changes in the aspect of the science he loved so well. But we must look
back over more than half a century, if we would form an estimate of
the position of astronomy when Encke’s most notable work was achieved.
At Seeberge, under Lindenau, Encke had been perfecting himself in the
higher branches of mathematical calculation. He took the difficult
work of determining the orbital motions of newly-discovered comets
under his special charge, and Dr. Bruhns tells us that every comet
which was detected during Encke’s stay at Seeberge was subjected to
rigid scrutiny by the indefatigable mathematician. Before long a
discovery of the utmost importance rewarded his persevering labours.
Pons had detected on November 26, 1818, a comet of no very brilliant
aspect, which was watched first at Marseilles, and then at Mannheim,
until December 29. Encke next took up the work, and tracked the comet
until January 12. Combining the observations made between December 22
and January 12, he assigned to the body a parabolic orbit. But he was
not satisfied with the accordance between this path and the observed
motions of the body. When he attempted to account for the motions of
the comet by means of an orbit of comparatively short period, he was
struck by the resemblance between the path thus deduced and that of
Comet I, 1805. Gradually the idea dawned upon him that a new era was
opening for science. Hitherto the only periodical comets which had been
discovered except Lexell’s—the ‘lost comet’—had travelled in orbits
extending far out into space beyond the paths of the most distant known
planets. But now Encke saw reason to believe that he had to deal with a
comet travelling within the orbit of Jupiter. On February 5, he wrote
to the eminent mathematician Gauss, pointing out the results of his
inquiries, and saying that he only waited for the encouragement and
authority of his former teacher to prosecute his researches to the end
towards which they already seemed to point. Gauss, in reply, not only
encouraged Encke to proceed, but counselled him as to the course he
should pursue. The result we all know. Encke showed conclusively that
the newly-discovered comet travels in a path of short period, and that
it had already made its appearance several times in our neighbourhood.
From the date of this discovery, Encke took high rank among the
astronomers of Europe. His subsequent labours by no means fell
short of the promise which this, his first notable achievement, had
afforded. If he effected less as an astronomical observer than many
of his contemporaries, he was surpassed by few as a manipulator of
those abstruse formulæ by which the planetary perturbations are
calculated. It was to the confidence engendered by this skill that
we owe his celebrated discovery of the acceleration of the motion of
the comet mentioned above. Assured that he had rightly estimated the
disturbances to which the comet is subjected, he was able to pronounce
confidently that some cause continually (though all but imperceptibly)
impedes the passage of this body through space, and so—by one of
those strange relations which the student of astronomy is familiar
with—the continually retarded comet travels ever more swiftly along a
continually diminishing orbit.
Bruhns’ Life of Encke is well worth reading, not only by those who
are interested in Encke’s fame and work as an astronomer, but by
the general reader. Encke the man is presented to our view, as well
as Encke the astronomer. With loving pains the pupil of the great
astronomer handles the theme he has selected. The boyhood of Encke, his
studies, his soldier life in the great uprising against Napoleon in
1813, and his work at the Seeberge Observatory; his labours on comets
and asteroids; his investigations of the transits of 1761 and 1769; his
life as an academician, and as director of an important observatory;
his orations at festival and funeral; and lastly, his illness and
death, are described in these pages by one who held Encke in grateful
remembrance as ‘teacher and master,’ and as a ‘fatherly friend.’
Not the least interesting feature of the work is the correspondence
introduced into its pages. We find Encke in communication with
Humboldt, with Bessel and Struve, with Hansen, Olbers, and Argelander;
with a host, in fine, of living as well as of departed men of science.
(From _Nature_, March 10, 1870.)
FOOTNOTES:
[1] Other green lines have since been discovered in the auroral
spectrum; and occasionally a red line is seen.
[2] In the _Quarterly Journal of Science_ for October 1866, a more
detailed but somewhat less popular account of the subject of the above
paper is presented. A few months earlier, a skilfully-written paper
on the same subject, from the pen of Mr. J. M. Wilson, of Rugby, had
appeared in the _Eagle_, a magazine written by and for members of
St. John’s College, Cambridge. Although my paper in the _Quarterly
Journal of Science_ was written quite independently of Mr. Wilson’s
(which, however, I had read), yet it chanced that in describing the
same mathematical relations, and the same sequence of events, I here
and there used language closely resembling his. I fear this led for a
while to some misconception; but I was fortunately able to show in Mr.
De la Rue’s address to the Astronomical Society, on the same subject,
passages yet more strikingly resembling some in Mr. Wilson’s paper
(written subsequently and quite independently). The fact would seem to
be that if two persons describe exactly the same events, and deal with
exactly the same mathematical relations, it is almost certain that in
more than one passage they will use somewhat similar expressions.
I was actually indebted to Mr. Wilson’s paper for one illustration,
however,—that derived from the movements of a supposed artificial
moon; and I think that had his paper appeared in a magazine printed
for general circulation, I should have referred to it. As it was,
this seemed useless so far as the readers of the _Quarterly Journal
of Science_ were concerned. The circumstances of the case were,
indeed, far from calling for a reference; while I had in a sense made
the illustration my own by detecting an important miscalculation in
the original (the amount of advance being either doubled or halved—I
forget which). Had I referred to Mr. Wilson’s paper, I must needs have
mentioned this mistake; and it would have appeared as though I had had
no other purpose in making the reference.
I mention these matters to explain what I fear my esteemed
fellow-collegian was disposed at the time to regard as either a wrong
or a slight. Nothing was further from my intention than either.
_VENUS ON THE SUN’S FACE._
More than a century ago scientific men were looking forward with eager
interest to the passage of the planet Venus across the sun’s face in
1769. The Royal Society judged the approaching event to be of such
extreme importance to the science of astronomy that they presented a
memorial to King George III., requesting that a vessel might be fitted
out, at Government expense, to convey skilful observers to one of the
stations which had been judged suitable for observing the phenomenon.
The petition was complied with, and after some difficulty as to the
choice of a leader, the good ship ‘Endeavour,’ of 370 tons, was placed
under the command of Captain Cook. The astronomical work entrusted to
the expedition was completely successful; and thus it was held that
England had satisfactorily discharged her part of the work of utilising
the rare phenomenon known as a transit of Venus.
A century passed, and science was again awaiting with interest the
approach of one of these transits. But now her demands were enlarged.
It was not one ship that was asked for, but the full cost and charge of
several expeditions. And this time, also, science had been more careful
in taking time by the forelock. The first hints of her requirements
were heard some fourteen years ago, when the Astronomer-Royal began
that process of laborious inquiry which a question of this sort
necessarily demands. Gradually, her hints became more and more
plain-spoken; insomuch that Airy—her mouthpiece in this case—stated
definitely in 1868 what he thought science had a right to claim from
England in this matter. When the claim came before our Government, it
was met with a liberality which was a pleasing surprise after some
former placid references of scientific people to their own devices.
The sum of ten thousand five hundred pounds was granted to meet the
cost of several important and well-appointed expeditions; and further
material aid was derived from the various Government observatories.
And now let us inquire why so much interest is attached to a phenomenon
which appears, at first sight, to be so insignificant. Transits,
eclipses, and other phenomena of that nature are continually occurring,
without any particular interest being attached to them. The telescopist
may see half-a-dozen such phenomena in the course of a night or two,
by simply watching the satellites of Jupiter, or the passage of our
moon over the stars. Even the great eclipse of 1868 did not attract so
much interest as the transit of Venus; yet that eclipse had not been
equalled in importance by any which has occurred in historic times,
and hundreds of years must pass before such another happens, whereas
transits of Venus are far from being so uncommon.
The fact is, that Venus gives us the best means we have of mastering a
problem which is one of the most important within the whole range of
the science of astronomy. I use the term important, of course, with
reference to the scientific significance and interest of the problem.
Practically, it matters little to us whether the sun is a million of
miles or a thousand millions of miles from us. The subject must in
any case be looked upon as an extra-parochial one. But science does
occasionally attach immense interest to extra-parochial subjects. And
this is neither unwise nor unreasonable, since we find implanted
in our very nature—and not merely in the nature of scientific men—a
quality which causes us to take interest in a variety of matters
that do not in the least concern our personal interests. Nor is this
quality, rightly considered, one of the least noble characteristics of
the human race.
That the determination of the sun’s distance is important, in an
astronomical sense, will be seen at once when it is remembered that
the ideas we form of the dimensions of the solar system are wholly
dependent on our estimate of the sun’s distance. Nor can we gauge the
celestial depths with any feeling of assurance, unless we know the
true length of that which is our sole measuring-rod. It is, in fact,
our basis of measurement for the whole visible universe. In some
respects, even if we knew the sun’s distance exactly, it would still
be an unsatisfactory gauge for the stellar depths. But that is the
misfortune, not the fault, of the astronomer, who must be content to
use the measuring-rod which nature gives him. All he can do is to find
out as nearly as possible its true length.
When we come to consider how the astronomer is to determine this
very element—the sun’s distance—we find that he is hampered with a
difficulty of precisely the same character.
The sun being an inaccessible object, the astronomer can apply no other
methods to determine its distance—directly—than those which a surveyor
would use in determining the distance of an inaccessible castle, or
rock, or tree, or the like. We shall see presently that the ingenuity
of astronomers has, in fact, suggested some other indirect methods.
But clearly the most satisfactory estimate we can have of the sun’s
distance is one founded on such simple notions and involving in the
main such processes of calculation as we have to deal with in ordinary
surveying.
There is, in this respect, no mystery about the solution of the famous
problem. Unfortunately, there is enormous difficulty.
When a surveyor has to determine the distance of an inaccessible
object, he proceeds in the following manner. He first very carefully
measures a base-line of convenient length. Then from either end of
the base-line he takes the bearing of the inaccessible object—that
is, he observes the direction in which it lies. It is clear that, if
he were now to draw a figure on paper, laying down the base-line to
some convenient scale, and drawing lines from its ends in directions
corresponding to the bearings of the observed object, these lines would
indicate, by their intersection, the true relative position of the
object. In practice, the mathematician does not trust to so rough a
method as construction, but applies processes of calculation.
Now, it is clear that in this plan everything depends on the base-line.
It must not be too short in comparison with the distance of the
inaccessible object; for then, if we make the least error in observing
the bearings of the object, we get an important error in the resulting
determination of the distances. The reader can easily convince himself
of this by drawing an illustrative case or two on paper.
The astronomer has to take his base-line for determining the sun’s
distance, upon our earth, which is quite a tiny speck in comparison
with the vast distance which separates us from the sun. It had been
found difficult enough to determine the moon’s distance with such a
short base-line to work from. But the moon is only about a quarter of
a million of miles from us, while the sun is more than ninety millions
of miles off. Thus the problem was made several hundred times more
difficult—or, to speak more correctly, it was rendered simply insoluble
unless the astronomer could devise some mode of observing which should
vastly enhance the power of his instruments.
For let us consider an illustrative case. Suppose there was a steeple
five miles off, and we had a base-line only two feet long. That would
correspond as nearly as possible to the case the astronomer has to deal
with. Now, what change of direction could be observed in the steeple
by merely shifting the eye along a line of two feet? There is a ready
way of answering. Invert the matter. Consider what a line of two feet
long would look like if viewed from a distance of five miles. Would
its length be appreciable, to say nothing of its being measurable? Yet
it is just such a problem as the measurement of that line which the
astronomer would have to solve.
But even this is not all. In our illustration only one observer is
concerned, and he would be able to use one set of instruments.
Suppose, however, that from one end of the two-feet line an observer
using one set of instruments took the bearings of the steeple; and
that, half a year after, another observer brought another set of
instruments and took the bearing of the steeple from the other end of
the two-feet line, is it not obvious how enormously the uncertainty
of the result would be increased by such an arrangement as this? One
observer would have his own peculiar powers of observation, his own
peculiar weaknesses: the other would have different peculiarities. One
set of instruments would be characterised by its own faults or merits,
so would the other. One series of observations would be made in summer,
with all the disturbing effects due to heat; the other would be made in
winter, with all the disturbing effects due to cold.
The observation of the sun is characterised by all these difficulties.
Limited to the base-lines he can measure on earth, the astronomer must
set one observer in one hemisphere, another in the other. Each observer
must have his own set of instruments; and every observation which one
has made in summer will have to be compared with an observation which
the other has made in winter.
Thus we can understand that astronomers should have failed totally when
they attempted to determine the sun’s distance without aid from the
other celestial bodies.
It may seem at first sight as though nothing the other celestial bodies
could tell the astronomer would be of the least use to him, since
these bodies are for the most part farther off than the sun, and even
those which, approach nearest to us are still far beyond the limits of
distance within which the simple plan followed by surveyors could be of
any service. And besides, it might be supposed that information about
the distance of one celestial body could be of no particular service
towards the determination of the distance of another.
But two things aid the astronomer at this point. First of all, he has
discovered the law which associates together the distances of all the
planets from the sun; so that if he can determine the distance of any
one planet, he learns immediately the distances of all. Secondly, the
planets in their motion travel occasionally into such positions that
they become mighty indices, tracing out on a natural dial-plate the
significant lesson from which the astronomer hopes to learn so much.
To take an instance from the motions of another planet than the one
we are dealing with. Mars comes sometimes so near the earth that the
distance separating us from him is little more than one-third of that
which separates us from the sun. Suppose that, at such a time, he
is seen quite close to a fixed star. That star gives the astronomer
powerful aid in determining the planet’s distance. For, to observers in
some parts of the earth, the planet will seem nearer to the star than
he will to observers elsewhere. A careful comparison of the effects
thus exhibited will give significant evidence respecting the distance
of Mars. And we see that the star has served as a fixed mark upon the
vast natural dial of the heavens, just as the division-marks on a
clock-face serve to indicate the position of the hands.
Now we can at once see why Venus holds so important a position in this
sort of inquiry. Venus is our nearest neighbour among the planets.
She comes several millions of miles nearer to us than Mars, our next
neighbour on the other side. That is the primary reason of her being
so much considered by astronomers. But there is another of equal
importance. Venus travels nearer than our earth to the sun. And thus
there are occasions when she gets directly between the earth and the
sun. At those times she is seen upon his face, and his face serves as
a dial-plate by which to measure her movements. When an observer at
one part of the earth sees her on one part of the sun’s face, another
observer at some other part of the earth will see her on another, and
the difference of position, if accurately measured, would at once
indicate the sun’s distance. As a matter of fact, other modes of
reading off the indications of the great dial-plate have to be adopted.
Before proceeding to consider those modes, however, we must deal with
one or two facts about Venus’s movements which largely affect the
question at issue.
Let us first see what we gain by considering the distance of Venus
rather than that of the sun.
At the time of a transit Venus is of course on a line between the earth
and the sun, and she is at somewhat less than a third of the sun’s
distance from us. Thus whatever effect an observer’s change of place
would produce upon the sun would be more than trebled in the case of
Venus. But it must not be forgotten that we are to judge the motions
of Venus by means of the dial-plate formed by the solar disc, and that
dial-plate is itself shifted as the observer shifts his place. Venus is
shifted three times as much, it is true; but it is only the balance of
change that our astronomer can recognise. That balance is, of course,
rather more than twice as great as the sun’s change of place.
So far, then, we have not gained much, since it has been already
mentioned that the sun’s change of place is not measurable by any
process of observation astronomers can apply.
It is to the fact that we have the sun’s disc, whereby to measure the
change, that we chiefly trust; and even that would be insufficient were
it not for the fact that Venus is not at rest, but travels athwart the
great solar dial-plate. We are thus enabled to make a time measurement
take the place of a measurement of space. If an observer in one place
sees Venus cross the sun’s face at a certain distance from the centre,
while an observer at another place sees her follow a path slightly
farther from the centre, the transit clearly seems longer to the former
observer than to the latter.
This artifice of exchanging a measurement of time for one of space—or
_vice versâ_—is a very common one among astronomers. It was Edmund
Halley, the friend and pupil of Sir Isaac Newton, who suggested its
application in the way above described. It will be noticed that what
is required for the successful application of the method is that one
set of observers should be as far to the north as possible, another as
far to the south, so that the path of Venus may be shifted as much as
possible. Clearly the northern observers will see her path shifted as
much to the south as it can possibly be, while the southern observers
will see the path shifted as far as possible towards the north.
One thing, however, is to be remembered. A transit lasts several hours,
and our observers must be so placed that the sun will not set during
these hours. This consideration sometimes involves a difficulty. For
our earth does not supply observing room all over her surface, and the
region where observation would be most serviceable may be covered by
a widely-extended ocean. Then again, the observing parties are being
rapidly swayed round by the rotating earth and it is often difficult
to fix on a spot which may not, through this cause, be shifted from a
favourable position at the beginning of the transit to an unfavourable
one at the end.
Without entering on all the points of difficulty involved by such
considerations as these, I may simply indicate the fact that the
astronomer has a problem of considerable complexity to solve in
applying Halley’s method of observation to a transit of Venus.
It was long since pointed out by the French astronomer Delisle that the
subject may be attacked another way—that, in fact, instead of noticing
how much longer the transit lasts in some places than in others, the
astronomer may inquire how much earlier it begins or ends in some
places than in others.
Here is another artifice, extremely simple in principle, though not
altogether so simple in its application. My readers must bear with
me while I briefly describe the qualities of this second method,
because in reality the whole question of the transit, and all the
points which have to be attended to in the equipment and placing of
the various observing parties, depend on these preliminary matters.
Without attending to them—or at least to such primary points as I
shall select—it would be impossible to form a clear conception of the
circumstances with which astronomers have to deal. There is, however,
no real difficulty about this part of the subject, and I shall only ask
of the reader to give his attention to it for a very brief space of
time.
Suppose the whole of that hemisphere of the earth on which the sun is
shining when the transit is about to begin were covered with observers
waiting for the event. As Venus sweeps rapidly onwards to the critical
part of her path, it is clear that some of these observers will get
an earlier view of the commencement of the transit than others will;
just as at a boat-race, persons variously placed round a projecting
corner of the course see the leading boat come into view at different
times. Some one observer on the outer rim of the hemisphere would be
absolutely the first to see the transit begin. Then rapidly other
observers would see the phenomenon; and in the course of a few minutes
some one observer on the outer rim of the hemisphere—almost exactly
opposite the first—would be absolutely the last to see the transit
begin. From that time the transit would be seen by all for several
hours—I neglect the earth’s rotation, for the moment—but the end of the
transit, like the beginning, would not be seen simultaneously by the
observers. First one would see it, then in succession the rest, and
last of all an observer almost exactly opposite the first.
Now, here we have had to consider four observers who occupy exceptional
positions. There is (1) the observer who sees the transit begin
earliest, (2) the one who sees it begin latest, (3) the one who sees it
end earliest, and (4) the one who sees it end latest. Let us consider
the first two only. Suppose these two observers afterwards compared
notes, and found out what was the exact difference of time between
their respective observations. Is it not clear that the result would
at once afford the means of determining the sun’s distance? It would
be the simplest of all possible astronomical problems to determine
over what proportion of her orbit Venus passed in the interval of time
which elapsed between these observations; and the observers would now
have learned that that portion of Venus’s orbit is so many miles long,
for they know what distance separated them, and it would be easy to
calculate how much less that portion of Venus’s orbit is. Thus they
would learn what the length of her whole orbit is, thence her distance
from the sun, and thence the sun’s distance from us.
The two observers who saw the transit end earliest and latest could do
the like.