition, and after his attention had been called to the matter by the notes which Mr. Lockyer appended to the English translation, should persist in treating the subject of nebulæ almost as if Mr. Huggins's discoveries had not been made, nor is there any logical propriety in his separation of star clusters into two groups,

*The change in the apparent position of the pole star arises from peculiarities in the earth's motion by which its pole does not always point to the same spot in the heavens. This source of change in the appearance of the stars, as seen from the earth, must not be confounded with changes arising from their proper motions.

We are often asked what sized telescopes will show such objects. This depends very much on climate and weather, Many of the easier clusters afford beautiful sights on clear nights, with refractors as small as three inches, which will also, give a notion of the brighter and larger nebula, such as those of Orion and Andromeda. Mr. With's 6-inch mirrors act beautifully, and with more power than might have been expected on many nebula. Larger apertures will of course do more; but the very largest are required to follow the observations of Ross, Lassell, Bond, etc.

See especially Celestial Chemistry, in our vol. vi., p. 387.

one of which is dealt with under the head of nebula. More information is needed before a complete classification can be made, but Mr. Lockyer has shown the right method by placing known telescopic clusters side by side with clusters visible to the naked eye. M.Guillemin strangely divides his description of nebula of regular form by interpolating in the midst of it remarks and sketches of some that are irregular in shape. Mr. Lockyer has corrected this awkwardness in his edition.

It is impossible to conceive of the laws of aggregation which operate upon nebulous matter, and nothing can be more surprising and extraordinary than the fantastical forms which some of the nebulæ assume. Waiting for information on this highly curious subject, we pass to the so-called "planetary nebulæ," which M. Guillemin erroneously describes as having uniformly luminous disks. Sir J. Herschel says of them, "They have, as their name imports, a near, and in some instances a perfect resemblance to planets presenting disks round or slightly oval, in some quite sharply terminated, in others a little hazy or softened at the borders. Their light is in some perfectly equable, in others mottled, and of a very peculiar texture, as if curdled."* He adds, "The largest of these objects is situated somewhat south of the parallel of B Ursa Majoris, and about 12m following that star. Its apparent diameter is 2′40′′, which, supposing it placed at a distance of not more than 61 Cygni, would imply a linear one seven times greater than that of the orbit of Neptune." The absence of the appearance of condensation in the centre of these planetary nebulæ has suggested the notion that they may be hollow shells, and, so far as they have been examined by Mr. Huggins, they afford evidence of gaseous

structure.

The

The discovery of variable nebulæ, and the evidence adduced of changes in the form of some of the principal nebulæ, show that these bodies are performing internal work, resulting in alterations in shape and possibly of constitution also. most remarkable of these changes is thus alluded to by Sir John Herschel, in his Catalogue of Nebula, etc., p. 24, No. 2197, "According to a letter from Mr. Eyre B. Powell, of Madras, a most extraordinary change has taken place in this nebula ( Argus) since my figure of it was delineated. He states that at the southern end of the curious oval vacuity close to the great star, which was decidedly closed when I depicted it, is now decidedly open. Should this be established, it will be the most extraordinary fact that has yet appeared in the history of a nebula." Those who have visited the southern hemisphere describe this nebula as an object of surpassing *Outlines of Astronomy.

grandeur, exceeding the great Orion nebula in splendour, and also in eccentric beauty of form.

What are nebulæ properly so-called? Are they gaseous matter resulting from the dissipation of the solid materials of former stars, or are they such matter in process of condensation? Both suppositions are probable, if our minds are impressed with the belief that incessant modification, the resolution of old forms, and the re-arrangement of their matter into new forms, is the rule throughout the universe. Hitherto, however, not even spectrum analysis has established a connection of this kind between nebula and stars. It may exist, but it is not yet proved; and if, on the one hand, the opponents of free speculation on these subjects ask the supporters of the nebular hypothesis for more proof than can at present be adduced, they are entitled to point out in reply that, in a matter subjected to so little positive investigation, negative evidence against that hypothesis is not entitled to much worth.

A few words on the two volumes before us. On the whole, the plates in the French edition are the best, and the type is larger and handsomer. Mr. Lockyer has been an "able editor" of the English edition, and if he had selected a publisher from whom students expect to receive works of a solid and enduring character, we have no doubt the popularity of the English version would have been as great in England as that of the French edition has been in France.

EQUIGRAPHIC PROJECTIONS OF THE GLOBE.

BY RICHARD A. PROCTOR, B.A.

(With Illustrations.)

In this paper the term "projection " is to be understood in the sense used in mapping-viz., to signify any method of construction by which the meridians and parallels of a map may be laid down.

Since it is impossible to represent any portion of a globe without distortion, the map-maker seeks to satisfy the conditions which seem most important for the particular purpose he may have in view. Thus he may propose to himself the construction of a map in which distances measured from the centre, or along a latitude-parallel, shall be correctly given, as in the equidistant projection, and in Flamsteed's projection, respectively, or in which errors of distance shall be distributed as equally as possible; or he may aim chiefly to obtain correctness of shape, either in large figures-a problem approximately solved in the conical projection, or in small figures, a problem completely solved in the stereographic and Mercator's projections, and which may be solved in an indefinite number of ways; or, again, he may propose that certain lines on the globe shall be represented by straight lines in the map-as great circles and rhumb-lines, for instance, are represented in the gnomonic and Mercator's projections respectively. These and many other problems may be proposed, and maps constructed to fulfil such conditions, will have a special value for special purposes. The problem I now propose to examine is that of the construction of maps in which equal areas on the globe shall be represented by equal areas on the map. M. Babinet, who first proposed such a construction, called it the homolographic projection of the globe; the term equigraphic seems preferable, however.

It is stated in Nichol's Cyclopædia of the Physical Sciences, that Cauchy, the celebrated mathematician, solved Babinet's problem, though it is not easy to see what difficulty Babinet could have found, since the problem admits of many simple solutions. I am unable to say whether Cauchy's solution corresponds with any of those I am about to indicate. The advantages of equigraphic projection for special purposes are obvious. Maps thus constructed are not necessarily much distorted; but of course when the whole of the sphere is represented in a single projection, as in the figures which illustrate this article, the distortion is very great in parts of the map.

The method illustrated in Fig. 1 results from the solution of the following problem :-Two neighbouring latitude-parallels