General Summary--Application--“CUI BONO.”
ZETETIC ASTRONOMY.
The term “zetetic” is derived from the Greek verb _zeteo_; which
means to search or examine--to proceed only by inquiry. None can
doubt that by making special experiments and collecting manifest and
undeniable facts, arranging them in logical order, and observing
what is naturally and fairly deducible, the result will be far more
consistent and satisfactory than by framing a theory or system and
assuming the existence of causes for which there is no direct evidence,
and which can only be admitted “for the sake of argument.” All theories
are of this character--“supposing instead of inquiring, imagining
systems instead of learning from observation and experience the true
constitution of things. Speculative men, by the force of genius may
invent systems that will perhaps be greatly admired for a time; these,
however, are phantoms which the force of truth will sooner or later
dispel; and while we are pleased with the deceit, true philosophy, with
all the arts and improvements that depend upon it, suffers. The real
state of things escapes our observation; or, if it presents itself
to us, we are apt either to reject it wholly as fiction, or, by new
efforts of a vain ingenuity to interweave it with our own conceits,
and labour to make it tally with our favourite schemes. Thus, by
blending together parts so ill-suited, the whole comes forth an absurd
composition of truth and error. * * These have not done near so much
harm as that pride and ambition which has led philosophers to think it
beneath them to offer anything less to the world than a complete and
finished system of nature; and, in order to obtain this at once, to
take the liberty of inventing certain principles and hypotheses, from
which they pretend to explain all her mysteries.”[1]
[1] “An Account of Sir Isaac Newton’s Discoveries.” By Professor
Maclaurin, M.A., F.R.S., of the Chair of Mathematics in the
University of Edinburgh.
Copernicus admitted, “It is not necessary that hypotheses should be
true, or even probable; it is sufficient that they lead to results
of calculation which agree with calculations. * * Neither let any
one, so far as hypotheses are concerned, expect anything _certain_
from astronomy; since that science can afford nothing of the kind;
lest, in case he should adopt for truth things feigned for another
purpose, he should leave this study more foolish than he came. * * The
hypothesis of the terrestrial motion was _nothing but an hypothesis_,
valuable only so far as it explained phenomena, and not considered
with reference to absolute truth or falsehood.” The Newtonian and all
other “systems of nature” are little better than the “hypothesis of
the terrestrial motion” of Copernicus. The foundations or premises are
always unproved; no proof is ever attempted; the necessity for it is
denied; it is considered sufficient that the assumptions shall _seem_
to explain the phenomena selected. In this way it is that one theory
supplants another; that system gives way to system as one failure after
another compels opinions to change. This will ever be so; there will
always exist in the mind a degree of uncertainty; a disposition to look
upon philosophy as a vain pretension; a something almost antagonistic
to the highest aspirations in which humanity can indulge, unless the
practice of theorising be given up, and the method of simple inquiry,
the “zetetic” process be adopted. “Nature speaks to us in a peculiar
language; in the language of phenomena, she answers at all times the
questions which are put to her; and such questions are experiments.”[2]
Not experiments only which corroborate what has previously been
_assumed_ to be true; but experiments in every form bearing on the
subject of inquiry, before a conclusion is drawn or premises affirmed.
[2] “Liebig’s Agricultural Chemistry,” p. 39.
We have an excellent example of zetetic reasoning in an arithmetical
operation; more especially so in what is called the “Golden Rule,” or
the “Rule-of-Three.” If one hundred weight of any article is worth a
given sum, what will some other weight of that article be worth? The
separate figures may be considered as the elements or facts of the
inquiry; the placing and working of these as the logical arrangement;
and the quotient or answer as the fair and natural deduction. Hence,
in every zetetic process, the conclusion arrived at is essentially a
quotient, which, if the details be correct, must, of necessity, be true
beyond the reach or power of contradiction.
In our courts of Justice we have also an example of the zetetic
process. A prisoner is placed at the bar; evidence for and against
him is advanced; it is carefully arranged and patiently considered;
and only such a verdict given as could not in justice be avoided.
Society would not tolerate any other procedure; it would brand with
infamy whoever should assume a prisoner to be guilty, and prohibit all
evidence but such as would corroborate the assumption. Yet such is the
character of theoretical philosophy!
The zetetic process is also the natural method of investigation; nature
herself teaches it. Children invariably seek information by asking
questions--by earnestly inquiring from those around them. Question
after question in rapid and exciting succession will often proceed
from a child, until the most profound in learning and philosophy will
feel puzzled to reply. If then both nature and justice, as well as the
common sense and practical experience of mankind demand, and will not
be content with less or other than the zetetic process, why should it
be ignored and violated by the learned in philosophy? Let the practice
of theorising be cast aside as one fatal to the full development of
truth; oppressive to the reasoning power; and in every sense inimical
to the progress and permanent improvement of the human race.
If then we adopt the zetetic process to ascertain the true figure
and condition of the Earth, we shall find that instead of its being
a globe, and moving in space, it is the directly contrary--A PLANE;
without motion, and unaccompanied by anything in the Firmament
analogous to itself.
If the Earth is a globe, and 25,000 miles in circumference, the surface
of all standing water must have a certain degree of convexity--every
part must be an arc of a circle, curvating from the summit at the
rate of 8 inches per mile multiplied by the square of the distance.
That this may be sufficiently understood, the following quotation is
given from the _Encyclopædia Britannica_, art. “Levelling.” “If a
line which crosses the plumb-line at right angles be continued for
any considerable length it will rise above the Earth’s surface (the
Earth being globular); and this rising will be as the square of the
distance to which the said right line is produced; that is to say, it
is raised eight inches very nearly above the Earth’s surface at one
mile’s distance; four times as much, or 32 inches, at the distance
of two miles; nine times as much, or 72 inches, at the distance of
three miles. This is owing to the globular figure of the Earth, and
this rising is the difference between the true and apparent levels;
the curve of the Earth being the true level, and the tangent to it
the apparent level. So soon does the difference between the true and
apparent levels become perceptible that it is necessary to make an
allowance for it if the distance betwixt the two stations exceeds two
chains.
[Illustration: FIG. 1.]
Let B. D. be a small portion of the Earth’s circumference, whose centre
of curvature is A. and consequently all the points of this arc will be
on a level. But a tangent B. C. meeting the vertical line A. D. in C.
will be the apparent level at the point B. and therefore D. C. is the
difference between the apparent and the true level at the point B.
The distance C. D. must be deducted from the observed height to have
the true difference of level; or the differences between the distances
of two points from the surface of the Earth or from the centre of
curvature A. But we shall afterwards see how this correction may be
avoided altogether in certain cases. To find an expression for C. D.
we have Euclid, third book, 36 prop. which proves that B. C² = C. D.
(2 _A D_ × _C D_); but since in all cases of levelling C. D. is
exceedingly small compared with 2 A. D., we may safely neglect C. D²
and then B C² = 2 A. D × C. D. or
B. C²
C. D = ------.
2 A. D
Hence the depression of the true level is equal to the square of the
distance divided by twice the radius of the curvature of the Earth.
For example, taking a distance of four miles, the square of 4 = 16,
and putting down twice the radius of the Earth’s curvature as in round
figures about 8000 miles, we make the depression on four miles
16 16 × 1760 176 528
= ---- of a mile = --------- yards = --- yards = --- feet,
8000 8000 50 50
or rather better than 10¹⁄₂ feet.
Or, if we take the mean radius of the Earth as the mean radius of its
curvature, and consequently 2 A. D = 7,912 miles, then 5,280 feet being
1 mile, we shall have C. D. the depression in inches
5280 × 12 × B C²
= ---------------- = 8008 B. C² inches.
7912
The preceding remarks suppose the visual ray C. B. to be a straight
line, whereas on account of the unequal densities of the air at
different distances from the Earth, the rays of light are incurvated
by refraction. The effect of this is to lessen the difference between
the true and apparent levels, but in such an extremely variable and
uncertain manner that if any constant or fixed allowance is made for
it in formulæ or tables, it will often lead to a greater error than
what it was intended to obviate. For though the refraction may at a
mean compensate for about a seventh of the curvature of the earth, it
sometimes exceeds a fifth, and at other times does not amount to a
fifteenth. We have, therefore, made no allowance for refraction in the
foregone formulæ.”
If the Earth is a globe, there cannot be a question that, however
irregular the _land_ may be in form, the _water_ must have a convex
surface. And as the difference between the true and apparent level, or
the degree of curvature would be 8 inches in one mile, and in every
succeeding mile 8 inches multiplied by the square of the distance,
there can be no difficulty in detecting either its actual existence
or proportion. Experiments made upon the sea have been objected to on
account of its constantly-changing altitude; and the existence of banks
and channels which produce a “a crowding” of the waters, currents, and
other irregularities. Standing water has therefore been selected, and
many important experiments have been made, the most simple of which
is the following:--In the county of Cambridge there is an artificial
river or canal, called the “Old Bedford.” It is upwards of twenty
miles long, and passes in a straight line through that part of the
fens called the “Bedford level” The water is nearly stationery--often
entirely so, and throughout its entire length has no interruption from
locks or water-gates; so that it is in every respect well adapted for
ascertaining whether any and what amount of convexity really exists.
A boat with a flag standing three feet above the water, was directed
to sail from a place called “Welney Bridge,” to another place called
“Welche’s Dam.” These two points are six statute miles apart. The
observer, with a good telescope, was seated in the water as a bather
(it being the summer season), with the eye not exceeding eight inches
above the surface. The flag and the boat down to the water’s edge were
clearly _visible throughout the whole distance!_ From this observation
it was concluded that the water did not decline to any degree from the
line of sight; whereas the water would be 6 feet higher in the centre
of the arc of 6 miles extent than at the two places Welney Bridge and
Welche’s Dam; but as the eye of the observer was only eight inches
above the water, the highest point of the surface would be at one mile
from the place of observation; below which point the surface of the
water at the end of the remaining five miles would be 16 feet 8 inches
(5² × 8 = 200 inches). This will be rendered clear by the following
diagram:--
[Illustration: FIG. 2.]
Let A B represent the arc of water from Welney Bridge to Welche’s Dam,
six miles in length; and A L the line of sight, which is now a tangent
to the arc A B; the point of contact, T, is 1 mile from the eye of the
observer at A; and from T to the boat at B is 5 miles; the square of 5
miles multiplied by 8 inches is 200 inches, or, in other words, that
the boat at B would have been 200 inches or above 16 feet below the
surface of the water at T; and the flag on the boat, which was 3 feet
high, would have been 13 feet below the line-of-sight, A T L!!
From this experiment it follows that the surface of standing water is
_not convex_, and therefore _that the Earth_ IS NOT A GLOBE! On the
Contrary, this simple experiment is all-sufficient to prove that the
surface of the water is parallel to the line-of-sight, and is therefore
horizontal, and that the Earth _cannot_ be other than A PLANE! In
diagram Figure 3 this is perfectly illustrated.
[Illustration: FIG. 3.]
A B is the line-of-sight, and C D the surface of the water equidistant
from or parallel to it throughout the whole distance observed.
Although, on account of the variable state of the water, objections
have been raised to experiments made upon the sea-shore to test the
convexity of the flood or ebb-tide level, none can be urged against
observations made from higher altitudes. For example,--the distance
across the Irish Sea between Douglas Harbour, in the Isle of Man, and
the Great Orm’s Head in North Wales is 60 miles. If the earth is a
globe, the surface of the water would form an arc 60 miles in length,
the centre of which would be 1,944 feet higher than the coast line
at either end, so that an observer would be obliged to attain this
altitude before he could see the Welsh coast from the Isle of Man: as
shown in the diagram, Figure 4.
[Illustration: FIG. 4.]
It is well known, however, that from an altitude not exceeding 100 feet
the Great Orm’s Head is visible in clear weather from Douglas Harbour.
The altitude of 100 feet could cause the line of sight to touch the
horizon at the distance of nearly 13 miles; and from the horizon to
Orm’s Head being 47 miles, the square of this number multiplied by 8
inches gives 1472 feet as the distance which the Welsh coast line would
be below the line of sight B C.--A representing the Great Orm’s Head,
which, being 600 feet high, its summit would be 872 feet below the
horizon.
Many similar experiments have been made across St. George’s Channel,
between points near Dublin and Holyhead, and always with results
entirely incompatible with the doctrine of rotundity.
Again, it is known that the horizon at sea, whatever distance it may
extend to the right and left of the observer on land, always appears
as a straight line. The following experiment has been tried in various
parts of the country. At Brighton, on a rising ground near the race
course, two poles were fixed in the earth six yards apart, and directly
opposite the sea. Between these poles a line was tightly stretched
parallel to the distant horizon. From the centre of the line the view
embraced not less than 20 miles on each side, making a distance of 40
miles. A vessel was observed sailing directly westwards; the line cut
the rigging a little above the bulwarks, which it did for several hours
or until the vessel had sailed the whole distance of 40 miles. This
will be understood by reference to the diagram, Figure 5.
[Illustration: FIG. 5.]
If the Earth were a globe, the appearance would be as represented in
Figure 6.
[Illustration: FIG. 6.]
[Illustration: FIG. 7.]
The ship coming into view from the east would have to ascend an
inclined plane for 20 miles until it arrived at the centre of the arc
A B, whence it would have to descend for the same distance. The square
of 20 miles multiplied by 8 inches gives 266 feet as the amount the
vessel would be below the line C D at the beginning and at the end of
the 40 miles.
If we stand upon the deck of a ship, or mount to the mast head; or go
to the top of a mountain, or ascend above the Earth in a balloon, and
look over the sea, the surface appears as a vast inclined plane rising
up until in the distance it intercepts the line of sight. If a good
mirror be held in the opposite direction, the horizon will be reflected
as a well-defined mark or line across the centre, as represented in
diagram, Figure 7.
Ascending or descending, the distant horizon does the same. It rises
and falls with the observer, and is always on a level with his eye. If
he takes a position where the water surrounds him--as at the mast-head
of a ship out of sight of land, or on the summit of a small island
far from the mainland, the surface of the sea appears to rise up on
all sides equally and to surround him like the walls of an immense
amphitheatre. He seems to be in the centre of a large concavity,
the edges of which expand or contract as he takes a higher or lower
position. This appearance is so well known to sea-going travellers that
nothing more need be said in its support. But the appearance from a
balloon is familiar only to a small number of observers, and therefore
it will be useful to quote from those who have written upon the subject.
“_The Apparent Concavity of the Earth as seen from a Balloon._--A
perfectly-formed circle encompassed the visible planisphere beneath,
or rather the concavo-sphere it might now be called, for I had
attained a height from which the surface of the Earth assumed a
regularly hollowed or concave appearance--an optical illusion
which increases as you recede from it. At the greatest elevation I
attained, which was about a mile-and-a-half, the appearance of the
World around me assumed a shape or form like that which is made
by placing two watch-glasses together by their edges, the balloon
apparently in the central cavity all the time of its flight at that
elevation.”--_Wise’s Aeronautics._
“Another curious effect of the aerial ascent was, that the Earth,
when we were at our greatest altitude, positively appeared _concave_,
looking like a huge dark bowl, rather than the convex sphere such
as we naturally expect to see it. * * * The horizon always appears
to be on a level with our eye, and seems to rise as we rise, until
at length the elevation of the circular boundary line of the sight
becomes so marked that the Earth assumes the anomalous appearance as
we have said of a _concave_ rather than a _convex_ body.”--_Mayhew’s
Great World of London._
Mr. Elliott, an American æronaut, in a letter giving an account of his
ascension from Baltimore, thus speaks of the appearance of the Earth
from a balloon:--
“I don’t know that I ever hinted heretofore that the æronaut may
well be the most sceptical man about the rotundity of the Earth.
Philosophy imposes the truth upon us; but the view of the Earth
from the elevation of a balloon is that of an immense terrestrial
basin, the deeper part of which is that directly under one’s feet.
As we ascend, the Earth beneath us seems to recede--actually to sink
away--while the horizon gradually and gracefully lifts a diversified
slope stretching away farther and farther to a line that, at the
highest elevation, seems to close with the sky. Thus upon a clear
day, the æronaut feels as if suspended at about an equal distance
between the vast blue oceanic concave above, and the equally expanded
terrestrial basin below.”
“The chief peculiarity of the view from a balloon, at a considerable
elevation, was the altitude of the horizon, which remained
practically on a level with the eye at an elevation of two miles,
causing the surface of the Earth to appear _concave_ instead of
_convex_, and to recede during the rapid ascent, whilst the horizon
and the balloon seemed to be stationary.”--_London Journal_, July 18,
1857.
During the important balloon ascents recently made for scientific
purposes by Mr. Coxwell and Mr. Glaisher, of the Royal Greenwich
Observatory, the same phenomenon was observed--
“The horizon always appeared on a level with the car.”--Vide
“Glaisher’s Report.”
The following diagram represents this appearance:--
[Illustration: FIG. 8.]
The surface of the earth C D appears to rise to the line-of-sight from
the balloon, and “seems to close with the sky” at the points H H in
the same manner that the ceiling and the floor of a long room, or the
top and bottom of a tunnel appear to approach each other, and from the
same cause, viz.: that they are _parallel to the line-of-sight, and
therefore horizontal_.
If the Earth’s surface were convex the observer, looking from a
balloon, instead of seeing it gradually ascend to the level of the eye,
would have to look downwards to the horizon H H, as represented in
figure 9, and the amount of dip in the line-of-sight C H would be the
greatest at the highest elevation.
[Illustration: FIG. 9.]
Many more experiments have been made than are here described, but the
selection now given is amply sufficient to prove that the surface of
water is horizontal, and that the Earth, taken as a whole, its land and
water together, is not a globe, has really no degree of sphericity; but
is “to all intents and purposes” A PLANE!
If we now consider the fact that when we travel by land or sea, and
from any part of the known world, in a direction towards the North
polar star, we shall arrive at one and the same point, we are forced
to the conclusion that what has hitherto been called the North Polar
region, is really THE CENTRE OF THE EARTH. That from this northern
centre the land diverges and stretches out, of necessity, towards a
circumference, which must now be called THE SOUTHERN REGION: which is
a vast circle, and not a pole or centre. That there is ONE CENTRE--THE
NORTH, and ONE CIRCUMFERENCE--THE SOUTH. This language will be better
understood by reference to the diagram Figure 10.
[Illustration: FIG. 10.]
N represents the northern centre; and S S S the southern
circumference--both icy or frozen regions. That the south is an
immense ring, or glacial boundary, is evident from the fact, that
within the antarctic circle the most experienced, scientific, and
daring navigators have failed in their attempts to sail, in a direct
manner, completely round it. Lieut. Wilkes, of the American Navy, after
great and prolonged efforts, and much confusion in his reckoning, and
seeing no prospect of success, was obliged to give up his attempt and
return to the north. This he acknowledged in a letter to Captain Sir
James Clarke Ross, with whose intention to explore the south seas he
had become acquainted, in which the following words occur: “I hope
you intend to circumnavigate the antarctic circle. I made 70 degrees
of it.” Captain Ross, however, was himself greatly confused in his
attempts to navigate the southern region. In his account of the voyage
he says, at page 96--“We found ourselves every day from 12 to 16 miles
by observation in advance of our reckoning.” “By our observations
we found ourselves 58 miles to the eastward of our reckoning in two
days.” And in this and other ways all the great navigators have been
frustrated in their efforts, and have been more or less confounded in
their attempts to sail round the Earth upon or beyond the antarctic
circle. But if the southern region is a pole or centre, like the
north, there would be little difficulty in circumnavigating it, for
the distance round would be comparatively small. When it is seen that
the Earth is not a sphere, but a plane, having only one centre, the
north; and that the south is the vast icy boundary of the world, the
difficulties experienced by circumnavigators can be easily understood.
Having given a surface or bird’s-eye view of the Earth, the following
sectional representation will aid in completing the description.
[Illustration: FIG. 11.]
E E represents the Earth; W W the “great deep,” or the waters which
surround the land; N the northern centre; and S S sections of the
southern ice. As the present description is purely zetetic, and as
every fact must therefore have its fullest value assigned to it, and
its consequences represented, a peculiarity must be pointed out in the
foregoing diagram. It will be observed that from about the points E E
the surface of the water rises towards the south S S. It is clearly
ascertained that the altitude of the water in various parts of the
world is much influenced by the pressure of the atmosphere--however
this pressure is caused--and it is well known that the atmospheric
pressure in the south is constantly less than it is in the north, and
therefore the water in the southern region must always be considerably
higher than it is in the northern. Hence the peculiarity referred to
in the diagram. The following quotation from Sir James Ross’s voyages,
p. 483, will corroborate the above statements:--“Our barometrical
experiments appear to prove that a gradual diminution of atmospheric
pressure occurs as we proceed southwards from the tropic of Capricorn.
* * * It has hitherto been considered that the mean pressure of the
atmosphere at the level of the sea was nearly the same in all parts of
the world, as no material difference occurs between the equator and
the highest northern latitudes. * * * The causes of the atmospheric
pressure being so _very much less_ in the southern than in the northern
hemispheres remains to be determined.”
Thus, putting all theories aside, we have seen that direct experiment
demonstrates the important truth, _that the Earth is an extended
Plane_. Literally, “Stretched out upon the waters;” “Founded on the
seas and established on the floods;” “Standing in the water and out
of the water.” How far the southern icy region extends horizontally,
or how deep the waters upon and in which the earth stands or is
supported are questions which cannot yet be answered. In Zetetic
philosophy the foundation must be well secured, progress must be made
step by step, making good the ground as we proceed; and whenever a
difficulty presents itself, or evidence fails to carry us farther,
we must promptly and candidly acknowledge it, and prepare for future
investigation; but never fill up the inquiry by theory and assumption.
In the present instance there is no practical evidence as to the extent
of the southern ice and the “great deep.” Who shall say whether the
depth and extent of the “mighty waters” _have_ a limit, or constitute
the “World without end?”
Having advanced direct and special evidence that the surface of the
earth is not convex, but, on the contrary, a vast and irregular plane,
it now becomes important that the leading phenomena upon which the
doctrine of rotundity has been founded should be carefully examined.
First, it is contended that because the hull of an outward-bound vessel
disappears before the mast head, the water is convex, and therefore the
Earth is a globe. In this conclusion, however, there is an assumption
involved, viz., that such a phenomenon _can only_ result from a convex
surface. Inquiry will show that this is erroneous. If we select for
observation a few miles of straight and level railway, we shall
find that the rails, which are parallel, appear in the distance to
approach each other. But the two rails which are nearest together do
so more rapidly than those which are farthest asunder, as shown in the
following diagram, Figure 12.
[Illustration: FIG. 12.]
Let the observer stand at the point A, looking in the direction of the
arrows; and the rails 1.2.3.4. will appear to join at the point B, but
the rail 5.6 will appear to have converged only as far as C towards B.
Again, let a train be watched from the point A in Figure 13.
[Illustration: FIG. 13.]
The observer looking from A, with his eye midway between the bottom
of the carriage and the rail, will see the diameter of the wheels
gradually diminish as they recede. The lines 1.2 and 1.4 will appear to
approach each other until at the point B they will come together, and
the space, including the wheels, between the bottom of the carriage
and the rail will there disappear. The floor of the carriage will seem
to be sliding without wheels upon the rail 1.2; but the lines 5.6 and
7.8 will yet have converged only to C and D.
The same phenomenon may be observed with a long row of lamps, where the
ground is a straight line throughout its entire length as represented
in Figure 14.
[Illustration: FIG. 14.]
The lines 1.2 and A D will converge at the point D and the pedestal of
the lamp at D will seem to have disappeared, but the line 3.4, which
represents the true altitude of the lamps, will only have converged to
the point C.
A narrow bank running along the side of a straight portion of railway,
upon which poles are placed for supporting the wires of the electric
telegraph will produce the same appearance, as shown in Figure 15.
[Illustration: FIG. 15.]
The bank having the altitude 1.3 and 2.4 will, in the distance of two
or three miles (according to its depth) disappear to the eye of an
observer placed at Figure 1; and the telegraph pole at Figure 2 will
seem not to stand upon a bank at all, but upon the actual railway. The
line 3.4 will merge into the line 1.2 at the point B, while the line
5.6 will only have descended to the position C.
[Illustration: FIG. 16.]
Many other familiar instances could be given to show the true law of
perspective; which is, that parallel lines appear in the distance
to converge to one and the same datum line, but to reach it at
different distances if themselves dissimilarly distant. This law being
remembered, it is easy to understand how the hull of an outward-bound
ship, although sailing upon a plane surface disappears before the
mast-head. In Figure 16, let A B represent the surface of the water;
C H the line of sight; and E D the altitude of the mast-head. Then,
as A B and C H are nearer to each other than A B and E D, they will
converge and appear to meet at the point H, which is the practical,
or, as it would be better to call it, the _optical_ horizon. The hull
of the vessel being contained within the lines A B and C H, must
gradually diminish as these converge, until at H, or the horizon,
it enters the vanishing point and disappears; but the mast-head
represented by the line E D is still _above_ the horizon at H, and will
require to sail more or less, according to its altitude, beyond the
point H before it sinks to the line C H, or, in other words, before the
lines A B and E D form the same angle as A B and C H.
It will be evident also that should the elevation of the observer be
greater than at C, the horizon or vanishing point would not be formed
at H, but at a greater distance; and therefore the hull of the vessel
would be longer visible. Or, if, when the hull has disappeared at H,
the observer ascends from the elevation at C to a higher position
nearer to E, it will again be seen. Thus all these phenomena which have
so long been considered as proofs of the Earth’s rotundity are really
optical sequences of the contrary doctrine. To argue that because the
lower part of an outward-bound ship disappears before the highest the
water must be round, is to _assume_ that a _round_ surface _only_
can produce this effect! But it is now shown that a _plane_ surface
_necessarily_ produces this effect; and therefore the assumption is
not required, and the argument involved is fallacious!
It may here be observed that no help can be given to this doctrine of
rotundity by quoting the prevailing theory of perspective. The law
represented in the foregoing diagrams is the “law of nature.” It may
be seen in every layer of a long wall, in every hedge and bank of the
roadside, and indeed in every direction where lines and objects run
parallel to each other; but no illustration of the contrary perspective
is ever to be seen! except in the distorted pictures, otherwise
cleverly and beautifully drawn as they are, which abound in our public
and private collections.
The theory which affirms that parallel lines converge only to one and
the same point upon the eye-line is an error. It is true only of lines
equidistant from the eye-line. It is true that parallel lines converge
to one and the same _eye-line_, but _meet it at different distances
when more or less apart from each other_. This is the true law of
perspective as shown by Nature herself; any other idea is fallacious
and will deceive whoever may hold and apply it to practice.
As it is of great importance that the difference should be clearly
understood, the following diagram is given. Let E L (Figure 17)
represent the eye-line and C the vanishing point of the lines, 1 C 2
C; then the lines 3.4.5.6, although converging _somewhere_ to the line
E L, will not do so to the point C, but 3 and 4 will proceed to D and 5
and 6 to H. It is repeated, that lines _equidistant_ from the _datum_
will converge on the _same point_ and at the _same distance_; but lines
_not_ equidistant will converge on the same _datum_ but at _different
distances_! A very good illustration of the difference is given in
Figure 18. Theoretic perspective would bring the lines 1, 2, and 3 to
the same _datum_ line E L and to the _same point_ A. But the true
or natural law would bring the lines 2 and 3 to the point A because
equidistant from the eye-line E L; but the line 1 being farther from
E L than either 2 or 3, would be taken beyond the point A on towards C,
until it formed the _same angle_ upon the line E L as 2 and 3 form at
the point A.
[Illustration: FIG. 17.]
[Illustration: FIG. 18.]
The subject of perspective will not be rendered sufficiently clear
unless an explanation be given of the cause and character of what is
technically called the “vanishing point.” Why do objects, even when
raised above the earth, vanish at a given distance? It is known,
and can easily be proved by experiment, that “the range of the eye,
or diameter of the field of vision is 110°; consequently this is
the _largest_ angle under which an object can be seen. The range of
vision is from 110° to 1°. * * The _smallest_ angle under which an
object can be seen is upon an average for different sights the 60th
part of a degree, or _one minute_ in space; so that when an object is
removed from the eye 3000 times its own diameter, it will only just
be distinguishable; consequently, the greatest distance at which we
can behold an object, like a shilling, of an inch in diameter is 3000
inches or 250 feet.”[3] It may, therefore, be very easily understood
that a line passing over the hull of a ship, and continuing parallel
to the surface of the water, must converge to the vanishing point at
the distance of about 3000 times its own elevation; in other words,
if the surface of the hull be 10 feet above the water it will vanish
at 3,000 times 10 feet; or nearly six statute miles; but if the
mast-head be 30 feet above the water, it will be visible for 90,000
feet or over 17 miles; so that it could be seen upon the horizon for
a distance of eleven miles _after the hull had entered the vanishing
point_! Hence the phenomenon of a receding ship’s hull being the
first to disappear, which has been so universally quoted and relied
upon as proving the rotundity of the Earth is fairly and logically
a proof of the very contrary! It has been misapplied in consequence
of an erroneous view of the law of perspective, and the desire to
support a theory. That it is valueless for such a purpose has already
been shown; and that, even if there were no question of the Earth’s
form involved, it could not arise from the convexity of the water, is
proved by the following experiment:--Let an observer stand upon the
sea-shore with the eye at an elevation of about six feet above the
water, and watch a vessel until it is just “hull down.” If now a good
telescope be applied the hull will be distinctly _restored to sight_!
From which it must be concluded that it had disappeared through the
influence of perspective, and not from having sunk behind the summit
of a convex surface! Had it done so it would follow that the telescope
had either carried the line-of-sight through the mass of water, or over
its surface and down the other side! But the power of “looking round a
corner” or penetrating a dense and extensive medium has never yet been
attributed to such an instrument! If the elevation of the observer be
much greater than six feet the distance at which the vanishing point is
formed will be so great that the telescope may not have power enough to
magnify or enlarge the angle constituting it; when the experiment would
appear to fail. But the failure would only be apparent, for a telescope
of sufficient power to magnify at the horizon or vanishing point would
certainly restore the hull at the greater distance.
[3] “Wonders of Science,” by Mayhew, p. 357.
[Illustration: FIG. 19.]
An illustration or proof of the Earth’s rotundity is also supposed to
be found in the fact that navigators by sailing due east or west return
in the opposite direction. Here, again, a supposition is involved,
viz., that upon a globe _only_ could this occur. But it is easy to
prove that it could take place as perfectly upon a circular plane
as upon a sphere. Let it first be clearly understood what is really
meant by sailing _due east and west_. Practically it is sailing at
right angles to north and south: this is determined ordinarily by the
mariners’ compass, but more accurately by the meridian lines which
converge to the northern centre of the Earth. Bearing this in mind,
let N in Figure 19 represent the northern centre; and the lines N. S.
the directions north and south. Then let the small arrow, Figure 1,
represent a vessel on the meridian of Greenwich, with its head W. at
right angles, or due west; and the stern E due east. It is evident that
in passing to the position of the arrow, Figure 2, which is still
due west or square to the meridian, the arc 1.2 must be described;
and in sailing still farther under the same condition, the arcs 2.3,
3.4, and 4.1 will be successively passed over until the meridian of
Greenwich, Figure 1, is arrived at, which was the point of departure.
Thus a mariner, by keeping the head of his vessel due west, or at right
angles to the north and south, practically circumnavigates a plane
surface; or, in other words, he describes a circle _upon a plane_,
at a greater or lesser distance from the centre N, and being at all
times square to the radii north and south, he is _compelled_ to do
so--_because_ the earth is a plane, having a central region, towards
which the compass and the meridian lines which guide him, converge. So
far, then, from the fact of a vessel sailing due west coming home from
the east, and _vice versa_, being a proof of the earth’s rotundity, it
is simply a phenomenon, consistent with and dependent upon its being
a plane! The subject may be perfectly illustrated by the following
simple experiment:--Take a round table, fix a pin in the centre; to
this attach a thread, and extend it to the edge. Call the centre the
north and the circumference the south; then, at any distance between
the centre and the circumference, a direction at right angles to the
thread will be due east and west; and a small object, as a pencil,
placed across or square to the thread, to represent a ship, may be
carried completely round the table without its right-angled position
being altered; or, the right-angled position firmly maintained, the
vessel must of necessity describe a circle on being moved from right
to left or left to right. Referring again to the diagram, Figure 19,
the vessel may sail from the north towards the south, upon the meridian
Figure 1, and there turning due west, may pass Cape Horn, represented
by D, and continue its westerly course until it passes the point C, or
the Cape of Good Hope, and again reaches the meridian, Figure 1, upon
which it may return to the north. Those, then, who hold that the earth
is a globe because it can be circumnavigated, have an argument which
is logically incomplete and fallacious. This will be seen at once by
putting it in the syllogistic form:--
A globe _only_ can be circumnavigated:
The Earth has been circumnavigated:
Therefore the Earth is a globe.
It has been shown that a _plane_ can be circumnavigated, and therefore
the first or major proposition is false; and, being so, the conclusion
is false. This portion of the subject furnishes a striking instance
of the necessity of, at all times, proving a proposition by direct
and immediate evidence, instead of quoting a natural phenomenon as a
proof of what has previously been assumed. But a theory will not admit
of this method, and therefore the zetetic process, or inquiry before
conclusion, entirely eschewing assumption, is the only course which
can lead to simple and unalterable truth. Whoever creates or upholds a
theory, adopts a monster which will sooner or later betray and enslave
him, or make him ridiculous in the eyes of practical observers.
Closely following the subject of circumnavigation, the gain and loss
of time discovered on sailing east and west is referred to as another
proof of rotundity. But this illustration is equally fallacious with
the last, and from the same cause, viz., the assumption that a _globe
only_ could produce the effect observed. It will be seen, by reference
to diagram, Figure 19, that the effect must take place equally upon a
plane as upon a globe. Let the ship, W E, upon the meridian, Figure 1,
at 12 at noon, begin to sail towards the position, Figure 2, which it
will reach the next day at 12, or in 24 hours: the sun during the same
24 hours will have returned only to Figure 1, and will require to move
for another hour or more until it reaches the ship at Figure 2, making
25 hours instead of 24, in which the sun would have returned to the
ship, if it had remained at Figure 1. In this way, the sun is more and
more behind the meridian time of the ship, as it proceeds day after day
upon its westerly course, so that on completing the circumnavigation
the ship’s time is a day later than the solar time, reckoning to and
from the meridian of Greenwich. But the contrary follows if the ship
sails from Figure 1 towards Figure 4, or the east, because it will meet
the sun one hour earlier than the 24 hours which would be required for
it to pass on to Figure 1. Hence, on completing the circle 1.4.3.2.1,
the time at the ship would be one day in advance of the time at
Greenwich, or the position Figure 1. Captain Sir J. C. Ross, at page
132, vol. 2, says--“November 25, having by sailing to the eastward
gained 12 hours, it became necessary, on crossing the 180th degree and
entering upon west longitude, in order to have our time correspond with
that of England, to have two days following of the same date, and by
this means lose the time we had gained, and still were gaining, as we
sailed to the eastward.”
In further illustration of this matter, and to impress the mind of the
readers with its importance as an evidence in support of the theory
of the earth’s sphericity, several authors have given the following
story:--Two brothers, twins, born within a few minutes of each other,
and therefore of the same age, on growing to manhood went to sea. They
both circumnavigated the earth, but in opposite directions; and when
they again met, one was a day older than the other!
Whatever truth there may be in this account, it is here shown to be no
more favourable to the idea of rotundity than it is to the opposite
fact that the earth is a plane; as both forms will permit of the same
effect.
Another phenomenon supposed to prove rotundity, is found in the fact
that Polaris, or the north polar star, gradually sinks to the horizon
as the mariner approaches the equator, on passing which it becomes
invisible. First, it is an ordinary effect of perspective for an object
to appear lower and lower as the observer recedes. Let any one try
the experiment of looking at a lighthouse, church spire, monument,
gas-lamp, or other elevated object, from the distance of a few yards,
and notice the angle at which it is observed: on going farther away,
the angle will diminish and the object appear lower, until, if the
distance be sufficiently great, the line-of-sight to the object, and
the apparently ascending surface of the Earth upon which it stands
will converge to the angle which constitutes the vanishing point; at
a single yard beyond which it will be invisible. This, then, is the
necessary result of the everywhere visible law of perspective operating
between the eye-line and the plane surface upon which the object
stands; and has no relation whatever to rotundity.
It is not denied that a similar depression of a distant object would
take place upon a globe; it is simply contended that it would not occur
upon a globe exclusively. But if the Earth is a sphere and the pole
star hangs over the northern axis, it would be impossible to see it for
a single degree beyond the equator, or 90 degrees from the pole. The
line-of-sight would become a tangent to the sphere, and consequently
several thousand miles out of and divergent from the direction of the
pole-star. Many cases, however, are on record of the north polar star
being visible far beyond the equator, as far even as the tropic of
Capricorn. In the _Times_ newspaper of May 13, 1862, under the head of
“Naval and Military Intelligence,” it is stated that Captain Wilkins
distinctly saw the Southern Cross and the polar star at midnight in
23·53 degrees of latitude, and longitude 35·46.
[Illustration: FIG. 20.]
This would be utterly impossible if the Earth were a globe, as shown
in the diagram, Figure 20. Let N represent the north pole, E E the
equator, C C the tropic of Capricorn, and P the polar star. It will
be evident that the line-of-sight C D being a tangent to the Earth
beyond the equator E must diverge from the axis N and could not by any
known possibility cause the star P to be visible to an observer at C.
No matter how distant the star P, the line C D being divergent from
the direction N P could never come in contact with it. The fact, then,
that the polar star has often been seen from many degrees beyond the
equator, is really an important argument against the doctrine of the
Earth’s rotundity.
It has been thought that because a pendulum vibrates more rapidly in
the northern region than at the equator, the Earth is thereby proved to
be a globe; and because the variation in the velocity is not exactly as
it should be if all the surface of the Earth were equidistant from the
centre, it has been concluded that the Earth is an oblate spheroid, or
that its diameter is rather less through the poles than it is through
the equator. The difference was calculated by Newton to be the 235th
part of the whole diameter; or that the polar was to the equatorial
diameter as 689 to 692. Huygens gave the proportion as 577 to 875 or
a difference of about one-third of the whole diameter. Others have
given still different proportions; but recently the difference of
opinion has become so great that many have concluded that the Earth
is really instead of oblate an _oblong_ spheroid. It is certain that
the question when attempted to be answered by measuring arcs of the
meridian, is less satisfactory than was expected. This will be evident
from the following quotation from the account of the ordnance survey
of Great Britain, which was conducted by the Duke of Richmond, Col.
Mudge, General Roy, Mr. Dalby, and others, who measured base lines on
Hounslow Heath and Salisbury Plain with glass rods and steel chains:
“when these were connected by a chain of triangles and the length
computed the result did not differ more than one inch from the actual
measurements--a convincing proof of the accuracy with which all the
operations had been conducted.
The two stations, of Beachy Head in Sussex and Dunnose in the Isle of
Wight, are visible from each other, and more than 64 miles asunder,
nearly in a direction from east to west; their exact distance was found
by the geodetical operations to be 339,397 feet (64 miles and 1477
feet). The azimuth, or bearing of the line between them with respect
to the meridian, and also the latitude of Beachy Head, were determined
by astronomical observations. From these data the length of a degree
perpendicular to the meridian was computed; and this, compared with the
length of a meridional degree in the same latitude, gave the proportion
of the polar to the equatorial axis. The result thus obtained, however,
differed considerably from that obtained by meridional degrees. It
has been found impossible to explain the want of agreement in a
satisfactory way. * * By comparing the celestial with the terrestrial
arcs, the length of degrees in various parallels was determined as in
the following table:--
Latitude of
middle point. Fathoms.
° ′ ″
Arbury Hill and Clifton 52 50 29·8 60,766
Blenheim and Clifton 52 38 56·1 60,769
Greenwich and Clifton 52 28 5·7 60,794
Dunnose and Clifton 52 2 19·8 60,820
Arbury Hill and Greenwich 51 51 4·1 60,849
Dunnose and Arbury Hill 51 35 18·2 60,864
Blenheim and Dunnose 51 13 18·2 60,890
Dunnose and Greenwich 51 2 54·2 60,884
This table presents a singular deviation from the common rule; for
instead of the degrees _increasing_ as we proceed from north to south,
they appear to _decrease_, as if the Earth were an _oblong_ instead
of an _oblate_ spheroid. * * The measurements of small arcs of the
meridian in other countries have presented similar instances.”[4]
[4] Encyclopedia of Geography, by Hugh Murray and several Professors
in the University of Edinburgh.
A number of French Academicians who measured above three degrees of
the meridian in Peru, gave as the result of their labours the first
degree of the meridian from the equator as 56,653 toises; whilst
another company of Academicians, who proceeded to Bothnia in Lapland,
gave as the result of their calculation 57,422 toises for the length
of a degree cutting the polar circle. But a more recent measurement
made by the Swedish Astronomers in Bothnia shows the French to have
been incorrect, having given the degree there 196 toises more than
the true length. Other observations have been made, but as no two sets
of experiments agree in result, it would be very unsatisfactory to
conclude from them that the Earth is an oblate spheroid.
Returning to the pendulum, it will be found to be equally
unsatisfactory as a proof of this peculiar rotundity of the Earth. It
is argued that as the length of a seconds pendulum at the equator is
39,027 inches, and 39,197 inches at the north pole, that the Earth
must be a globe, having a less diameter through its axis than through
its equator. But this proceeds upon the _assumption_ that the Earth
_is_ a globe having a “centre of attraction of gravitation,” towards
which all bodies gravitate or fall; and as the pendulum is a falling
body under certain restraint, the fact that it oscillates or falls
more rapidly at the north than it does at the equator, is a proof that
the north is nearer to the centre of attraction, or the centre of
the Earth, than is the equatorial region; and, of course, if nearer,
the radius must be shorter; and therefore the “Earth is a spheroid
flattened at the poles.” This is very ingenious and very plausible,
but, unfortunately for its character as an argument, the essential
evidence is wanting that the Earth is a globe at all! whether oblate
or oblong, or truly spherical, are questions logically misplaced.
It should also be first proved that _no other_ cause could operate
besides greater proximity to the centre of gravity, to produce the
variable oscillations of a pendulum. This not being attempted, the
whole subject must be condemned as logically insufficient, irregular,
and worthless for its intended purpose. Many philosophers have ascribed
the alterations in the oscillations of a pendulum to the diminished
temperature of the northern centre. That the heat gradually and almost
uniformly diminishes on passing from the equator to the north is well
ascertained. “The mean annual temperature of the whole Earth at the
level of the sea is 50° Fah. For different latitudes it is as under:--
Degrees. Inches.
Latitude (Equator) 0 84·2 Length of Pendulum 39,027
„ „ 10 82·6 „ „ „
„ „ 20 78·1 „ „ „
„ „ 30 71·1 „ „ „
„ „ 40 62·6 „ „ „
„ (London) 50 53·6 „ „ 39,139
„ „ 60 45·0 „ „ „
„ „ 70 38·1 „ „ „
„ „ 80 33·6 „ „ „
„ (Pole) 90 00·0 „ „ 39,197[5]”
[5] “Million of Facts,” by Sir Richard Phillips, p. 475.
“All the solid bodies with which we are surrounded are constantly
undergoing changes of bulk corresponding to the variations of
temperature. * * The expansion and contraction of metals by heat and
cold form subjects of serious and careful attention to chronometer
makers, as will appear by the following statements:--The length of the
pendulum vibrating seconds, in vacuo, in the latitude of London (51°
31′ 8″ north), at the level of the sea, and at the temperature of 62°,
has been ascertained with the greatest precision to be 39·13929 inches:
now, as the metal of which it is composed is constantly subject to
variation of temperature, it cannot but happen that its _length_ is
constantly varying; and when it is further stated that if the “bob”
be let down ¹⁄₁₀₀th of an inch, the clock will lose 10 seconds in 24
hours; that the elongation of ¹⁄₁₀₀₀th of an inch will cause it to lose
one second per day; and that a change of temperature equal to 30° Fah.
will alter its length ¹⁄₅₀₀₀th part and occasion an error in the rate
of going of 8 seconds per day, it will appear evident that some plan
must be devised for obviating so serious an inconvenience.”[6]
[6] “Noad’s Lectures on Chemistry,” p. 41.
From these data it is readily seen that the variations in the rate
of a pendulum as it is carried from the equator towards the north
are sufficiently explained, without supposing that they arise from a
peculiar spheroidal form of the Earth.
Others have attributed the variable motions of the pendulum to
increased density of the air on going northwards. That the condition
of the air must have some influence in this respect will be seen
from the following extract from experiments on pendulums by Dr.
Derham, recorded in numbers 294 and 480 of the _Philosophical
Transactions_:--“The arches of vibration _in vacuo_ were larger than
in the open air, or in the receiver before it was exhausted; the
enlargement or diminution of the arches of vibration were _constantly
proportional_ to the _quantity of air_, or rarity, or density of it,
which was left in the receiver of the air-pump. And as the _vibrations_
were _longer_ or _shorter_, _so_ the _times_ were accordingly, viz.,
two seconds in an hour when the vibrations were longest, and less and
less as the air was re-admitted, and the vibrations shortened.”
Thus there are two distinct and tangible causes which necessarily
operate to produce the variable oscillations of a pendulum, without
supposing any distortion in the supposed rotundity of the Earth. First,
if the pendulum vibrates in the air, which is colder and therefore
denser in the north than at the equator, it must be more or less
resisted in its passage through it; and, secondly, if it vibrates _in
vacuo_, the temperature being less, the length must be less, the arcs
of vibration less, and the velocity greater. In going towards the
equator, the temperature increases, the length becomes greater, the
arcs increase, and the times of vibration diminish.
Another argument for the globular form of the Earth is the
following:--The degrees of longitude radiating from the north pole
gradually increase in extent as they approach the equator; beyond which
they again converge towards the south. To this it is replied that no
actual measurement of a degree of longitude has ever been made south of
the equator! If it be said that mariners have sailed round the world
in the southern region and have _computed_ the length of the degrees,
it is again replied that such evidence is unfavourable to the doctrine
of rotundity. It will be seen from the following table of what the
degrees of longitude would be if the earth were a globe of 25,000
miles circumference, and comparing these with the results of practical
navigation, that the diminution of degrees of longitude beyond the
equator is purely imaginary.
Latitudes at different longitudes:--
Latitude 1 = 59·99 nautical miles.
10 = 59·09 „ „
20 = 56·38 „ „
30 = 51·96 „ „
34 = 49·74 (Cape Town)
40 = 45·96 „ „
45 = 42·45 (Port Jackson, Sydney)
50 = 38·57 „ „
56 = 33·55 (Cape Horn)
60 = 30·00 „ „
65 = 25·36 „ „
70 = 20·52 „ „
75 = 15·53 „ „
80 = 10·42 „ „
85 = 5·53 „ „
86 = 4·19 „ „
87 = 3·14 „ „
88 = 2·09 „ „
89 = 1·05 „ „
90 = 0·00 „ „
According to the above table (which is copied from a large Mercator’s
chart in the library of the Mechanics’ Institute, Royal Hill,
Greenwich), the distance round the Earth at the Antarctic circle would
only be about 9,000 miles. But practical navigators give the distance
from the Cape of Good Hope to Port Jackson as 8,000 miles; from Port
Jackson to Cape Horn as 8,000 miles; and from Cape Horn to the Cape
of Good Hope, 6,000 miles, making together 22,000 miles. The average
longitude of these places is 45°, at which parallel the circuit of
the Earth, if it be a globe, should only be 14,282 miles. Here, then,
is an error between the theory of rotundity and practical sailing of
7,718 miles. But there are several statements made by Sir James Clarke
Ross which tend to make the disparity even greater: at page 236, vol.
2, of “South Sea Voyages,” it is said “From near Cape Horn to Port
Philip (in Melbourne, Australia) the distance is 9,000 miles.” These
two places are 143 degrees of longitude from each other. Therefore
the whole extent of the Earth’s circumference is a mere arithmetical
question. If 143 degrees make 9,000 miles, what will be the distance
made by the whole 360 degrees into which the surface is divided? The
answer is, 22,657 miles; or, 8,357 miles more than the theory of
rotundity would permit. It must be borne in mind, however, that the
above distances are nautical measure, which, reduced to statute miles,
gives the actual distance round the Southern region at a given latitude
as 26,433 statute miles; or nearly 1,500 miles more than the largest
circumference ever assigned to the Earth at the equator.
But actual measurement of a degree of longitude in Australia or some
other land far south of the equator can alone place this matter beyond
dispute. The problem to be solved might be given as the following:--A
degree of longitude in England at the latitude of 50° N. is 38·57
nautical or 45 statute miles; at the latitude of Port Jackson in
Australia, which is 45° S., a degree of longitude, if the Earth is a
globe, should be 42·45 nautical or 49·52 statute miles. But if the
Earth is a plane, and the distances above referred to as given by
nautical men are correct, a degree of longitude on the parallel of Port
Jackson will be 69·44 statute miles, being a difference of 19·92 or
nearly 20 statute miles. In other words, a degree of longitude along
the southern part of Australia ought to be, _if the Earth is a plane_,
nearly 20 miles greater than a degree of longitude on the southern
coast of England. This is the point which has yet to be settled. The
day is surely not far distant when the scientific world will demand
that the question be decided by proper geodetical operations! And
this not altogether for the sake of determining the true figure of
the Earth, but also for the purpose of ascertaining, if possible, the
cause of the many anomalies observed in navigating the southern region.
These anomalies have led to the loss of many vessels and the sacrifice
of a fearful amount of life and property. “In the southern hemisphere,
navigators to India have often fancied themselves east of the Cape when
still West, and have been driven ashore on the African coast, which
according to their reckoning lay behind them. This misfortune happened
to a fine frigate, the “Challenger,” in 1845.”[7] “Assuredly there are
many shipwrecks from alleged errors in reckoning which _may_ arise
from a somewhat false idea of the general form and measurement of the
Earth’s surface. Such a subject, therefore, ought to be candidly and
boldly discussed.”[8]
[7] “Tour through Creation,” by the Rev. Thomas Milner, M.A.
[8] “The Builder,” Sept. 20, 1862, in a “review” of a
recently-published work on Astronomy.
It is commonly believed that surveyors when laying out railways
and canals, are obliged to allow 8 inches per mile for the Earth’s
curvature; and that if this were not done in the latter case the water
would not be stationary, but would flow on until at the end of one
mile in each direction, although the canal should have the same depth
throughout, the surface would stand 8 inches higher in the middle than
at the ends. In other words, that the bottom of a canal in which the
allowance of 8 inches per mile had not been made, would be a chord
to the surface of the contained water, which would be an arc of a
circle. To this it is replied, that both in regard to railways and
canals, wherever an allowance has been attempted the work has not
been satisfactory; and so irregular were the results in the earlier
days of railway, canal, and other surveying, that, the most eminent
engineers abandoned the practice of the old “forward levelling” and
allowing for convexity; and adopted what is now called the “double
sight” or “back-and-fore sight” method. It was considered that whether
the surface were convex or horizontal, or whether the convexity were
more or less than the supposed degree, would be of no consequence in
practice if the spirit level or theodolite were employed to read both
backwards and forwards; for whatever degree of convexity existed,
one “sight” would compensate for the other; and if the surface were
horizontal, the same mode of levelling would apply. So important did
the ordnance department of the Government consider this matter, that it
was deemed necessary to make the abandonment of all ideas of rotundity
compulsory, and in a standing order (No. 6) of the House of Lords as to
the preparation of sections for railways, &c., the following language
is used, “That the section be drawn to the same _horizontal_ scale as
the plan; and to a vertical scale of not less than one inch to every
one hundred feet; and shall show the surface of the ground marked on
the plan, the intended level of the proposed work, the height of every
embankment, and the depth of every cutting; and a _datum_ HORIZONTAL
LINE, which shall be _the same throughout the whole length of the
work_, or any branch thereof respectively; and shall be referred to
some fixed point stated in writing on the section, near some portion of
such work; and in the case of a canal, cut, navigation, turnpike, or
other carriage road, or railway, near either of the termini.” No. 44
of the standing orders of the House of Commons is similar to the above
order (No. 6) of the House of Lords.
Thus it is evident that the doctrine of the Earth’s rotundity cannot
be mixed up with the practical operations of civil engineers and
surveyors, and to prevent the waste of time and the destruction of
property which necessarily followed the doings of some who were
determined to involve the convexity of the Earth’s surface in their
calculations, the very Government of the country has been obliged to
interfere! Every survey of this and other countries, whether ordnance
or otherwise, is now carried out in connection with a horizontal datum,
and therefore, as no other method proves satisfactory, it is virtually
an admission by all the most practical scientific men of the day that
the Earth _cannot be other than a plane_!
An argument for the Earth’s convexity is thought by many to be found
in the following facts:--“Fluid or semi-fluid substances in a state
of motion invariably assume the globular form, as rain, hail, dew,
mercury, and melted lead, which, poured from a great height becomes
divided into spherical masses, as in the manufacture of small shot,
&c.” “There is abundant evidence from geology that the Earth has been
a fluid or semi-fluid mass, and it could not, therefore, continue in
a state of motion through space without becoming spherical.” Without
denying that the Earth has been, at some former period, in a pulpy or
semi-fluid state, it is requisite to prove beyond all doubt that it
has a motion upon axes and through space, or the conclusion that it
is therefore spherical is premature and illogical. It will be shown
in a subsequent part of this work, that such axial and orbital motion
does not exist, and therefore any argument founded upon and including
it as a fact is necessarily fallacious. In addition to this, it may
be remarked that the tendency in falling fluids to become globular is
owing to what has been called “attraction of cohesion” (not “attraction
of gravitation”), which is very limited in its operation. It is
confined to small quantities of matter. If, in the manufacture of
small shot, the melted metal is allowed to fall in masses of several
ounces or pounds, instead of being divided into particles weighing
only a few grains, it will never take a spherical form, and shot of
an inch in diameter could not be made by this process. Bullets of
even half-an-inch diameter can only be made by casting the metal into
spherical moulds. In tropical countries, the rain instead of falling in
drops or small globules, often comes down in large irregular masses,
which have no approximation whatever to sphericity. So that it is
manifestly unjust to affirm of large masses of matter like the Earth
that which only belongs to minute portions or a few grains in weight.
The whole matter taken together entirely fails as an argument for the
Earth’s rotundity.
Those who hold that the Earth is a globe will often affirm, with
visible enthusiasm, that in an eclipse of the Moon there is proof
positive of rotundity. That the shadow of the Earth upon the Moon is
always round; and that nothing but a globe could, in all positions,
cast a circular shadow. Here again the essential requirements of an
argument are wanting. It is _not proved_ that the Moon is eclipsed _by
a shadow_. It is _not proved_ that the _Earth moves_ in an orbit, and
therefore takes _different positions_. It is _not proved_ that the Moon
receives her light from the Sun, and that therefore her surface is
darkened by the Earth intercepting the Sun’s light. It will be shown
in the proper place that the Earth has no motion in space or on axes;
that it is not a shadow which eclipses the Moon; that the Moon is not
a reflector of the Sun’s light, but is _self-luminous_; and therefore
could not possibly be obscured by _a shadow_ from any object whatever.
The subject is only introduced here because it forms one of the
category of supposed evidences of the Earth’s rotundity. But to call
that an argument where every necessary proposition is assumed, is to
stultify both the judgment and the reasoning powers!
Many place great reliance upon what is called the “spherical excess”
observed in levelling, as a proof of the Earth’s rotundity. In
Castle’s Treatise on Levelling it is stated that “the angles taken
between any three points on the surface of the Earth by the theodolite,
are, strictly speaking, spherical angles, and their sum must exceed 180
degrees; and the lines bounding them are not the chords as they should
be, but the tangents to the Earth. This excess is inappreciable in
common cases, but in the larger triangles it becomes necessary to allow
for it, and to diminish each of the angles of the observed triangle by
one-third of the spherical excess. To calculate this excess, divide the
area of the triangle in feet by the radius of the Earth in seconds and
the quotient is the excess.”
The following observation as made by surveyors, also bears upon the
subject:--If a spirit-level or theodolite be “levelled,” and a given
point be read upon a graduated staff at the distance of about or
more than 100 chains, this point will have an altitude slightly in
excess of the altitude of the cross-hair of the theodolite; and if the
theodolite be removed to the position of the graduated staff and again
levelled, and a backward sight taken to the distance of 100 chains,
another excess of altitude will be observed; and this excess will
go on increasing as often as the experiment or backward and forward
observation is repeated. From this it is argued that the line of sight
from the spirit-level or theodolite is a tangent, and that the surface
of the Earth is therefore spherical.
Of a similar character is the following observation:--If a theodolite
or spirit-level be placed upon the sea-shore, and “levelled,” and
directed towards the sea, the line of the horizon will be observed to
be a given amount below the cross-hair of the instrument, to which a
certain dip, or inclination from the level will have to be given to
bring the cross-hair and the sea horizon together. It is concluded that
as the sea horizon is always observed to be below the cross-hair of the
“levelled” theodolite, the line of sight is a tangent, the surface of
the water convex, and therefore the Earth is a globe.
[Illustration: FIG. 21.]
The conclusion derived from the last three observations is exceedingly
plausible, and would completely satisfy the minds of scientific men
as to the Earth’s sphericity if a perfect explanation could not be
given. The whole matter has been specially and carefully examined;
and one very simple experiment will show that the effects observed do
not arise from rotundity in the Earth’s surface, but from a certain
peculiarity in the instruments employed. Take a convex lens or a
magnifying glass and hold it over a straight line drawn across a
sheet of paper. If the glass be so held that a part of the straight
line can be seen _through_ it, and another part seen _outside_ it, a
difference in the _direction_ of the line will be observed, as shown
in the diagram Figure 21. Let A B C represent a straight line. If a
lens is now held an inch, or more, according to its focal length,
over the part of the line A B, and the slightest amount out of its
centre, that part of the line A B which passes under the lens will
be seen in the direction of the figures 1.2; but if the lens be now
moved a little out of its central position in the opposite direction,
the line B C will be observed at 3.4, or below B C. A lens is a
magnifying glass because it _dilates_ or spreads out from its centre
the objects observed through it Therefore whatever is magnified by it
is seen a little out of its axis or centre. This is again necessitated
by the fact that the axis or actual centre is always occupied by the
cross-hair. Thus the line-of-sight in the theodolite or spirit-level
not being axial or absolutely central, reads upon a graduated staff
a position which is necessarily slightly divergent from the axis of
vision; and this is the source of that “spherical excess” which has so
long been considered by surveyors as an important proof of the Earth’s
rotundity. In this instance, as, indeed, in all the others given as
evidence that the Earth is a globe, the premises do not fully warrant
the conclusion--which is premature,--drawn before the whole subject is
fairly examined; and when other causes are amply sufficient to explain
the effects observed.
SECTION 2.
THE EARTH NO AXIAL OR ORBITAL MOTION.
If a ball be allowed to drop from the mast-head of a ship _at rest_, it
will strike the deck at the foot of the mast. If the same experiment
be tried with a ship _in motion_, the same result will be observed.
Because, in the latter case, the ball is acted upon simultaneously by
two forces at right angles to each other--one, the momentum given to it
by the moving ship in the direction of its own motion, and the other
the force of gravity, the direction of which is square to that of the
momentum. The ball being acted upon by the two forces together will not
go in the direction of either, but will take a diagonal course, as
shown in the following diagram, Figure 22.
[Illustration: FIG. 22.]
[Illustration: FIG. 23.]
The ball passing from A to C by the force of gravity, and having at
the moment of its liberation received a momentum from the ship in the
direction A B, will by the conjoint action of the two forces, take the
direction A D, falling at D, just as it would have fallen at C had the
vessel remained at rest. In this way, it is contended by those who
hold that the Earth is a moving sphere, a ball allowed to fall from
the mouth of a deep mine reaches the bottom in an apparently vertical
direction, the same as it would if the Earth were motionless. So far,
there need be no discussion--the explanation is granted. But now let
the experiment be modified in the following way:--Let the ball be
thrown _upwards from_ the mast-head of a moving vessel; it will partake
as before of two motions, the upward and the horizontal, and will take
a diagonal course upwards and with the vessel until the two forces
expend themselves, when it will begin to fall by the force of gravity
only, and drop into the water far behind the ship, which is still
moving horizontally. Diagram Figure 23 will illustrate this effect. The
ball being thrown upwards in the direction A C, and the vessel moving
from A to B, will cause it to pass in the direction A D, arriving at D
when the vessel reaches B; the two forces having expended themselves
when the ball arrives at D, it will begin to descend by the force of
gravity in the direction D B H, but during its fall the vessel will
have reached the position S, so that the ball will drop far behind
it at the point H. To bring the ball from D to S _two forces_ would
be required, as D H and D W; but as D W does not exist, the force of
gravity operates _alone_, and the ball necessarily falls behind the
vessel at a distance proportionate to the altitude attained at D, and
the time occupied in falling from D to H.
The same result will be observed on throwing a ball directly upwards
from a railway carriage when in rapid motion, as shown in the following
Figure 24. While the carriage or tender passes from A to B, the ball
thrown from A to C will reach the position D, but while the ball then
comes down by the force of gravity, _operating alone_, to the point H,
the carriage will have advanced to W, so that the ball will always drop
more or less behind the carriage, according to the force first given
to it in the direction A C and the time occupied in ascending to D,
and thence descending to H. It is therefore demanded that if the Earth
had a motion upon axes from west to east, and a ball, instead of being
dropped down a mine or allowed to fall from the mast head of a ship,
be _shot upwards_ into the air; from the moment of its beginning to
descend the surface of the Earth would turn from under its direction,
and it would fall behind or to the west of its line of descent. On
making the experiment _no such effect is observed_, and therefore the
conclusion is unavoidable, that the Earth DOES NOT MOVE UPON AXES!
[Illustration: FIG. 24.]
[Illustration: FIG. 25.]
The following experiment has been tried, with the object of obtaining
definite results. If the Earth is a globe, having a circumference of
25,000 miles at the equator, the circumference at the latitude of
London (51°) will be about 16,000 statute miles; so that the motion of
the Earth’s surface, if 25,000 miles in 24 hours at the equator, in
England would be more than 700 feet per second. An air-gun was firmly
fixed to a strong post, as shown at A in Figure 25, and carefully
adjusted by a plumb-line, so that it was perfectly vertical. On
discharging the gun, the ball ascended in the direction A C, and
invariably (during several trials) descended within a few inches of
the gun at A; twice it fell back upon the very mouth of the barrel.
The average time that the ball was in the atmosphere was 16 seconds;
and, as half the time would be required for the ascent and half for the
descent, it is evident that if the Earth had a motion once round its
axis in 24 hours, the ball would have passed in 8 seconds to the point
D, while the air-gun would have reached the position B H. The ball
then commencing its descent, requiring also 8 seconds, would in that
time have fallen to the point H, while the Earth and the gun would
have advanced as far as W. The time occupied being 8 seconds, and the
Earth’s velocity being 700 feet per second, the progress of the Earth
and the air-gun to W, in advance of the ball at H, would be 5,600 feet!
In other words, in these experiments, the ball, which always fell back
to the place of its detachment, should have fallen 5,600 feet, or
considerably more than one statute mile to the west of the air-gun!
Proving beyond all doubt that the supposed axial motion of the Earth
DOES NOT EXIST!
The same experiment ought to suffice as evidence against the
assumed motion of the Earth in an orbit; for it is difficult, if
not impossible, to understand how the behaviour of the ball thrown
from a vertical air-gun should be other in relation to the Earth’s
forward motion in space than it is in regard to its motion upon axes.
Besides, if it is proved _not_ to move upon axes, the assumption
that it moves in an orbit round the Sun is useless for theoretical
purposes, and there is no necessity for either denying or in any
way giving it farther consideration. But that no point may be taken
without direct evidence, let the following experiment be tried:--Take
two carefully-bored iron tubes, about two yards in length, and place
them, one yard asunder, on the opposite sides of a wooden frame, or
a solid block of wood or masonry; so adjust them that their axes of
vision shall be perfectly parallel to each other, and direct them to
the plane of some notable fixed star, a few seconds previous to its
meridian time. Let an observer be stationed at each tube; and the
moment the star appears in the first tube, let a knock or other signal
be given, to be repeated by the observer at the second tube when he
first sees the star. A distinct period of time will elapse between the
signals given, showing that the same star is not visible at the same
moment by two lines of sight parallel to each other and only one yard
asunder. A slight inclination of the second tube towards the first
would be required for the star to be seen at the same moment. If now
the tubes be left in their position for six months, the same star will
be visible at the same meridian time, without the slightest alteration
being required in the direction of the tubes. From which result it
is concluded that if the Earth had moved _a single yard_ in an orbit
through space there would at least be the difference of time indicated
by the signals, and the slight inclination of the tube which the
difference in position of one yard required. But as no such difference
in the direction of the tube is required, the conclusion is unavoidable
that in six months a given meridian upon the Earth has not moved a
single yard, and that therefore the Earth has not the slightest degree
of orbital motion--or motion at right angles to the meridian of a given
star! It will be useless to say in explanation that the stars are so
infinitely distant that a difference in the angle of inclination of the
tube in six months could not be expected, as it will be proved in a
subsequent section that _all_ the stars are within a few thousand miles
from the Earth’s surface!
SECTION 3.
THE TRUE DISTANCE OF THE SUN AND STARS.
As it is now demonstrated that the Earth is a plane, the distance of
the Sun and Stars may readily be measured by plane trigonometry. The
base line in any operation being horizontal and always a carefully
measured one, the process becomes exceedingly simple. Let the altitude
of the Sun be taken on a given day at 12 o’clock at the high-water
mark on the sea shore at Brighton, in Sussex; and at the same hour
at the high-water mark of the River Thames, near London Bridge; the
difference in the Sun’s altitude taken simultaneously from two stations
upon the same meridian, and the distance between the stations, or the
length of the base line ascertained, are all the elements required for
calculating the exact distance of the Sun from London or Brighton;
but as this distance is the hypothenuse of a triangle, whose base is
the Earth’s surface, and vertical side the zenith distance of the
Sun, it follows that the distance of the Sun from that part of Earth
to which it is vertical is less than the distance from London. In the
Diagram, Figure 26, let L B represent the base line from London to
Brighton, a distance of 51 statute miles. The altitude at L and at B
taken at the same moment of time will give the distance L S or B S.
The angle of altitude at L or B, with the length of L S or B S, will
then give the vertical distance of the Sun S from E, or the place which
is immediately underneath it. This distance will be thus found to be
considerably less than 4,000 miles.
[Illustration: FIG. 26.]
The following are the particulars of an observation made, a few years
ago, by the officers engaged in the Ordnance survey. Altitude of the
Sun at London 55° 13′; altitude taken at the same time, on the grounds
of a public school, at Ackworth, in Yorkshire, 53° 2′; the distance
between the two places in a direct line, as measured by triangulation,
is 151 statute miles. From these elements the true distance of the Sun
may be readily computed; and proved to be under 4,000 miles!
Since the above was written, an officer of the Royal Engineers, in the
head-quarters of the Ordnance Survey, at Southampton, has furnished the
following elements of observations recently made:--
Southern Station, Sun’s altitude, 45°
Northern ditto, „ „ 38°
Distance between the two stations, 800 statute miles.
The calculation made from these elements gives the same result, viz.,
that the actual distance of the Sun from the Earth is less than 4,000
miles.
The same method of measuring distances applies equally to the Stars;
and it is easy to demonstrate, beyond the possibility of doubt, so long
as assumed premises are excluded, that all the visible objects in the
firmament are contained within the distance of 6,000 miles!
From these demonstrable distances it follows unavoidably that the
_magnitude_ of the Sun, Moon, Stars, &c., is very small--much smaller
than the Earth from which they are measured; and to which therefore
they cannot possibly be other than secondary, and subservient.
SECTION 4.
THE SUN MOVES IN A CIRCLE OVER THE EARTH, CONCENTRIC WITH THE NORTH
POLE.
As the Earth has been shown to be fixed, the motion of the Sun is a
visible reality; and if it be observed from any northern latitude, and
for any period before and after the time of southing, or passing the
meridian, it will be seen to describe an arc of a circle; an object
moving in an arc cannot return to the centre of such arc without having
completed a circle. This the Sun does visibly and daily. To place the
matter beyond doubt, the observation of the Arctic navigators may be
referred to. Captain Parry, and several of his officers, on ascending
high land in the vicinity of the north pole, repeatedly saw, for 24
hours together, the sun describing a circle upon the southern horizon.
SECTION 5.
THE DIAMETER OF THE SUN’S PATH IS CONSTANTLY CHANGING--DIMINISHING FROM
DECEMBER 21ST TO JUNE 15TH, AND ENLARGING FROM JUNE TO DECEMBER.
This is a matter of absolute certainty, proved by what is called, in
technical language, the northern and southern declination, which is
simply saying that the Sun’s path is nearest the north pole in summer,
and farthest away from it in winter. This difference in position gives
rise to the difference of altitude, as observed at various periods of
the year, and which is shewn in the following table, given in “The
Illustrated London Almanack,” for 1848, by Mr. Glaisher, of the Royal
Observatory, Greenwich.
“Sun’s altitude at the time of Southing, or being on the meridian:--
Sun’s Time of Southing.
altitude. M. S. (Common clock, or
London mean time.)
June 15 62° 0 4 before noon.
„ 30 61²⁄₃° 3 18 afternoon.
July 15 59²⁄₃° 5 38 „
„ 31 56¹⁄₂° 6 4 „
Aug. 15 52¹⁄₂° 0 11 „
„ 31 47° 0 5 „
Sep. 15 38²⁄₃° 4 58 before noon.
„ 30 35¹⁄₂° 10 6 „
Oct. 31 24° 16 14 „
Nov. 30 17° 10 58 „
Dec. 21 12° 0 27 „
„ 31 15° 3 29 afternoon.
Jan. 1 15¹⁄₂° 3 36 „
„ 15 17° 9 33 „
„ 31 21° 13 41 „
Feb. 15 25° 14 28 „
„ 29 30¹⁄₂° 12 43 „
March 15 {On the Equator} 36° 9 2 „
{ at 6 a.m. } 38¹⁄₂° 0 0 „
„ 21 42¹⁄₂° 4 10 before noon.
April 15 48° 0 8 „
„ 30 53° 2 58 „
May 15 57° 3 54 „
„ 31 60° 2 37 „
In the following diagram (Fig. 27) A A A represent the Sun’s daily path
on December 21st, and B B B the same on June 15th. N the North Pole, S
the Sun, E Great Britain. The figures 1 2 3 the Arctic Circle, and 4 5
6 the extent of sunlight. The arrows show the direction of the Sun’s
motion.
[Illustration: FIG. 27.]
SECTION 6.
CAUSE OF DAY AND NIGHT, SEASONS, &c.