Chapter XVIII: Eclipsing Stars

Stellar eclipses are necessarily included among the phenomena of spectroscopic binaries. For the planes of a proportion of these systems must pass through the earth, with the result that the circulating bodies occult one another when they cross the line of conjunction. The circumstance is particularly valuable as supplying a datum unattainable with the spectroscope for star couples differently conditioned. The rapid loss and recovery of light which tell us that one body is passing in front of the other, tell us, at the same time, that they revolve in an orbit seen edge on—that is to say, making an angle of 90° with the “tangent plane” of the sphere. Radial velocities are, accordingly, measured in their true proportions, and the masses of stars giving double spectra become strictly determinable. The duration of eclipse, moreover, indicates the density of the obscured and obscuring globes; and where the dimensions of even one of their orbits is known, it supplies a measure for their actual diameters. Thus precise evaluations of the light-changes and radial velocities of these singular objects go hand in hand; both kinds of research are equally necessary to the advancement of knowledge concerning systems which are peculiarly interesting because they are, more than any others in the sidereal world, accessible to investigation.

The circumstances of stellar eclipses are endlessly varied, and their differences are full of meaning. They are central when the orbit is directed straight towards us; they are partial when it deviates from coincidence with the line of vision. Then the interposing body may be dark or bright; it may be larger or smaller than the globe behind it. Supposing it to be sensibly obscure and the transit central, the eclipse will be either total or annular. The first case is not known, although quite likely to occur; no complete periodical disappearances have been witnessed. The second has not been definitely attested. Its inevitable indication would obviously be a stationary minimum. While the two discs are superposed, the light must remain steadily at its lowest level; and if the eclipse be annular, the discs are, _ipso facto_, superposed during an appreciable interval, the length of which bears an inverse ratio to the depth of the obscuration.

While a bright and dark pair can undergo but one eclipse in each revolution, two are the portion of a couple radiant in both its members. If they are alike in size and brilliancy and pass one another centrally, the eclipses will be equal and the loss of light one-half. And it is noteworthy that in nature this seems to be a somewhat prevalent arrangement. Several systems are known in which it may subsist; spectroscopic observations can peremptorily decide whether it does, in fact, subsist or not. The principle of their decision lies on the surface. Eclipses necessarily take place at points of the orbit where radial motion approximates to zero. If they are duplicated in each period, the cessation of movement marks at one, the transition from speed of approach to speed of recession; at the next, the turning-point where speed of recession changes to speed of approach. A minimum of light, that is to say, precedes each reversal of movement. If, on the other hand, the eclipses are single, occurring only once in a revolution, the cycle of motion to and from the eye is completed in the interval between them. The criterion is thus absolute and unmistakable; only the faintness of the stars impedes its general application. Where unequal eclipses alternate, however, the spectroscope is not needed to inform us that they take place two and two in each circuit. They are then evidently due to the mutual occultations of disparate stars; and the species of combination they indicate is frequently met with. It is varied to the utmost, as might be expected, by gradations of disparity, in the production of which deficient luminosity may concur with inferiority of size, or be partially neutralised by its superiority. Thus as each globe in its turn comes in front of the other, there results a double series of eclipses, the odd ones (dating from a fixed epoch) being perfectly similar each to each, but differing in depth and duration from those of the even or intermediate series.

Further diversities arise through slight tilting of the orbits. The corresponding eclipses are partial, even to the limit of evanescence, when the star discs just escape contact. And it may be noted that the second eclipse in each revolution, properly belonging to a luminous pair, may be suppressed where the path traversed is at the same time sensibly inclined and considerably eccentric. Partial eclipses are doubtless the rule, central ones the exception; but their discrimination is often a matter of some delicacy. Indeed, the photometric study of such phases is an art in itself, the practice of which demands skill, vigilance, and patience beyond the common. The aid of photography, lately enlisted for it, is likely to enhance its security and precision.

Eclipsing stars, once more, are close binaries circulating nearly in the line of sight. Not any intrinsic peculiarity, but our situation in space, determines their special character. Relatively to us, they are periodically variable, as Spica or Castor would become were our place suitably shifted. Their changes are of a distinctive kind; they are short, sharp, and decisive. When well developed, that is to say; for photographic photometry may ere long afford the means of detecting occultations barely adumbrated by a drop not perhaps exceeding one-tenth of a magnitude. All members of the class so far have been recognised by their variation in brightness; their accompanying circulatory motion, inferred in all cases, has been verified in only a few. The following list gives the designations, periods, and phases of the eclipsing stars with which astronomers had made acquaintance down to the end of 1902. They are enumerated in the order of their discovery.

┌──────────┬─────────────────┬───────────┬─────────────┬─────────┐
│Chandler’s│ Name. │ Period. │Light Range. │Duration │
│ No. │ │ │ │of Phase.│
├──────────┼─────────────────┼───────────┼─────────────┼─────────┤
│ │ │d. h. m. s.│ m. m.│ h. m.│
│ 1090│ Algol │ 2 20 48 55│ 2·3 to 3·4│ 9 20│
│ 3109│ S Cancri │ 9 11 37 45│ 8·2 „ 9·8│ 21 30│
│ 1411│ λ Tauri │ 3 22 52 12│ 3·4 „ 4·2│ 10 0│
│ 5374│ δ Libræ │ 2 7 51 23│ 5·0 „ 6·2│ 12 0│
│ 5484│ U Coronæ │ 3 10 51 12│ 7·5 „ 8·9│ 9 42│
│ 6546│ RS Sagittarii │ 2 9 58 36│ 6·4 „ 7·6│ 10 40│
│ 320│ U Cephei │ 2 11 49 38│ 7·1 „ 9·4│ 11 0│
│ 6189│ U Ophiuchi │ 0 20 7 43│ 6·0 „ 6·7│ 5 20│
│ 7488│ Y Cygni │ 1 11 57 26│ 7·1 „ 7·9│ 9 0│
│ 2610│ R Canis Majoris│ 1 3 15 46│ 5·9 „ 6·7│ 5 0│
│ 5949│ R Aræ │ 4 10 12 42│ 6·9 „ 8·0│ 9 30│
│ 3055│ X Carinæ │ 0 12 59 30│ 7·9 „ 8·6│ 6 39│
│ 5144│ Y Boötis │ 2 14 24 0│ 8·0 „ 8·6│ 4 0│
│ 3416│ S Velorum │ 5 22 24 35│ 7·8 „ 9·3│ 15 11│
│ 6442│ Z Herculis │ 3 23 50 0│ 6·9 „ 8·0│ 6 36│
│ 7399│ W Delphini │ 4 19 21 12│ 9·3 „ 12·1│ 14 0│
│ 6636a│ RX Herculis │ 0 21 20 33│ 7·0 „ 7·8│ 4 8│
│ 2781│R^2 Puppis │ 6 10 19 36│ 9·1 „ 10·8│ 17 0│
│ │U^3 Cygni │ 4 13 45 2│ 8·7 „ 11·4│ 13 0│
│ │V^2 Cygni │ 6 0 8 48│10·8 „ 12·8│ │
│ 3707│R^2 Velorum │ 1 20 30 2│10·0 „ 10·9│ 3 20│
│ 6773│ U Scuti │ 0 22 54 0│ 9·1 „ 9·6│ 5 0│
│ 7318│ UW Cygni │ 3 10 49 12│10·5 „ 12·0│ 8 30│
│ 6927│ U Sagittæ │ 3 9 19 12│ 6·5 „ 9·1│ 12 0│
│ 7891│ UZ Cygni │31 7 17 46│ 8·9 „ 11·85│ 48 0│
│ │ RV Lyræ │ 3 14 22 23│11·0 „ 12·8│ │
│ │14, 1902 Persei │ 3 1 21 32│ 9·4 „ 12·0│ │
└──────────┴─────────────────┴───────────┴─────────────┴─────────┘

Algol (β Persei) is the model eclipsing star. Goodricke’s sagacious conjecture that such was its nature, adopted and developed by Pickering, obtained experimental confirmation after a lapse of 107 years. Vogel’s spectrographs showed in 1889 that, previously to each obscuration, the star was swiftly receding from the earth, while recovered brightness was attended by a somewhat greater velocity of approach. The excess is simply due to the fact that the system is travelling towards the sun at the leisurely pace of 2⅓ miles a second. The true orbital speed is sensibly uniform; accelerations, pointing to ellipticity in the track pursued, have not been detected. One eclipse takes place in each revolution; the eclipsing body is to all intents and purposes a gigantic planet; it gives no perceptible light. The sun round which it circulates is, on the contrary, peculiarly brilliant for its size, partly because its absorption, being of the helium type, produces little or no mellowing effect upon its keen white rays.

Much has been learned about the system formed by these contrasted globes. Its visible member travels at the rate of 26⅓ miles a second; and since the period of revolution comprises 247,735 seconds, the distance of its centre from the centre of gravity slightly exceeds 1,000,000 miles. The length of the eclipse, moreover, gives the actual size of the star. It has a diameter of slightly more than 1,000,000 miles, or about five-fourths that of the sun. The dimensions of the satellite, too, are approximately known. From the loss of light through its interposition, Professor Pickering in 1880[564] calculated the ratio of its diameter to that of its primary to be as 764 to 1000. The ratio should be increased if the transit were not central, which it does not appear to be. For the eclipse is not annular, since there is no pause at minimum; the flow of change is continuous; the turning of the luminous tide is not appreciably delayed; decline is immediately succeeded by restoration. The orbit is not then level with the eye; and Mr. Yendell considers that an inclination of 7° would agree best with the light-curve.[565] In Vogel’s opinion it is such as to imply for the dark body a diameter of 830,000 miles, an estimate which can hardly be far from the truth.[566] Admitting with him that the two stars are of equal density—possibly a hazardous assumption—we can infer their masses, knowing their respective volumes, and the circulatory speed of one of them. They are in the proportion of two to one, and both spheres together contain two-thirds as much matter as our sun. They are, accordingly, at least four times more tenuous; but the consequence cannot be said to discredit the postulate in view of the extreme rarefaction characterising white stars in general and helium stars in particular. The distance of Algol from its satellite (always on Vogel’s hypothesis of equal densities) is 3,230,000 miles, leaving an interval between their surfaces of scarcely more than 2,250,000 miles. But we shall find that even closer degrees of contiguity are compatible with stability in the mechanism of the stellar heavens.

The period of Algol has long been known to vary minutely but continuously. But as to the nature, law, or cause of these inequalities nothing had been ascertained, and little had even been surmised, prior to Dr. Chandler’s discussion of them in 1888.[567] He proved them to be slowly compensatory, not indefinitely progressive. Consistently in advance of their due time down to about the year 1804, the obscurations of the star then began to fall behind it, and the delay had in 1843 accumulated to 156 minutes. A gradual process of restoration thereupon set in, and the normal epoch was reached near the beginning of 1873. It was, however, quickly transcended, for acceleration was still going forward, and may not attain its term for some years yet to come.[568] These irregularities are evidently comprised in a cycle of considerably more than a century; they can scarcely, for that very reason, be accounted for on gravitational principles; since a third body, revolving in so long a period, would be too distant to perturb markedly the movements of the close pair traversing an inner circuit. Dr. Chandler hence resorted to another mode of explanation.[569] He proposed to account for the alternate anticipations and retardations of Algol’s eclipses on the principle of the equation of light. They might result, he pointed out, from the description, by the occulting pair, of an orbit so wide that the transmission of light across it takes close upon 300 minutes. The star’s phases would then be observed too soon or too late according as they occurred on the hither or the farther side of the great ellipse. They would be shifted by turns backward and forward in time just as are the eclipses of Jupiter’s satellites while the earth performs its annual circuits. The system of Algol is, on this view, triple. Two dark masses and a vividly shining one unite to form it. The revolutions of the eclipsing pair round the common centre of gravity, which is at a distance from it just equal to that of Uranus from the sun, are accomplished in about 130 years, at the rate of 2·7 miles a second. Its members are at present nearer to us than their mean place, and their occultations consequently forerun the mean times; this will continue until towards the year 1934, when, on the passage of the ascending node, a coincidence of epochs should be observed. Two other criteria are applicable to Chandler’s theory. If it be true, Algol’s approaching systemic movement of 2·3 miles a second should disappear within the next decade, neutralised by orbital velocity at that time directed away from the sun. Again, the wide circuits performed in a plane supposed to make an angle of 20° with the line of sight, might be directly traceable as undulations impressed upon the straight track of the star’s proper motion. Minute fluctuations of position simulating the looked-for effects have indeed been observed; but whether they are merely casual, or represent an actual, though almost evanescent phenomenon, is too delicate a question to be decided off-hand.[570] Twenty years hence the waves of disturbance may have defined themselves;[571] scarcely sooner.

An alternative hypothesis to Chandler’s was put forward by M. Tisserand early in 1895.[572] Rejected by the former investigator as insufficient, it assumed in the hands of the latter an extremely plausible form. No third body is demanded by it; a slight flattening of the globe of Algol, together with a moderate degree of ellipticity in the orbit of its satellite, meet the needs of explanation. The combined effect would be to produce a slow revolution of the orbital major axis, occasioning just such an inequality in the times of conjunction as that discussed by Dr. Chandler; and the fundamental postulated cause is likely to be present. Algol must have a rapid rotation; otherwise its system could not long subsist. That is to say, the maximum length of its axial period is 2^d 21^h, the period of its revolution. This implies an equatorial speed of 13½ miles a second, and a consequent equatorial bulging of very considerable amount. One of the conditions stipulated by Tisserand may then be granted, and the second can scarcely be absent, since the eccentricity of stellar orbits rarely falls short of the degree required. Verification may be procured by the spectroscopic detection of variations of velocity in different sections of Algol’s path. But the crucial test of the theory is of the photometric kind. At intervals of 120 years, if it correspond with fact, the shortest and longest radii of the ellipse traversed would, owing to the progression of the apsides, alternately point towards the earth. In the first case, the eclipses would be abbreviated by periastral acceleration; in the second, they would be long, because the movement at apastron should be slow. Their duration at present approaches to being the longest possible; if they shorten notably from 1910 onward, Tisserand’s hypothesis will be amply confirmed, while their failure to do so will compel its final rejection. Chandler’s, on the other hand, will remain in possession of the field should the alleged periodical disturbance of Algol’s proper motion be definitively established. Thus the rival theories alike wait on the future, and invite the award of events.

As the upshot of a careful series of measurements with the Yale heliometer, Dr. Chase[573] ascribes to Algol a parallax of 0·035″, equivalent to a light-journey of ninety-three years. If actually so remote, it gives just eighty times as much light as the sun from a surface not very greatly larger, but fifty-two times more brilliant—an inference surprising indeed, but not incredible.

A second Algol-variable was recognised by Hind in 1848.[574] Usually of 8·2 magnitude, S Cancri loses and regains more than three-fourths of its light in 21½ hours, divided between 8½ of decline and thirteen of restoration. The dissymmetry of the phases is increased by a remarkable pause in the brightening after minimum, as if a secondary cause of obscuration had supervened. Nor should it be forgotten that Schmidt observed on 14th April 1882 an excessive darkening of the star, which remained for a whole hour sunk nearly to the twelfth magnitude. The period which, until lately, was the longest ascertained for any member of its class, is subject to a cyclical disturbance embracing at least 300 light-cycles.[575] The deviations of the computed minima sometimes run up to forty minutes. It will be of great interest to determine whether they imply the presence of a third attractive body, or whether spheroidal deformation will suffice to account for them. The dimness of S Cancri places it for the present beyond the reach of useful spectrographic research. Its density has, however, been calculated by Mr. H. N. Russell of Princeton University,[576] from the ratio between its period of revolution and the duration of the eclipses suffered by it, with the result of showing that the star is composed of materials forty times more attenuated than those of the sun! And this is an upper limit.

Shortly after Hind’s detection of S Cancri, Baxendell found that its peculiarities were shared by λ Tauri, a radiantly white star of 3·4 magnitude. Its eclipses, as in several other cases, deepen more quickly than they lighten. They occur at intervals of 3^d 23^h, and last ten hours. They do not, indeed, come off quite punctually. An oscillatory disturbance of unknown law affects them, which occasions “errors” from the computed epochs, amounting at times to three hours.[577] Plassmann regards λ Tauri as continuously variable.[578] He noticed in 1891 a secondary dip in brightness fifty hours after the chief minimum, besides two intermediate maxima; and the Pulkowa photographs lent in 1897[579] some partial countenance to his views. They showed the spectrum to be occasionally and unequally double, the fainter rays, by their relatively large displacements, betraying their origin from a mass greatly inferior to that of the star characterised by the less mobile, and more intense absorption-lines they accompany. Thus M. Plassmann’s second eclipse[580] is real, though inconspicuous. No orbital elements have yet been assigned to this star. M. Bélopolsky regarded his materials as inadequate for purposes of computation; and indeed the movements derived from his plates were of a somewhat problematic nature. They greatly need elucidation, which it ought not to be very difficult to supply. The spectrum of λ Tauri is of pure helium type. The calculated density of the pair is about one-tenth that of the sun.

The fourth Algol variable is an all but perfect timekeeper. The phases of δ Libræ have been watched since 1858 without the detection of any assured irregularity. They last twelve hours, of which 5½ are spent in a decline from 5·0 to 6·2 magnitude, and 6½ in the reversal of the process. The eclipsing body appears to be wholly obscure, but the spectrographic method has not been applied to the system. The limit of density found for it by Mr. H. N. Russell is one-twenty-fifth that of the sun.

The phases of U Coronæ are very similar to those of Algol, but the intervening time is longer—eighty-three in lieu of sixty-nine hours. Each pair, too, is similarly composed of a bright and dark member, and their mean density comes out nearly the same. The analogy is completed by the presence of a variation in the period, evidently akin to the disturbances of Algol,[581] and explicable, doubtless, on an identical principle. U Coronæ, however, is a comparatively faint object; at high light it is of only 7·5 magnitude, and consequently offers scant facilities for research.

The eclipsing system designated RS Sagittarii, discovered by Gould in 1874, was subjected in 1896 to exact inquiries by Alexander W. Roberts of Lovedale, South Africa.[582] From them it appears that the coupled stars are alike in size, but so unlike in lustre that one gives more than twice as much light as the other. There result two unequal minima in each revolution; at the first, the combined magnitude of 6·6 drops to 7·6, at the second, to 6·9. The former has, besides, a duration of 10^h 40^m, the latter of only seven hours; whence the orbit is found to have an eccentricity of 0·25, the long, deep eclipse occurring at apastron, the slighter phase coinciding with the rapid sweep through periastron. The intervals of time from each to the next are of 2^d 10^h very nearly; and their equality implies that the major axis of the path pursued is directed towards the earth. The plane of the ellipse, however, must be somewhat inclined, since the mutual transits of the globes circulating in it are not central; and the amount of its inclination may be determined when the course of light-change is more accurately known. The gravitational period (as it may be called) is, of course, double the eclipse-period, or 4^d 20^h; but the mass of the system can be ascertained only by spectroscopic means. Its brighter member proves to be of about one-sixth, the dim component of one-fifth, the solar density.[583] All these particulars have been gathered from the photometric relations of these intimately conjoined bodies. From their dynamical relations, truths no less remarkable will perhaps before long be elicited.

FIG. 21.—Photometric Curves of Algol Variables (Pickering).
]

At Moscow, in 1880, U Cephei was added by Ceraski to the Algol family. This object is distinguished by the abruptness and extent of its changes. In four and a half hours it descends from 7·1 to 9·4 magnitude, this profound obscuration lasting for about two hours, after which brightness returns, almost, if not quite as quickly as it departed. The light-curve, determined photometrically by Professor Pickering, is shown in Fig. 21.

He explains its singularities on the hypothesis of a total eclipse by a large semi-obscure body,[584] and alleges confirmatory evidence in a barely perceptible secondary minimum corresponding to the transit of the brilliant over the dusky globe. Chandler and Yendell, nevertheless, deny the reality of the minor eclipse;[585] and Wilsing vainly endeavoured in 1890[586] to bring the observed phases of U Cephei into harmony with any conceivable form of the occultation-theory. And the star, by its faintness, evades spectrographic tests for motion. Some increase of blue absorption is, however, stated to occur at its minima; and this is noteworthy as an instance, unique among Algol variables, of alteration in the quality of their diminished rays. Irregularities of the same type as those of Algol affect the period of U Cephei. If dependent on the light-equation principle, they signify the description, by the eclipsing couple, of an orbit larger than the Saturnian, in a period of between thirty and forty years.[587] Changes in radial motion, due to deflection in this wide path, would, if measurable, lend authenticity to an ingenious speculation, which may otherwise be superseded by Tisserand’s hypothesis[588] of a revolving major axis. Mr. Russell finds U Cephei to be a considerably more tenuous body than Algol.

The exceedingly short period of U Ophiuchi—20^h 8^m—and the halving of its light at minimum, suggest that it is composed of twin suns, alternately occulting one another. The period of revolution would, in that case, be twice the period of variation, and the globes would have more room to circulate than if one of them were dark. For then the brief intervals between the eclipses would represent each a complete round of the orbit, and the duration of the phases would imply such close proximity of the bright and the dark stars that the gap dividing their surfaces would scarcely exceed three-tenths of their joint radii. Such an arrangement is possible; a single spectrographic impression, taken five hours before or after a minimum, would show whether it actually subsists. If it do, the spectral lines will be single, though shifted; if not, they should appear incipiently double, and the movements indicated might unhesitatingly be taken to be included in a cycle twice the length of the eclipse-interval.

Discovered by Sawyer in 1881, U Ophiuchi showed to Chandler’s patient scrutiny individualities that should not be passed over.[589] Thus the return of light after minimum is interrupted by a pause similar to that observed in S Cancri, but which tends to become obliterated in a “mean curve.” Its reality has not been established photometrically (see Fig. 21), but may emerge with the application of finer methods. The circumstance, too, is worth remark that—again like S Cancri—U Ophiuchi was once caught sight of during an abnormally obscure phase.[590] An inequality of its period, comprised within thirty-seven to forty years, further noticed by Chandler, is perhaps visibly reflected in the disturbance of the star’s proper motion.

A still more curiously interesting object of the same class is met with in Y Cygni. Here, at least, as M. Dunér virtually demonstrated in 1892,[591] eclipses are duplicated; two occur in the course of each revolution. Its phases, first recognised by Chandler, 9th December 1886, range from 7·1 to 7·9 magnitude, and are completed in nine hours. But they were soon perceived to recur with conspicuous irregularity.[592] Towards the middle of 1888 they were no less than seven hours behind their calculated times, which shortly afterwards began to be largely anticipated. Perturbations on such a scale had never previously been betrayed by the occultations of a binary; and the task of accounting for them by inequalities of light-transmission was evidently a formidable one. The problem they offer was, however, destined to receive a different, and, we may add, a definitive solution.

When Dunér came to discuss the results of his own observations at Upsala in 1891–92, and to compare them with those made elsewhere, he was at once struck with a persistent discrepancy between the odd and the even sets of minima. The first, third, fifth, and so on, from an assigned epoch, obeyed a law of recurrence quite distinct from that conformed to by the intervening obscurations. Thus in November 1891, the intervals from an even to an odd minimum, and from an odd to an even minimum, differed by no less than nine hours, forty-three minutes. Clearly, the constant sum of these discrepant periods gives the true time-measure of systemic circulation. Two bright bodies, then, eclipse each other, and they seem to be matched “to a hair”; their eclipses, moreover, must be central, since the loss of light amounts to just one-half. The disparity of their intervals depends primarily upon the eccentricity of the orbit; secondarily, upon the situation of the line of apsides. It vanishes when the line in question points directly towards the earth; it attains a maximum when it is viewed at right angles, for then the right and left sections of the eclipse being traversed respectively with the least and greatest possible velocities, the succession of alternate occultations reaches the limit of time-inequality. Dunér’s final conclusions regarding the system were expressed as follows:—[593]

“The variable star Y Cygni consists of two stars of equal size and equal brightness, which move about their common centre of gravity in an elliptical orbit whose major axis is eight times the radius of the stars. The period of an anomalistic revolution[594] is 2·996933 days, and the eccentricity is 0·145. A minimum occurred while the stars were at periastron, on 8th December 1885. The line of apsides of the orbit, which then coincided with the line of sight, completes one revolution in the plane of the orbit in 41·1 tropical years.”

The next coincidence of the kind, if the above elements are correct, should take place in 1906. The compelling cause of the orbit’s gyration remains to be investigated. It may be found in disturbance exercised by an unseen, exteriorly revolving mass upon the conjoined suns; or their own spheroidal shape may be solely concerned in producing it; the question has an important bearing upon the construction of all such systems. The linear dimensions of the orbit of Y Cygni will unquestionably be determined ere long with the spectroscope, whence the mass of the bodies travelling in it will at once follow. A mean density less than one-sixth the solar is ascribed to them with some confidence.[595]

The variations of R Canis Majoris, detected by Sawyer in 1887, have been traced, as it were, only in outline. Their period is 28^h 16^m, five hours of which are occupied by the phases, and since the star fades to half its normal lustre, they are likely to be conditioned much as are those of Y Cygni. Two similar globes presumably undergo them in turn, mutually revolving in double the period of their occultations.

The character of R Aræ was noticed by Mr. A. W. Roberts in 1891.[596] He considers the eclipses, which recur once in 4^d 10^h, to be not always of the same depth; but this symptom of intrinsic variability in one or both of the transiting stars needs to be verified. The curve at minimum is symmetrical.

The nature of X Carinæ—another southern variable discovered by Roberts in 1892—is still dubious. It changes from 7·9 to 8·6 magnitude in 6^h 39^m, and remains constant only during 6^h 20^m. So that the phases extend over more than half the period of variation, which must evidently be doubled to give the period of revolution, since no eclipse can possibly have a duration of more than one-half the occulted body’s orbital circuit. The alternate minima of X Carinæ are thought by Roberts[597] to be, to a very small extent, unequal, and to succeed each other at slightly different intervals. If this be so, the system is composed of two stars, one a little brighter than the other, pursuing a nearly circular track in a period of twenty-six hours, and in such close contiguity that the times during which their discs overlap are longer than the intervals of their apparent separation. The actual subsistence, however, of this, or some analogous arrangement has yet to be proved.

The variations of Y Boötis are also more or less enigmatical.[598] They are limited to six-tenths of a magnitude, and have a period rather shorter than that of Algol. The eclipsing character of this eighth-magnitude star, suggested by Parkhurst in 1893,[599] was confirmed, on the strength of a year’s observations, by Yendell. Chandler, nevertheless, expresses doubts as to its genuineness, which is compromised by extraordinary anomalies, hardly amenable to explanatory efforts. The predicted minima do not always occur, and their failures seem capricious and inconsequential. But if they depended, as Parkhurst thinks they must,[600] upon a certain critical inclination of the orbit, causing transits to be occasionally missed, a law of periodicity should be traceable in the lapsed phenomena.

The obscurations of S Velorum recorded themselves on the plates of the Cape “Durchmusterung,” and the record was duly interpreted by Mr. Ray Woods in 1894.[601] They are marked by the same peculiarities as those of U Cephei, and probably indicate total effacements of a radiant sun by the prolonged transits across it of a voluminous, but dimly shining companion sphere, the diameter of which, according to Roberts,[602] cannot fall short of half the distance between the revolving bodies. Their respective densities, as estimated by him, are 0·61 and 0·03 that of the sun,[603] the dusky mass proving, on the assumed data, to be twenty times more rarefied than the brilliant one. A disparity so extreme cannot readily be admitted as real. If only the star could be elevated on the photometric scale,[604] the taking of a few spectrographs would at once acquaint us with the true plan of its system; but its faintness—7·8 magnitude—must long continue to baffle experiments of this kind.

A modified specimen of the Y Cygni sub-class is met with in Z Herculis. Its eclipsing character was announced by Chandler in 1894;[605] about a month later, Hartwig and Dunér independently detected in it a double sequence of disparate minima, with periods respectively of forty-seven and forty-nine hours. Hence the revolution of a pair of unequally bright stars in a period of just four days was inferred with virtual certainty.[606] In M. Dunér’s words, “Z Herculis consists of two stars of equal size, one of which is twice as bright as the other. These stars revolve round their common centre of gravity in an elliptical orbit, the semi-axis major of which is six times the diameter of the stars. The plane of the orbit passes through the sun, the eccentricity is 0·2475, and the line of apsides is inclined at an angle of 4° to the line of sight.” The chief minimum lasts 6·6 hours, and occurs not far from apastron. The secondary phase is hurried through in four hours, when the stars are moving with nearly their greatest speed. It is, however, unlikely that this relation will continue unchanged;[607] since it may be taken almost as an axiom that orbits so conditioned pivot round in space, turning their longest axes successively in every direction.

The first Algol variable photographically discovered was W Delphini. On 18th July 1895, Miss Louisa D. Wells missed a 9·3 magnitude star from a Harvard plate exposed 26th September 1891,[608] while upon seventy-one earlier and subsequent ones it was normally imprinted. The one tell-tale photograph had been taken during eclipse, when it sinks to 12·1 magnitude—that is to say, eleven-twelfths of its light are cut off by the interposing body. Pickering[609] believes the latter to be partially luminous and very large, affording prolonged totalities, but the photometric curve (see Figure 21) hardly warrants this assumption. It is fairly sharp at minimum, not flat, like that of U Cephei, and corresponds better with a partial occultation by a wholly dark satellite than with the central transit of one dimly radiative. The period is not constant.[610] Deviations from regularity amounting to one hour had become manifest early in 1898.

The phases of a seventh-magnitude star (DM + 12° 3557) named RX Herculis were discovered by Sawyer in 1898.[611] They range over eight-tenths of a magnitude, and recur at intervals of 21^h 21^m. Like those of U Ophiuchi, they probably indicate the revolution, in double that period, of two equal stars; and since the minimum brightness is just one-half the maximum, their mutual occultations may be total.

The variability of R^2 Puppis (CPD − 41° 1681), noticed by Professor Kapteyn during his inspection of the Cape Durchmusterung negatives, was verified and defined by Mr. Innes in 1899.[612] The period at first assigned of nearly thirteen days was abridged to one-half that length by Mr. Roberts’s investigations.[613] The light fades at minimum to one-third its full amount, through the intervention of a dimly luminous mass.

U^3 Cygni and V^2 Cygni were both detected by Madame Ceraski in studying photographs of the sky taken at Moscow.[614] They undergo analogous changes, investigated at Harvard College in 1899–1900.[615] Those of U^3 Cygni are remarkable for their extent, the greatest known in an eclipsing star, unless (which is doubtful) W Delphini should be bracketed with it. V^2 Cygni, at full brightness, ranks little higher than the eleventh magnitude, and descends, once in six days, nearly to the thirteenth. It is thus an object at the limit of detailed observation. Innumerable systems of the same kind must lie beyond that limit. The twenty-first star on our list—R^2 Velorum—suspected as an Algol variable by Innes in 1901, was verified and investigated by Roberts.[616] Of the remaining six objects enumerated, U Sagittæ was found by M. Schwab of Ilmenau to vary after the manner of U Cephei;[617] and UZ Cygni, detected by Mrs. Fleming in 1902, is remarkable for a period more than thrice as long as that of S Cancri. UW Cygni, RV Lyræ, and the still unnamed star in Perseus have been recently discovered by Mr. Stanley Williams.

Algol variables, without any recognised exception, show first-type spectra. They are either helium or Sirian stars. This specialty is unaccountable, and may perhaps vanish with the widening of experience; for many close binaries exempt from eclipses belong to the solar class, and no reason is apparent why those happening to revolve in planes coincident with the visual ray should differ in quality of light from those revolving in orbits variously inclined to it. Nor is it yet quite certain that the eclipse-theory accounts for certain minor phenomena in the stars to which it applies. Thus some of their light-curves, as drawn visually, are marked by peculiarities incapable of being explained as the outcome of purely dynamical relations. They may, however, turn out to be illusory or subjective; their reality is not incontrovertible. Again, the exceptionally low minima recorded for S Cancri and U Ophiuchi need confirmation. The possibility of mistake is not excluded so long as each remains an isolated event.

Three varieties of eclipsing stars may be distinguished. The first includes bright and dark pairs, like Algol and its companion, revolving in slightly oblique orbits. One partial occultation takes place in each revolution. The intimate association which they present of bodies at opposite extremes of luminosity is not a little remarkable. In the second variety, exemplified by U Cephei, a brilliant star circulates round a larger, but far less lustrous globe. One prolonged totality marks the orbital period. The secondary minima, theoretically inevitable in such cases, have not been certainly observed. Vanishing stars, could they be discovered, would appropriately illustrate this mode of construction where the contrast in light-power had reached its limit. Finally, the third species of occulting systems consists of stars undergoing nearly equal double eclipses, the period of revolution comprising two periods of variation. Y Cygni is a typical example. If the loss of light amount to one-half, or eight-tenths of a magnitude, and the alternate minima be of the same intensity, the eclipses are total; for two similar stars, one is temporarily substituted. If, owing to the inclination of their path, they only partially conceal one another, the phases will be slighter, yet still equal. Their disparity, in odd and even series, shows at once that the balance of luminosity is tilted; and indications are not wanting that its level is disturbed rather by inequalities of intrinsic lustre than of shining area.

The time-keeping of eclipse-stars is a subject demanding profound and persistent study. The minutest irregularities traceable in it may be of far-reaching significance.[618] On what principle they should be explained, is still largely an open question. Possibly several forms of action conspire, even in the same system, to produce the sum-total of their deviations. In no case has the presence of a third body been proved; in no case have perturbations of the ordinary gravitational type been suspected. On the other hand, the occulting and the occulted globes must be deformed through rotation; hence one true cause for the observed inequalities falls within our ken; whether it is a _sufficient_ cause alone remains doubtful. Essentially, however, increase of knowledge regarding these marvellous combinations depends upon the development of spectrographic methods. Surely, although perhaps in slow succession, they will yield the secrets of their construction to a mode of inquiry that continually gains power and accuracy, and is capable of dealing directly with the most recondite springs of celestial mechanics.