under Professor De Morgan's notice. It is known that the sun, carrying
with him his family of planets, is speeding swiftly through space--his
velocity being estimated as probably not falling short of 20,000 miles
per hour. It follows, of course, that the real paths of the planets in
space are not closed curves, but spirals of different orders. How, then,
can the theory of Copernicus be right, according to which the planets
circle in closed orbits round the sun? Here was Mr. Reddie's difficulty;
and like the other, it appeared to his mind as a great discovery. He was
no whit concerned by the thought that astronomers ought surely to have
noticed the difficulty before. It did not seem in the least wonderful
that he, lightly reading a book or two of popular astronomy, should
discover that which Laplace, the Herschels, Leverrier, Airy, Adams, and
a host of others, who have given their whole lives to astronomy, had
failed to notice. Accordingly, Mr. Reddie forwarded to the British
Association (in session at Newcastle) a paper controverting the theory
of the sun's motion. The paper was declined with thanks by that bigoted
body 'as opposed to Newtonian astronomy.' 'That paper I published,' says
Mr. Reddie, 'in September 1863, with an appendix, in both thoroughly
exhibiting the illogical reasoning and absurdities involved in the
theory; and with what result? The members of Section A of the British
Association, and Fellows of the Royal Society and of the Royal
Astronomical Society, to whom I sent copies of my paper, were, without
exception, _dumb_.' Professor De Morgan, however, having occasion to
examine Mr. Reddie's publications some time after, was in no sort dumb,
but in very plain and definite terms exhibited their absurdity. After
all, however, the real absurdity consisted, not in the statements which
Mr. Reddie made, nor even in the conclusions which he drew from them,
but in the astounding simplicity which could suppose that astronomers
were unaware of the facts which their own labours had revealed.
In my correspondence with Mr. Reddie I recognised the real source of the
amazing self-complacency displayed by the true paradoxist. The very
insufficiency of the knowledge which a paradoxist possesses of his
subject, affords the measure of his estimate of the care with which
other men have studied that subject. Because the paradoxist is ready to
pronounce an opinion about matters he has not studied, it does not seem
strange to him that Newton and his followers should be equally ready to
discuss subjects they had not inquired into.
Another very remarkable instance was afforded by Mr. Reddie's treatment
of the subject of comets. And here, by the way, I shall quote a remark
made by Sir John Herschel soon after the appearance of the comet of
1861. 'I have received letters,' he said, 'about the comets of the last
few years, enough to make one's hair stand on end at the absurdity of
the theories they propose, and at the ignorance of the commonest laws of
optics, of motion, of heat, and of general physics, they betray in their
writers.' In the present instance, the correspondence showed that the
paradoxist supposed the parabolic paths of some comets to be regarded by
astronomers as analogous to the parabolic paths traversed by
projectiles. He expressed considerable astonishment when I informed him
that, in the first place, projectiles do not travel on truly parabolic
paths; and secondly, that in all respects their motion differs
essentially from that which astronomers ascribe to comets. These last
move more and more quickly until they reach what is called the vertex of
the parabola (the point of such a path which lies nearest to the sun):
projectiles, on the contrary, move more and more slowly as they approach
the corresponding point of their path; and further, the comet first
approaches and then recedes from the centre of attraction--the
projectile first recedes from and then approaches the attracting centre.
The earth-flatteners form a considerable section of the paradoxical
family. They experienced a practical rebuff, a few years since, which
should to some degree have shaken their faith in the present chief of
their order. To do this chief justice, he is probably far less confident
about the flatness of the earth than any of his disciples. Under the
assumed name of Parallax he visited most of the chief towns of England,
propounding what he calls his system of zetetic astronomy. Why he should
call himself Parallax it would be hard to say; unless it be that the
verb from which the word is derived signifies primarily to shift about
or dodge, and secondarily to alter a little, especially for the worse.
His employment of the word zetetic is less doubtful, as he claims for
his system that it alone is founded on the true seeking out of Nature's
secrets.
The experimental basis of the theory of Parallax is mainly this: Having
betaken himself to a part of the Bedford Canal, where there is an
uninterrupted water-line of about six miles, he tested the water surface
for signs of curvature, and (as he said) found none.
It chanced, unfortunately, that a disciple--Mr. John Hampden, of
Swindon--accepted the narrative of this observation in an unquestioning
spirit; and was so confident that the Bedford Canal has a truly plane
surface, that he wagered five hundred pounds on his opinion, challenging
the believers in the earth's rotundity to repeat the experiment. The
challenge was accepted by Mr. Wallace, the eminent naturalist; and the
result may be anticipated. Three boats were to be moored in a line,
three miles or so between each. Each carried a mast of given length. If,
when the summits of the first and last masts were seen in a line
through a telescope, the summit of the middle mast was not found to be
above the line, then Mr. Hampden was to receive five hundred pounds from
Mr. Wallace. If, on the contrary, the top of the middle mast was found,
as the accepted theory said it should be, to be several feet above the
line joining the tops of the two outer masts, then Mr. Hampden was to
lose the five hundred pounds he had so rashly ventured. Everything was
conducted in accordance with the arrangements agreed upon. The editor of
a well-known sporting paper acted as stakeholder, and unprejudiced
umpires were to decide as to what actually was seen through the
telescope. It need scarcely be said that the accepted theory held its
own, and that Mr. Hampden lost his money. He scarcely bore the loss with
so good a grace as was to have been expected from a philosopher merely
desirous of ascertaining the truth. His wrath was not expended on
Parallax, whom he might have suspected of having led him astray; nor
does he seem to have been angry with himself, as would have seemed
natural. All his anger was reserved for those who still continued to
believe in the earth's rotundity. Whether he believed that the Bedford
water had risen under the middle boat to oblige Mr. Wallace, or how it
came to pass that his own chosen experiment had failed him, does not
appear.
The subsequent history of this matter has been unpleasant. It
illustrates, unfortunately but too well, the mischief which may ensue
from the tricks of those who make a trade of paradox--tricks which would
be scarce possible, however, if text-books of science were more
carefully written, and by those only who are really acquainted with the
subject of which they treat.
The book which originally led to Mr. Hampden's misfortunes, and has
misled not a few, ought to have deceived none. I have already mentioned
the statement on which Parallax (whose true name is Rowbotham) rested
his theory. Of course, if that statement had been true--if he had, with
his eye a few inches from the surface of the water of the Bedford Canal,
seen an object close to the surface six miles from him--there manifestly
would have been something wrong in the accepted theory about the earth's
rotundity. So, also, if a writer were to announce a new theory of
gravity, stating as the basis of his theory that a heavy missile which
he had thrown into the air had gone upwards on a serpentine course to
the moon, any one who accepted the statement would be logically bound to
admit at least that the fact described was inconsistent with the
accepted theory. But no one would accept such a statement; and no one
should have accepted Mr. Rowbotham's statement.
His statement was believed, however, and perhaps is still believed by
many. Twenty years ago De Morgan wrote that 'the founder of the zetetic
astronomy gained great praise from provincial newspapers for his
ingenuity in proving that the earth is a flat, surrounded by ice,' with
the north polar ice in the middle. 'Some of the journals rather incline
to this view; but the "Leicester Advertiser" thinks that the statement
"would seem to invalidate some of the most important conclusions of
modern astronomy;" while the "Norfolk Herald" is clear that "there must
be great error on one side or the other." ... The fact is worth noting
that from 1849-1857 arguments on the roundness or flatness of the earth
did itinerate. I have no doubt they did much good, for very few persons
have any distinct idea of the evidence for the rotundity of the earth.
The "Blackburn Standard" and "Preston Guardian" (December 12 and 16,
1849) unite in stating that the lecturer ran away from his second
lecture at Burnley, having been rather too hard pressed, at the end of
his first lecture, to explain why the large hull of a ship disappeared
before the masts. The persons present and waiting for the second
lecture assuaged their disappointment by concluding that the lecturer
had slipped off the ice edge of his flat disc, and that he would not be
seen again till he peeped up on the opposite side.' ... 'The zetetic
system,' proceeds De Morgan, 'still lives in lectures and books; as it
ought to do, for there is no way of teaching a truth comparable to
opposition. The last I heard of it was in lectures at Plymouth, in
October 1864. Since this time a prospectus has been issued of a work
entitled "The Earth not a Globe;" but whether it has been published I do
not know.'
The book was published soon after the above was written, and De Morgan
gives the following quaint account of it: 'August 28, 1865. The zetetic
astronomy has come into my hands. When in 1851 I went to see the Great
Exhibition I heard an organ played by a performer who seemed very
desirous of exhibiting one particular stop. "What do you think of that
stop?" I was asked. "That depends on the name of it," said I "Oh! what
can the name of it have to do with the sound? 'that which we call a
rose,' etc." "The name has everything to do with it: if it be a flute
stop I think it very harsh; but if it be a railway-whistle stop, I think
it very sweet." So as to this book: if it be childish, it is clever; if
it be mannish, it is unusually foolish. The flat earth floating
tremulously on the sea; the sun moving always over the flat, giving day
when near enough, and night when too far off; the self-luminous moon,
with a semi-transparent invisible moon created to give her an eclipse
now and then; the new law of perspective, by which the vanishing of the
hull before the masts, usually thought to prove the earth globular,
really proves it flat;--all these and other things are well fitted to
form exercises for a person who is learning the elements of astronomy.
The manner in which the sun dips into the sea, especially in tropical
climates, upsets the whole. Mungo Park, I think, gives an African
hypothesis which explains phenomena better than this. The sun dips into
the Western ocean, and the people there cut him in pieces, fry him in a
pan, and then join him together again; take him round the under way, and
set him up in the East. I hope this book will be read, and that many
will be puzzled by it; for there are many whose notions of astronomy
deserve no better fate. There is no subject on which there is so little
accurate conception as on that of the motions of the heavenly
bodies.[51] The author, though confident in the extreme, neither
impeaches the honesty of those whose opinion he assails, nor allots them
any future inconvenience: in these points he is worthy to live on a
globe and to rotate in twenty-four hours.'
I chanced to reside near Plymouth when Mr. Rowbotham lectured there in
October 1864. It will readily be understood that, in a town where there
are so many naval men, his lectures were not altogether so successful as
they have sometimes been in small inland towns. Numbers of naval
officers, however, who were thoroughly well assured of the fact that the
earth is a globe, were not able to demolish the crafty arguments of
Parallax publicly, during the discussions which he challenged at the
close of each lecture. He was too skilled in that sort of evasion which
his assumed name (as interpreted by Liddell and Scott) suggests, to be
readily cornered. When an argument was used which he could not easily
meet, or seem to meet, he would say simply: 'Well, sir, you have now had
your fair share of the discussion; let some one else have his turn.' It
was stated in the newspapers that one of his audience was so wrathful
with the lecturer on account of these evasions, that he endeavoured to
strike Parallax with a knobbed stick at the close of the second lecture;
but probably there was no real foundation for the story.
Mr. Rowbotham did a very bold thing, however, at Plymouth. He undertook
to prove, by observations made with a telescope upon the Eddystone
Lighthouse from the Hoe and from the beach, that the surface of the
water is flat. From the beach usually only the lantern can be seen. From
the Hoe the whole of the lighthouse is visible under favourable
conditions. Duly on the morning appointed, Mr. Rowbotham appeared. From
the Hoe a telescope was directed towards the lighthouse, which was well
seen, the morning being calm and still, and tolerably clear. On
descending to the beach it was found that, instead of the whole lantern
being visible as usual, only half could be seen--a circumstance
doubtless due to the fact that the air's refractive power, which usually
diminishes the dip due to the earth's curvature by about one-sixth part,
was less efficient that morning than usual. The effect of the
peculiarity was manifestly unfavourable to Mr. Rowbotham's theory. The
curvature of the earth produced a greater difference than usual between
the appearance of a distant object as seen from a certain high station
and from a certain low station (though still the difference fell short
of that which would be shown if there were no air). But Parallax claimed
the peculiarity observable that morning as an argument in favour of his
flat earth. It is manifest, he said, that there is something wrong about
the accepted theory; for it tells us that so much less of the lighthouse
should be seen from the beach than from the Hoe, whereas less still was
seen. And many of the Plymouth folk went away from the Hoe that morning,
and from the second lecture, in which Parallax triumphantly quoted the
results of the observation, with the feeling which had been expressed
seven years before in the 'Leicester Advertiser,' that 'some of the most
important conclusions of modern astronomy had been seriously
invalidated.' If our books of astronomy, in referring to the effects of
the earth's curvature, had only been careful to point out how surveyors
and sailors and those who build lighthouses take into account the
modifying effects of atmospheric refraction, and how these effects have
long been known to vary with the temperature and pressure of the air,
this mischief would have been avoided. It would not be fair to say of
the persons misled on that occasion by Parallax that they deserved no
better; since the fault is not theirs as readers, but that of careless
or ill-informed writers.
Another experiment conducted by Parallax the same morning was creditable
to his ingenuity. Nothing better, perhaps, was ever devised to deceive
people, apparently by ocular evidence, into the belief that the earth is
flat--nor is there any clearer evidence of the largeness of the earth's
globe compared with our ordinary measures. On the Hoe, some ninety or a
hundred feet above the sea-level, he had a mirror suspended in a
vertical position facing the sea, and invited the bystanders to look in
that mirror at the sea-horizon. To all appearance the line of the
horizon corresponded exactly with the level of the eye-pupils of the
observer. Now, of course, when we look into a mirror whose surface is
exactly vertical, the line of sight to the eye-pupils of our image in
the mirror is exactly horizontal; whereas the line of sight from the
eyes to the image of the sea-horizon is depressed exactly as much as the
line from the eyes to the real sea-horizon. Here, then, seemed to be
proof positive that there is no depression of the sea-horizon; for the
horizontal line to the image of the eye-pupil seemed to coincide exactly
with the line to the image of the sea-horizon. It is not necessary to
suppose here that the mirror was wrongly adjusted, though the slightest
error of adjustment would affect the result either favourably or
unfavourably for Parallax's flat-earth theory. It is a matter of fact
that, if the mirror were perfectly vertical, only very acute vision
could detect the depression of the image of the sea-horizon below the
image of the eye-pupil. The depression can easily be calculated for any
given circumstances. Parallax encouraged observers to note very closely
the position of the eye-pupil in the image, so that most of them
approached the image within about ten inches, or the glass within about
five. Now, in such a case, for a height of one hundred feet above the
sea-level the image of the sea-horizon would be depressed below the
image of the eye-pupil by less than three hundredths of an inch--an
amount which could not be detected by one eye in a hundred. The average
diameter of the pupil itself is one-fifth of an inch, or about seven
times as great as the depression of the sea-horizon in the case
supposed. It would require very close observation and a good eye to
determine whether a horizontal line seen on either side of the head were
on the level of the centres of the eye-pupils, or lower by about
one-seventh of the breadth of either pupil.
The experiment is a pretty one, however, and well worth trying by any
one who lives near to the sea-shore and sea-cliffs. But there is a much
more effective experiment which can be much more easily tried--only it
is open to the disadvantage that it at once demolishes the argument of
our friend Parallax. It occurred to me while I was writing the above
paragraph. Let a very small mirror (it need not be larger than a
sixpence) be so suspended to a small support and so weighted that when
left to itself it hangs with its face perfectly vertical--an arrangement
which any competent optician will easily secure--and let a fine
horizontal line or several horizontal lines be marked on the mirror;
which, by the way, should be a metallic one, as its indications will
then be altogether more trustworthy. This mirror can be put into the
waistcoat pocket and conveniently carried to much greater height than
the mirror used by Parallax. Now, at some considerable height--say five
or six hundred feet above the sea-level, but a hundred or even fifty
will suffice--look into this small mirror while _facing_ the sea. The
true horizon will then be seen to be visibly below the centre of the
eye-pupil--visibly in this case because the horizontal line traced on
the mirror can be made to coincide with the sea-horizon exactly, and
will then be found _not_ to coincide with the centre of the eye-pupil.
Such an instrument could be readily made to show the distance of the
sea-horizon, which at once determines the height of the observer above
the sea-level. For this purpose all that would be necessary would be a
means of placing the eye at some definite distance from the small
mirror, and a fine vertical scale on the mirror to show the exact
depression of the sea-horizon. For balloonists such an instrument would
sometimes be useful, as showing the elevation independently of the
barometer, whenever any portion of the sea-horizon was in view.
The mention of balloon experiences leads me to another delusive argument
of the earth-flatteners.[52] It has been the experience of all
aeronauts that, as the balloon rises, the appearance of the earth is by
no means what would be expected from the familiar teachings in our books
of astronomy. There is a picture in most of these books representing the
effect of ascent above the sea-level in depressing the line of sight to
the horizon, and bringing more and more into view the convexity of the
earth's globe. One would suppose, from the picture, that when an
observer is at a great height the earth would appear to rise under him,
like some great round and well-curved shield whose convexity was towards
him. Instead of this, the aeronaut finds the earth presenting the
appearance of a great hollow basin, or of the concave side of a
well-curved shield. The horizon seems to rise as he rises, while the
earth beneath him sinks lower and lower. A somewhat similar phenomenon
may be noted when, after ascending the landward side of a high cliff, we
come suddenly upon a view of the sea--invariably the sea-horizon is
higher than we expected to find it. _Only_, in this case, the surface of
the sea seems to rise from the beach below towards the distant horizon
convexly not concavely; the reason of which I take to be this, that the
waves, and especially long rollers or uniform large ripples, teach the
eye to form true conceptions of the shape of the sea-surface even when
the eye is deceived as to the position of the sea-horizon. Indeed, I
should much like to know what would be the appearance of the sea from a
balloon when no land was in sight (though I do not particularly wish to
make the observation myself): the convexity discernible, for the reason
just named, would contend strangely with the concavity imagined, for the
reason now to be indicated.
The deception arises from the circumstance that the scene displayed
below and around the balloon is judged by the eye from the experience of
more familiar scenes. The horizon is depressed, but so little that the
eye cannot detect the depression, especially where the boundary of the
horizon is irregular. It is here that the text-book pictures mislead;
for they show the depression as far too great to be overlooked, setting
the observer sometimes about two thousand miles above the sea-level. The
eye, then, judges the horizon to be where it usually is--on the same
level as the observer; but looking downwards, the eye perceives, and at
once appreciates if it does not even exaggerate, the great depth at
which the earth lies below the balloon. The appearance, then, as judged
by the eye, is that of a mighty basin whose edge rises up all round to
the level of the balloon, while its bottom lies two or three miles or
more below the balloon.