By A.M. CLERKE.
Science needed two thousand years to disentangle the earth's orbital
movement from the revolutions of the other planets, and the
incomparably more arduous problem of distinguishing the solar share in
the confused multitude of stellar displacements first presented itself
as possibly tractable a little more than a century ago. In the lack
for it as yet of a definite solution there is, then, no ground for
surprise, but much for satisfaction in the large measure of success
attending the strenuous attacks of which it has so often been made the
object.
Approximately correct knowledge as to the direction and velocity of
the sun's translation is indispensable to a profitable study of
sidereal construction; but apart from some acquaintance with the
nature of sidereal construction, it is difficult, if not impossible,
of attainment. One, in fact, presupposes the other. To separate a
common element of motion from the heterogeneous shiftings upon the
sphere of three or four thousand stars is a task practicable only
under certain conditions. To begin with, the proper motions
investigated must be established with _general_ exactitude. The errors
inevitably affecting them must be such as pretty nearly, in the total
upshot, to neutralize one another. For should they run mainly in one
direction, the result will be falsified in a degree enormously
disproportionate to their magnitude. The adoption, for instance, of
system of declinations as much as 1" of arc astray might displace to
the extent of 10° north or south the point fixed upon as the apex of
the sun's way (see L. Boss _Astr. Jour._, No. 213). Risks on this
score, however, will become less formidable with the further advance
of practical astronomy along a track definable as an asymptote of
ideal perfection.
Besides this obstacle to be overcome, there is another which it will
soon be possible to evade. Hitherto, inquiries into the solar movement
have been hampered by the necessity for preliminary assumptions of
some kind as to the relative distances of classes of stars. But all
such assumptions, especially when applied to selected lists, are
highly insecure; and any fabric reared upon them must be considered to
stand upon treacherous ground. The spectrographic method, however,
here fortunately comes into play. "Proper motions" are only angular
velocities. They tell nothing as to the value of the perspective
element they may be supposed to include, or as to the real rate of
going of the bodies they are attributed to, until the size of the
sphere upon which they are measured has been otherwise ascertained.
But the displacement of lines in stellar spectra give directly the
actual velocities relative to the earth of the observed stars. The
question of their distances is, therefore, at once eliminated. Now the
radial component of stellar motion is mixed up, precisely in the same
way as the tangential component, with the solar movement; and since
complete knowledge of it, in a sufficient number of cases, is rapidly
becoming accessible, while knowledge of tangential velocity must for a
long time remain partial or uncertain, the advantage of replacing the
discussion of proper motions by that of motions in line of sight is
obvious and immediate. And the admirable work carried on at Potsdam
during the last three years will soon afford the means of doing so in
the first, if only a preliminary investigation of the solar
translation based upon measurements of photographed stellar spectra.
The difficulties, then, caused either by inaccuracies in star
catalogues or by ignorance of star distances may be overcome; but
there is a third, impossible at present to be surmounted, and not
without misgiving to be passed by. All inquiries upon the subject of
the advance of our system through space start with an hypothesis most
unlikely to be true. The method uniformly adopted in them--and no
other is available--is to treat the _inherent_ motions of the stars
(their so-called _motus peculiares_) as pursued indifferently in all
directions. The steady drift extricable from them by rules founded
upon the science of probabilities is presumed to be solar motion
visually transferred to them in proportions varying with their
remoteness in space, and their situations on the sphere. If this
presumption be in any degree baseless, the result of the inquiry is
_pro tanto_ falsified. Unless the deviations from the parallactic line
of the stellar motions balance one another on the whole, their
discussion may easily be as fruitless as that of observations tainted
with systematic errors. It is scarcely, however, doubtful that law,
and not chance, governs the sidereal revolutions. The point open to
question is whether the workings of law may not be so exceedingly
intricate as to produce a grand sum total of results which, from the
geometrical side, may justifiably be regarded as casual.
The search for evidence of a general plan in the wanderings of the
stars over the face of the sky has so far proved fruitless. Local
concert can be traced, but no widely diffused preference for one
direction over any other makes itself definitely felt. Some regard,
nevertheless, _must_ be paid by them to the plane of the Milky Way;
since it is altogether incredible that the actual construction of the
heavens is without dependence upon the method of their revolutions.
The apparent anomaly vanishes upon the consideration of the
profundities of space and time in which the fundamental design of the
sidereal universe lies buried. Its composition out of an indefinite
number of partial systems is more than probable; but the inconceivable
leisureliness with which their mutual relations develop renders the
harmony of those relations inappreciable by short-lived terrestrial
denizens. "Proper motions," if this be so, are of a subordinate kind;
they are indexes simply to the mechanism of particular aggregations,
and have no definable connection with the mechanism of the whole. No
considerable error may then be involved in treating them, for purposes
of calculation, as indifferently directed, and the elicited solar
movement may genuinely represent the displacement of our system
relative to its more immediate stellar environment. This is perhaps
the utmost to be hoped for until sidereal astronomy has reached
another stadium of progress.
Unless, indeed, effect should be given to Clerk Maxwell's suggestion
for deriving the absolute longitude of the solar apex from
observations of the eclipses of Jupiter's satellites (Proc. Roy. Soc.,
vol. xxx., p. 109). But this is far from likely. In the first place,
the revolutions of the Jovian system cannot be predicted with anything
like the required accuracy. In the second place, there is no certainty
that the postulated phenomena have any real existence. If, however, it
be safe to assume that the solar system, cutting its way through
space, virtually raises an ethereal counter-current, and if it be
further granted that light travels less _with_ than _against_ such a
current, then indeed it becomes speculatively possible, through slight
alternate accelerations and retardations of eclipses taking place
respectively ahead of and in the wake of the sun, to determine his
absolute path in space as projected upon the ecliptic. That is to say,
the longitude of the apex could be deduced together with the resolved
part of the solar velocity; the latitude of the apex, as well as the
component of velocity perpendicular to the plane of the ecliptic,
remaining, however, unknown.
The beaten track, meanwhile, has conducted two recent inquirers to
results of some interest. The chief aim of each was the detection of
systematic peculiarities in the motions of stellar assemblages after
the subtraction from them of their common perspective element. By
varying the materials and method of analysis, Prof. Lewis Boss,
Director of the Albany Observatory, hopes that corresponding
variations in the upshot may betray a significant character. Thus, if
stars selected on different principles give notably and consistently
different results, the cause of the difference may with some show of
reason be supposed to reside in specialties of movement appertaining
to the several groups. Prof. Boss broke ground in this direction by
investigating 284 proper motions, few of which had been similarly
employed before (_Astr. Jour._, No. 213). They were all taken from an
equatorial zone 4° 20' in breadth, with a mean declination of +3°,
observed at Albany for the catalogue of the Astronomische
Gesellschaft, and furnished data accordingly for a virtually
independent research of a somewhat distinctive kind. It was carried
out to three separate conclusions. Setting aside five stars with
secular movements ranging above 100", Prof. Boss divided the 279 left
available into two sets--one of 185 stars brighter, the other of 144
stars fainter than the eighth magnitude. The first collection gave for
the goal of solar translation a point about 4° north of [alpha] Lyræ,
in R.A. 280°, Decl. +43°; the second, one some thirty-seven minutes of
time to the west of [delta] Cygni, in R.A. 286°, Decl. +45°. For a
third and final solution, twenty-six stars moving 40"-100" were
rejected, and the remaining 253 classed in a single series. The upshot
of their discussion was to shift the apex of movement to R.A. 289°,
Decl. +51°. So far as the difference from the previous pair of results
is capable of interpretation, it would seem to imply a predominant set
toward the northeast of the twenty-six swifter motions subsequently
dismissed as prejudicial, but in truth the data employed were not
accurate enough to warrant so definite an inference. The Albany proper
motions, as Prof. Boss was careful to explain, depend for the most
part upon the right ascensions of Bessel's and Lalande's zones, and
are hence subject to large errors. Their study must be regarded as
suggestive rather than decisive.
A better quality and a larger quantity of material was disposed of by
the latest and perhaps the most laborious investigator of this
intricate problem. M. Oscar Stumpe, of Bonn (_Astr. Nach._, Nos.
2,999, 3,000), took his stars, to the number of 1,054, from various
quarters, if chiefly from Auwers' and Argelander's lists, critically
testing, however, the movement attributed to each of not less than 16"
a century. This he fixed as the limit of secure determination, unless
for stars observed with exceptional constancy and care. His discussion
of them is instructive in more ways than one. Adopting, the additional
computative burden imposed by it notwithstanding, Schonfeld's
modification of Airy's formulæ, he introduced into his equations a
fifth unknown quantity expressive of a possible stellar drift in
galactic longitude. A negative result was obtained. No symptom came to
light of "rotation" in the plane of the Milky Way.
M. Stumpe's intrepid industry was further shown in disregard of
customary "scamping" subterfuges. Expedients for abbreviation vainly
spread their allurements; every one of his 2,108 equations was
separately and resolutely solved. A more important innovation was his
substitution of proper motion for magnitude as a criterion of
remoteness. Dividing his stars on this principle into four groups, he
obtained an apex for the sun's translation corresponding to each as
follows:
Number of Proper motion. Apex.
Group included stars. " " ° °
I. 551 0.16 to 0.32 R.A. 287.4 Decl. +42.
II. 340 0.32 to 0.64 " 279.7 " 40.5
III. 105 0.64 to 1.28 " 287.9 " 32.1
IV. 58 1.28 and upward " 285.2 " 30.4
Here again we find a marked and progressive descent of the apex toward
the equator with the increasing swiftness of the objects serving for
its determination, leading to the suspicion that the most northerly
may be the most genuine position, because the one least affected by
stellar individualities of movement.
By nearly all recent investigations, moreover, the solar _point de
mire_ has been placed considerably further to the east and nearer to
the Milky Way than seemed admissible to their predecessors; so that
the constellation Lyra may now be said to have a stronger claim than
Hercules to include it; and the necessity has almost disappeared for
attributing to the solar orbit a high inclination to the medial
galactic plane.
From both the Albany and the Bonn discussions there emerged with
singular clearness a highly significant relation. The mean magnitudes
of the two groups into which Prof. Boss divided his 279 stars were
respectively 6.6 and 8.6, the corresponding mean proper motions 21".9
and 20".9. In other words, a set of stars on the whole six times
brighter than another set owned a scarcely larger sum total of
apparent displacement. And that this approximate equality of movement
really denoted approximate equality of mean distance was made manifest
by the further circumstance that the secular journey of the sun proved
to subtend nearly the same angle whichever of the groups was made the
standpoint for its survey. Indeed, the fainter collection actually
gave the larger angle (13".73 as against 12".39), and so far an
indication that the stars composing it were, on an average, nearer to
the earth than the much brighter ones considered apart.
A result similar in character was reached by M. Stumpe. Between the
mobility of his star groups, and the values derived from them for the
angular movement of the sun, the conformity proved so close as
materially to strengthen the inference that apparent movement measures
real distance. The mean brilliancy of his classified stars seemed, on
the contrary, quite independent of their mobility. Indeed, its changes
tended in an opposite direction. The mean magnitude of the slowest
group was 6.0, of the swiftest 6.5, of the intermediate pair 6.7 and
6.1. And these are not isolated facts. Comparisons of the same kind,
and leading to identical conclusions, were made by Prof. Eastman at
Washington in 1889 (Phil. Society Bulletin, vol. xii, p. 143;
Proceedings Amer. Association, 1889, p. 71).
What meaning can we attribute to them? Uncritically considered, they
seem to assert two things, one reasonable, the other palpably absurd.
The first--that the average angular velocity of the stars varies
inversely with their distance from ourselves--few will be disposed to
doubt; the second--that their average apparent luster has nothing to
do with greater or less remoteness--few will be disposed to admit.
But, in order to interpret truly, well ascertained if unexpected
relationships, we must remember that the sensibly moving stars used to
determine the solar translation are chosen from a multitude sensibly
fixed; and that the proportion of stationary to traveling stars rises
rapidly with descent down the scale of magnitude. Hence a mean struck
in disregard of the zeros is totally misleading; while the account is
no sooner made exhaustive than its anomalous character becomes largely
modified. Yet it does not wholly disappear. There is some warrant for
it in nature. And its warrant may perhaps consist in a preponderance,
among suns endowed with high _physical_ speed, of small or slightly
luminous over powerfully radiative bodies. Why this should be so, it
would be futile, even by conjecture, to attempt to explain.--_Nature._
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