**Abstract**

Paleomagnetic findings show that the North pole has changed its place several times. Charles H Hapgood suggested that the previous North pole was in Hudson Bay. Belcher Islands 56.2N 80W was a likely place for the pole. It is 33.80º from the North pole. There are two ways how the pole wandering could take place.

There is a stationary planet and the axis of rotation turns within it.

There is a stationary axis of rotation and the planet itself turns (gyroscopic effect).

In the case 1 the axial tilt of the Earth would have changed several times. However the Earth’s axial tilt 23,4º is close to the values of Mars 25,2º and Saturn 26,7º. In the beginning they have likely been equal ones. The difference of the values depends on different precessions. So the case 2 is more likely the true one. The latitude of the North pole has remained 90N. There has always existed arctic climate at the North pole.

When a fluid body rotates freely about its axis the gravity gives it a form of an ellipsoid of rotation. Its form depends on the mass and the speed of rotation. The Earth is such a fluid body with a chin crust. To research the consequences of the turn of the Earth we must use a mathematical ellipsoid of rotation instead of the real Earth. The error is not big as the Earth is already very close to an ellipsoid of rotation.. I call this mathematical body “the Globe” and the real planet “the Earth”.

I suppose that the planet Earth itself has turned an angle around one of its equatorial diagonals. Its axis of rotation has kept its position.

**Fig 1**

In
the figure 1 there is an ellipsoid of rotation, G, in an xyz
co-ordinate. The x-axis is vertically to the figure. Let's turn the
co-ordinate an angle δ
around x-axis to a position XYZ. Now the ellipsoid G turns with the
XYZ co-ordinate to a position G’. We give the ellipsoids the
present values of the Earth, the equatorial radius is 6378388 meter
and the polar one 6356912 meter, we get the Globes G and G’. The
real Globe G turns to a position G’. The immaterial mathematical
ellipsoid G remains. Its axis of rotation is jointed permanently with
the z-axis. All elevations are measured from the Globe G. **Hudson
Bay was at the present geographical North pole. **The latitude of
Belcher Islands was 90N before the turn of the Earth. The latitude of
a place before the turn of the Earth was its present distance from
Belcher Islands. **There was no interglacial warm period but a
change of latitudes. **Let’s take a piece of string and mark it
with some color at 10°-intervals.
Stick its other end with a pin at Belcher Island on a globe map. On
the string you can find the latitude of the place before the last
turn of the Earth. The Siberian mammoths lived on the latitudes of
present Mediterranean and North Africa

Calculation
of the elevation after the turn of the Earth. New York as an
example.**the turn of
co-ordinates**

X=x

Y=y*cos(δ)+z*sin(δ)

Z=-y*sin(δ)+z*cos(δ)**change
to the polar
co-ordinate**x=r*cos(Φ)*cos(ψ)

y=r*cos(Φ)*sin(ψ)

z=r*sin(Φ)

x=cosΦ *cosψ

y=cosΦ *sinψ

z=sinΦ

X=cosΦ*cosψ

Z=sinΦ*cosδ-cosΦ*sinψ*sinδ

**Fig
2: Ice Age follows every turn of the Earth.**

The difference between the radii of the
two Globes, G and G’, gives the elevation at any place. In figure 2
there are the elevations over the entire Globe, calculated by C++. As
you can see the surface of the Globe rises over 5000 meter in the
most part of Asia and Europe and in Patagonia. Elevation maximum was
close to 12 km.. It means that there was an Ice Age in these areas. I
call pole meridians the meridian of Belcher Island (80W) and the
meridian 170E,. They divide the globe into two symmetrical
hemispheres. The origin of the co-ordinate in the figure 2 (and in
all the next ones) is 10E as it is 90º
from the pole meridians. The earth's surface rose within two **Up-areas
**(the red areas ) and sank in two **Down-areas **(the blue and
green areas). Sea level sank and uncovered large areas. The surface
remains unchanged on the lines between these areas (zero lines). The
zero lines intersect at the origins. The pole meridians pass through
the points of elevation maximum and minimum (yellow points). The
maximum elevations was 11.95 km at MAX1=61.78N 100E and MAX2=61.78S
80W and the minimum ones -11.95 km at MIN1=28N 80W and MIN2=28S 100E.
The shape of the Earth differs now a lot from the Globe. The gravity
forces the shape of the Earth change continuously towards the Globe.
The Earth's surface must sink within Up-areas and rise within
Down-areas, the sea level must rise.

**Fig 3:
There is a symmetry as regards the origins. **

If the theory is true there should be the corresponding symmetry on the real Earth too. The origin lies on the maps at the point 0N10E In figure 3 there is a red line that is a copy of the coastline of northwestern Africa. It is turned 180º around the point 0N 10E. It coincides with the coastline of southeastern Africa very well. It continues along Rift valley and Lake Tanganyika. There is indeed symmetry as regards the point 0N 10E.

**Fig 4:
Flow paths**

As the viscosity of magma is very great
it is possible that the pressure can vary on the equipotential
surfaces of the Earth. The local pressure depends on the elevation at
the place. Magma flows from every point of the Earth to the direction
of the lowest pressure. We have a point P on the surface of the Earth
(fig 4) and we find the point P_{1} where the elevation is
the minimum among all the points at a distance **r** from the
point P. Magma flows now from the point P to the point P_{1 }.
I have used the points on the coordinate axes with 1º
space as the starting points P, but it can be any point on the
Earth's surface. I have used **a step** **r =1****º**
( r = 111 km). If we proceed in the same way from the point P_{1}
we will come finally to either point of minimum elevation **P**_{min}
(MIN1 or MIN2). If we proceed similarly from point P toward the
maximum elevation, we will come finally to either point of maximum
elevations **P**_{max} (MAX1 or MAX2). We get lines
that go from **P**_{max }to **P**_{min}
(fig 4). I call them **flow paths**. Magma flows from every point
of the Earth towards the points P_{min} and the flow paths
show the direction for the magma flow. For simplicity I have kept the
Earth as a sphere, that it is very close to. However it brings about
minor inaccuracy, especially in the Polar regions.

**Fig 5: Magma flow.**

According to
Bernoulli's equation the increase in the kinetic energy of
frictionless fluids is equal to the consumption of its potential
energy p_{1}-p_{2 }= c_{2}^{2}/2g-c_{1}^{2}/2g.
The potential energy is proportional to the elevation difference
p_{1}-p_{2 }= C*(e_{1}-e_{2}). As
magma is far from frictionless, all the elevation difference is
needed to sustain the velocity of magma, the rest of it converts into
heat by friction. Thus the beginning velocity c_{1 }= 0, so
e_{1}-e_{2 }= c^{2}/2g+heat. As the friction
is usually proportional to the square of velocity, we get e_{1}-e_{2
}= C*c^{2}. Thus the velocity of magma is v=C*√(e_{1}-e_{2})
(fig 5). We have to use relative values of velocity instead of
absolute ones as the proportion of the developed heat is unknown.

**Fig 6: Acceleration of magma flow
(a=v _{2}-v_{1}).**

The acceleration of the magma flow is
positive in the red areas (fig 6) but negative in the blue ones. The
acceleration of magma brings about stress in the crust. There is
tension in the areas of positive acceleration but compression where
the acceleration is negative one. The crust breaks up with tension
and folds with compression. The brown stripes in the figure indicate
the lines of equal velocity. I call them **isovelos**.

**Fig 7:
Orientation of landscapes.**

We have a line A-B, not parallel to isovelos I (fig 7). As the crust moves with magma along the flow paths tends the line A-B to turn parallel to the flow paths when the acceleration is positive one (7a), because the velocity is greater at a point B than at a point A. Line A-B tends to turn parallel to the isovelos when the acceleration is negative one (7b). The direction of the Andes is almost N-S up to latitude 16ºS and it turns then abruptly transversely (fig 6). Quite obviously they have turned along the flow paths as long as the acceleration has been positive one but transversely when acceleration has changed to negative. So a separate region can take a new orientation without that the entire continent turns. Thus the paleomagnetic theory is no liable method to show the place of the earlier Poles.

**Fig 8:
Accumulation of mass.**

There are two points P_{1 }and
P_{2} on a flow path F (fig 8a). The distances of point P_{1}
from the adjacent flow paths F_{1} and F_{2} are D_{11
}and D_{12}, and in the same way the distances of point
P_{2 }are D_{21} and D_{22 }. If we connect
points N_{1}, N_{2} , N_{3} and_{ }N_{4}
to the center of the Earth we get a pyramid (fig 8b) where D_{1}
is the distance between F_{1} and F_{2} in the inflow
site and D_{2 }is the similar distance in the outflow site_{
}. Magma flows into this pyramid through a triangle A_{1}
and leaves it through A_{2}. As we use relative values of
velocity we can take the average density ρ=1,
then the mass inflow in a time unit is m_{1 }= v_{1 * }A_{1}
and the outflow m_{2 }= v_{2 * }A_{2}. There
is accumulation of mass (positive or negative) inside the pyramid Ac
= v_{1 * }A_{1}-v_{2 * }A_{2}. As the
heights of the triangles A_{1} and A_{2} are
practically equal, the distances D_{1} and D_{2} can
substitute for the areas of the triangles. So we get Ac = v_{1 *
}D_{1}-v_{2 * }D_{2}. The accumulation
per a distance unit is ac = v_{1}- D_{2}/D_{1 *
}v_{2}. If the elevation difference is very small the
outflow v_{2 }stops. The pressure in the pyramid grows and
lifts magma up. There grows an uplift. That kind of situation is
found along the zero lines. In fact we can find an uplift on the zero
lines along the southwestern coast of Africa and its symmetrical
counterpart, the eastern coast of New Zealand and further along
Tonga-Kermadec Ridge, and along the northern coast of Horn of Africa
(fig 2).

As the points N are with
1º space on the flow
paths the distances D_{11 }+ D_{12 }and D_{21}
+ D_{22 }are longer than D_{1 }and D_{2 }but
in the ratio D_{2}/D_{1 }it will be compensated more
or less.

**Fig 9:
Accumulation rate (ar).**

Accumulation rate is the difference of
adjacent values of accumulation along a flow path from P_{max}
to P_{min} , ar = ac_{2} - ac_{1} (fig 9). In
most cases the accumulation rate is positive even though the
accumulation itself decreases in Up-areas. Both decr>.001 and
incr>.001 mean the same accumulation rate. A positive accumulation
rate decreases the elevation difference and slows down the magma
flow. The earth's surface will rise in Down-areas. The yellow areas
indicate a very great accumulation rate in Down-area. One result of
it is a long uplift in Caribbean. The Greater Antilles and Yucatan
are parts of it. It continues as Clarion Fracture Zone in the
Pacific. In Australia there is a corresponding uplift from Exmouth
Plateau to Barkly Tableland.

**Fig 10:
Convergence of flow paths (c= D**_{1}**/D**_{2}**)**.

As all the flow paths pass
from points P_{max} to points P_{min} , covering the
entire earth, they have to diverge (c<1) in the Up-areas and
converge (c>1) in the Down-areas. There are some exceptions
anyway, red lines in the blue area.(figure 10).

**Fig 11:
Length of flow paths.**

The length of the flow path varies (fig 11) but as the departures and the arrivals are common for all of them, the average elevation difference is inversely proportional to the length of the flow path, i.e. amount of steps. So is the average velocity and the mass that has moved in a time unit.

**Fig 12:
Distribution of the accumulation.**

As the accumulation in a time unit is
greater along a shorter flow path than along a longer one we must
multiply the basic acceleration by a coefficient inversely
proportional to the amount of steps, a**cc =
(v**_{1}**-D**_{2}**/D**_{1}***v**_{2}**)*100/amount**.
Its distribution over the Earth is shown in figure 12. The
accumulation decreases along flow paths from the points P_{max}
toward zero line and increases then toward the points P_{min }.
The Earth approaches the shape of the Globe. This process makes the
sea level rise. There has been a great negative accumulation in the
beginning of flow paths, it means a strong flow of mass away. It has
caused Grahamland and the southern end of South America to turn along
with it. It has consumed the crust. That is to be seen in Scotia Sea
and Scotia Basin. A similar consumption is noticed westward in
South-east Pacific Basin too. A corresponding consumption is noticed
on both sides of the point 61.78ºN
100ºE, The East
Siberian plateau eastward and The West Siberian plain westward.

**Fig 13:
Emerging continents.**

All the previous cases represent the
situation just after the turn of the Earth. If we add the
accumulation, multiplied by a time related coefficient, to the
elevation in figure 2, we get the elevation at the moment in
question. **E = e+(v**_{1}**-D**_{2
}**/****D**_{1}***v**_{2}**)*100/amount*TIME**.
If we select the time coefficient so that the sub-equatorial Africa
rises above the sea-level (yellow areas in figure 13), we get the
present situation. Then the chosen TIME coefficient is 335. The
greatest part of Down-area will rise above the zero-level but the
continental blocks only emerge above sea-level. Both the coast lines
of northwestern Africa and southeastern Africa corresponds with the
border line of the yellow area quite accurately. So does the western
coast of North America. Its broken eastern coast is far inside the
yellow area. It means that there is no continental block eastward.
North America has obviously separated from Europe and moved westward,
and so has done South America from Africa, as Wegener proposed. The
large areas around the points P_{max} cannot sink below zero
level as figure 13 shows but the sinking stops at zero level.

**Fig 14:
Changes in elevation difference.**

The changes in elevations change the elevation difference as well. If we use the same TIME coefficient as in the previous chapter, we will get the present situation (fig 14). When the elevation difference diminishes enough the magma flow slows down and stops finally and there will grow an uplift (blue stripes in the figure 14). One of these uplifts begins from Corsica and Sardinia continuing as Atlas mountains in Northwest Africa. Its symmetrical counterpart begins from Cape Rise and continues as Drakensberg in South Africa. The largest of these uplifts are the Mid-Atlantic Ridge and its counterparts. According to the Archimedes' law the highest mountain chains grows always in seas.

**Ocean effect**The sinking of
crust increases toward the points of elevation minimum (fig 2), so
does the sea bottom too. The oceans grow deeper and deeper as
approaching these points along the flow paths. It decreases the
elevation difference. This ocean effect has not taken account in this
study. It brings about a moving of the mountain changes in figure 14
toward the points of elevation maximum. It means that the
Mid-Atlantic Ridge in South Atlantic moves westwards but eastwards in
North Atlantic its most northern part turns toward Iceland because
the flow paths under the ocean are very long there.

**Fig 15:
The past of the Earth.**

By choosing some smaller value for the TIME coefficient we can survey the past of the Earth. If we chose the value 170 we get the moment when Novaya Semliya took its shape. Lesser Antilles emerge at the same time but we must bear in mind the later effect of the orientation (fig 7). Its influence has been very significant in Lesser Antilles.

We can also predict a future situation by choosing the TIME coefficient greater than 335.

**Fig 16:
Trapped magma.**

An interesting case is the Tibetan plateau. A diagrammatic drawing 16 illustrates the case. The elevation of the Tibetan plateau was very high just after the turn of the Earth (figure 16a) and it remained high. Magma flow met higher pressure A former high mountain chain, Himalayas blocks the advance. The magma had no possibility to move forward but to take other ways. When the elevation in Siberia had sunk to lower level than in Tibet (figure 16b) the magma began flow from the high plateau back towards Siberia, bringing about an uplift Kunlun Shan. A similar case but in smaller scale is going on in Europe. The Scandinavian mountain chain stopped the magma flow that now is reversing and lifts the crust in West Finland. South of Himalayas the magma goes on flowing towards the point of elevation minimum. So the elevation sink there. It increases the elevation difference and pressure against the mountain chain. When the pressure grows big enough it breaks Himalayas at 100E making the mountain chains turn southward. In this event erupts enormous amount magma. It had brought about peninsula Malaya and Sumatra island. It caused the disastrous tsunami too. It will be repeating. There was a great eruption in the western end of Himalayas too.

**Fig 17:
Negative accumulation rate.**

There are stripes where the accumulation rate is negative. The surface sinks there (fig 17). It brings about rifts and ridges. One of them has created the Greater Antilles (notice the bend of Cuba Island). It continues as Clarion Fracture Zone in the Pacific. In the Atlantic it brings about Puerto Rico Trench. As these rifts alternate with high uplifts they bring about a very unstable crust like the stripes from Altai through Pamir to Iran and another one through Korea and Japan.

**Fig 18:
Changes in the Earth's moment of inertia.**

As mass moves from one place to another
the moment of inertia of the Earth changes. The principal axes of the
ellipsoid of inertia changes too. As the Earth spins about one of the
principal axes the spin axis must also change. In accordance with the
"Law for conservation of angular momentum" the spin angular
momentum is constant. We have a body, composed of all the pyramids
(fig 8b) along a flow path from P_{max} to P_{min}
(fig 18). It consists of two parts B_{1 }and B_{2}.
B_{1} is composed of all the pyramids that have lost mass. B_{2}
is composed of all the pyramids that have gained mass. These moving
of mass change the moment of inertia. These changes will be
compensated so that the center of mass of the body B_{1}
(point c_{1}) rises and the center of mass of the body B_{2}
(point c_{2}) sinks. It takes place so that heavy material
from the core rises (case c_{1}) and sinks (case c_{2})._{
}So the moment of inertia remains unchanged. If every layer
inside the bodies B_{1} and B_{2} is homogeneous, the
centers of gravity of areas A_{1 }and A_{2} , points
c'_{1} and c'_{2} , lie on the same radius of the
earth as points c_{1} and c_{2} . We can now compute
their coordinates on the Earth's surface.

**Fig 19:
The correction stripes of moment of inertia.**

Small momentary changes in the great moment of inertia of the Earth will be corrected by changes in the liquid core as shown in the previous chapter. These corrections are seen on the surface as uplifts (red stripes) and subsidence (blue stripes). We can see that the red stripe follows the northern coast of Asia lifting it above sea-level. The lifting is especially clear along Tien Shan. James Bay, by Hudson Bay, is the place of the strongest subsidence. The blue stripe crosses the Rocky Mounts along the Valley of Colorado. It crosses the coast line at Los Angeles. Basins are typical on the blue stripes. The "trans Atlantic cable break" was caused presumably by this phenomenon too. During a serious Earth quake a considerable motion of mass takes place. That will be compensated by another Earth quake at some place on the opposite site of the Earth.

These kind of corrections of the moment of inertia are like a house of cards resting on nothing, only the spinning of the Earth keeps it up. The higher it rises the more uncertain is the balance, especially when the spinning is slowing down. Finally the house of cards will collapse. So the correction of the moment of inertia is possible only to a certain limit. When that limit is exceeded the deformities of the core disappear and the principal axes take their proper stand and the Earth turns.

**Fig 20:
Isostasy.**

J.H. Pratt's idea of isostasy implies that there is a certain level of compensation where the pressure due to the weight of the overlying mater is same everywhere. If we have a continental column and an oceanic one lying on this level their weights are equal. But the center of mass of the continental column is situated higher as its average density is smaller (fig 20). Thus its moment of inertia is greater . As the distribution of the continents on the Earth is uneven, the principal axes never coincides with the geometrical axes of the ellipsoid (the Globe).

**Summary**

The Earth is a liquid heavenly body.

When it cooled off enough it got a solid crust that uniformly covered the entire planet. All was covered by a shallow sea.

There is left only 40% of that original crust, the continental plates. Another heavenly body approached near enough to tear 60% of the crust off. Water filled the hole uncovering a continent Pangaia on the opposite side of the Earth. Now the terrestrial life was possible.

Since then the Earth was not an ellipsoid any more. The moment of inertia changed and with it the Earth turned.

Whenever the Earth differs from a shape of rotation ellipsoid the gravity moves its masses so that its shape approaches an ellipsoid again. The gravity is the only force needed. It is a real force. It is capable to move continents, contrary to fictitious convection forces. The moving of masses change the moment of inertia of the Earth,

**I=mr****²**. As the angular momentum,**L=I****ω**is constant, the angular velocity**ω**ought to change. But as the Earth is a liquid body, the small changes in the moment of inertia will bee compensated by inner changes in the Earth. That distort however the shape of the Globe. Finally the abnormality grows big enough and the ellipsoid of inertia turns with its principal axes. As the rotation axis must join one of them the Earth turns so that a principal axis meets the rotation axis. Because of the uneven distribution of continents the Earth is unable to get the shape of an exact ellipsoid before than the continents had broken into pieces that are scattered evenly over the Earth.

**The last turn of the Earth take
place about 12000 years ago.**

Platon told that Atlantis sank 9000 years before Solon, it is 11300 years ago.

Russians found a frozen mammoth in Siberia, at Beresovka. It was nothing if not decayed. It had suffocated 12000 years ago. A very interesting thing was a flowering butter cup in its mouth. So it had been grazing in summer-time, suffocated and not decayed! It is hard to find any other explanation but it had been moved from Mediterranean latitudes to present Siberia and lifted suddenly to an altitude of several thousand meters.

Mankind's collective memory about a great catastrophe. The common knowledge of deluge. Psalm 114 tells: “The Red Sea hurried out of their way, the mountains skipped like rams”. An old Finnish ballad tells that when we go to the Last Judgement the stars are dancing on the sky. It is really the dancing stars one can see at the moment of turning the Earth.

The Theory of Continental Drift has
gained almost an indisputable approval. According to this theory,
among other things, an Indian plate is pushing below an Eurasian
plate lifting it several kilometers. The thickness of the solid crust
within continents is about 50 Km. Its density is circa 2.7 g/cm^{3}.
In that case the pressure under the continental plate is about 13500
bars. It would be impossible to push there any Indian plate.
Especially when there the dominating temperature is so high that all
material melts. So would happen to the pushing Indian plate too. The
ancient truth tells:” You can’t push with a rope”.

E-mail:
heikki.ruohonen@pp.inet.fi

Heikki Ruohonen

MSc Engineering

Elotie 1 A 10

Fin-20780 Kaarina

Finland