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.
[Illustration:
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.