_THE SUN'S DISTANCE_
The question of the sun's distance arises naturally from the
consideration of his temperature, since the intensity of the radiations
emitted as compared with those received and measured, depends upon it.
But the knowledge of that distance has a value quite apart from its
connection with solar physics. The semi-diameter of the earth's orbit is
our standard measure for the universe. It is the great fundamental datum
of astronomy--the unit of space, any error in the estimation of which is
multiplied and repeated in a thousand different ways, both in the
planetary and sidereal systems. Hence its determination was called by
Airy "the noblest problem in astronomy." It is also one of the most
difficult. The quantities dealt with are so minute that their sure grasp
tasks all the resources of modern science. An observational inaccuracy
which would set the moon nearer to, or farther from us than she really
is by one hundred miles, would vitiate an estimate of the sun's distance
to the extent of sixteen million![748] What is needed in order to attain
knowledge of the desired exactness is no less than this: to measure an
angle about equal to that subtended by a halfpenny 2,000 feet from the
eye, within a little more than a thousandth part of its value.
The angle thus represented is what is called the "horizontal parallax"
of the sun. By this amount--the breadth of a halfpenny at 2,000 feet--he
is, to a spectator on the rotating earth, removed at rising and setting
from his meridian place in the heavens. Such, in other terms, would be
the magnitude of the terrestrial radius as viewed from the sun. If we
knew this magnitude with certainty and precision, we should also know
with certainty and precision--the dimensions of the earth being, as they
are, well ascertained--the distance of the sun. In fact, the one
quantity commonly stands for the other in works treating professedly of
astronomy. But this angle of parallax or apparent displacement cannot be
directly measured--cannot even be perceived with the finest instruments.
Not from its smallness. The parallactic shift of the nearest of the
stars as seen from opposite sides of the earth's orbit, is many times
smaller. But at the sun's limb, and close to the horizon, where the
visual angle in question opens out to its full extent, atmospheric
troubles become overwhelming, and altogether swamp the far more minute
effects of parallax.
There remain indirect methods. Astronomers are well acquainted with the
proportions which the various planetary orbits bear to each other. They
are so connected, in the manner expressed by Kepler's Third Law, that
the periods being known, it only needs to find the interval between any
two of them in order to infer at once the distances separating them all
from one another and from the sun. The plan is given; what we want to
discover is the scale upon which it is drawn; so that, if we can get a
reliable measure of the distance of a single planet from the earth, our
problem is solved.
Now some of our fellow-travellers in our unending journey round the sun,
come at times well within the scope of celestial trigonometry. The orbit
of Mars lies at one point not more than thirty-five million miles
outside that of the earth, and when the two bodies happen to arrive
together in or near the favourable spot--a conjuncture which occurs
every fifteen years--the desired opportunity is granted. Mars is then
"in opposition," or on the _opposite_ side of us from the sun, crossing
the meridian consequently at midnight.[749] It was from an opposition of
Mars, observed in 1672 by Richer at Cayenne in concert with Cassini in
Paris, that the first scientific estimate of the sun's distance was
derived. It appeared to be nearly eighty-seven millions of miles
(parallax 9·5"); while Flamsteed deduced 81,700,000 (parallax 10") from
his independent observations of the same occurrence--a difference quite
insignificant at that stage of the inquiry. But Picard's result was just
half Flamsteed's (parallax 20"; distance forty-one million miles); and
Lahire considered that we must be separated from the hearth of our
system by an interval of _at least_ 136 million miles.[750] So that
uncertainty continued to have an enormous range.
Venus, on the other hand, comes closest to the earth when she passes
between it and the sun. At such times of "inferior conjunction" she is,
however, still twenty-six million miles, or (in round numbers) 109 times
as distant as the moon. Moreover, she is so immersed in the sun's rays
that it is only when her path lies across his disc that the requisite
facilities for measurement are afforded. These "partial eclipses of the
sun by Venus" (as Encke termed them) are coupled together in pairs,[751]
of which the components are separated by eight years, recurring at
intervals alternately of 105-1/2 and 121-1/2 years. Thus, the first
calculated transit took place in December, 1631, and its companion
(observed by Horrocks) in the same month (N.S.), 1639. Then, after the
lapse of 121-1/2 years, came the June couple of 1761 and 1769; and again
after 105-1/2, the two last observed, December 8, 1874, and December 6,
1882. Throughout the twentieth century there will be no transit of
Venus; but the astronomers of the twenty-first will only have to wait
four years for the first of a June pair. The rarity of these events is
due to the fact that the orbits of the earth and Venus do not lie in the
same plane. If they did, there would be a transit each time that our
twin-planet overtakes us in her more rapid circling--that is, on an
average, every 584 days. As things are actually arranged, she passes
above or below the sun, except when she happens to be very near the line
of intersection of the two tracks.
Such an occurrence as a transit of Venus seems, at first sight, full of
promise for solving the problem of the sun's distance. For nothing would
appear easier than to determine exactly either the duration of the
passage of a small, dark orb across a large brilliant disc, or the
instant of its entry upon or exit from it. And the differences in these
times (which, owing to the comparative nearness of Venus, are quite
considerable), as observed from remote parts of the earth, can be
translated into differences of space--that is, into apparent or
parallactic displacements, whereby the distance of Venus becomes known,
and thence, by a simple sum in proportion, the distance of the sun. But
in that word "exactly" what snares and pitfalls lie hid! It is so easy
to think and to say; so indefinitely hard to realise. The astronomers of
the eighteenth century were full of hope and zeal. They confidently
expected to attain, through the double opportunity offered them, to
something like a permanent settlement of the statistics of our system.
They were grievously disappointed. The uncertainty as to the sun's
distance, which they had counted upon reducing to a few hundred thousand
miles, remained at many millions.
In 1822, however, Encke, then director of the Seeberg Observatory near
Gotha, undertook to bring order out of the confusion of discordant, and
discordantly interpreted observations. His combined result for both
transits (1761 and 1769) was published in 1824,[752] and met universal
acquiescence. The parallax of the sun thereby established was 8·5776",
corresponding to a mean distance[753] of 95-1/4 million miles. Yet this
abolition of doubt was far from being so satisfactory as it seemed.
Serenity on the point lasted exactly thirty years. It was disturbed in
1854 by Hansen's announcement[754] that the observed motions of the moon
could be drawn into accord with theory only on the terms of bringing the
sun considerably nearer to us than he was supposed to be.
Dr. Matthew Stewart, professor of mathematics in the University of
Edinburgh, had made a futile attempt in 1763 to deduce the sun's
distance from his disturbing power over our satellite.[755] Tobias Mayer
of Göttingen, however, whose short career was fruitful of suggestions,
struck out the right way to the same end; and Laplace, in the seventh
book of the _Mécanique Céleste_,[756] gave a solar parallax derived from
the lunar "parallactic inequality" substantially identical with that
issuing from Encke's subsequent discussion of the eighteenth-century
transits. Thus, two wholly independent methods--the trigonometrical,
or method by survey, and the gravitational, or method by
perturbation--seemed to corroborate each the upshot of the use of the
other until the nineteenth century was well past its meridian. It is
singular how often errors conspire to lead conviction astray.
Hansen's note of alarm in 1854 was echoed by Leverrier in 1858.[757] He
found that an apparent monthly oscillation of the sun which reflects a
real monthly movement of the earth round its common centre of gravity
with the moon, and which depends for its amount solely on the mass of
the moon and the distance of the sun, required a diminution in the
admitted value of that distance by fully four million miles. Three years
later he pointed out that certain perplexing discrepancies between the
observed and computed places both of Venus and Mars, would vanish on the
adoption of a similar measure.[758] Moreover, a favourable opposition of
Mars gave the opportunity in 1862 for fresh observations, which,
separately worked out by Stone and Winnecke, agreed with all the newer
investigations in fixing the great unit at slightly over 91 million
miles. In Newcomb's hands they gave 92-1/2 million.[759] The
accumulating evidence in favour of a large reduction in the sun's
distance was just then reinforced by an auxiliary result of a totally
different and unexpected kind.
The discovery that light does not travel instantaneously from point to
point, but takes some short time in transmission, was made by Olaus
Römer in 1675, through observing that the eclipses of Jupiter's
satellites invariably occurred later, when the earth was on the far
side, than when it was on the near side of its orbit. Half the
difference, or the time spent by a luminous vibration in crossing the
"mean radius" of the earth's orbit, is called the "light-equation"; and
the determination of its precise value has claimed the minute care
distinctive of modern astronomy. Delambre in 1792 made it 493 seconds.
Glasenapp, a Russian astronomer, raised the estimate in 1874 to 501,
Professor Harkness adopts a safe medium value of 498 seconds. Hence, if
we had any independent means of ascertaining how fast light travels, we
could tell at once how far off the sun is.
There is yet another way by which knowledge of the swiftness of light
would lead us straight to the goal. The heavenly bodies are perceived,
when carefully watched and measured, to be pushed forward out of their
true places, in the direction of the earth's motion, by a very minute
quantity. This effect (already adverted to) has been known since
Bradley's time as "aberration." It arises from a combination of the two
movements of the earth round the sun and of the light-waves through the
ether. If the earth stood still, or if light spent no time on the road
from the stars, such an effect would not exist. Its amount represents
the proportion between the velocities with which the earth and the
light-rays pursue their respective journeys. This proportion is,
roughly, one to ten thousand. So that here again, if we knew the rate
per second of luminous transmission, we should also know the rate per
second of the earth's movement, consequently the size of its orbit and
the distance of the sun.
But, until lately, instead of finding the distance of the sun from the
velocity of light, there has been no means of ascertaining the velocity
of light except through the imperfect knowledge possessed as to the
distance of the sun. The first successful terrestrial experiments on the
point date from 1849; and it is certainly no slight triumph of human
ingenuity to have taken rigorous account of the delay of a sunbeam in
flashing from one mirror to another. Fizeau led the way,[760] and he was
succeeded, after a few months, by Léon Foucault,[761] who, in 1862, had
so far perfected Wheatstone's method of revolving mirrors, as to be able
to announce with authority that light travelled slower, and that the sun
was in consequence nearer than had been supposed.[762] Thus a third line
of separate research was found to converge to the same point with the
two others.
Such a conspiracy of proof was not to be resisted, and at the
anniversary meeting of the Royal Astronomical Society in February, 1864,
the correction of the solar distance took the foremost place in the
annals of the year. Lest, however, a sudden bound of four million miles
nearer to the centre of our system should shake public faith in
astronomical accuracy, it was explained that the change in the solar
parallax corresponding to that huge leap, amounted to no more than the
breadth of a human hair 125 feet from the eye![763] The Nautical Almanac
gave from 1870 the altered value of 8.95", for which Newcomb's result of
8.85", adopted in 1869 in the Berlin Ephemeris, was substituted some ten
years later. In astronomical literature the change was initiated by Sir
Edmund Beckett in the first edition (1865) of his _Astronomy without
Mathematics_.
If any doubt remained as to the misleading character of Encke's
deduction, so long implicitly trusted in, it was removed by Powalky's
and Stone's rediscussions, in 1864 and 1868 respectively, of the transit
observations of 1769. Using improved determinations of the longitude of
the various stations, and a selective judgment in dealing with their
materials, which, however indispensable, did not escape adverse
criticism, they brought out results confirmatory of the no longer
disputed necessity for largely increasing the solar parallax, and
proportionately diminishing the solar distance. Once more in 1890, and
this time with better success, the eighteenth-century transits were
investigated by Professor Newcomb.[764] Turning to account the
experience gained in the interim regarding the optical phenomena
accompanying such events, he elicited from the mass of somewhat
discordant observations at his command, a parallax (8·79") in close
agreement with the value given by sundry modes of recent research.
Conclusions on the subject, however, were still regarded as purely
provisional. A transit of Venus was fast approaching, and to its
arbitrament, as to that of a court of final appeal, the pending question
was to be referred. It is true that the verdict in the same case by the
same tribunal a century earlier had proved of so indecisive a character
as to form only a starting-point for fresh litigation; but that century
had not passed in vain, and it was confidently anticipated that
observational difficulties, then equally unexpected and insuperable,
would yield to the elaborate care and skill of forewarned modern
preparation.
The conditions of the transit of December 8, 1874, were sketched out by
Sir George Airy, then Astronomer-Royal, in 1857,[765] and formed the
subject of eager discussion in this and other countries down to the very
eve of the occurrence. In these Mr. Proctor took a leading part; and it
was due to his urgent representations that provision was made for the
employment of the method identified with the name of Halley,[766] which
had been too hastily assumed inapplicable to the first of each
transit-pair. It depends upon the difference in the length of time taken
by the planet to cross the sun's disc, as seen from various points of
the terrestrial surface, and requires, accordingly, the visibility of
both entrance and exit at the same station. Since these were, in 1874,
separated by about three and a half hours, and the interval may be much
longer, the choice of posts for the successful use of the "method of
durations" is a matter of some difficulty.
The system described by Delisle in 1760, on the other hand, involves
merely noting the instant of ingress or egress (according to situation)
from opposite extremities of a terrestrial diameter; the disparity in
time giving a measure of the planet's apparent displacement, hence of
its actual rate of travel in miles per minute, from which its distances
severally from earth and sun are immediately deducible. Its chief
attendant difficulty is the necessity for accurately fixing the
longitudes of the points of observation. But this was much more sensibly
felt a century ago than it is now, the improved facility and certainty
of modern determinations tending to give the Delislean plan a decided
superiority over its rival.
These two traditional methods were supplemented in 1874 by the camera
and the heliometer. From photography, above all, much was expected.
Observations made by its means would have the advantages of
impartiality, multitude, and permanence. Peculiarities of vision and
bias of judgment would be eliminated; the slow progress of the
phenomenon would permit an indefinite number of pictures to be taken,
their epochs fixed to a fraction of a second; while subsequent leisurely
comparison and measurement could hardly fail, it was thought, to educe
approximate truth from the mass of accumulated evidence. The use of the
heliometer (much relied on by German observers) was so far similar to
that of the camera that the object aimed at by both was the
determination of the relative positions of the _centres_ of the sun and
Venus viewed, at the same absolute instant, from opposite sides of the
globe. So that the principle of the two older methods was to ascertain
the exact times of meeting between the solar and planetary limbs; that
of the two modern to determine the position of the dark body already
thrown into complete relief by its shining background. The former are
"methods by contact," the latter "methods by projection."
Every country which had a reputation to keep or to gain for scientific
zeal was forward to co-operate in the great cosmopolitan enterprise of
the transit. France and Germany each sent out six expeditions;
twenty-six stations were in Russian, twelve in English, eight in
American, three in Italian, one in Dutch occupation. In all, at a cost
of nearly a quarter of a million, some fourscore distinct posts of
observation were provided; among them such inhospitable, and all but
inaccessible rocks in the bleak Southern Ocean, as St. Paul's and
Campbell Islands, swept by hurricanes, and fitted only for the
habitation of seabirds, where the daring votaries of science, in the
wise prevision of a long leaguer by the elements, were supplied with
stores for many months, or even a whole year. Siberia and the Sandwich
Islands were thickly beset with observers; parties of three
nationalities encamped within the mists of Kerguelen Island,
expressively termed the "Land of Desolation," in the sanguine, though
not wholly frustrated hope of a glimpse of the sun at the right moment.
M. Janssen narrowly escaped destruction from a typhoon in the China seas
on his way to Nagasaki; Lord Lindsay (now Earl of Crawford and
Balcarres) equipped, at his private expense, an expedition to Mauritius,
which was in itself an epitome of modern resource and ingenuity.
During several years, the practical methods best suited to insure
success for the impending enterprise formed a subject of European
debate. Official commissions were appointed to receive and decide upon
evidence; and experiments were in progress for the purpose of defining
the actual circumstances of contacts, the precise determination of which
constituted the only tried, though by no means an assuredly safe road to
the end in view. In England, America, France, and Germany, artificial
transits were mounted, and the members of the various expeditions were
carefully trained to unanimity in estimating the phases of junction and
separation between a moving dark circular body and a broad illuminated
disc. In the previous century, a formidable and prevalent phenomenon,
which acquired notoriety as the "Black Drop" or "Black Ligament," had
swamped all pretensions to rigid accuracy. It may be described as
substituting adhesion for contact, the limbs of the sun and planet,
instead of meeting and parting with the desirable clean definiteness,
_clinging_ together as if made of some glutinous material, and
prolonging their connection by means of a dark band or dark threads
stretched between them. Some astronomers ascribed this baffling
appearance entirely to instrumental imperfections; others to atmospheric
agitation; others again to the optical encroachment of light upon
darkness known as "irradiation." It is probable that all these causes
conspired, in various measure, to produce it; and it is certain that its
_conspicuous_ appearance may, by suitable precautions, be obviated.
The organisation of the British forces reflected the utmost credit on
the energy and ability of Lieutenant-Colonel Tupman, who was responsible
for the whole. No useful measure was neglected. Each observer went out
ticketed with his "personal equation," his senses drilled into a species
of martial discipline, his powers absorbed, so far as possible, in the
action of a cosmopolitan observing machine. Instrumental uniformity and
uniformity of method were obtainable, and were attained; but diversity
of judgment unhappily survived the best-directed efforts for its
extirpation.
The eventful day had no sooner passed than telegrams began to pour in,
announcing an outcome of considerable, though not unqualified success.
The weather had proved generally favourable; the manifold arrangements
had worked well; contacts had been plentifully observed; photographs in
lavish abundance had been secured; a store of materials, in short, had
been laid up, of which it would take years to work out the full results
by calculation. Gradually, nevertheless, it came to be known that the
hope of a definitive issue must be abandoned. Unanimity was found to be
as remote as ever. The dreaded "black ligament" gave, indeed, less
trouble than was expected; but another appearance supervened which took
most observers by surprise. This was the illumination due to the
atmosphere of Venus. Astronomers, it is true, were not ignorant that the
planet had, on previous occasions, been seen girdled with a lucid ring;
but its power to mar observations by the distorting effect of refraction
had scarcely been reckoned with. It proved, however, to be very great.
Such was the difficulty of determining the critical instant of internal
contact, that (in Colonel Tupman's words) "observers side by side, with
adequate optical means, differed as much as twenty or thirty seconds in
the times they recorded for phenomena which they have described in
almost identical language."[767]
Such uncertainties in the data admitted of a corresponding variety in
the results. From the British observations of ingress and egress Sir
George Airy[768] derived, in 1877, a solar parallax of 8·76" (corrected
to 8·754"), indicating a mean distance of 93,375,000 miles. Mr. Stone
obtained a value of ninety-two millions (parallax 8·88"), and held any
parallax less than 8·84" or more than 8·93" to be "absolutely negatived"
by the documents available.[769] Yet, from the same, Colonel Tupman
deduced 8·81",[770] implying a distance 700,000 miles greater than Stone
had obtained. The best French observations of contacts gave a parallax
of about 8·88"; French micrometric measures the obviously exaggerated
one of 9·05".[771]
Photography, as practised by most of the European parties, was a total
failure. Utterly discrepant values of the microscopic displacements
designed to serve as sounding lines for the solar system, issued from
attempts to measure even the most promising pictures. "You might as well
try to measure the zodiacal light," it was remarked to Sir George Airy.
Those taken on the American plan of using telescopes of so great focal
length as to afford, without further enlargement, an image of the
requisite size, gave notably better results. From an elaborate
comparison of those dating from Vladivostock, Nagasaki, and Pekin, with
others from Kerguelen and Chatham Islands, Professor D. P. Todd, of
Amherst College, deduced a solar distance of about ninety-two million
miles (parallax 8·883" ±0·034"),[772] and the value was much favoured by
concurrent evidence.
On the whole, estimates of the great spatial unit cannot be said to have
gained any security from the combined effort of 1874. A few months
before the transit, Mr. Proctor considered that the uncertainty then
amounted to 1,448,000 miles;[773] five years after the transit,
Professor Harkness judged it to be still 1,575,950 miles;[774] yet it
had been hoped that it would have been brought down to 100,000. As
regards the end for which it had been undertaken, the grand campaign had
come to nothing. Nevertheless, no sign of discouragement was apparent.
There was a change of view, but no relaxation of purpose. The problem,
it was seen, could be solved by no single heroic effort, but by the
patient approximation of gradual improvements. Astronomers, accordingly,
looked round for fresh means or more refined expedients for applying
those already known. A new phase of exertion was entered upon.
On September 5, 1877, Mars came into opposition near the part of his
orbit which lies nearest to that of the earth, and Dr. Gill (now Sir
David) took advantage of the circumstance to appeal once more to him for
a decision on the _quæstio vexata_ of the sun's distance. He chose, as
the scene of his labours, the Island of Ascension, and for their plan a
method recommended by Airy in 1857,[775] but never before fairly tried.
This is known as the "diurnal method of parallaxes." Its principle
consists in substituting successive morning and evening observations
from the same spot, for simultaneous observations from remote spots, the
rotation of the earth supplying the necessary difference in the points
of view. Its great advantage is that of unity in performance. A single
mind, looking through the same pair of eyes, reinforced with the same
optical appliances, is employed throughout, and the errors inseparable
from the combination of data collected under different conditions are
avoided. There are many cases in which one man can do the work of two
better than two men can do the work of one. The result of Gill's skilful
determinations (made with Lord Lindsay's heliometer) was a solar
parallax of 8·78", corresponding to a distance of 93,080,000 miles.[776]
The bestowal of the Royal Astronomical Society's gold medal stamped the
merit of this distinguished service.
But there are other subjects for this kind of inquiry besides Mars and
Venus. Professor Galle of Breslau suggested in 1872[777] that some of
the minor planets might be got to repay astronomers for much
disinterested toil spent in unravelling their motions, by lending aid to
their efforts towards a correct celestial survey. Ten or twelve come
near enough, and are bright enough for the purpose; in fact, the absence
of sensible magnitude is one of their chief recommendations, since a
point of light offers far greater facilities for exact measurement than
a disc. The first attempt to work this new vein was made at the
opposition of Phocæa in 1872; and from observations of Flora in the
following year at twelve observatories in the northern and southern
hemispheres, Galle deduced a solar parallax of 8·87".[778] At Mauritius
in 1874, Lord Lindsay and Sir David Gill applied the "diurnal method" to
Juno, then conveniently situated for the purpose; and the continued use
of similar occasions affords an unexceptionable means for improving
knowledge of the sun's distance. They frequently recur; they need no
elaborate preparation; a single astronomer armed with a heliometer can
do all the requisite work. Dr. Gill, however, organized a more complex
plan of operations upon Iris in 1888, and upon Victoria and Sappho in
1889. A novel method was adopted. Its object was to secure simultaneous
observations made from opposite sides of the globe just when the planet
lay in the plane passing through the centre of the earth and the two
observers, the same pair of reference-stars being used on each occasion.
The displacements caused by parallax were thus in a sense doubled, since
the star to which the planet seemed approximated in the northern
hemisphere, showed as if slightly removed from it in the southern, and
_vice versâ_. As the planet pursued its course, fresh star-couples came
into play, during the weeks that the favourable period lasted. In these
determinations, only heliometers were employed. Dr. Elkin, of Yale
college, co-operated throughout, and the heliometers of Dresden,
Göttingen, Bamberg, and Leipzig, shared in the work, while Dr. Auwers of
Berlin was Sir David Gill's personal coadjutor at the Cape. Voluminous
data were collected; meridian observations of the stars of reference for
Victoria occupied twenty-one establishments during four months; the
direct work of triangulation kept four heliometers in almost exclusive
use for the best part of a year; and the ensuing toilsome computations,
carried out during three years at the Cape Observatory, filled two bulky
tomes[779] with their details. Gill's final result, published in 1897,
was a parallax of 8·802", equivalent to a solar distance of 92,874,000;
and it was qualified by a probable error so small that the value might
well have been accepted as definitive but for an unlooked-for discovery.
The minor planet Eros, detected August 14, 1898, was found to pursue a
course rendering it an almost ideal intermediary in solar
parallax-determinations. Once in thirty years, it comes within fifteen
million miles of the earth; and although the next of these choice epochs
must be awaited for some decades, an opposition too favourable to be
neglected occurred in 1900. At an International Conference, accordingly,
held at Paris in July of that year, a plan of photographic operations
was concerted between the representatives of no less than 58
observatories.[780] Its primary object was to secure a large stock of
negatives showing the planet with the comparison-stars along the route
traversed by it from October, 1900, to March, 1901,[781] and this at
least was successfully attained. Their measurement will in due time
educe the apparent displacements of the moving object as viewed
simultaneously from remote parts of the earth; and the upshot should be
a solar parallax adequate in accuracy to the exigent demands of the
twentieth century.
The second of the nineteenth-century pair of Venus-transits was looked
forward to with much abated enthusiasm. Russia refused her active
co-operation in observing it, on the ground that oppositions of the
minor planets were trigonometrically more useful, and financially far
less costly; and her example was followed by Austria; while Italian
astronomers limited their sphere of action to their own peninsula.
Nevertheless, it was generally held that a phenomenon which the world
could not again witness until it was four generations older should, at
the price of any effort, not be allowed to pass in neglect.
The persuasion of its importance justified the summoning of an
International Conference at Paris in 1881, from which, however, America,
preferring independent action, held aloof. It was decided to give
Delisle's method another trial; and the ambiguities attending and
marring its use were sought to be obviated by careful regulations for
insuring agreement in the estimation of the critical moments of ingress
and egress.[782] But in fact (as M. Puiseux had shown[783]), contacts
between the limbs of the sun and planet, so far from possessing the
geometrical simplicity attributed to them, are really made up of a
prolonged succession of various and varying phases, impossible either to
predict or identify with anything like rigid exactitude. Sir Robert Ball
compared the task of determining the precise instant of their meeting or
parting, to that of telling the hour with accuracy on a watch without a
minute hand; and the comparison is admittedly inadequate. For not only
is the apparent movement of Venus across the sun extremely slow, being
but the excess of her real motion over that of the earth; but three
distinct atmospheres--the solar, terrestrial, and Cytherean--combine to
deform outlines and mask the geometrical relations which it is desired
to connect with a strict count of time.
The result was very much what had been expected. The arrangements were
excellent, and were only in a few cases disconcerted by bad weather. The
British parties, under the experienced guidance of Mr. Stone, the late
Radcliffe observer, took up positions scattered over the globe, from
Queensland to Bermuda; the Americans collected a whole library of
photographs; the Germans and Belgians trusted to the heliometer; the
French used the camera as an adjunct to the method of contacts. Yet
little or no approach was made to solving the problem. Thus, from 606
measures of Venus on the sun, taken with a new kind of heliometer at
Santiago in Chili, M. Houzeau, of the Brussels Observatory, derived a
solar parallax of 8.907", and a distance of 91,727,000 miles.[784] But
the "probable errors" of this determination amounted to 0.084" either
way: it was subject to a "more or less" of 900,000, or to a total
uncertainty of 1,800,000 miles. The "probable error" of the English
result, published in 1887, was less formidable,[785] yet the details of
the discussion showed that no great confidence could be placed in it.
The sun's distance came out 92,560,000 miles; while 92,360,000 was given
by Professor Harkness's investigation of 1,475 American
photographs.[786] Finally, Dr. Auwers deduced from the German
heliometric measures the unsatisfactorily small value of 92,000,000
miles.[787] The transit of 1882 had not, then, brought about the desired
unanimity.
The state and progress of knowledge on this important topic were summed
up by Faye and Harkness in 1881.[788] The methods employed in its
investigation fall (as we have seen) into three separate classes--the
trigonometrical, the gravitational, and the "phototachymetrical"--an
ungainly adjective used to describe the method by the velocity of light.
Each has its special difficulties and sources of error; each has
counter-balancing advantages. The only trustworthy result from celestial
surveys, was at that time furnished by Gill's observations of Mars in
1877. But the method by lunar and planetary disturbances is unlike all
the others in having time on its side. It is this which Leverrier
declared with emphasis must inevitably prevail, because its accuracy is
continually growing.[789] The scarcely perceptible errors which still
impede its application are of such a nature as to accumulate year by
year; eventually, then, they will challenge, and must receive, a more
and more perfect correction. The light-velocity method, however,
claimed, and for some years justified, M. Faye's preference.
By a beautiful series of experiments on Foucault's principle, Michelson
fixed in 1879 the rate of luminous transmission at 299,930 (corrected
later to 299,910) kilometres a second.[790] This determination was held
by Professor Todd to be entitled to four times as much confidence as any
previous one; and if the solar parallax of 8·758" deduced from it by
Professor Harkness errs somewhat by defect, it is doubtless because
Glasenapp's "light-equation," with which it was combined, errs slightly
by excess. But all earlier efforts of the kind were thrown into the
shade by Professor Newcomb's arduous operations at Washington in
1880-1882.[791] The scale upon which they were conducted was in itself
impressive. Foucault's entire apparatus in 1862 had been enclosed in a
single room; Newcomb's revolving and fixed mirrors, between which the
rays of light were to run their timed course, were set up on opposite
shores of the Potomac, at a distance of nearly four kilometres. This
advantage was turned to the utmost account by ingenuity and skill in
contrivance and execution; and the deduced velocity of 299,860
kilometres = 186,328 miles a second, had an estimated error (30
kilometres) only one-tenth that ascribed by Cornu to his own result in
1874.
Just as these experiments were concluded in 1882, M. Magnus Nyrén, of
St. Petersburg, published an elaborate investigation of the small
annular displacements of the stars due to the successive transmission of
light, involving an increase of Struve's "constant of aberration" from
20·445" to 20·492". And from the new value, combined with Newcomb's
light-velocity, was derived a valuable approximation to the sun's
distance, concluded at 92,905,021 miles (parallax = 8·794"). Yet it is
not quite certain that Nyrén's correction was an improvement. A
differential method of determining the amount of aberration, struck out
by M. Loewy of Paris,[792] avoids most of the objections to the absolute
method previously in vogue; and the upshot of its application in 1891
was to show that Struve's constant might better be retained than
altered, Loewy's of 20·447" varying from it only to an insignificant
extent. Professor Hall had, moreover, deduced nearly the same value
(20·454") from the Washington observations since 1862, of Alpha
Lyræ (Vega); whence, in conjunction with Newcomb's rate of light
transmission, he arrived at a solar parallax of 8·81".[793] Inverting
the process, Sir David Gill in 1897 derived the constant from the
parallax. If the earth's orbit have a mean radius, as found by him, of
92,874,000 miles, then, he calculated, the aberration of
light--Newcomb's measures of its velocity being supposed exact--amounts
to 20.467". This figure can need very slight correction.
Professor Harkness surveyed in 1891,[794] from an eclectic point of
view, the general situation as regarded the sun's parallax. Convinced
that no single method deserved an exclusive preference, he reached a
plausible result through the combination, on the principle of least
squares--that is, by the mathematical rules of probability--of all the
various quantities upon which the great datum depends. It thus summed up
and harmonised the whole of the multifarious evidence bearing upon the
point, and, as modified in 1894,[795] falls very satisfactorily into
line with the Cape determination. We may, then, at least provisionally,
accept 92,870,000 miles as the length of our measuring-rod for space.
Nor do we hazard much in fixing 100,000 miles as the outside limit of
its future correction.
FOOTNOTES:
[Footnote 748: Airy, _Month. Not._, vol. xvii., p. 210.]
[Footnote 749: Mars comes into opposition once in about 780 days; but
owing to the eccentricity of both orbits, his distance from the earth at
those epochs varies from thirty-five to sixty-two million miles.]
[Footnote 750: J. D. Cassini, _Hist. Abrégée de la Parallaxe du Soleil_,
p. 122, 1772.]
[Footnote 751: The present period of coupled eccentric transits will, in
the course of ages, be succeeded by a period of single, nearly central
transits. The alignments by which transits are produced, of the earth,
Venus, and the sun, close to the place of intersection of the two
planetary orbits, now occur, the first a little in front of, the second,
after eight years less two and a half days, a little behind the node.
But when the first of these two meetings takes place very near the node,
giving a nearly central transit, the second falls too far from it, and
the planet escapes projection on the sun. The reason of the liability to
an eight-yearly recurrence is that eight revolutions of the earth are
accomplished in only a very little more time than thirteen revolutions
of Venus.]
[Footnote 752: _Die Entfernung der Sonne: Fortsetzung_, p. 108. Encke
slightly corrected his results of 1824 in _Berlin Abh._, 1835, p. 295.]
[Footnote 753: Owing to the ellipticity of its orbit, the earth is
nearer to the sun in January than in June by 3,100,000 miles. The
quantity to be determined, or "mean distance," is that lying midway
between these extremes--is, in other words, half the major axis of the
ellipse in which the earth travels.]
[Footnote 754: _Month. Not._, vol. xv., p. 9.]
[Footnote 755: _The Distance of the Sun from the Earth determined by the
Theory of Gravity_, Edinburgh, 1763.]
[Footnote 756: _Opera_, t. iii., p. 326.]
[Footnote 757: _Comptes Rendus_, t. xlvi., p. 882. The parallax 8·95"
derived by Leverrier from the above-described inequality in the earth's
motion, was corrected by Stone to 8·91". _Month. Not._, vol. xxviii., p.
25.]
[Footnote 758: _Month. Not._, vol. xxxv., p. 156.]
[Footnote 759: _Wash. Obs._, 1865, App. ii., p. 28.]
[Footnote 760: _Comptes Rendus_, t. xxix., p. 90.]
[Footnote 761: _Ibid._, t. xxx., p. 551.]
[Footnote 762: _Ibid._, t. lv., p. 501. The previously admitted velocity
was 308 million metres per second; Foucault reduced it to 298 million.
Combined with Struve's "constant of aberration" this gave 8.86" for the
solar parallax, which exactly agreed with Cornu's result from a
repetition of Fizeau's experiments in 1872. _Comptes Rendus_, t. lxxvi.,
p. 338.]
[Footnote 763: _Month. Not._, vol. xxiv., p. 103.]
[Footnote 764: _Astr. Papers of the American Ephemeris_, vol. ii., p.
263.]
[Footnote 765: _Month. Not._, vol. xvii., p. 208.]
[Footnote 766: Because closely similar to that proposed by him in _Phil.
Trans._ for 1716.]
[Footnote 767: _Month. Not._, vol. xxxviii., p. 447.]
[Footnote 768: _Ibid._, p. 11.]
[Footnote 769: _Ibid._, p. 294.]
[Footnote 770: _Ibid._, p. 334.]
[Footnote 771: _Comptes Rendus_, t. xcii., p. 812.]
[Footnote 772: _Observatory_, vol. v., p. 205.]
[Footnote 773: _Transits of Venus_, p. 89 (1st ed.).]
[Footnote 774: _Am. Jour. of Sc._, vol. xx., p. 393.]
[Footnote 775: _Month. Not._, vol. xvii., p. 219.]
[Footnote 776: _Mem. Roy. Astr. Soc._, vol. xlvi., p. 163.]
[Footnote 777: _Astr. Nach._, No. 1,897.]
[Footnote 778: Hilfiker, _Bern Mittheilungen_, 1878, p. 109.]
[Footnote 779: _Annals of the Cape Observatory_, vols. vi., vii.]
[Footnote 780: _Rapport sur l'État de l'Observatoire de Paris pour
l'Année 1900_, p. 7.]
[Footnote 781: _Observatory_, vol. xxiii., p. 311; Newcomb, _Astr.
Jour._, No. 480.]
[Footnote 782: _Comptes Rendus_, t. xciii., p. 569.]
[Footnote 783: _Ibid._, t. xcii., p. 481.]
[Footnote 784: _Bull. de l'Acad._, t. vi., p. 842.]
[Footnote 785: _Month. Not._, vol. xlviii., p. 201.]
[Footnote 786: _Astr. Jour._, No. 182.]
[Footnote 787: _Astr. Nach._, No. 3,066.]
[Footnote 788: _Comptes Rendus_, t. xcii., p. 375; _Am. Jour. of Sc._,
vol. xxii., p. 375.]
[Footnote 789: _Month. Not._, vol. xxxv., p. 401.]
[Footnote 790: _Am. Jour. of Sc._, vol. xviii., p. 393.]
[Footnote 791: _Nature_, vol. xxxiv., p. 170; _Astron. Papers of the
American Ephemeris_, vol. ii., p. 113.]
[Footnote 792: _Comptes Rendus_, t. cxii., p. 549.]
[Footnote 793: _Astr. Journ._, Nos. 169, 170]
[Footnote 794: _The Solar Parallax and its Related Constants_,
Washington, 1891.]
[Footnote 795: _Astr. and Astrophysics_, vol. xiii., p. 626.]