the soul of the astronomer, this is Delisle’s method of utilising a
transit. It has obviously one serious disadvantage as compared with
the other. An observer at one side of the earth has to bring his
observations into comparison with those made by an observer at the
other side of the earth. Each uses the local time of the place at which
he observes, and it has been calculated that for the result to be of
value there must not be an error of a single second in their estimates
of local time. Now, does the reader appreciate the full force of this
proviso? Each observer must know so certainly in what exact longitude
he is, that his estimate of the time when true noon occurs shall not be
one second wrong! This is all satisfactory enough in places where there
are regular observatories. But matters are changed when we are dealing
with such places as Woahoo, Kerguelen Land, Chatham Island, and the
wilds of Siberia.
In the transit[3] of 1874 there are many such difficulties to be
encountered. In fact, it is almost impossible to conceive a transit
the circumstances of which are more inconvenient. On the other hand,
however, the transit is of such a nature that if once the preliminary
difficulties are overcome, we can hope more from its indications than
from those of any other transit which will happen in the course of the
next few centuries.
The transit will begin earliest for observers in the neighbourhood
of the Sandwich Islands, latest for observers near Crozet Island,
far to the south-east of the Cape of Good Hope. It ends earliest for
observers far to the south-west of Cape Horn, latest for observers in
the north-eastern part of European Russia. Thus we see that, so far as
the application of our second method is concerned, the suitable spots
are not situated in the most inviting regions of the earth’s surface.
As the transit happens on December 8, 1874, the principal northern
stations will be very bleak abodes for the observers. The southern
stations are in yet more dreary regions,—notwithstanding the fact that
the transit occurs during the summer of the southern hemisphere.
For the application of Halley’s method we require stations where
the whole transit will be visible; and as the days are very short
at the northern stations in December, it is as respects these that
we encounter most difficulty. However, it has been found that many
places in Northern China, Japan, Eastern Siberia, and Manchouria are
suitable for the purpose. The best southern stations for this method
lie unfortunately on the unexplored Antarctic continent and the islands
adjacent to it; but Crozet Island, Kerguelen Land, and some other
places more easy of access than the Antarctic continent, will serve
very well. Indeed, England has so many stations to occupy elsewhere
that it is doubtful whether she will care to undertake the dangerous
and difficult task of exploring the Antarctic wastes to secure the best
southern stations. The work may fairly be left to other nations, and
doubtless will be efficiently carried out.
What England will actually undertake has not yet been fully decided
upon. We may be quite certain that she will send out a party to Woahoo
or Hawaii to observe the accelerated commencement of the transit.
She will also send observers to watch the retarded commencement, but
whether to Crozet Island, Kerguelen Land, Mauritius, or Rodriguez is
uncertain. Possibly two parties will be sent out for this purpose, and
most likely Rodriguez and Mauritius will be the places selected. It
had been thought until lately that the sun would be too low at some of
the places when the transit begins, but a more exact calculation of
the circumstances of the transit has shown this to be a mistake. Both
Crozet Island and Kerguelen Land are very likely to be enveloped in
heavy mists when the transit begins—that is, soon after sunrise—hence
the choice of Mauritius and Rodriguez as the most suitable station.
England will also be called on to take an important part in observing
the accelerated end of the transit. A party will probably be sent to
Chatham Island or Campbell Island, not far from New Zealand. It had
been thought that at the former island the sun would be too low; but
here, again, a more exact consideration of the circumstances of the
transit has led astronomers to the conclusion that the sun will be
quite high enough at this station.
The Russian observers are principally concerned with the observation
of the retarded end of the transit, nearly all the best stations lying
in Siberia. But there are several stations in British India where
this phase can be very usefully observed; and doubtless the skilful
astronomers and mathematicians who are taking part in the survey of
India will be invited—as at the time of the great eclipse—to give their
services in the cause of science. Alexandria, also, though inferior
to several of the Indian stations, will probably be visited by an
observing party from England.
It will be seen that England will thus be called on to supply about
half-a-dozen expeditions to view the transit. All of these will be sent
out in pursuance of Delisle’s mode of utilising a transit, so that, for
reasons already referred to, it will be necessary that they should be
provided with instruments of the utmost delicacy, and very carefully
constructed.[4] They will have to remain at their several stations for
a long time before the transit takes place—several months, at least—so
that they may accurately determine the latitude of the temporary
observatories they will erect. This is a work requiring skilled
observers and recondite processes of calculation. Hence it is that the
cost of sending out these observing parties is so considerable.
The only English party which will apply Halley’s method of observation
is the one which will be stationed at Mauritius, under Lord Lindsay.
This part of their work will be comparatively easy, the method only
requiring that the duration of the transit should be carefully
timed. In fact, one of the great advantages of Halley’s method is
the smallness of the expense it involves. A party might land the day
before the transit, and sail away the day after, with results at
least as trustworthy as those which a party applying Delisle’s method
could obtain after several months of hard work. It is to this, rather
than any other cause, that the small expense of the observations
made in 1769 is to be referred. And doubtless had it been decided
by our astronomical authorities to apply Halley’s method solely or
principally, the expense of the transit-observations would have been
materially lessened. There would, however, have been a risk of failure
through the occurrence of bad weather at the critical stations; whereas
now—as other nations will doubtless avail themselves of Halley’s
method—the chance that the transit-observations will fail through
meteorological causes is very largely diminished. Science will owe much
to the generosity of England in this respect.
It is, indeed, only recently that the possibility of applying Halley’s
method has been recognised. It had been thought that the method must
fail totally in 1874. But on a more careful examination of the
circumstances of the transit, a French astronomer, M. Puiseux, was
enabled to announce that this is not the case. Almost simultaneously I
published calculations pointing to a similar result; but having carried
the processes a few steps further than M. Puiseux, I was able to show
that Halley’s method is not only available in 1874, but is the more
powerful method of the two.
Unfortunately, there is an element of doubt in the inquiry, of which
no amount of care on the part of our observers and mathematicians will
enable them to get rid. I refer to the behaviour of Venus herself. It
is to the peculiarity we are now to consider that the _quasi_-failure
of the observations made in 1769 must be attributed. It is true that
Mr. Stone, the first-assistant at the Greenwich Observatory, has
managed to remove the greater part of the doubts which clouded the
results of those observations. But not even his skill and patience can
serve to remove the blot which a century of doubt has seemed to throw
upon the most exact of the sciences. We shall now show how much of the
blame of that unfortunate century of doubt is to be ascribed to Venus.
At a transit, astronomers confine their attention to one particular
phase—the moment, namely, when Venus just seems to lie wholly within
the outline of the sun’s disc. This at least was what Halley and
Delisle both suggested as desirable. Unfortunately, Venus had not
been consulted, and when the time of the transit came she declined
to enter upon or leave the sun’s face in the manner suggested by the
astronomers. Consider, for example, her conduct when entering on the
sun’s face:—
At first, as the black disc of the planet gradually notched the edge of
the sun’s disc, all seemed going on well. But when somewhat more than
half of the planet was on the sun’s face, it began to be noticed that
Venus was losing her rotundity of figure. She became gradually more and
more pear-shaped, until at last she looked very much like a peg-top
touching with its point the edge of the sun’s disc. Then suddenly—‘as
by a lightning flash,’ said one observer—the top lost its peg, and then
gradually Venus recovered her figure, and the transit proceeded without
further change on her part until the time came for her to leave the
sun’s face, when similar peculiarities took place in a reversed order.
Here was a serious difficulty indeed. For when was the moment of true
contact? Was it when the peg-top figure seemed just to touch the edge
of the sun? This seemed unlikely, because a moment after the planet
was seen well removed from the sun’s edge. Was it when the rotund part
of the planet belonged to a figure which would have touched the sun’s
edge if the rotundity had been perfect elsewhere? This, again, seemed
unlikely, because at this moment the black band connecting Venus and
the sun was quite wide. And, besides, if this were the true moment of
contact, what eye could be trusted to determine the occurrence of a
relation so peculiar? Yet the interval between this phase and the final
or peg-top phase lasted several seconds—as many as twenty-two in one
instance in 1769—and the whole success of the observation depended on
exactness within three or four seconds at the outside.
We know that Venus will act in precisely the same manner in 1874. If
we had been induced to hope that improvements in our telescopes would
diminish the peculiarity, the observations of the transit of Mercury,
in November 1868, would have sufficed to destroy that hope, for even
with the all but perfect instruments of the Greenwich Observatory,
Mercury assumed the peg-top disguise in the most unpleasing manner.
It may be asked, then, What do astronomers propose to do in 1874 to
prevent Venus from misleading them again as she did in 1769? Much has
already been done towards this end. Mr. Stone undertook a series of
careful researches to determine the law according to which Venus may be
expected to behave, or to misbehave herself; and the result is, that he
has been able to tell the observers exactly what they will have to look
for, and exactly what it is most important that they should record. In
1769, observers recorded their observations in such doubtful terms,
owing to their ignorance of the real significance of the peculiarities
they witnessed, that the mathematicians who had to make use of those
observations were misled. _Hinc illæ lacrymæ._ Hence it is that an
undeserved reproach has fallen upon the ‘exact science.’
The amount of the error resulting from the misinterpretation of the
observations made in 1769 was, however, very small indeed, when its
true character is considered. It is, indeed, easy to make the error
seem enormous. The sun’s distance came out some four millions of miles
too large, and that seems no trifling error. Then, again, the resulting
estimate of the distance of Neptune came out more than a hundred
million miles too great; while even this enormous error was as nothing
when compared with that which resulted when the distances of the fixed
stars were considered.
But this is an altogether erroneous mode of estimating the effect of
the error. It would be as absurd to count up the number of hairs’
breadth by which the geographer’s estimates of the length and breadth
of England may be in error. In all such matters it is relative and not
absolute error we have to consider. A microscopist would have made a
bad mistake who should over-estimate the length of a fly’s proboscis
by a single hair’s breadth; but the astronomer had made a wonderfully
successful measurement of the sun’s distance who deduced it within
three or four millions of miles of the true value. For it is readily
calculable that the error in the estimated relative bearing of the sun
as seen from opposite sides of the earth corresponds to the angle which
a hair’s breadth subtends when seen from a distance of 125 feet.
The error was first detected when other modes of determining the sun’s
distance were applied by the skilful astronomers and physicists of
our own day. We have no space to describe as fully as they deserve
the ingenious processes by which the great problem has been attacked
without aid from Venus. Indeed, we can but barely mention the
principles on which those methods depend. But to the reader who takes
interest in astronomy, we can recommend no subject as better worth
studying than the masterly researches of Foucault, Leverrier, and
Hansen upon the problem of the sun’s distance.
The problem has been attacked in four several ways. First, the
tremendous velocity of light has been measured by an ingenious
arrangement of revolving mirrors; the result combined with the
known time occupied by light in travelling across the earth’s orbit
immediately gives the sun’s distance. Secondly, a certain irregularity
in the moon’s motion, due to the fact that she is most disturbed by the
sun when traversing that half of her path which is nearest to him, was
pressed into the service with similar results. Thirdly, an irregularity
in the earth’s motion, due to the fact that she circles around the
common centre of gravity of her own mass and the moon’s, was made a
means of attacking the problem. Lastly, Mars, a planet which, as we
have already mentioned, approaches us almost as nearly as Venus, was
found an efficient ally.
The result of calculations founded on these methods showed that the
sun’s distance, instead of being about 95,000,000 miles, is little
more than 91,500,000 miles. And recently a re-examination of the
observations made upon Venus in 1769 led Mr. Stone to believe that they
point to a similar result.
Doubtless, however, we must wait for the transit of Venus in 1874
before forming a final decision as to the estimate of the sun’s
distance which is to take its place in popular works on astronomy
during the next century or so. Nothing but an unlooked-for combination
of unfavourable circumstances can cause the failure of our hopes.
Certainly, if we should fail in obtaining satisfactory results in 1874,
the world will not say that the generosity of the English Government
has been in fault, since it would be difficult to find a parallel in
the history of modern science to the munificence of the grant which
has been made this year for expeditions to observe a phenomenon whose
interest and importance are purely scientific.
(From _St. Paul’s_, October 1869.)
FOOTNOTES:
[3] The reader will remember the time at which the essay appeared. For
several reasons it seems well to leave the essay unaltered. In the
second series of Light Science a later stage is presented, and the
account is carried up to the present date in my work on _The Transits
of Venus_.
[4] It is held to be of the utmost importance that all the observing
parties should use similar telescopes.
_BRITAIN’S COAL CELLARS._
It would have been deemed a strange thought in the days of the Tudors
to suggest that England’s greatness would one day depend,—or seem to
depend,—on her stores of coal, a mineral then regarded as only an
unpleasant rival of the wood-log for household fires. When Shakespeare
put into the mouth of Faulconbridge the words—
This England never did, nor never shall,
Lie at the proud foot of a conqueror,
But when it first did help to wound itself,
he would have thought it a singular proviso that England should be
watchful of her coal stores if she would preserve her position among
the nations. And yet there is a closer connection between the present
greatness of Britain and the mighty coal cellars underlying certain
British counties than we are commonly prepared to acknowledge. Saxon
steadiness and Norman energy have doubtless played their part in
placing Britain in the position she now holds; but whatever may have
been the case in past ages of our history, it is certain that at
present there is much truth in Liebig’s assertion that England’s power
is in her coal. The time may come again, as the time has been, when we
shall be less dependent on our coal stores,—when bituminous bankruptcy
will not be equivalent to national bankruptcy; but if all our coal
mines were at this moment rendered unworkable, the power of England
would receive a shock from which it would be ages in recovering.
I have quoted an assertion made many years since by Baron Liebig. The
assertion was accompanied by another not less striking. ‘Civilisation,’
he said, ‘is the economy of power; and English power is coal.’ It is
on this text that I propose now to comment. There has recently been
issued a Blue Book, bearing in the most important manner on the subject
of England’s coal-supply. For five years fifteen eminent Commissioners
have been engaged in examining the available evidence respecting the
stores of coal contained in the various coal-fields of Great Britain.
Their inquiries were commenced soon after the time when the fears of
the country on this subject were first seriously awakened; and were
directed specially to ascertain how far those fears were justified
by the real circumstances of the case. It will be well to compare
the various opinions which were expressed before the inquiries were
commenced, with the results which have now been obtained.
In the first place it should be noticed that the subject had attracted
the attention of men of science many years ago. Some forty years[5]
have passed since Dr. Buckland, in one of the Bridgewater Treatises,
pointed to the necessity for a careful examination of our coal stores,
lest England should drift unawares into what he called ‘bituminous
bankruptcy.’ At that time the quantity of coal raised annually in
England amounted to but about forty millions of tons. Ten years later
the annual yield had risen to about fifty millions of tons; and then
another warning voice was raised by Dr. Arnold. Ten more years passed,
and the annual yield had increased to 83,635,214 tons, when Mr. Hull
made the startling announcement that our coal stores would last us but
about two centuries, unless some means were adopted to check the lavish
expenditure of our black diamonds.
But it was undoubtedly the address of Sir W. Armstrong to the British
Association, in 1863, which first roused the attention of the country
to the importance of the subject. ‘The greatness of England,’ he said,
‘depends much upon the superiority of her coal, in cheapness and
quality, over that of other nations. But we have already drawn from our
choicest mines a far larger quantity of coal than has been raised in
all other parts of the world put together; and the time is not remote
when we shall have to encounter the disadvantages of increased cost
of working and diminished value of produce.’ Then he summed up the
state of the case as he viewed it. ‘The entire quantity of available
coal existing in these islands has been calculated to amount to 80,000
millions of tons, which, at the present rate of consumption, would be
exhausted in 930 years; but with a continued yearly increase of 2¾
millions of tons would only last 212 years.’
Other statements were not wanting, however, which presented matters in
a more favourable light. Mr. Hussey Vivian, M.P., expressed the opinion
that South Wales alone could supply all England with coals for 500
years. Mr. R. C. Taylor, of the Geological Society, said that our coal
stores would suffice for 1,700 years. And there were some who adopted a
yet more sanguine view of our position.