regarding thoughtfully the stately motion of the sidereal system,
as exhibited on a magnified, and, therefore, appreciable scale by
a powerful telescope, should speak of the connection between this
movement and the intrinsic worth of a sovereign. The natural thought
with most men would be that ‘too much learning’ had made the astronomer
mad. Yet, when we come to inquire closely into the question of a
sovereign’s intrinsic value, we find ourselves led to the diurnal
motion of the stars, and that by no very intricate path. For, What
is a sovereign? A coin containing so many grains of gold mixed with
so many grains of alloy. A grain, we know, is the weight of such and
such a volume of a certain standard substance—that is, so many cubic
inches, or parts of a cubic inch, of that substance. But what is an
inch? It is determined, we find, as a certain fraction of the length
of a pendulum vibrating seconds in the latitude of London. A second,
we know, is a certain portion of a mean solar day, and is practically
determined by a reference to what is called a sidereal day—the
interval, namely, between the successive passages by the same star of
the celestial meridian of any fixed place. This interval is assumed to
be constant, and it has, indeed, been described as the ‘one constant
element’ known to astronomers.
We find, then, that there is a connection, and a very important
connection, between the motion of the stars and our measures, not
merely of value, but of weight, length, volume, and time. In fact, our
whole system of weights and measures is founded on the apparent diurnal
motion of the sidereal system, that is, on the real diurnal rotation
of the earth. We may look on the meridian-plane in which the great
transit-telescope of the Greenwich Observatory is made to swing, as
the gigantic hand of a mighty dial, a hand which, extending outwards
among the stars, traces out for us, by its motion among them, the exact
progress of time, and so gives us the means of weighing, measuring,
and valuing terrestrial objects with an exactitude which is at present
_beyond_ our wants.
The earth, then, is our ‘chief time-piece,’ and it is of the
correctness of this giant clock that I am now to speak.
But how can we test a time-piece whose motions we select to regulate
every other time-piece? If a man sets his watch every morning by the
clock at Westminster, it is clearly impossible for him to test the
accuracy of that clock by the motions of his watch. It would, indeed,
be possible to detect any gross change of rate; but for the purpose of
illustration I assume, what is indeed the case, that the clock is very
accurate, and therefore that minute errors only are to be looked for
even in long intervals of time. And just as the watch set by a clock
cannot be made use of to test the clock for small errors, so our best
time-pieces cannot be employed to detect slow variations, if any such
exist, in the earth’s rotation-period.
Sir William Herschel, who early saw the importance of the subject,
suggested another method. Some of the planets rotate in such a manner,
and bear such distinct marks upon their surface, that it is possible,
by a series of observations extending over a long interval of time, to
determine the length of their rotation-period within a second or two.
Supposing their rotation uniform, we at once obtain an accurate measure
of time. Supposing their rotation _not_ uniform, we obtain—(1) a hint
of the kind of change we are looking for; and (2), by the comparison of
two or more planets, the means of guessing how the variation is to be
distributed between the observed planets and our earth.
Unfortunately, it turned out that Jupiter, one of the planets
from which Herschel expected most, does _not_ afford us exact
information-his real surface being always veiled by his dense and
vapour-laden atmosphere. Saturn, Venus, and Mercury are similarly
circumstanced, and are in other respects unfavourable objects for
this sort of observation. Mars only, of all the planets, is really
available. Distinctly marked (in telescopes of sufficient power) with
continents and oceans, which are rarely concealed by vapours, this
planet is in other respects fortunately situated. For it is certain
that whatever variations may be taking place in planetary rotations
must be due to external agencies. Now, Saturn and Jupiter have their
satellites to influence (perhaps appreciably in long intervals of time)
their rotation-movements. Venus and Mercury are near the sun, and are
therefore in this respect worse off than the earth, whose rotation
is in question. Mars, on the other hand, farther removed than we are
from the sun, having also no moon, and being of small dimensions
(a very important point, be it observed, since the tidal action of
the sun depends on the dimensions of a planet), is likely to have a
rotation-period all but absolutely constant.
Herschel was rather unfortunate in his observations of Mars. Having
obtained a rough approximation from Mars’ rotation in an interval
of two days—this rough approximation being, as it chanced, only
thirty-seven seconds in excess of the true period, he proceeded to
take three intervals of one month each. This should have given a much
better value; but, as it happened, the mean of the values he obtained
was forty-six seconds too great. He then took a period of two years,
and being misled by the erroneous values he had already obtained, he
_missed one rotation_, getting a value two minutes too great. Thirty
years ago, two German astronomers, Beer and Madler, tried the same
problem, and taking a period of seven years, obtained a value which
exceeds the true value by only one second. Another German, Kaiser,
by combining more observations, obtained a value which is within
one-fifteenth of a second of the true value. But a comparison of
observations extending over 200 years has enabled me to obtain a value
which I consider to lie within one-hundredth part of a second of the
truth. This value for Mars’ rotation-period is 24 hours 37 minutes
22·73 seconds.
Here, then, we have a result so accurate, that _at some future time_
it may serve to test the earth’s rotation-period. We have compared
the rotation-rate of our test-planet with the earth’s rate during the
past 200 years; and therefore, if the earth’s rate vary by more than
one-hundredth of a second in the next two or three hundred years, we
shall—or rather our descendants will—begin to have some notion of the
change at the end of that time.
But in the meantime, mankind being impatient, and not willing to leave
to a distant posterity any question which can possibly be answered
_now_, astronomers have looked around them for information available at
once on this interesting point. The search has not been in vain. In
fact, we are able to announce, with an approach to positiveness, that
our great terrestrial time-piece is actually _losing time_.
In our moon we have a neighbour which has long been in the habit of
answering truthfully questions addressed to her by astronomers. Of
old, she told Newton about gravitation, and when he doubted, and
urged opposing evidence offered—as men in his time supposed—by the
earth, she set him on the right track, so that when in due time the
evidence offered by the earth was corrected, Newton was prepared
at once to accept and propound the noble theory which rendered his
name illustrious. Again, men wished to learn the true shape of the
earth, and went hither and thither measuring its globe; but the moon,
meanwhile, told the astronomer who remained at home a truer tale. They
sought to learn the earth’s distance from the sun, and from this and
that point they turned their telescopes on Venus in transit; but the
moon set them nearer the truth, and that not by a few miles, but by
2,000,000 miles or more. We shall see that she has had something to say
about our great terrestrial time-piece.
One of the great charms of the science of astronomy is, that it enables
men to _predict_. At such and such an hour, the astronomer is able
to say, a celestial body will occupy such and such a point on the
celestial sphere. You direct a telescope towards the point named, and
lo! at the given instant, the promised orb sweeps across the field
of view. Each year there is issued a thick octavo volume crowded
with such predictions, three or four years in advance of the events
predicted; and these predictions are accepted with as little doubt by
astronomers as if they were the records of past events.
But astronomers are not only able to predict—they can also trace
back the paths of the celestial bodies, and say: ‘At such and such
a long-past epoch, a given star or planet occupied such and such a
position upon the celestial sphere.’ But how are they to verify such
a statement? It is clear that, in general, they cannot do so. Those
who are able to appreciate (or better, to make use of) the predictions
of astronomy, will, indeed, very readily accord a full measure of
confidence to calculations of past events. They know that astronomy
is justly named the most exact of the sciences, and they can see that
there is nothing, in the nature of things, to render retrospection
more difficult than prevision. But there are hundreds who have no such
experience of the exactness of modern astronomical methods—who have,
on the contrary, a vague notion that modern astronomy is merely the
successor of systems now exploded; perhaps even that it may one day
have to make way in its turn for new methods. And if all other men were
willing to accept the calculations of astronomers respecting long-past
events, astronomers themselves would be less easily satisfied. Long
experience has taught them that the detection of error is the most
fruitful source of knowledge; therefore, wherever such a course is
possible, they always gladly submit their calculations to the test of
observation.
Now, looking backward into the far past, it is only here and there
that we see records which afford means of comparison with modern
calculations. The planets had swept on in their courses for ages
with none to note them. Gradually, observant men began to notice and
record the more remarkable phenomena. But such records, made with very
insufficient instrumental means, had in general but little actual
value: it has been found easy to confirm them without any special
regard to accuracy of calculation.
There is one class of phenomena, however, which no inaccuracy of
observation can very greatly affect. A total eclipse of the sun is an
occurrence so remarkable, that (1) it can hardly take place without
being recorded, and (2) a very rough record will suffice to determine
the particular eclipse referred to. Long intervals elapse between
successive total eclipses visible at the same place on the earth’s
surface, and even partial eclipses of noteworthy extent occur but
seldom at any assigned place. Very early, therefore, in the history of
modern astronomy, the suggestion was made, that eclipses recorded by
ancient historians should be calculated retrospectively. An unexpected
result rewarded the undertaking. It was found that ancient eclipses
could not be fairly accounted for without assigning a slower motion to
the moon in long-past ages than she has at present!
Here was a difficulty which long puzzled mathematicians. One after
another was foiled by it. Halley, an English mathematician, had
detected the difficulty, but no English mathematician was able to
grapple with it. Contented with Newton’s fame, they had suffered their
Continental rivals to shoot far ahead in the course he had pointed out.
But the best Continental mathematicians were defeated. In papers of
acknowledged merit, adorned by a variety of new processes, and showing
a deep insight into the question at issue, they yet arrived, one and
all, at the same conclusion—failure.
Ninety years elapsed before the true explanation was offered by the
great mathematician Laplace. A full exposition of his views would be
out of place in such a paper as the present, but, briefly, they amount
to this:—
The moon travels in her orbit, swayed chiefly by the earth’s
attraction. But the sun, though greatly more distant, yet, owing to
the immensity of his mass, plays an important part in guiding our
satellite. His influence tends to relieve the moon, in part, from the
earth’s sway. Thus she travels in a wider orbit, and with a slower
motion, than she would have but for the sun’s influence. Now the earth
is not at all times equally distant from the sun, and his influence
upon the moon is accordingly variable. In winter, when the earth
is nearest to the sun, his influence is greatest. The lunar month,
accordingly (though the difference is very slight), is longer in
winter than in summer. This variation had long been recognised as the
moon’s ‘annual equation;’ but Laplace was the first to point out that
the variation is itself slowly varying. The earth’s orbit is slowly
changing in shape—becoming more and more nearly circular year by year.
As the greater axis of her orbit is unchanging, it is clear that the
actual extent of the orbit is slowly increasing. Thus, the moon is
slightly released from the sun’s influence year by year, and so brought
more and more under the earth’s influence. She travels, therefore,
continually faster and faster, though the change is indeed but a very
minute one;—only to be detected in long intervals of time. Also the
moon’s _acceleration_, as the change is termed, is only temporary, and
will in due time be replaced by an equally gradual retardation.
When Laplace had calculated the extent of the change due to the cause
he had detected, and when it was found that ancient eclipses were
now satisfactorily accounted for, it may well be believed that there
was triumph in the mathematical camp. But this was not all. Other
mathematicians attacked the same problem, and their results agreed so
closely that all were convinced that the difficulty was thoroughly
vanquished.
A very noteworthy result followed from Laplace’s calculations.
Amongst other solutions which had been suggested, was the supposition
(supported by no less an authority than Sir Isaac Newton, who lived to
see the commencement of the long conflict maintained by mathematicians
with this difficulty), that it is not the moon travelling more quickly,
but our earth rotating more slowly, which causes the observed
discrepancy. Now it resulted from Laplace’s labours—as he was the first
to announce—that the period of the earth’s rotation has not varied by
one-tenth of a second per century in the last two thousand years.
The question thus satisfactorily settled, as was supposed, was
shelved for more than a quarter of a century. The result, also, which
seemed to flow from the discussion—the constancy of the earth’s
rotation-movement—was accepted; and, as we have seen, our national
system of measures was founded upon the assumed constancy of the day’s
duration.
But mathematicians were premature in their rejoicings. The question
has been brought, by the labours of Professor Adams—co-discoverer
with Leverrier of the distant Neptune—almost exactly to the point
which it occupied a century ago. We are face to face with the very
difficulties—somewhat modified in extent, but not in character—which
puzzled Halley, Euler, and Lagrange. It would be an injustice to
the memory of Laplace to say that his labours were thrown away.
The explanation offered by him is indeed a just one. But it is
insufficient. Properly estimated it removes only half the difficulty
which had perplexed mathematicians. It would be quite impossible to
present in brief space, and in form suited to these pages, the views
propounded by Adams. What, for instance, would most of our readers
learn if we were to tell them that, ‘when the variability of the
eccentricity is taken into account, in integrating the differential
equations involved in the problem of the lunar motions—that is, when
the eccentricity is made a function of the time—non-periodic or secular
terms appear in the expression for the moon’s mean motion’—and so
on? Let it suffice to say that Laplace had considered only the work
of the sun in diminishing the earth’s _pull_ on the moon, supposing
that the slow variation in the sun’s _direct_ influence on the moon’s
motion in her orbit must be self-compensatory in long intervals of
time. Adams has shown, on the contrary, that when this variation is
closely examined, no such compensation is found to take place; and that
the effect of this want of compensation is to diminish by more than
one-half the effects due to the slow variation examined by Laplace.
These views gave rise at first to considerable controversy.
Pontécoulant characterised Adams’s processes as ‘analytical
conjuring-tricks,’ and Leverrier stood up gallantly in defence of
Laplace. The contest swayed hither and thither for a while, but
gradually the press of new arrivals on Adams’s side began to prevail.
One by one his antagonists gave way; new processes have confirmed his
results, figure for figure; and no doubt now exists, in the mind of any
astronomer competent to judge, of the correctness of Adams’s views.
But, side by side with this inquiry, another had been in progress. A
crowd of diligent labourers had been searching with close and rigid
scrutiny into the circumstances attending ancient eclipses. A new light
had been thrown upon this subject by the labours of modern travellers
and historians. One remarkable instance of this may be cited. Mr.
Layard has identified the site of Larissa with the modern Nimroud.
Now, Xenophon relates that when Larissa was besieged by the Persians,
an eclipse of the sun took place, so remarkable in its effects (and
therefore undoubtedly total), that the Median defenders of the town
threw down their arms, and the city was accordingly captured. And
Hansen has shown that a certain estimate of the moon’s motion makes the
eclipse which occurred on August 15, 310 B.C., not only _total_, but
_central_ at Nimroud. Some other remarkable eclipses—as the celebrated
sunset eclipse (total) at Rome, 399 B.C.; the eclipse which enveloped
the fleet of Agathocles as he escaped from Syracuse; the famous eclipse
of Thales, which interrupted a battle between the Medes and Lydians;
and even the partial eclipse which (possibly) caused the ‘going back
of the shadow upon the dial of Ahaz’—have all been accounted for
satisfactorily by Hansen’s estimate of the moon’s motion: so also have
nineteen lunar eclipses recorded in the Almagest.
This estimate of Hansen’s, which accounts so satisfactorily for solar
and lunar eclipses, makes the moon’s rate of motion increase more than
twice as fast as it should do according to the calculations of Adams.
But before our readers run away with the notion that astronomers have
here gone quite astray, it will be well to present, in a simple manner,
the extreme minuteness of the discrepancy about which all the coil has
been made.
Suppose that, just in front of our moon, a false moon exactly equal to
ours in size and appearance (see _note_ at the end of this paper) were
to set off with a motion corresponding to the present motion of the
moon, save only in one respect—namely, that the false moon’s motion
should not be subject to the change we are considering, termed _the
acceleration_. Then one hundred years would elapse before our moon
would fairly begin to show in advance. She would, in that time, have
brought only one one-hundred-and-fiftieth part of her breadth from
behind the false moon. At the end of another century she would have
gained four times as much; at the end of a third, nine times as much:
and so on. She would not fairly have cleared her own breadth in less
than twelve hundred years. But the _whole_ of this gain, minute as it
is, is not left unaccounted for by our modern astronomical theories.
_Half_ the gain is explained, the other half remains to be interpreted;
in other words, _the moon travels further by about half her own breadth
in twelve centuries than she should do according to the lunar theory_.
But in this difficulty, small as it seems, we are not left wholly
without resource. We are not only able to say that the discrepancy is
probably due to a gradual retardation of the earth’s rotation-movement,
but we are able to place our finger on a very sufficient cause for such
a retardation. One of the most firmly established principles of modern
science is this—that where _work is done_, force is, in some way or
other, expended. The _doing of work_ may show itself in a variety of
ways— in the generation of heat, in the production of light, in the
raising of weights, and so on; but in every case an equivalent force
must be expended. If the brakes are applied to a train in motion,
intense heat is generated in the substance of the brake. Now, the force
employed by the brakesman is _not_ equivalent to the heat generated.
Where, then, is the balance of force expended? We all know that the
train’s motion is retarded, and this loss of motion represents the
requisite expenditure of force. Now, is there any process in nature
resembling, in however remote a degree, the application of a brake to
check the earth’s rotation? There is. The tidal wave, which sweeps,
twice a day, round the earth, travels in a direction contrary to the
earth’s motion of rotation. That this wave ‘does work,’ no one can
doubt who has watched its effects. The mere rise and fall in open
ocean may not be strikingly indicative of ‘work done;’ but when we
see the behaviour of the tidal wave in narrow channels, when we see
heavily-laden ships swept steadily up our tidal rivers, we cannot but
recognise the expenditure of force. Now, where does this force come
from? Motion being the great ‘force-measurer,’ what motion _suffers_
that the tides may _work_? We may securely reply, that the only
motion which _can_ supply the requisite force is the earth’s motion
of rotation. Therefore, it is no mere fancy, but a matter of absolute
certainty, that, though slowly, still very surely, our terrestrial
globe is losing its rotation-movement.
Considered as a time-piece, what are the earth’s errors? Suppose, for
a moment, that the earth was _timed_ and _rated_ two thousand years
ago, how much has she _lost_, and what is her ‘rate-error?’ She has
lost in that interval nearly one hour and a quarter, and she is losing
now at the rate of one second in twelve weeks. In other words, the
length of a day is now more by about one eighty-fourth part of a second
than it was two thousand years ago. At this rate of change, our day
would merge into a lunar month in the course of thirty-six thousand
millions of years. But after a while, the change will take place more
slowly, and some trillion or so of years will elapse before the full
change is effected.
Distant, however, as is the epoch at which the changes we have been
considering will become effective, the subject appears to us to have
an interest apart from the mere speculative consideration of the
future physical condition of our globe. Instead of the recurrence of
ever-varying, closely intermingled cycles of fluctuation, we see, now
for the first time, the evidence of cosmical decay—a decay which, in
its slow progress, may be but the preparation for renewed genesis—but
still, a decay which, so far as the races at present subsisting upon
the earth are concerned, must be looked upon as finally and completely
destructive.[2]
(From _Chambers’s Journal_, October 12, 1867.)
_ENCKE THE ASTRONOMER._