As a sequel to the story of Galileo, I think it may be interesting to
inquire what the evidence, as _we now have it_, proves with regard
to the truth of the Copernican theory, there being two opposite and
contradictory errors on this subject, and these not merely popular
errors, but shared to some extent by educated and otherwise learned
men. But I must, before proceeding, remind my readers that I use the
word _Copernican_ simply to signify the system of modern astronomy,
that in which the Sun is the centre round which the Earth and the other
planets revolve, and not as meaning the precise theory of Copernicus,
which (as I have said) was overthrown by Kepler, when he discovered
that the planetary orbits were not circular but elliptical, the Sun,
moreover, not being strictly in the centre, but in one of the foci of
the orbit.
Now it is a plain fact, which all persons must perceive, that either
the Earth revolves on its axis in twenty-four hours (more accurately
23 hours 56 mins. 5 secs.), or else that the whole of the celestial
bodies are carried round the Earth in that same time. It is also a fact
no less perceptible to _careful_ observers, that either the Sun goes
round the Earth in the course of a year, or else that the Earth goes
round the Sun. The question is how these facts are to be accounted for.
The first of the two errors I have just mentioned is that which
supposes the Copernican theory to have been directly and conclusively
proved. This I imagine to be very common, and to arise from the
elementary books learnt by schoolboys, which state (naturally enough)
the modern theory of astronomy without the reasons that support it.
We need not dwell long on this point. Persons who have got this
erroneous impression misunderstand the nature of the evidence. Some
things in astronomy can be positively proved from observation, as,
for instance, the existence of sun-spots. Many things in mechanics,
chemistry, optics, and other branches of physical study can be
demonstrated by experiment. The motion of the Earth round the Sun
cannot, however, be so treated. It is inferred, and very rightly so,
from the fact that it explains completely and easily all the observed
phenomena, while, on the other hand, there are certain things which, as
_far as our present knowledge goes_, cannot be explained in any other
way; and the same argument applies to the rotation of the Earth on its
axis. But though all this is perfectly clear so far, who can possibly
say that as science progresses some explanation may not be hereafter
found consistent with the antagonistic theory--consistent, let us say,
with the system of Tycho Brahé, or some modification of it? I need
not add that I consider the future discovery of such explanation as so
improbable, that one may practically dismiss the idea, but I should be
sorry to deny it as being conceivably possible.
The other, and opposite, error is that of certain well-meaning but
ill-informed persons, who imagine that the Copernican theory is even
now doubtful and liable to be overthrown--liable, I mean, in a real and
practical sense, and not by distant contingencies, such as those at
which I have just hinted, and which may be considered as shadowy and
intangible. I do not suppose that amongst educated men there are many
such scientific recusants; but at any rate it may be useful to give a
short summary of the evidence on which the Copernican conclusion is
based. In doing this I fear I shall tire the patience of my readers by
partly repeating Galileo’s own arguments, which I have already quoted
in discussing the Dialogue. This cannot easily be avoided, for much
of his reasoning is so sound and so forcible, that after the lapse of
more than two centuries we can add but little to it. On the other hand,
there are grave mistakes that must be shunned; and, moreover, there
have been discoveries made since the day when the Dialogue was written,
of inestimable importance.
The best way of treating the question is to resume the history of
astronomical research from the point where we dropped it; that is, at
the time when Galileo first made known to the world the result of his
observations.
It ought to be clearly understood that from the moment the telescope
was turned on the heavens, the old system of astronomy was doomed, and
nothing could finally have saved it. For a time prejudice and other
more creditable feelings kept it floating on the sea of speculation,
but such a state of things could not last; and the startling
information that men like Galileo, Fabricius, and Scheiner imparted
to the scientific world, could not fail to expel the old theory of
the universe from the minds of men--at least, men of intellectual
capacity--gradually and slowly, but yet most surely.
Now we have seen what the revelations were which the telescope at once
displayed, even in its comparatively rude and imperfect state. There
were the spots on the Sun, the satellites of Jupiter, the phases of
Venus, the greater apparent size of the superior planets (Mars and the
rest) when on the opposite side of the Earth from the Sun, this last
phenomenon being quite inconsistent with the system of Ptolemy.
One consequence of all this was that the less enlightened men of
the old school indulged in a violent antipathy to the new-fangled
instrument, which threatened to overthrow their time-honoured
traditions, and simply refused to believe in the telescope and its
results. Thus the principal professor of philosophy at Padua, when
invited by Galileo to look through his glass at the Moon and the
planets, pertinaciously refused to do so. Simplicio, who, of course,
represents in the Dialogue the prejudices of men of this stamp, admits
(as we have seen) his feelings on this subject, and his suspicions that
the new discoveries were to be attributed to optical errors. He was
willing to be corrected if mistaken, but such had hitherto been his
opinion.
It was not, however, to be expected that men of sound sense would
allow themselves to be misled for any length of time by fallacies such
as these. Continued observations carefully made are sure to correct
mere optical errors, and after a reasonable interval it must have been
evident that the phenomena discerned through the telescope were facts
that had to be dealt with--not phantoms to be ignored.
Thus, when it was found that the planet Venus presented to the eye
phases such as the Moon does, instead of always appearing like a round
body, it became evident that she revolved, not as Ptolemy supposed,
round the Earth, but round the Sun, an inference subsequently confirmed
by the observation of her transits over the Sun’s disc.
This being so, the adherents of Ptolemy had to meet this difficulty:
here was a planet much nearer to the Earth than to the Sun,[24] and
yet revolving round the latter in preference to the former. There was
clearly, then, _some_ attractive force belonging to the Sun (whatever
its nature might be), greater than that of the Earth, which Venus
obeyed; the same was true of Mercury, with the difference that this
planet was much nearer to the Sun. Then as regards the superior
planets, Mars, Jupiter, Saturn, the probability that the Sun was
the great central power that controlled their movements was a very
strong one. There is but little to add on these topics to Galileo’s
own forcible argument in the third day’s dialogue; he is, however,
inaccurate in his figures, and states that Mars appears sixty times as
large when in opposition to the Sun, as at conjunction. More recent
observations have shown that he appears rather more than thirty times
as large when at his nearest point to the Earth, than he does when
near his conjunction with the Sun, and consequently at his farthest
point from the Earth; but this variation is quite sufficient for the
argument, and proves incontestably that if Mars revolves round the
Earth as in any way the centre of his orbit, it must be in an ellipse
of so great eccentricity as no one could reasonably imagine him to
do; indeed, the anti-Copernicans of Galileo’s day knew nothing of the
elliptic motions of the planets; neither, as we have seen, did Galileo
himself.
The same argument, drawn from the apparent size of the planet at
different periods, applies also to Jupiter and Saturn--the other
exterior planets were discovered much later--only not so strikingly as
in the case of Mars. The improbability, if we once admit that all the
planets revolve round the Sun, that the Earth, occupying the position
it does, should be at rest, while the Sun, controlling the motions
of the planets (vast bodies, some of them), circled, nevertheless,
round the Earth; the improbability, I say, of this is so great as to
be almost overwhelming; at any rate, unless the difficulties of the
counter hypothesis were shown to be insurmountable, which, as we know,
is far from being the case. It was of course possible, without going
the lengths of the Paduan professor, and setting oneself against the
telescope altogether, to admit the facts but deny the inferences; to
grant, for instance, that Mars appeared to have a diameter more than
six times as great in one position as in another, and to attribute
it, as I hinted just now, to some extraordinary eccentricity in his
orbit round the Earth; but it is not wise to look through a telescope
with the eyes of the body open and the eyes of the mind closed;
and generally it is but right to be guided by clear and distinct
probabilities when discussing questions of natural philosophy on
scientific grounds--and it is of these alone that I am at the present
moment speaking.
It must be borne in mind distinctly that the discovery of the moon-like
phases of Venus, showing her to revolve round the Sun, was simply
conclusive as against the old system of Ptolemy, which had so long been
the received system of astronomy. The theory of Tycho Brahé, or some
modification of it, was the only one that could henceforth be adopted.
But when you dethrone an ancient theory which has for centuries held
an almost undisputed sway, you have to reconsider your whole position,
and compromises such as that of Tycho are not always adequate to the
emergency.
But these considerations formed only a part of this complicated
controversy. The anti-Copernicans of the seventeenth century would
not even admit the revolution of the Earth on its own axis, and were
consequently forced to hold that the whole of the heavenly bodies were
carried round this our globe in twenty-four hours. In ancient times,
when men knew little or nothing of the sizes and distances of the
Sun, the planets, or the stars, such a belief was quite reasonable
and natural; they thought the stars were set as if they were jewels
in a hollow sphere, which was turned round its poles each day. But
the astronomers of Galileo’s day knew something far more accurate
than this; he himself, as we observed in the Dialogue, greatly
under-estimated the distance and the size of the Sun, and had but a
very imperfect idea of the enormous interval that separates us from the
stars; yet he evidently perceived the improbability of all these vast
and remote bodies revolving with an almost inconceivable velocity round
the Earth every twenty-four hours. And what must be _our_ judgment
on such a subject, seeing that we know the Sun’s mean distance to be
about 92,000,000 miles, more than nineteen times as much as Galileo’s
estimate? And yet some of the planets are farther and much farther
from us than the Sun. Then as regards the stars, α Centauri, the
nearest of them, is calculated to be more than 20,000,000,000,000 miles
distant; but this calculation supposes the truth of the Copernican
theory, and that we may not seem to argue in a circle, we will not use
it, but content ourselves with saying that, from certain reasons about
which there can be no mistake, we are sure that the distance of the
stars is very considerably greater than even the remotest planet in
our own system, which is Neptune. Now, this planet’s distance from the
Sun is computed at 2,775,000,000 miles, and if, indeed, he is carried
daily round the Earth in a circle, it must be with a velocity exceeding
that of light; the stars, therefore, with a velocity far greater still.
Now, nothing with which we are acquainted moves with so great a speed
as light--or, as some men call it, _radiant energy_, meaning thereby
to include heat as well as light in the term--a speed estimated at
186,000 miles in a second of time. Are we then to believe that the
stars are carried in a circle round the Earth every day at a velocity
much exceeding even this? It seems almost enough to ask such a question
without pausing for the answer. The simple rotation of the Earth on its
own axis explains all the phenomena without resorting to such extreme
suppositions as those just mentioned.
It is remarkable that no one of any note--at least, in modern times,
for I am not so sure about the ancients--ever appears to have
suggested the intermediate theory of the Earth revolving on its axis,
and yet remaining stationary as regards any motion of translation.
With our present knowledge of astronomy we could not entertain such
an opinion, though in the early part of the seventeenth century it
might have been considered plausible. Since, however, it has not been
maintained by any noteworthy author, we need not further discuss it.
The reader will bear in mind what has already been said on this
branch of the subject in the second day’s dialogue,[25] and it is not
necessary to repeat it in detail. It may, however, be useful to mention
a few experiments of a later date, which have tended to confirm the
truth of the Earth’s diurnal revolution.
Before the close of the seventeenth century it was observed that a
diminution of gravity occurred at, and near, the equator. This was
proved by the vibration of the pendulum, an experiment associated
chiefly with the name of Richer; and it has, if I mistake not, been
since then carefully tested by spring balances. This phenomenon is
owing partly to the spheroidal figure of the Earth--itself the result
of the rotation on the axis--but principally to the centrifugal
tendency being greater at the equator, from the higher velocity of
rotation.
I have already alluded to the trade winds, and the argument to be drawn
from them, which I think a sound and strong one; but I need not dwell
on it further.
It is, however, well worth remembering that in our own day another
proof has been given, which has been generally allowed to be an
important one. It is the result of an experiment of Foucault, and is
simply this: if a pendulum, with a heavy weight attached to it, be
made to oscillate in a plane due north and south, say in the latitude
of Paris, the pendulum, after a time, and supposing it to continue in
movement long enough for the purpose of observation, will oscillate
in a direction slightly north-east and south-west. Now the pendulum
moves naturally always in the same direction, backwards and forwards,
as originally started, and if the Earth were shaped like a cylinder
no change would be detected; but the spherical form of the Earth, as
it rotates on its axis, here makes the whole difference; the floor
of the room where the pendulum vibrates is carried round the axis of
rotation, as everything else is, but the plane of oscillation remaining
the same--or parallel to the original one--it no longer points north
and south. At the equator this phenomenon would disappear, and in the
southern hemisphere it would be the other way: that is, the pendulum
would vibrate north-west and south-east.
The same thing is exemplified by the small machine called the
gyroscope, where a heavy disc, so adjusted as to revolve freely in any
given direction, independently of the frame in which it is placed, will
continue, when once set in rapid motion, to spin in the same plane,
directed, for instance, to any one star that happens at the time to be
due north or due south of us, while the frame moves round it with the
rotation of the Earth.
I think, then, on the whole, we may say that those persons who, in
the present state of our knowledge on the subject, are not convinced
that the Earth revolves on its own axis, would not be satisfied by any
evidence whatever.
Returning now to the general question of Copernicanism, we find that
for some time after the trial of Galileo, things remained much _in
statu quo_; unless we except the observation of the transit of Venus,
in 1639; but, as that eventful seventeenth century was drawing to its
close, there came on the scene some thoughtful and able astronomers,
who could not only utilise the knowledge of their predecessors, but
could also guess, with more or less accuracy, what that law--hitherto
unknown--might be, which governed the planets and our own Earth in
their movements. It was about this time that the Royal Society was
founded in London, and a stimulus was thus given to investigation and
to experiment. The third law of Kepler, which states that in all the
planetary orbits the square of the periodic time of revolution is in
a constant proportion to the cube of the mean distance, suggested the
existence of another law, not yet discovered, a law of attraction, on
which this itself depended. Among the astronomers of that day three
names deserve special mention, Wren, Hooke, and Halley, because each
of them guessed with some accuracy at the true doctrine--as it is now
known to be--that the planets are attracted to the Sun by a force which
acts inversely as the square of the distance. Hooke, in particular,
deserves the credit of having applied this law to the path of a
projectile, under certain circumstances, as well as to the planetary
orbits; but though he thus lighted upon true conclusions, he appears
to have been deficient in mathematical skill, and therefore unable to
verify his results. It is, however, only just to the memory of Horrox,
who was carried off by an early death, to mention that the true theory
of the identity of terrestrial and astronomical gravity had occurred
to his mind; if he had lived twenty or thirty years longer, he might
have survived in history as the discoverer of the great problem.
Be this as it may, there now arose another man greater than his
predecessors, and greater than all his contemporaries; he also was an
Englishman, by name Isaac Newton. What others guessed, or concluded
on insufficient evidence, became, in his powerful hands, clear and
well-grounded truths, proved, so far as such things could be proved, by
rigid mathematical reasoning, and established on a solid basis, which
time has not shaken, and which subsequent investigation has confirmed.
Others had supposed the existence of the law of attraction by which the
Sun acted on the planets; many persons had understood the existence of
terrestrial gravitation. Newton showed that these two are identical;
and, moreover, that every particle of matter attracts every other
particle _mutually_, and according to the one universal law, that of
the inverse square of the distance; so that a vast planet revolving
round the Sun obeys the same law as a pebble dropped from one’s hand to
the Earth. The popular story of his having been suddenly led to this
conclusion by the sight of an apple falling is apparently fabulous; and
what really occurred is this: he sat alone one day in a garden, and
fell into a speculation (as men of scientific mind are apt to do) on
the power of gravity, that is, of gravity as we feel it here on the
Earth. Then it struck him that however high you ascend, even on the
loftiest mountains, no sensible diminution in this remarkable force
takes place; so, he said to himself: why not as high as the Moon? If
so, perhaps she is retained in her orbit by this very power. And again
if so, what then? To which question his active mind gave the just and
true answer, that it was probably one and the same force that acted at
the surface of the Earth, at the distance of the Moon, and finally, as
regulating the action of the Sun on the planets.
It seems that there was an error, which it is unnecessary to explain in
detail, in Newton’s first calculations; but that when, after a lapse of
time and with the error corrected, he again returned to them, he found
the motion of the Moon to be exactly accounted for by his theory.
Again, in dealing with the complicated problem of the action of the
heavenly bodies one upon the other, that is, when the disturbing force,
for instance, of a third body is brought to bear on the motions of
two others, although Hooke and others had as a conjecture put forth
the existence of such mutual action, yet Newton was the first who
thoroughly grappled with it.
The mutual attraction of matter, so far as things terrestrial are
concerned, had occurred to the inquiring intellect of Francis Bacon;
but it was left for Newton to propound it as the great principle that
governs the physical universe.
Now let us see how all this bears on the truth of the Copernican
system. Newton proved--and I may add that the improved methods of
mathematics which have been adopted since his day make the proofs more
simple and easy--that if any body moves in an ellipse, or indeed, in
one of the other conic sections, the law of force, tending to the
focus, is that of the inverse square of the distance.[26] Conversely,
he proved that a body under the action of a central force, varying in
intensity as the inverse square of the distance, will move in a conic
section.
Then if the Moon moved in an ellipse, as it was easy to perceive that
she did, and if her motion corresponded precisely with what it would
be on the theory of universal gravitation; if also, as seemed evident,
the planets revolved in ellipses, then the inference that the law
of gravitation, as stated by Newton, was true became irresistible;
not susceptible, as before stated, of direct and absolute proof, but
established conclusively by a sound and legitimate induction.
What I have just stated shows that Kepler’s first law corresponds
with Newton’s discovery; but the same is true of the two other laws.
It would of course be out of place here to go minutely into all the
evidence which can be gathered in support of the doctrine of universal
gravitation. I may briefly state that all of Kepler’s laws are
simply explicable by that hypothesis, and that the evidence derives
additional confirmation from the following curious fact: observation
shows that Kepler’s laws, though approximately true, are not strictly
and accurately so; if the planets were mere particles revolving round
the Sun, they would then be quite rigidly true, but the planets have
a certain mass (though very small compared to the Sun) and so do in
some measure attract the Sun as well as being attracted by him, and
they, moreover, exercise a disturbing influence on each other. These
perturbations, however, have been calculated, and the result is that
they agree with what ought reasonably to be expected, supposing the
theory of universal gravitation to be true. This confirmatory proof has
been acquired, I need not add, since the time of Newton by the labours
of astronomers, Laplace and others, who have succeeded him, and who
have had the advantage of that more manageable method of mathematical
calculation to which I have just alluded.
Supposing then the law of gravitation to be established by sufficient
proof, we may now ask what must become of the old systems of
astronomy? What must befall Ptolemy and even Tycho Brahé?
It is obvious that they could do nothing but collapse. If the law
of gravitation were once admitted to be true, the idea of the Sun
revolving round the Earth must be dismissed as impossible. Here it is
right to remark that (assuming the law of universal gravitation) it
is not, strictly and scientifically speaking, correct to say that any
one heavenly body revolves round another, but that they both revolve
round their common centre of gravity. In the case of the Earth and the
Sun, so vastly superior is the mass of the latter that the centre of
gravity is far away within his volume, and the disturbance exercised
on him by the Earth is scarcely appreciable; so also, in the case of
the Moon and the Earth, the centre of gravity is within the latter,
but at a considerable distance from its own centre; and here there is
a distinctly appreciable oscillation of the Earth, arising from this
very cause, during each revolution of the Moon in her orbit. When two
bodies are more nearly equal in mass, as is probably the case with the
double stars that have been observed in recent times, then the two
revolve round a centre of gravity lying between them, exterior to both
of them. It is believed that this is actually the fact in the instance
I am here alluding to of the double stars, and there is some reason for
supposing that the curve in which they revolve is an ellipse. This, if
true, would clearly indicate that the law of gravitation, as stated by
Newton, extends not only through our own solar system, but over the
whole material universe.
And there is one remarkable property of this mysterious agency which
we term gravitation, and that is its instantaneous action even at the
greatest distances. Light travels with an enormous and yet a finite
velocity, so that it takes a few years to arrive at the Earth from even
the nearest stars. The force of gravity knows no such limit, nor is its
action retarded by even the minutest fraction of time.
Nor, again, is it impeded, as in the case of light, by any screen or
obstacle of whatever nature. Furthermore, it does not lose anything of
its intensity, as light does, by being diffused over a larger surface;
it varies as the _mass_ of the bodies concerned, but not in the least
according to the extent of their surfaces. Given the same distance, no
diffusion weakens its force.
Great as was the evidence adduced by Newton for the truth of his
theory, there were some real difficulties in the way of its reception.
I need not allude to these in detail; they are explained in treatises
on physical astronomy for the benefit of those who are interested in
the subject. Briefly, I may say that subsequent research and careful
calculations have removed the difficulties, and thereby confirmed the
already existing evidence.
Then, as regards terrestrial gravity, experiments have been
made--notably at the mountain Schehallion, in Scotland--throwing
additional light upon it, and indicating that not merely the Earth as a
whole, but any great mass, such as a mountain, exercises an appreciable
attractive force.
Newton seems to have expected that some further discovery would take
place, at no distant period, as to the nature of this occult agency
which operates so powerfully in the heavens and on the Earth. In one
of his letters he strongly disclaims the opinion that gravity is
essential to matter and inherent in it; he thinks it is “inconceivable
that inanimate brute matter should, without the mediation of something
else which is not material, operate on and affect other matter
without mutual contact... that gravity should be innate, inherent,
and essential to matter, so that one body may act upon another at a
distance through a _vacuum_, without the mediation of anything else by
and through which their action and force may be conveyed from one to
another, is to me so great an absurdity that I believe no man who has
in philosophical matters a competent faculty of thinking can ever fall
into it.”
And yet we see that what he thought absurd is still apparently true,
and that, great as was Newton’s sagacity in discovering and proving the
effects of this great cosmical law, he failed when he came to speculate
on the more remote causes of it. Since his time, other ingenious
theorists have imagined hypotheses in the hopes of accounting for it;
but their efforts have not met with any great success, and the last
word of science on the subject is that the cause of gravitation remains
undiscovered.
But if the attempt to trace the ultimate cause of the law of
gravitation has been a failure, the proof of its operation in the
physical universe has been a marvellous success, and that not only in
the present day, when difficulties have been removed and fresh evidence
has been added, but, to a certain extent, even in Newton’s own time,
and especially here in his own country. Indeed, we cannot suppress a
feeling of admiration when we contemplate the revolution in astronomy
brought about by this quiet, unobtrusive man, who is said to have spent
thirty-five years of his long life within the walls of Trinity College,
Cambridge, of which he was a Fellow, and who, though twice elected to
represent the University in Parliament, never opened his lips in the
House of Commons. I may, perhaps, be here permitted to insert a passage
from a work to which I have previously alluded, Whewell’s “History of
the Inductive Sciences,” well worth quoting both for its eloquence and
its truth. After recounting, with some detail, the circumstances of
this great epoch in astronomical knowledge, he proceeds:
Such, then, is the great Newtonian induction of universal
gravitation, and such its history. It is indisputably and
incomparably the greatest scientific discovery ever made,
whether we look at the advance which it involved, the extent
of the truth disclosed, or the fundamental and satisfactory
nature of this truth. As to the first point, we may observe
that any one of the five steps into which we have separated
the doctrine [these were, 1st, that the force attracting
_different_ planets to the sun, and, 2nd, the force attracting
the _same_ planet in different parts of its orbit, is as the
inverse square of the distances; 3rd, that the earth exerts
such a force on the moon, and that this is identical with
terrestrial gravity; 4th, that there is a _mutual_ attraction
of the heavenly bodies on one another; 5th, that there exists
a mutual attraction of _all particles of matter_ throughout
the universe] would of itself have been considered as an
important advance, would have conferred distinction on the
persons who made it, and the time to which it belonged. All the
five steps made at once formed not a leap, but a flight; not
an improvement merely, but a metamorphosis; not an epoch, but
a termination. Astronomy passed at once from its boyhood to
mature manhood. Again, with regard to the extent of the truth,
we obtain as wide a generalisation as our physical knowledge
admits when we learn that every particle of matter, in all
times, places, and circumstances, attracts every other particle
in the universe by one common law of action. And by saying
that the truth was of a fundamental and satisfactory nature, I
mean that it assigned, not a rule merely, but a cause, for the
heavenly motions; and that kind of cause which most eminently
and peculiarly we distinctly and thoroughly conceive, namely,
mechanical force. Kepler’s laws were merely _formal_ rules,
governing the celestial motions according to the relations
of space, time, and number; Newton’s was a _causal_ law,
referring these motions to mechanical reasons. It is no doubt
conceivable that future discoveries may both extend and further
explain Newton’s doctrines; may make gravitation a case of
some wider law, and may disclose something of the way in which
it operates--questions with which Newton himself struggled.
But, in the meantime, few persons will dispute that, both in
generality and profundity, both in width and depth, Newton’s
theory is without a rival or neighbour.[27]
The effect of all this on the Copernican system and the evidence on
which it rested, was to raise that system from a simple though strong
probability, a question on which at any rate something might be said
for and against it, to a probability of almost overwhelming force; for
it not only showed how the heavenly bodies moved, but it explained the
cause of their motions, and in a word furnished the key that unlocked
the arcana of Nature. When you came to know not only how the Moon and
the planets moved, but the law which regulated their movements, and
when you found that all fitted into one harmonious whole (at least with
some minor exceptions), it was not easy to refuse assent to a theory
supported by such powerful evidence.
Yet in saying this we are perhaps rather viewing the question from
our present standpoint, than as a contemporary would have done. As
a matter of fact, Newton’s hypothesis, though eagerly received in
England, met with a long opposition on the Continent, and particularly
in France, where Descartes’ theory of vortices reigned supreme for many
years. It must not be supposed that these Cartesian philosophers were
anti-Copernicans; far otherwise, only they accounted for the celestial
motions in a different way from Newton, and, as every one now admits,
in a wrong way.
I have already remarked that there were some apparent difficulties in
the application of the law of universal gravitation to all the heavenly
bodies, and that these have been removed by subsequent calculation. One
of these difficulties, if indeed it could be so called (for it hardly
amounted to that), has been solved within living memory. It was noticed
that the planet Uranus showed signs of perturbation from some unknown
reason; and even the work I have just quoted, “Whewell’s History of
the Inductive Sciences,” published in 1847, contains the following
sentence: “Uranus still deviates from his tabular place, and the cause
remains yet to be discovered.” Two astronomers, one French and one
English, Le Verrier and Adams, found out the cause by discovering the
existence, each independently of the other, of an exterior planet
revolving in an orbit more distant by far than that of Uranus; to this
planet the name of Neptune has been given, and his existence is one
more confirmatory proof of the theory of gravitation.
The Copernican system had been built up and consolidated by Newton’s
great discovery; but another piece of evidence, of a most important
character, was added by the investigations of Bradley, Professor of
Astronomy at Oxford, and afterwards Astronomer Royal; this careful
observer, while engaged in endeavouring to detect such an apparent
motion of the fixed stars (so called) as would indicate an annual
parallax, noticed that another motion existed different from that
which the annual parallax would produce, and for which he could not
account; the apparent orbits described by the stars observed depended
on the distance of the stars from the pole of the ecliptic; the
phenomenon was different from anything hitherto discovered, and one
or two modes of explanation were tried in vain. Accident, however,
turned Bradley’s thoughts in the right direction; he was one day in
a boat on the Thames, and observed that the vane on the mast gave a
different apparent direction to the wind, according as the boat sailed
in different courses. Here, then, was the solution of the difficulty:
it was already known from Römer’s investigations that light moved with
a finite velocity, and if so it would naturally produce the same effect
as that observed in the boat, or to take an illustration very commonly
given, like that which any one finds when moving along rapidly in a
shower of rain, in which latter case the rain seems to fall not in the
direction it has when one is at rest, but in a direction compounded of
that and the one opposite to the person’s line of motion.
Bradley soon drew the correct conclusion, that light acted in precisely
the same way upon the Earth as it moved in its orbit, and that the
_apparent_ annual displacement of the stars, as detected by him, arose
from this sole cause. All the great astronomers who followed him have
agreed with his conclusions, and the phenomenon in question, which is
called the aberration of light, has conferred a lasting fame on its
discoverer. And the remarkable point about it is this, that not only
does it give a fresh illustration to the Copernican theory, but it
is one of the very few scientific facts that cannot (so far as our
knowledge of the subject goes) be explained in any other way. It is,
therefore, generally considered as a critical test of the truth of the
system.
There are two other phenomena, on which however I do not propose to
dwell at any length, known as precession and nutation, which it is
not easy to explain otherwise than by the modern theory of astronomy
and the principle of gravitation; the latter of these two owed its
discovery to Bradley, and the former to Hipparchus, who could not have
been aware of its real cause, though he had observed the fact of its
occurrence.
But passing on from these, I may call attention to one most remarkable
result of modern scientific research, connected with the stars. In
Galileo’s day, it was a drawback to the Copernican theory that none of
the stars showed the smallest annual parallax; in popular language,
none of them seemed to undergo any change of place, however small,
when observed at opposite points of the Earth’s orbit, or as the
opponents would have said, the Earth’s imagined orbit. A displacement
of this kind, I need hardly repeat, must not be confounded with that
other motion which Bradley observed and explained. This was one of
Tycho Brahé’s reasons for rejecting the Copernican system, and it
was one of the best arguments used by the opponents of Galileo. As
the enormous distance of the stars from the Earth was, as we have
already seen, at that time unknown, the celestial distances generally
being under-estimated even by the best astronomers, the argument had
an apparent force, which no one now would attribute to it. Galileo
himself had some hope of overcoming the difficulty by discovering some
annual displacement in certain stars, but it is needless to add that
his instruments were unequal to such a task. Subsequent observers
tried various methods, but without any real success until the present
century, when Bessel and other observers found that a star called
61 Cygni had a certain annual parallax; and not long afterwards,
Henderson, making his observations at the Cape of Good Hope on a
conspicuous star in the constellation of the Centaur, a constellation
belonging to the southern hemisphere, found at length that this star,
which in fact is a double star, and known as α Centauri, had a parallax
of nearly 1″; subsequent calculations show it to be probably rather
less, that is to say about 0″·91. This means that it is more than
twenty billions of miles distant, and that light takes more than three
years to travel from α Centauri to the earth. It is, however, believed
to be much the nearest of all the stars, no other coming within double
of the distance.
Now it is difficult to evade the conclusion which naturally follows
from these results, that the Earth really does move in an annual orbit
round the Sun. It is no part of my present task to give a list of the
stars of which the parallax has been found, but I may say there are
several others besides the two I have named; and I know of no method
of accounting for the fact in any way but by the annual motion of the
Earth, unless we suppose some instrumental error to have occurred.
There have been so many of these in times past that it may seem rash to
exclude such a possibility, but, considering the perfection of modern
scientific instruments, it is in the highest degree improbable; and we
may fairly reckon the parallaxes of the stars as a strong confirmation
of the already strong evidence in favour of the Copernican theory--a
theory which, as we have seen, was, from a purely scientific point of
view, very probable in the days of Galileo, overwhelmingly probable
after the great discovery of Newton, and at the present time, with all
the light that subsequent research and observation have thrown on it,
scarcely short of a moral certainty.
I may repeat once more that it has not, indeed, that absolute physical
certainty, arising from direct experiment, which has been obtained in
other scientific investigations; but, allowing for this faint element
of instability, we may fairly say that no truth of natural philosophy
stands on a firmer basis.
And for Galileo, who lived before the day when, as Whewell says,
“Astronomy passed from boyhood to mature manhood,” we may fairly say
that, after we have censured his faults and his errors, after we have
ascertained that he was not a hero or a “martyr of science,” we must
still recognise the fact that he was one of the greatest natural
philosophers of his day, pre-eminent in astronomy, in mechanics,
in mathematics. To his honour also be it added, that his religious
faith, and his respect for the Church and her authority, so far as we
can judge, never failed. Whatever his defects may have been--want of
prudence, want of candour, want of consideration for others--we can
easily perceive that he would never have been willingly drawn into any
controversy intended to provoke antagonism between Religion and Science.
In the present age, unhappily, there have been men who have taken
the other course, and have contributed their share towards exciting
antagonism, heedless of the consequences. Some have done this
unwittingly, arguing on the side of religion, but without a proper
supply of sound scientific information; others, on the opposite
side, have shown so bitterly hostile a spirit to Revelation, if not
even to Natural Religion, as to render it more than ever difficult
to re-establish that concord between the two studies, that of the
supernatural and that of the physical, which should never have been
interrupted.
This, however, is so wide a subject that I must not be led into it. Yet
I may briefly remark that two of the greatest lights of the Catholic
Church, men whose teaching and whose writings have exercised an undying
influence, have both, either by words explicitly, or implicitly by
their example, contributed to encourage a sound knowledge of natural
philosophy, and in harmony with Christian theology.
They both lived when physical science was in its infancy, though at
intervals of nearly 800 years apart. St. Augustine, who flourished
towards the latter part of that period dominated by the corrupt
civilisation of ancient Rome, amongst his voluminous works devoted
one treatise to the interpretation of the Book of Genesis, “De Genesi
ad Litteram;” and he takes the opportunity of cautioning those whom
he addresses against the risk of exciting the ridicule of unbelievers
by a mistaken adherence to a rigidly literal interpretation of Holy
Scripture. He was, I believe, one of the first that interpreted the six
days of Creation in the non-literal sense, though his particular theory
is not one in accordance with modern scientific opinion. I allude to
him not for the details of natural philosophy, but as enunciating a
principle, which some subsequent authors have not followed as they
might have done.
St. Thomas Aquinas lived in those middle ages of which he was one of
the most brilliant ornaments. The power of his intellect is admitted by
those who have little sympathy with his teaching; his literary industry
is a standing marvel; and I have already observed that besides the
theological and metaphysical works on which he expended so much labour,
he wrote a treatise on the astronomy of Aristotle. It may be said this
is no very great matter, but I mention it as illustrating the breadth
of mind of this great saint and theologian, who could spare time for
a study of physical science without neglecting the more solemn duties
of his calling. His active mind was alive to every source from whence
wisdom and learning could be imbibed; and if he had lived in the age of
Galileo, I have sometimes fancied that he would have thrown some oil on
the troubled waters, would have counselled prudence to the adventurous
astronomer, patience and forbearance to his antagonists. But it is of
no avail to indulge in speculations such as these. Each age of the
world has its difficulties, moral and intellectual, and we can neither
hurry the stream of human thought onwards nor drive it backwards.
So again it is with the dispositions of individuals; if Galileo had
been gifted with the calm, dignified reserve of Newton, instead of
being the vivacious, loquacious Italian that he in fact was, he might
have lived and died in peace.
And now, if I may be permitted to recur once more to the subject of
gravitation, I have a word to say as to the lesson which this great
all-pervading law seems to teach. It has nothing to do with any
question of revealed Religion; but does it not bear the unmistakable
signs of the action of an all-wise, an all-powerful Creator? It may
possibly be the result of some other, though unknown, law; and even
then it brings us back to the same point. The result in nature remains
the same, and that result is written in characters that cannot be
ignored. Mathematicians have occupied themselves in making suppositions
as to the effects of imaginary laws of gravity, some of which might,
no doubt, ensure sufficient order and regularity to maintain this
world, and the countless worlds that people space, while others would
cause hopeless confusion. The striking thing is that the existing law
perfectly answers its purpose.
Only let us imagine that no law of attraction acted upon matter at all,
nor any force of whatever kind--what would be the result? There would
be no coherence, no abode for human or animal life--nothing but chaos
and anarchy.
If, then, we contrast this imagined picture with the one actually
before us, we are, I think, forcibly led to the conclusion that the
physical universe owes its origin, its existence, its harmony to an
Omnipotent Being, unseen, yet not unknown, intangible to the senses,
ever present to the intelligence.
And now, in order to avoid misapprehension, I venture to restate
briefly the propositions I have sought to establish.
I have maintained that the Catholic Church has a right to lay her
restraining hand on the speculations of Natural Science, just as much
as she has in the case of other speculative inquiries. Those who do
not believe in her prerogatives will, of course, deny such right _in
toto_; but I contend that if you grant the existence of this right at
all, you cannot exclude Physical Science from its operation.
On the other hand, in the particular case of Galileo, I have not
attempted to defend all the proceedings of the Cardinals of the Index
and the Cardinals of the Inquisition. For it must be remembered
it was no gentle rebuke with which the Copernican system and the
individual Galileo were visited; no such light condemnation as that
of placing on the Index of prohibited books all Copernican works as
being _inopportune_, or again, that of a caution to Galileo to be more
prudent, was deemed adequate to the emergency--if, indeed, any one even
thought of them.
So with the facts of the history before us, I think any sweeping
defence of the proceedings in question would be unnecessary from an
ecclesiastical point of view, and from a scientific point of view
untenable.
Moreover, I must add, as an indispensable premiss to the conclusion
just stated, I have also maintained that the censures pronounced by
the Cardinals on both occasions were not dogmatic decisions, such
as Catholic theologians hold to be infallible; but disciplinary
enactments, varying with the changing characters of different ages.
Then again, referring to the scientific questions involved, we may
see that Astronomy, considered historically, is divided into three
periods--the ancient one before the invention of the telescope, that
is, up to the time of Galileo; the intermediate one, when the telescope
was in use but the law of universal gravitation as yet unknown--from
Galileo until the publication of the “Principia” of Newton; and the
modern one, from Newton downwards. During the first period it seemed
highly probable to the whole world, with the exception of a few gifted
intellects, that this Earth was the centre of the Universe, and that
all the heavenly bodies revolved round it; during the second period,
when the telescope had shed a light so powerful and so brilliant upon
astronomical research that men could not absolutely close their eyes
to it even if they wished, the balance of probability passed into the
opposite scale, and the more intelligent men of science guessed at the
truth, however indistinctly. But some elements of uncertainty remained;
and this circumstance, taken in connection with the irrelevant
arguments so much in vogue at that time, must in all fairness be
allowed as an excuse for the many good men, ecclesiastics and others,
who opposed the Copernican doctrine. After the great step made by
Newton it was no longer a question of balancing probabilities, for the
weights were almost all transferred to one scale, and the probabilities
of the truth of the Heliocentric System (to give it for once its
accurate name) became overwhelming. The subsequent investigations
of Bradley and others have gone further still, and have converted
this strong, overpowering probability into something approaching
indefinitely near to a moral certainty.
Beyond this we cannot reasonably expect to go; _physical_ certainty
is not to be attained when we have to traverse the vast distances of
celestial space, and human infirmity must be content to recognise the
boundary beyond which it may not pass, the limit imposed on finite
minds by the Infinite.
THE END.
CHARLES DICKENS AND EVANS, CRYSTAL PALACE PRESS
FOOTNOTES
[1] Nicetas of Syracuse (whose date I am not able to give) seems to
have been aware of the diurnal movement of the earth round its axis.
[2] M. de l’Épinois has, since then, published a still more complete
collection of the various documents he had obtained permission to
inspect at Rome; but this work is, unfortunately, out of print.
[3] “Principium 7^m.--Sancta Sedes Apostolica cui divinitus commissa
est custodia depositi, potestas pascendi universam Ecclesiam ad salutem
animarum, potest sententias theologicas vel quatenus cum theologicis
nectuntur proscribere ut sequendas vel proscribere ut non sequendas,
non unice ex intentione definitivâ sententiâ infallibiliter decidendi
veritatem, sed etiam absque ilia ex necessitate et intentione vel
simpliciter vel pro determinatis adjunctis prospiciendi _securitati_[4]
doctrinæ Catholicæ. In hujusmodi declarationibus licet non sit
doctrinæ _veritas infallibilis_, quia hanc decidendi ex hypothesi
non est intentio; est tamen _infallibilis securitas_. Securitatem
dico tum objectivam doctrinæ declaratæ [vel simplicitea vel pro
talibus adjunctis], tum subjectivam quatenus omnibus tutum est eam
amplecti, et tutum non est, nec absque violatione debitæ submissionis
erga magisterium divinitus constitutum fieri potest, ut eam amplecti
recusent.
“Coroll. C. Falsum est, auctoritatem propter quam debeatur assensus
intellectus, solam esse auctoritatem Dei revelantis seu Ecclesiæ vel
Pontificis infallibiliter definientis; sunt enim gradus assensus
religiosi multiplices. In præsenti distinguendus est assensus _fidei
proprie et immediate divinæ_ propter auctoritatem Dei revelantis;
assensus fidei quam supra diximus _mediate divinam_ propter
auctoritatem infallibilitur definientis doctrinam ut veram non tamen
ut revelatam; assensus _religiosus_ propter auctoritatem universalis
providentiæ ecclesiasticæ in sensu declarato.”--_De Divina Traditione
et Scriptura_, p. 116, et seq. Ed. 1870.
[4] “Non coincidere hæc duo, infallibilem veritatem et securitatem,
manifestum est vel ab eo, quod secus nulla doctrina probabilis aut
probabilior posset dici sana et secura.”
[5] It happens, curiously enough, that the doctrine of the perfect
immobility of the Sun, which so shocked the Qualifiers of the
Inquisition, is simply discarded by modern astronomers. No one now
holds that the Sun is the centre of the whole universe, or that he is
immovable. It is generally supposed that he travels in space, though
not round any _known_ centre, and the Earth and Planets with him.
[6] “Dico, che quando ci fosse vera dimostratione che il Sole stia nel
centro del mondo, e la terra nel 3 cielo, e che il Sole non circonda la
terra, ma la terra circonda il Sole, allora bisogneria andar con molta
consideratione in esplicare le Scritture che paiono contrarie, e più
sotto dire che non l’ intendiamo, che dira che sia falso quello che si
dimostra. Ma io non crederò che ci sia tale dimostratione fin che non
mi sia mostrata, etc.”--_Extract from Cardinal Bellarmine’s Letter to
F. Foscarini._
[7] A brief but interesting résumé of the Aristotelian physics is given
in Whewell’s “History of the Inductive Sciences,” a work to which I
shall have occasion to refer more than once.
[8] It is said that a weight dropped from the top of a very high
tower falls slightly to the _east_, because the velocity of the axial
rotation is greater at the summit of the tower than at its foot, and
the stone or ball dropped partakes of the motion of the _highest_ part
of the tower from which it falls; this is perfectly true in theory;
and experiments, made not only from the summits of towers but also in
mines, tend to confirm it.
[9] Simplicio having said that the cause why parts of the earth are
carried downwards was gravity, Salviati answers: “Voi errate, Signor
Simplicio, voi dovevate dire, che ciaschedun sa, ch’ ella si chiama
gravità; ma io non vi domando il nome, ma dell’ essenza della cosa:
della quale essenza voi non sapete punto più di quello, che voi
sappiate dell’ essenza del movente le Stelle in giro; eccetuatone il
nome, che a questa è stato posto, e fatto familiare, e domestico per
la frequente esperienza, che mille volte il giorno noi ne veggiamo; ma
non è, che realmente noi intentiamo più, che principio, o che virtù
sia quella, che muove la pietra in giù, di quel noi sappiamo chi la
muova in sù, separata del proiciente; o chi muova la Luna in giro,
eccettochè (come ho detto) il nome, che più singolare e proprio gli
abbiamo assegnato di gravità; dovechè a quello con termine più generico
assegniamo virtù impressa, a quello diamo intelligenza o assistente, o
informante; e a infiniti altri moti diamo loro per cagione la natura.”
[10] It is curious that the notion of the universe being shaped
as a curve returning into itself has been started by some modern
German philosophers, founders of what has been called “non-Euclidian
geometry.” The investigations of astronomers, however, rather point to
the conclusion that the stellar universe has no centre, no symmetrical
figure, though speculations such as these must always be uncertain.
[11] To speak of the circumference of a circle of infinite radius as
being identical with a straight line (though practically true enough)
is not rigidly accurate. We should say that they approximate infinitely
to one another, or in mathematical phraseology, they are equal to each
other _in the limit_.
[12] It is not intended here to deny what some writers state--that
the _friction_ caused by the Earth’s rotation does in some degree act
upon the tidal wave. It is remarkable, so far as can be ascertained
from observations taken at some small island at a distance from any
continent, that the tidal wave of the Ocean only rises, even at the
spring, about five or six feet. The enormous rise of water at some
places arises from the tidal wave being driven into estuaries, mouths
of rivers, and other narrow channels.
[13] These are the author’s words, spoken by Salviati: “Tra tutti
gli nomini grandi, che sopra tal mirabile effetto di natura hanno
filosofato, più mi maraviglio del Keplero, che di altri, il quale
d’ingegno libero, e acuto, e che aveva in mano i moti attribuiti alla
terra, abbia poi dato l’orecchio, e assenso a _predominii della Luna
sopra l’acqua_, e a proprietà occulte, e simili fanciullezze.”
[14] It is not intended to imply that these two Schools of thought
stand on anything like the same scientific level.
[15] The spots on the Sun were seen at about the same period of time by
Fabricius and by Father Scheiner, a Jesuit, as already mentioned.
[16] I must not be understood as implying that even doctrinal decisions
promulgated by the Roman Congregations _in their own name_ are
considered by theologians to be infallible; such character belonging
only to decisions addressed by the Pope himself to the Church.
[17] A curious instance of popular unacquaintance with astronomy was
afforded some months ago, when the planet Venus, which one would think
was a well-known object to most people, was mistaken for “the Star of
Bethlehem;” and this mistake was by no means confined to the ignorant,
but was shared by persons of education.
The planet was at the time a brilliant “morning star;” and the effect
on the eye is more striking in these circumstances than when it is
seen, as is very commonly the case, in the evening, shortly after
sunset. I suppose this would account in some measure for the delusion.
In clearer and finer skies than those of England, Venus is sometimes so
brilliant in the early morning as to startle an unaccustomed observer.
[18] Dr. Ward makes a curious mistake in one point; he speaks in one
of the articles of _The Dublin Review_ (which he then edited) of
Copernicanism as destroying the old ideas as to _above and below_;
that is to say, for instance, your idea of ascending on high towards
heaven was thereby nullified, and ascending from the surface of the
earth meant going in any direction which the earth’s rotation might
place above your head at any particular moment. But Dr. Ward, who
was doubtless thinking of the very old and exploded notion that the
earth was a flat surface, does not seem to have been aware that this
objection applies in principle to the Ptolemaic system also; Ptolemy
knew that the earth was spherical in its shape, and consequently that
what would be _above_ a person in the eastern parts of India, to take
an example, would be widely different from that which would be so at
the westernmost point of Africa. It may, however, be admitted that an
additional cause for bewilderment was presented by the diurnal rotation
of the Earth, since it then appeared that the same point in space
_above_ you at noon would be far away _below_ you at midnight.
[19] Quoted from an article in the “Revue des Questions Historiques,”
1867, “Galilée, son Procès, sa Condemnation, d’après des documents
inédits,” by M. Henri de l’Épinois.
[20] Tycho Brahé discovered two out of the principal inequalities in
the Moon’s motion--known to astronomers as the Variation and the Annual
Equation; the third, which is the most obvious of all and is called the
Evection, was discovered by Ptolemy.
[21] The figurative interpretation, however, in this instance is as
old as St. Augustine, though his speculations lead him to a different
conclusion from that of modern scientific men; namely, that of
supposing the actual creation to be the work of one moment.
[22] It is, I think, Mr. Proctor who uses this argument in one of his
works, to prove how very doubtful a thing is the existence of highly
organised and rational beings on the other planets.
[23] It is quite possible, as Mr. Lockyer has recently argued, that
many objects that appear to us as stars, are in reality nebulæ in a
more or less advanced stage of condensation.
[24] The _relative_ distances could be computed geometrically, even
before the absolute distances were known, and in fact were so; Kepler’s
third law affords a simple rule for calculating them, but they were
known even previously.
[25] I may, perhaps, be permitted to recall to the reader’s mind, in a
note, one or two of the main objections urged by the anti-Copernicans.
One of these was that it would leave the atmosphere behind, the true
answer to which is that the atmosphere itself is attracted by the
force of gravity to the earth, and is carried round by the rotation,
as everything else is; this Galileo did not perfectly understand, as
may be seen by his remarks, both in the second and the fourth day’s
dialogue. Another was this--and it was put forward by no less a man
than Tycho Brahé--a stone dropped from a high tower ought to fall to
the westward of the tower, because the tower would be carried on to the
east by the earth’s rotation, and the stone would not; this, however,
being contrary to experience. The real fact is that the stone partakes
of the rotatory movement as much as the tower does, the two forces of
rotation and gravity being combined according to the second law of
motion, while the stone is falling; this Galileo did know. Supposing
a very high tower, the stone ought to fall slightly to the east, on
account of the superior velocity of rotation at the top of the tower to
that at the bottom. It is said this experiment has been successfully
tried, as stated in note, page 55.
[26] There are other laws, besides that of the inverse square of the
distance, which would cause a body to move in an ellipse, at least if
the force acting on it were placed, not in the focus, but in the centre
of the orbit. The question has been discussed with reference to some of
the binary stars which appear to move round one another in ellipses. No
doubt is thereby raised as to the prevalence of the law of the inverse
square in our own solar system, where it has been verified by long and
careful observation; the doubt (I think we may say a comparatively
slight one) is whether the same law extends to the whole stellar
universe, where, of course, accurate observation is impracticable.
[27] I do not think the truth of this is affected by any of the
great modern discoveries; though that of the Conservation of Energy
approaches more nearly than others to Universal Gravitation in its
importance.
Transcriber’s Notes
Punctuation, hyphenation, and spelling were made consistent when a
predominant preference was found in the original book; otherwise they
were not changed.
Simple typographical errors were corrected; unbalanced quotation
marks were remedied when the change was obvious, and otherwise left
unbalanced.
Original text uses “loadstone”, not “lodestone”.
Footnotes, originally at the bottoms of pages, have been collected and
moved to the end of this eBook.
Page 22: The symbol in “Locus sigilli” is a version of a Maltese cross.
Footnote 4, originally on page 27, is a sub-note of footnote 3.
End of Project Gutenberg's Galileo and his Judges, by F. R. Wegg-Prosser