**Planetary
Heat Engine Theory**

**Taras K Revised 15 May 2004****
**(First Edition- 26 August 2000)

**Abstract:**

This
simple theoretical heat engine model uses an ice-air cycle. The “engine”
converts radiant solar energy into planetary mechanical energy. The
mechanical energy produced is in the form of increased planetary wobble. Wobble or ‘free Eulerian precession’ is
like a pendulum oscillation within a rotating frame, it increases a planet's
rotational kinetic energy, while keeping its angular momentum constant.
On Earth, wobble energy could possibly cause geological deformation as well as
dissipate into internal heat by friction. Calculations are included for
several cases, showing the theoretical power output of this heat engine process
on an earth-like planet. The predicted energy output of this heat engine
cycle is big enough to drive many geophysical processes that are now generally
considered to be powered by other sources. Friction heating of a
planetary interior can provide a governor mechanism for heat engine output and
regulate internal planet temperature.

**A Planetary Heat Engine Theory:**

For
many years people have known that wind, ocean currents, and rain are powered by
the sun.^{(1)} Geological
processes like wind and water erosion are thus solar powered. The solar heat engine idea can be expanded
to explain some other planetary phenomena, including: daily rotation and wobble, plate tectonics, glaciation, and the
melting of subterranean lava. This
may seem like an outrageous assertion.
How could solar energy spin the Earth? power tectonic
motion? cause an ice age? or heat a planet’s interior?
Answers to these questions may be found by studying the behavior of a freely
turning inertial body, like a planet, as it is perturbed by the thermodynamic
mass transport of a multi-phase substance, like water, on the body and in its
atmosphere.

First, a brief discussion of solid body rotation . . . the bottom line
is— Extra energy often causes spinning things to wobble.^{(2,3)}
Rotary motion can be simulated or calculated knowing a body’s inertia
and its initial spin conditions. The inertia (a tensor) is generally
written as a 3 x 3 matrix, which has diagonal form when expressed in
the principal axis basis.^{(4)} The three diagonal elements are
then the three principal moments of inertia.^{(5)} If not equal,
the principal moments can be ordered: maximum, intermediate, and minimum
moments of inertia. The maximum and minimum axes have stable spin.^{(6)}
The intermediate axis sits in an energy saddle and is a chaotic neutral
point for the spin axis. When turning about one of these principal axes
the body’s angular velocity remains constant over time (simple spin). When
turning about any other axes the angular momentum remains constant, but not the
angular velocity vector. This kind of
“complex spin” motion is demonstrated by a wobbly USA football pass. 200 years ago, Leonhard Euler analyzed this
motion and predicted that the Earth would wobble slightly, with a ten-month
period.

In energy terms, a free body
with three different principal moments of inertia and a fixed net angular
momentum has simple stable spin at its lowest and highest kinetic energy levels.
All other energy levels imply a wobble. There are energy saddles
associated with the intermediate inertial axis, which can produce interesting
quasi-stable and variable-frequency polarity reversing behavior.

Note ~ Spin, rotation, and
turning, as used in this paper, all mean essentially the same thing.

Planets and other objects frequently turn nearly about their maximum inertial
axis, as this is the lowest kinetic energy state for a given amount of angular
momentum. If a body is free of external torques, yet has a way to
dissipate internal mechanical energy, it will approach the maximum inertial
axis spin state over time, as its rotational kinetic energy decreases. A classic example of this is the spinning,
bullet-like, Explorer 1 satellite with its energy-absorbing whip antennas;
within a few days it was turning end over end. . . its lowest energy
state.^{(7)}

The
Earth now turns very close to its lowest-energy, maximum inertial axis, but
with a slight wobble. Our planet oscillates
a bit, causing the geographical positions of the North and South Poles to
describe various approximately circular paths, up to about 20 meters in
diameter. The frequency spectrum of the solid earth’s oscillation has
two major peaks. There is a 12 month
period ‘annual’ peak, with harmonics.
An internal oscillation within the {solid earth, atmosphere, and oceans}
system causes the annual wobble. Seasonal changes in weather and
solar flux are synchronized with this annual component. With reference
to the solid earth, the annual wobble is called a ‘forced oscillation’. In addition to this annual term, there is 14
month period ‘Chandler Wobble’ spectral component due to ‘free oscillation’ of
the above system as a whole; this is akin to the solid body wobbles or 'Free
Eulerian Precession' discussed earlier. These wobble components combine
so that the astronomical latitude of a point on the ground changes by up to 20
meters (~ 0.7 arcseconds or 1/5000 ^{th} of a degree) in a
combined semi-period of six and a half months. The International Earth
Rotation Service has observations of the wobble going back to 1846.^{(8)}
The energy source of the Chandler Wobble continues to be a topic of
considerable discussion in geophysics.^{(9)}

When
a surface area's astronomical latitude or "spin latitude" changes as
a result of wobble, its perpendicular distance from the rotation axis changes
(except right near the Equator). This variation in distance causes
variation in centripetal potential. When a planet is solid and rigid the
changes in potential can be quite significant. For a totally rigid,
earth-size planet, turning once a day, the change in centripetal potential,
from equator to pole, is about 10^{5} joules / kg, which
is equivalent to 11 km of height change at one gee. This is at a
constant radial distance from the planet's center of mass and is separate from
gravitational potential changes due to non-spherically symmetric mass
distribution.

The
next figure shows how wobble induces rigid surface potential changes during
oscillation of the surface relative to its spin axis.

Color, digital versions of some
figures may be found on the web at:
www.icarusengineering.com

In the figures, the energy
reference frame turns around the planet's fixed angular momentum vector at the
rate of daily rotation, hence the ellipsoidal equipotentials (shown
exaggerated) and almost-fixed position of the spin axis. On Earth, near
45 degrees spin latitude, the slope of an equipotential relative to a
constant radius arc is about 1:580
( pi / 2
times the average slope from zero spin latitude to a pole). Thus, near
45 degrees, a 17 meter change in spin latitude produces an equivalent
height change of 17 meters / 580 or about 3 cm. (17 meters
along the surface is about 0.6 arcsecond of latitude.)

On Earth, even in the case of large tectonic
oscillations, the shifting of the surface relative
to its spin axis would be very slow compared to the rate of daily rotation.
This is because Earth's principal moments of inertia are nearly equal
(less than 1/2 percent different). This near-symmetry also means
that the rotation vector is always within 1/10 degree of the angular
momentum vector.

Real
planets are not totally rigid; they flex and flow somewhat in response to
changes in centripetal potential.^{(10)} A "Rigidity
Index" can be used to compare the actual situation to the idealized rigid
case. The rigidity index is defined as the ratio of the actual surface
potential change to a theoretical rigid case. This is a simplified way
of expressing what is traditionally described with Love numbers.^{(11)}
The rigidity index can be a function of location as well as
other variables. The
average planet-wide index
effects the period
of any "Tectonic Oscillations" (Chandler-type wobbles).
This average should be weighted to emphasize the effects of
45-degree latitude areas. On the Earth we can compare the actual
observed Chandler 'free
oscillation' period of 14 months
with Euler’s calculated period of 10 months for a rigid, 0.33 %
oblate Earth; this gives an average rigidity index of about 0.7

Multiplying this rigidity index by the 3 cm rigid body height change,
calculated previously, gives about 2 cm. In theory, this means that
often much of the mid-latitude surface land mass of the Earth goes
energetically "up and
down" by 2 cm. in little over
a year. This motion is rather similar to that of a piston. And
this movement could, perhaps, become the stroke of a huge planetary heat
engine.

The
fluctuations in potential of surface areas produce no power by themselves, if
there are no changes in mass distribution. The power comes from varying
the surface loading with movable water mass.
In this simple engine analogy, mass is added to the "surface
pistons" in the form of snow and ice at the tops of their strokes and
removed by melting and evaporation at the bottoms. The mechanical energy
from one cycle is equal to the difference in surface loading times the stroke
length. If the surface is loaded with
an ice mass 1000 km x 1000 km
x 0.1 meter on the
"down" stroke and empty on the "up" stroke the variation in
mass loading is 10^{14} kilograms, producing a weight force
variation of 10^{15} newtons. With a potential height
‘stroke’ of 2 cm, this force difference yields 2 x 10^{13} joules
of energy. Over a period of 14 months this correspond to a power output
of about 600 kW or 800 HP. The energy from one cycle above is
equal to approximately 2 % of the kinetic energy in the original 17 meter wobble. This corresponds to
an energy 'Q' of about minus 350. For small wobbles, Energy is
proportional to Amplitude squared; so a 2 percent increase in energy results in
a 1 percent increase in amplitude. The author does not currently know
whether ice mass ‘forcing’ has actually been historically significant on Earth,
and more references on the subject are sought.^{(12)}

To
model the efficiency of this heat engine cycle, the thermal energy required to
return the mass of ice to the top of a stroke is compared with the mechanical
energy output. To return the ice mass, it is melted and evaporated.
Once the H_{2}O is vaporized and in the atmosphere, wind can
move it around; allowing it to re-freeze and fall on ground that is at the top
of a stroke. How much energy is required? The combined heat of
fusion and vaporization for water is about 2.5 x 10^{6}
joules / kg, plus there's the pressure-volume work of 10^{5}
joules needed to push 1 kg (~1 cubic meter) of vapor into atmospheric
pressure. In the case above, with 10^{14} kg of ice, it means
that at least 2.6 x 10^{20} joules of solar energy go into each cycle.
Dividing the output of 2 x 10^{13} joules by the
solar input gives a thermodynamic efficiency of 8 x 10^{-8}
or eight millionths of a percent— not very much! However the
energy output and efficiency of the cycle are proportional to the length of the
stroke, which could, perhaps at times, increase dramatically. Another
way to look at the cycle efficiency is to convert the heat of
fusion + vaporization + P-V work into an equivalent (1 gee)
height change— 2.6 x 10^{6} joules / kg
corresponds to 265 km of height change at 9.8 m/s^{2}, thus
the maximum efficiency for a rigid-earth, ice-air cycle (90 degree amplitude
oscillation) would be the ratio of the centripetal equipotential oblateness to
this height--- 11 km / 265 km = about 4%.
At the current rigidity index of
0.7 the maximum efficiency would be about 3%. These numbers are presented
for comparison only, rigidity indices will most likely lessen as wobble amplitudes
increase and also rigidity may become longitudinally polarized, i.e.,
the wobble pole path could become very elliptical or otherwise elongated.

What is
needed for this type of heat engine to work?

**Spin Rate**
A planetary spin rate fast enough to
produce substantially oblate equipotentials (imaginary "sea level"
surfaces) in the planet’s combined gravitational and centripetal acceleration
field **Rigidity**
A rigid or semi-rigid planet that resists deformation by changing relationship to equipotentials **Complex spin**
A motion producing changes in "Spin Latitude" of surface areas. In various forms this motion is known as: ‘Wobble', 'Free Nutation’, ‘Free Eulerian Precession’, ‘True Polar Wander’, ‘Pole Shifts’, or “Tectonic Oscillation”. **Heat**
A source of radiant heat, like a very close-by star, that is located approximately perpendicular to the planetary spin axis **Heat Sink**
A heat sink to low temperature, like space. **Working Fluid**
An atmosphere containing a
compound, such as water or CO |

The following calculations are for a variety of hypothetical heat engine cycles on an earth-like planet. The first case is similar to the one worked through in the text. The other cases show how much power could be produced if wobble amplitude were increased.

:Heat Engine Calculations for an Earth-Like Planet | |||||

Wobble Oscillation Amplitude | |||||

Compared to Typical - | 1x typ. | 500x | 30,000x | 300,000x | |

20 th Century Values | |||||

Meters at Surface | 17 | 7,500 | 450,000 | 4,500,000 | |

degrees, minutes, secconds | 0.6" | 4' | 4 deg. | 40 deg. | |

Oscillation Amplitude, rad | 2.7E-06 | 1.2E-03 | 7.0E-02 | 7.0E-01 | |

Oscillation Period, days | 430 | 430 | 602 | 1003 | |

Mean Latitude, degrees | 45 | 45 | 45 | 45 | |

Rigidity Index, ratio | 0.7 | 0.7 | 0.5 | 0.3 | |

Centripetal Equipotential | |||||

Oblateness, m | 11000 | 11000 | 11000 | 11000 | |

Potential "Height" Change, m | 0.021 | 9 | 389 | 1500 | |

Surface Area m ^2 | 1E+12 | 5E+12 | 1E+13 | 2E+13 | |

Variation in Ice Thickness, m | 0.1 | 1 | 10 | 100 | |

Ice Mass per Cycle, kg | 1.0E+14 | 5.0E+15 | 1.0E+17 | 2.0E+18 | |

Heat per Cycle, joules | 2.5E+20 | 1.3E+22 | 2.5E+23 | 5.0E+24 | |

Srface Load Change, N | 9.8E+14 | 4.9E+16 | 9.8E+17 | 1.96E+19 | |

Energy per Cycle, joules | 2.0E+13 | 4.4E+17 | 3.8E+20 | 2.9E+22 | |

Power Output, watts | 5.4.E+05 | 1.2E+10 | 7.3E+12 | 3.4E+14 | |

Horse Power | 723 | 1.6E+07 | 9.8E+09 | 4.5E+11 | |

Energy in Wobble, joules | 1.1E+15 | 2.2E+20 | 5.6E+23 | 3.2E+25 | |

Cycle Output / EiW(above) | 1.8E-02 | 2.1E-03 | 6.9E-04 | 9.2E-04 | |

System "-Q" | 3.5E+02 | 3.1E+03 | 9.2E+03 | 6.9E+03 | |

Energy Flux Ratio* | 5.5E+01 | 4.9E+02 | 1.5E+03 | 1.1E+03 | |

Heat Eng. efficiency, (ratio) | 8.1E-08 | 3.6E-05 | 1.5E-03 | 5.9E-03 | |

Power / Planet's Solar Flux | 3.2E-12 | 7.0E-08 | 4.3E-05 | 2.0E-03 | |

Cycle / Earth Spin Energy | 6.7E-17 | 1.6E-12 | 1.4E-09 | 1.1E-07 | |

Yearly Output / ESE | 5.7E-17 | 1.4E-12 | 8.6E-10 | 4.0E-08 | |

Water, Heat of Fusion & Vap. | 2.5E+06 | ||||

( joules / kg ) | & Mars-Like ? | ||||

Total Earth Solar Flux, W | 1.7E+17 | Revised | |||

Earth (mantle) Spin Energy, J | 3E+29 | Apr-02 | |||

The energy
flux ratio, above* is an interesting
parameter. It shows the number of cycles whose energy output equals the
total kinetic energy in the wobble oscillation. It is like Q / 2 pi .
When the ratio is multiplied by the
cycle period, the resulting time scales are roughly seventy to three thousand
years, in the different cases. This gives an indication of how long
oscillations would take to build up, without any damping. The calculations assume uniform planet-wide
rigidity, if continental crust (surface piston area) stays more rigid than the
planet-wide average, then the cycle may self-excite more easily. This is because a smaller average rigidity
index means that less kinetic energy is needed for a given size wobble.

A key
factor governing cycle power output is the timing between the surface potential
changes and the variations in surface loading.
The previous calculations assume the most powerful timing
relationship. Any actual feedback mechanisms that connect Earth's wobble
to global snowfall distribution are not yet known. Theoretically, in
large oscillations the variations of an area's spin latitude could produce
self-energizing feedback via local changes in sun angle and atmospheric
pressure-altitude. This process is
shown in the graphs of the preceding figure. In smaller amplitude
oscillations the strongest feedback may come from variations in ocean currents.
These variations are caused by the movements of the oceans relative to
the planet's spin axis. Changes in ocean currents could likely produce
rapid changes in worldwide snowfall distribution and stronger currents could
perhaps generate much bigger snowstorms than we now experience.

Wobble induced Coriolis accelerations produce ocean currents by making the
waters turn in their basins. With a wobble of 20 meters
(3 x 10^{-6} radians) the net swirl induced over a 7 month
period is about 3 x 10^{-6 }revolutions per day, which
corresponds to a flow rate of about 100 meters / day around the
periphery of a 10,000 km diameter basin. This is small compared to
typical ocean currents, but it extends to all ocean depths. For wobbles
less than 1 radian, or so, the undamped swirl is roughly proportional to the wobble
amplitude.

The
constant angular momentum heat engine modeled here, if not limited by damping,
would continue to pump kinetic energy into the planet until it was spinning
close to its minimum inertial axis, where rotation has the maximum kinetic
energy for a given angular momentum. As noted before, damping tends to
do the opposite, inducing maximum inertial axis spin. By way of a side note~
There are heat engine models that rely on tidal transfer
of angular momentum between a planet and its parent star, such cycles can increase planetary spin rate without inducing wobble. These angular momentum
exchanging cycles will hopefully be discussed in future papers.

On
oscillating planets damping can come from many processes. Energy is dissipated by ocean tides and
currents; they can damp wobble, as can subterranean friction. Underground
friction heating may be particularly important to the cycle, because in
addition to providing damping, it could regulate the heat engine’s wobble
production.

When mechanical energy is dissipated inside an earth-like
planet it generates heat at high temperatures. In this way, a planetary
phase-change heat engine could pump a small fraction of Earth's incident solar
heat flux down into the planet’s incandescent interior. We do not normally consider that heat might
“naturally” get from a relatively cool place (Earth’s surface and atmosphere)
to a much hotter place (Earth’s interior). Man-made machines that move heat “uphill” (against a temperature
gradient) are called ‘heat pumps’.

Friction heating of the Earth's crust and mantle would likely reduce rigidity.
This reduces the fluctuations of potential at a given wobble
amplitude. Smaller potential fluctuations
produce less heat engine power output for the same variations in surface
loading. So wobble production can
depend on internal heat content. The
next figure shows how surface potential changes are related to planetary
rigidity.

::

Note
that the rigid planet need not be spherical, though it makes the diagram
simpler. It's the rigid, constant
radius motion (relative to the spin axis) that produces the upper circular arc
C1-C2-C3.

There
are many factors governing planetary heat engines. The dynamics of a spinning, visco-elastic, cosmic body that is
perturbed by heat-driven shifting of surface mass could be quite
intricate. The motion could be seen as
a sort of "planetary dance".
And this kind of heat engine “dancing” activity would surely leave some
significant marks . . . such as evidence of fluctuating ice
deposits or indications of varying Coriolis currents in deep sea sedimentation.

The "unrigid" part of planetary behavior during tectonic
oscillations could cause a complicated pattern of changing strain within a
planet. These cyclic strains might be drivers of plate tectonics,
particularly during orogenies and glacial epochs. Also, strains tend to
release heat in localized areas underground, creating 'hot spots'. This
is because movement, and its associated friction heating, generally occur at
the weakest (often hottest) place.
Comparing the Earth’s tectonic motion patterns with those produce by
various types of theoretical tectonic oscillations could prove quite
interesting.

Possibly some of the heat-flow and isotope-ratio data fit problems
experienced with current geophysical paradigms^{(13)} may be resolved
by the energy production of planetary heat engine cycles. As can be seen in the power output chart the
theoretical mechanical output of an earth-like engine could become geologically
significant at fairly small wobble amplitudes.
The second column case in the chart produces 1.5 x 10^{10} watts
with less than one tenth of a degree of wobble. What might that mean in geological terms? To get a rough idea of the energy scale we
can compare this heat engine output to the potential energy in a large
non-isostatically compensated mountain range. If the mountain range is 10,000 km long, 200 km wide, and 6 km high, then the volume is about 6 x 10^{15} cubic
meters. At a density of 3000 kg/m^{3,}
it has a mass of 1.8 x 10^{19} kg, with a weight of about 1.8 x 10^{20
}newtons. If the range is
triangular in cross section then the center of gravity is 2000 meters
above the base. 2000 meters
times 1.8 x 10^{20 }newtons equals
3.6 x 10^{23 }joules of energy.
This energy divided by the 1.5 x
10^{10} watt engine output
equals 2.4 x 10^{13} seconds,
or about 760,000 years, not very long
in the geological time frame.

The friction heat produced by the engine cycles may also be
significant. The theoretical power
output of the engine in the fourth column case -- 3 x 10^{14 }watts
is an order of magnitude greater than Earth’s current outward
subterranean heat flux of approximately 3 x 10^{13} watts.^{(14)} So heat engine activity could possibly
account for the heat production now ascribed to ‘radioactive decay’ and
‘primordial heat’. We now know of
little direct evidence showing ancient wobble amplitudes, but do have some evidence
of fluctuating ice age glacial deposits, these might be indicative of
“ice-engine” activity.

It is an
intriguing possibility that there could be a feedback relationship between the
output of a phase-change heat engine and planetary rigidity--- As a planet cools and hardens, the engine
modeled here would produce more power and “rev up” (more wobble). This would produce more friction and heat
the planet until it became fluid or elastic enough inside to slow or shut-down
the engine cycle. This feedback process provides an internal
thermostatic action for spinning planetary bodies. Perhaps it’s an
aspect of Gaia theory.^{(15)} Animals that thermoregulate are
called warm blooded. . . but
who ever heard of a "warm blooded planet"?

**Acknowledgments:**

Thanks to
Caltech geology professors James Westphal and Gene Shoemaker for conveying the
vision of rocks moving and forming a dynamic system. Thanks to Bob
Leighton, CIT professor and family friend, for teaching how to analyze
situations and make quick mental calculations. Thanks to Caltech
professor E. C. Stone for a wonderful
Feynman I physics course, which
encouraged the author’s interest in dynamics.
Thanks to math professors Bohnenblust and Dean for a great course in
numerical modeling. Thanks to classmate
Mike Purucker for pointing out a possible correlation between episodes of
geomagnetic reversals and ice ages (circa 1975). Thanks to Jacques
Labeyrie for fascinating discussions, including many on geophysics (c 1991).
Thanks to John Dickenson for suggesting that the cause-effect
relationship between glaciation and planetary shifting could work two ways
(c1998). Thanks to CIT professor Tom Caughey for interesting rotational
dynamics discussions. Thanks to Joe Kirschvink, CIT professor and former
Lloyd House-mate for valuable discussions and references. Thanks to Professor David Stevenson for
valuable discussions and comments.
Thanks to Professor Bill
Iwan, Professor Tom Caughey and the
Caltech Civil Engineering Department for hosting the author's seminar talk on
Planetary Heat Engines (5-11-2000). Thanks to Dr. Dan Gezari for
organizing an informal lunch seminar at NASA Goddard (2-11-2000). Thanks
to Cari and Bob Leidig for reading over early manuscripts and giving many
helpful suggestions. And particular
thanks to James Lovelock for the Gaia Hypothesis, which stimulated a lot of
thought on self-regulation and Earth's dynamics.

Taras
K, Copyright 2004

**References:**

(1) Gamow, ch 6

(2) Feynman, vol 1, ch 20-4

(3) Munk and MacDonald, ch 2

(4) Apostol, vol II, chs 2, 3 & 4

(5) Goldstein, ch 5

(6) Webster, ch VII, arts. 84-88

(7) Personal communication with Professor Tom
Caughey, Caltech, 1999; also Leighton and Vogt, B-17, p. 91

(8) IERS Website- http://hpiers.obspm.fr/

(9) Anderson- TotE; Cannon;
Cazenave; Chao, et. al.; Gross; Lambeck- TCAR, TEVR ch 5;
Munk and MacDonald, ch 10-6; White

(10) Lambeck- __GG__

(11) Munk and MacDonald, ch 5

(12) Chao, et. al.

(13) Anderson- AtotE:HaHDaH, TIoE:DESFtTD

(14) Skinner
and Porter, Figure CI.1, p. 15

(15) Lovelock

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Introductory Physics__, Addison-Wesley Publishing Co., 1969. [handy
practical stuff]

Lovelock, James __Ages of Gaia,__
W. W. Norton and Co. , New York, 1990.

Lovelock, James __Gaia: A new look at
life on Earth,__ Oxford University Press, 1995. [recent edition of an
important book, which many years ago, prompted my interest in the Earth's
energy balance]

Miller, Russel __Continents in
Collision__, Time Life Books, 1983.

Mound; Mitrovica; Evans; and Kirschvink
"A sea level test for inertial interchange true polar wander
events" *Geophys. J. Int., *vol. 136, pp. F5-F10, 1999

Munk and MacDonald __The Rotation of
the Earth,__ Cambridge University Press, 1960. [a classic text]

National Geographic __Atlas of the
World__, (Revised Sixth Edition).

Pratt, David "Poleshifts:
Theosophy and Science Contrasted" (website), January 2000
http://ourworld.compuserve.com/homepages/dp5/pole1.htm#c [interesting
material on mythology, historical perspectives, etc.]

Skinner and
Porter __The Blue Planet__, Wiley, John & Sons Inc., 1994.

Steinberger and O'Connell
"Changes of the Earth's Rotation Axis Owing to Advection of Mantle Density
Heterogeneities", *Nature*, 8 May 1997, pp 169-173.

Webster, Arthur Gordon __The Dynamics
of Particles and of Rigid, Elastic, and Fluid Bodies__, third edition, B. G. Teubner, Leipzig, 1925.
[this text really goes into the details, great figures!]

White, John __Pole Shift__, Doubleday and Company, 1980. [lots
of wild ideas collected here]

Wilson, J. Tuzo __Continents Adrift__,
Scientific American, Inc., W.H. Freeman and Co., 1972. [a very influential and popular
classic]

Woodhouse,
John "Mapping the Upper Mantle", *Journal of Geophysical
Research, *vol. 89 no. B7, July 10, 1984. [shows interesting mantle
density/rigidity features]