Chapter V:

New Theory Results Must Equal Old Theory Results
When and Where Applicable

A new theory, law, or principle is acceptable if, and only if, the new theory, law, or principle provides the same results as an older, accepted, theory, law, or principle where that older, accepted, theory, law, or principle is known to apply.  One example of this concept is the comparison of Albert Einstein’s Special Relativity Theory to Classical Mechanics.  Classical Mechanics defines Kinetic Energy of a mass as follows:

Where “K.E.” represents the Kinetic Energy of the object or particle, “m” represents the mass of the object or particle in motion and “v” represents the velocity of the object or particle.  Albert Einstein theorized the equivalency of mass and energy represented by the following relationship:

E  =  mc²

Where “E” represents the Total Energy of the system (Kinetic Energy plus Rest Energy), “m” represents the mass of the object or particle whether it is at rest or in motion, and “c” represents the speed of light in a vacuum.  This equation is applicable to all objects or particles that have “rest mass” moving at any velocity from zero to a velocity approaching that of the speed of light, c = 2.99729×10⁸ meters/second.  However, if the velocity of an object or particle is much, much less than the speed of light, the Kinetic Energy of that object or particle will reduce to the value determined by the Classical Mechanics expression for Kinetic Energy given above where the Classical Mechanics expression applies.  Einstein’s equation for the relationship of Mass and Energy, E = mc², represents the Total Energy of an object or particle with mass, m.  This equation must be used when the mass is moving at a “relativistic velocity.”  In other words, this equation must be used when the mass is moving at a significant fraction of the speed of light in a vacuum, c, in order to account for relativistic mass increase.  In order to determine the relativistic Kinetic Energy, the Energy of the Rest Mass, the equivalent energy liberated if the mass at rest was converted 100% into energy, is subtracted from the Total Mass Energy as follows:

Kinetic Energy = Total Energy - Rest Energy

Where the total mass is a function of the rest mass and the ratio of velocity to the speed of light as follows:

A binomial expansion of the (1-v²/c²)^-1/2 term can be performed to determine the Kinetic Energy of a particle with rest mass, m₀, if it is assumed that the velocity of the mass, v, is much, much less than the speed of light in a vacuum, c.  Relativistic equations should always reduce to the classical physics accepted values when conditions are such that the relativistic effects are very, very insignificant.  A binomial expansion of the Kinetic Energy equation is performed to determine what Kinetic Energy is equal to relative to mass at velocities much, much smaller than the speed of light.

Further reducing the above equation, Kinetic Energy of the mass, m₀, can be expressed as follows:

If the velocity, v, of the mass, m₀, is assumed to be much, much less than the speed of light, c, the ratio v/c is extremely small.  If v/c is extremely small, then the ratio of v/c to the 4^th power or greater will be essentially equal to zero and those terms can be ignored and “thrown out” of the equation.  The equation for Kinetic Energy of the mass, m₀, can be further reduced as follows which demonstrates that in the conditions where relativistic physics is insignificant, the relativistic equation for Kinetic Energy reduces to the classical physics equation for Kinetic Energy:

The reduction of a relativistic expression for Kinetic Energy to the classical expression of Kinetic Energy is an example of a new theory, in this case Einstein’s Special Relativity Theory, providing the same result as an older accepted theory, in this case Classical Physics, when the conditions are present where the old theory is known to apply.  This principle must be adhered to anytime a new theory is being evaluated.

Newton’s Law of Gravity as It Applies to Large Masses and Nuclear Gravitation Field Theory

The classical physics approach to the Newton’s Law of Gravity indicates that relatively large masses are required to measure any substantial Gravitational Fields of Attraction.  Assuming no amplification of gravity, the gravitational field measured external to any given object of mass is proportional to the total rest mass of all the nucleons in the nucleus and all the electrons around the nucleus of all the atoms which make up a given mass as long as the gravitational field is measured outside that given mass.  In addition, the gravitational field is inversely proportional to the square of the distance from the centroid of the given object of mass as long as the gravitational field is measured outside the object and the object is either a point source or a sphere.  The planet Earth, where we live, is a typical example of a large spherical mass that provides a significant gravitational field.  Since we stand on the surface of the Earth, the gravitational field that we experience from the Earth is based upon the total rest mass of all the atoms that make up the Earth.  Earth’s total mass is 5.98×10²⁴kg.  Earth’s equatorial radius is 6.378×10⁶meters.  Earth’s mean density is 5,522 kg/meter³.  The density of pure water at 77^oF or 25^oC is 1,000 kg/meter³.  Therefore, the Specific Gravity (SG) of the Earth is 5.522, which is a reasonable value for a planet made mostly of rock.  Using Newton’s Law of Gravity and Newton’s Second Law of Motion, the acceleration of gravity at the Earth’s surface can be calculated.  Newton’s Second Law of motion states:

F  =  ma

Where “F” represents the force applied to the object or particle, “m” represents the mass of the object or particle, and “a” represents the resultant acceleration of the object or particle.

Newton’s Law of Gravity is applied to 1 kg mass on Earth in following calculation.  “M_Earth” represents the mass of the Earth, “m” represents a 1 kilogram mass on the Earth’s surface, “R_Earth” represents the radius of the Earth, and “G” represents the Universal Gravitation Constant:

F = 9.87 Newtons = 9.87 kg-m/sec²

Rearranging the equation for Newton’s Second Law of Motion:

a = 9.87 meters/sec² = 32.4 ft/sec²

In actuality, the acceleration at the Earth’s surface is slightly less at the equator and rises as one moves toward the poles.  The rotation of the Earth on its axis results in a centrifugal force acting in the opposite direction of the gravitational acceleration.  Therefore, the effective gravitational acceleration is slightly reduced for all points on Earth except the North and South Pole.  The circumference of the Earth is equal to 2πR_Earth or 4.074×10⁷ meters (40,740 kilometers).  The Earth makes one complete rotation on its axis in a period of 24 hours.  The velocity of Earth’s rotation at any given Latitude can be calculated using the following equation:

Where “R_Earth” represents the Earth’s radius and “t” represents the time for the Earth to rotate one complete turn on its axis = 23 hours, 56 minutes = 23.93 hours, which is the Siderial Day, vice the Solar Day.  The maximum rotational velocity will be sensed at the Earth’s equator because the Latitude at the equator is 0^o and the cosine of 0^o is a maximum value of 1.  The rotational velocity at the equator is calculated below:

Likewise, the centripetal acceleration, “a,” at any given Latitude on the Earth, can be determined by the following equation:

The centripetal acceleration produced by the Earth rotating on its axis results in a centrifugal force tending to throw one off the Earth.  The maximum centrifugal force will be sensed at the Earth’s equator because the Latitude at the equator is 0^o and the cosine of 0^o is a maximum value of 1.  The centripetal acceleration is calculated below:

a = 0.0338 meters/sec²

Therefore, the total acceleration at the Earth’s surface at the Equator is:

a = 9.84 meters/sec² = 32.3 ft/sec²

NOTE:

The accepted value for g = 32.2 ft/sec2 which is within the accuracy of my calculations.  I assumed the Earth was a perfect sphere.  In actuality, the Earth is slightly flattened at the poles.  The value for Earth’s radius used in the above calculation is an average value.

There is no such condition that exists where there is actual “zero-gravity” except when an observer is, theoretically, placed at an infinite distance from any mass that is producing a gravitational field.  It is extremely misleading to the general public when it is stated by the news media on television that the astronauts in the Space Shuttle are in “zero-gravity” because they are “floating around.”  They are still in the presence of the Earth’s relatively strong gravitational field.  The Space Shuttle and the astronauts inside the Shuttle are in a continuous free fall condition as the Space Shuttle orbits the Earth.  The astronauts and the Space Shuttle are falling toward the Earth with the same acceleration rate.  Therefore, the net acceleration between the astronauts and the Space Shuttle is zero, giving the astronauts the sensation of floating in “zero gravity.”  The astronauts inside the Space Shuttle experience the same sensation that an occupant in an elevator would experience just after the elevator cable has given way and the elevator falls towards the bottom of the elevator shaft.

Let’s assume the orbit of the Space Shuttle is about 100 miles above the surface of the Earth.  Using Newton’s Law of Gravity and Newton’s Second Law of Motion, it can be determined how fast the Space Shuttle must be traveling relative to the Earth’s surface to maintain its orbit.  The following equations can be used to demonstrate the speed the Space Shuttle must be traveling to maintain an orbit at 100 miles above the surface of the Earth.  In this equation, “R” represents the distance of the Space Shuttle from the center of the Earth, which is equal to R_Earth, the Earth’s radius, plus 100 miles; “G” represents the Universal Gravitation Constant; M_Earth represents the mass of the Earth; and m represents the mass of the Space Shuttle, crew, and payload.

Solving for v, the velocity of the Space Shuttle, the following equation is obtained:

v = 7823.9 meters/sec = 7.8239 km/sec = 4.8596 miles/sec

The results are very close to the nominal 5 miles per second assumed for the orbital velocity of a spacecraft or satellite just above the Earth’s atmosphere.

The assumption that the Nuclear Attraction Force that holds the nucleus together is the same as the Force of Gravity still remains consistent with the observation of Newton’s Law of Gravity on a macroscopic scale.  The “Strong Nuclear Force” can be explained to be the same as Newton’s Law of Gravity on a macroscopic scale because the Electrostatic Repulsion Force does not have any significant repulsion effect on a macroscopic scale as long as the masses used for measurement of the gravitational field are neutral in charge.  Most atoms and molecules that make up the Earth are in an overall neutral charge state because the positive charges in the nucleus are neutralized by the negative charges of the “orbiting” electrons about the atom.  Ionic compounds, such as Sodium Chloride (table salt), found in solution in all the Oceans of the Earth, are balanced in charge because the same amount of Sodium (Na⁺) ions and Chloride (Cl^-) ions exist to form the ionic compound.  Therefore, for all practical purposes, the overall charge on the Earth, including its atmosphere, is neutral. Newton’s Law states Gravity is directly proportional to mass and inversely proportional to the square of the distance from the center of mass, assuming the mass is a sphere as an atom, a ball, or the planet Earth.  As long as the gravitational field measurement instrumentation is outside the mass of interest, the measured Force of Gravity will be proportional to the integration of the mass of all the atoms and molecules that make up the total mass of interest.  If the mass producing the gravitational field is significant enough, then the Gravitational Attraction Force can be detected by the instrumentation.

Kepler’s Laws of Orbital Motion, Gravity, and the Nuclear Gravitation Field Theory

On the macroscopic scale where Newton’s Law of Gravity and Kepler’s Law of Orbital Motion apply, any changes to the assumed source of Gravity cannot affect those laws where the laws have been demonstrated to apply.  Previously I have demonstrated that Newton’s Law of Gravity is not affected by the assumption that Gravity is the same as the “Strong Nuclear Force.”  As noted previously, Newton’s Law of Gravity is represented by the following equation:

Likewise, it can be demonstrated that Kepler’s Laws of Orbital Motion are also unaffected by that assumption.  Kepler’s Laws apply to massive objects such as planets, moons, and stars and macroscopic objects such as spacecraft and satellites.  Kepler’s Laws of Orbital Motion are provided below:

1. Planets do not move in perfect circles in their orbits about the Sun.  They travel, instead in elliptical paths, with the Sun at one of the foci.  Both foci are located on the major axis of the ellipse.  The distance of a planet from the Sun will change as it moves along its orbit (See Figure 5-1).



2. A line drawn from a planet to the Sun will sweep out equal areas in equal times as the planet moves along its orbit.  At the time when a planet comes closest to the Sun, its perihelion, the planet is moving faster than when it is at its most distant point, its aphelion (See Figure 5-2).



3. The square of the orbital period of a planet is proportional to the cube of the average distance of that planet from the Sun and is represented by the equation  P² = a³  (See Table 5-1).

The orbital period of a planet is the time it takes the planet to complete one orbit around the Sun in Earth years.  The average distance of the planet from the Sun turns out to be the same as half the length of the major axis of the ellipse of the orbit, or, in other words, the “Semi-major Axis” and is measured in units of Earth-Sun distance, or Astronomical Units.  The farther a planet is from the Sun, the longer its period of orbit around the Sun.

Reference: “The Space-Age Solar System,” Joseph F. Baugher, Page 15

Figure 5-1: Kepler’s First Law of Orbital Motion

Reference: http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Figure 5-2: Kepler’s Second Law of Orbital Motion

Reference: http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Table 5-1: The Sun's Planets and Their Properties

Planet	Semimajor Axis “a” in A.U.	Period “P” in Years	P2	a3	Eccentricity	Ecliptic Inclination	Mass in Earth Mass Units
Mercury	0.39	0.241	0.0581	0.0594	0.206	7.0	0.056
Venus	0.72	0.615	0.378	0.373	0.007	3.39	0.82
Earth	1.00	1.000	1.000	1.000	0.017	0.00	1.000
Mars	1.52	1.88	3.534	3.512	0.093	1.85	0.108
Jupiter	5.20	11.86	140.7	140.6	0.049	1.30	318
Saturn	9.5	29.46	867.9	857.3	0.054	2.49	95.1
Uranus	19.2	84.01	7,058	7,078	0.047	0.77	14.5
Neptune	30.1	164.79	27,156	27,271	0.009	1.77	17.2
Pluto	39.72	250.3	62,650	62,665	0.25	17.2	0.002

Reference:  “The Space-Age Solar System,” Joseph F. Baugher, Appendix D

Figure 5-3: Parameters of an Ellipse

Reference: http://www.xahlee.org/SpecialPlaneCurves_dir/Ellipse_dir/ellipse.html

The eccentricity of an orbit represents the deviation from the orbit being a perfect circle.  If the eccentricity = 0.000, then the orbit is a perfect circle.  Note from Table 5-1, above, that the planet Venus has the most nearly circular orbit of all the planets with an eccentricity of 0.007.  Neptune is a close second with an eccentricity of 0.009.  Earth is in third position with an eccentricity of 0.017.  Eccentricity of an ellipse is defined by the following equation:

The variable, “b,” represents the Semi-minor axis of the ellipse and the variable, “a,” represents the Semi-major axis of the ellipse (See Figure 5-3).  In the case of a circle, b and a are equal and the value inside the square root would be 0.  That result is expected because the eccentricity of a circle is 0.

Planetary orbits about a single star of a mass different than that of the Sun can also be considered.  Kepler's Law can be modified to correct for the mass of the star in Solar masses.  As is the case with our Solar System, the mass of the planets are assumed to be much smaller than that of the star.  Kepler’s Law is modified as follows:

The mass of the star, M_*, is given in Solar Mass Units where the Sun’s mass equals 1.

For a more general case where the orbits of double stars around each other are considered, Kepler’s Law of Orbital Motion is modified to take into account the masses of each of the two stars in the system.  M_*1 represents the mass of the first star and M_*2 represents the mass of the second star in the double star system.  Stellar masses are in units of Solar mass where the Sun’s mass equals 1.

Since the macroscopic objects of consideration in evaluating Kepler’s Laws of Orbital Motion are neutral in charge, Electrostatic Forces would not affect the Gravitational Fields associated with these macroscopic objects.  Therefore, assuming the “Strong Nuclear Force” that holds the protons and neutrons together in the nucleus is the same as the Gravitational Attraction Force does not affect Kepler’s Laws of Motion.

Newton’s Law of Gravity and Kepler’s Laws of Orbital Motion apply under all macroscopic conditions except under the condition where the observer is in the presence of a very strong gravitational field.  Such a gravitational field is only naturally present in relative proximity to a star such as our Sun, near a collapsed star such as a white dwarf, neutron star, or a “black hole.”  In relatively large gravitational fields such as these, Einstein’s General Relativity Theory must be applied to account for the gravitational bending or warping of “Space-Time.”  The scientific term for this General Relativistic effect is “Space-Time Compression.”  The amount of “Space-Time Compression” is directly related to the intensity of the gravitational field.  The planet Mercury is actually near enough to the Sun that it orbits in a gravitational field strong enough to warp “Space-Time” to a measurable degree.  Mercury’s orbit does not quite follow Newton’s Law of Gravity or Kepler’s Laws of Orbital Motion.  Mercury’s orbit deviates slightly from its classical physics predicted orbit because of the Sun’s gravitational field “warping Space-Time.”  The deviation in Mercury’s orbit can be accounted for by applying Einstein’s General Relativity Theory to the calculation of Mercury’s orbit.  See “Tests of Einstein’s General Theory of Relativity,” below:

Tests of Einstein’s General Theory of Relativity

Reference: http://www.stg.brown.edu/projects/classes/ma8/papers/amiller/cosmo/tests.html

NOTE:

The hyperlink to the above Referenced Website is no longer available.

Einstein’s theory of relativity, although intriguing as a purely theoretical model, directly challenged many contemporary Newtonian views of his time.  His theory gained validity as it predicted various natural phenomena more accurately than former theories.  Several important observations and experiments, such as one that utilized the Mössbauer effect to support the existence of a redshift, put relativity to the test.

Example 1:

Before Einstein's General Relativity Theory, astronomers could not explain why Mercury, the nearest planet to the Sun, revolved in an orbit that was not perfectly elliptical.  This phenomenon, referred to as the precession of Mercury’s perihelion (Mercury's perihelion is the point in its orbit during which it is closest to the Sun), has puzzled scientists who historically attacked the problem using Newtonian physical laws.  Einstein's field equations, which describe the extent of the warping of Space-Time by massive objects, and his geodesic equations, which describe the path of objects moving through warped Space-Time, predicted very accurately the seemingly anomalous precession of Mercury's orbit.  Because of Mercury's proximity to the Sun, it experiences a distortion of its orbit by the significant curvature in Space-Time caused by the Sun.

Example 2:

Not only do Einstein's theorems predict that masses will be affected by curvature of Space-Time by massive objects, but that even light particles move in curved paths in warped Space-Time fields generated by massive objects.  This prediction was been clearly supported during a partial solar eclipse in 1919.  If photons, or light particles, are affected by curved Space-Time, then we would expect that the light sent from stars would be deflected from its original path by massive objects, such as the Sun.  However, the bright light cast by the Sun made scientific observations of starlight that passed close by the Sun extremely difficult.  Normally, detection of this starlight is prevented by sunlight, which floods and overpowers the starlight by many degrees of magnitude.

During a solar eclipse, when the Sun’s light is obscured by the position of the moon, astronomers can avoid this problem.  By taking pictures of the blocked Sun and the surrounding sky, they can determine whether the position of the starlight is different than it should be in areas where Space-Time is not warped.  Indeed, this hypothesis was confirmed by painstaking observations made in 1919 and during subsequent eclipses.  Einstein's General Relativity Theory, again, correctly predicted that Space-Time curved by massive objects would even affect the path of light.

Figure 5-4:  General Relativity:  Gravity Warping Space-Time

Reference: http://archive.ncsa.uiuc.edu/Cyberia/NumRel/NumRelHome.html

Planetary Science:  Mercury

Reference: http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node98.html

Mercury, the closest planet to the Sun, is only 36 million miles away from the Sun's blazing surface.  Its highly eccentric orbit brings it within 28.5 million miles of the Sun, battering Mercury's surface and heating up the little planet to over 600 degrees Kelvin.  Its diameter is about 3,301 miles, and its mass about 54% that of the Earth's.  It goes around the Sun in just under 88 days and rotates on its axis every 59 days.  The successful prediction by Albert Einstein that Mercury's orbit would be found to advance by 43 inches per century is usually regarded as a confirmation of the General Theory of Relativity.  Night surface temperature is thought to be about 100^oK, midday temperature over 600^oK.  In 1974 and 1975, the U.S. Mariner space probe revealed that Mercury has a moonlike heavily cratered surface, and a slight magnetic field.

Figure 5-5:  Mercury’s Orbit

The deviation from Newtonian Physics that occurs in strong gravitational fields has already been considered and accounted for using Einstein’s General Relativity Theory.  Assuming the Gravitational Attraction Force is the same as the “Strong Nuclear Force” does not affect General Relativistic effects on a macroscopic scale.  Therefore, Newton’s Law of Gravity, Kepler’s Laws of Orbital Motion, or Einstein’s General Relativity Theory as applied to planetary motion are not affected by assuming the Gravitational Attraction Force is the same as the “Strong Nuclear Force” holding the protons and neutrons together in the nucleus.

Einstein’s General Relativity Theory may also be applicable to the nucleus in the form of quantized gravity if the “Strong Nuclear Force” and “Gravity” are one and the same.  An analysis is performed later to determine the approximate gravitational field of the Uranium-238 nucleus to determine if the field is strong enough to result in significant “Space-Time Compression.”  If the gravitational field is strong enough, the resultant “Space-Time Compression” can affect the apparent gravitational field strength as a function of distance from the center of the nucleus and can affect the solutions to the Schrodinger Wave Equation which has both a time dependent component and a spatial dependent component.  The Schrodinger Wave Equation will be addressed a bit later when Quantum Mechanics associated with electron energy levels about the nucleus and the nuclear energy levels for the protons and neutrons is evaluated.

Whether or not the “Strong Nuclear Force” and Gravity are one and the same force has absolutely no effect on Kepler’s Laws of Orbital Motion or Einstein’s General Relativity Theory from a macroscopic point of view.  Therefore, evaluation to determine if the “Strong Nuclear Force” and Gravity are one and the same force will not affect the results of Kepler’s Laws of Orbital Motion or the study of gravitational fields in the vicinity of large masses such as our Sun, Neutron Stars, or Black Holes.

Index and Direct Links to Other Chapters of Nuclear Gravitation Field Theory
and Nuclear Gravitation Field Theory Home Page/Table of Contents:

Nuclear Gravitation Field Theory

1. Purpose for Evaluation of the Strong Nuclear Force and the Force of Gravity



2. Executive Summary



3. The Classical Physics Evaluation of Electrostatics and Gravity
1. The Electrostatic Repulsion Force
2. Newton’s Law of Gravity - The Attractive Force of Masses
3. Comparison of Electrostatic Repulsion and Gravitational Attraction



4. Nuclear Gravitation Field Theory:  Major Stumbling Blocks to Overcome



5. New Theory Results Must Equal Old Theory Results When and Where Applicable
1. Newton’s Law of Gravity as It Applies to Large Masses and Nuclear Gravitation Field Theory
2. Kepler’s Laws, Gravity, and Nuclear Gravitation Field Theory



6. Structure of the Nucleus of the Atom



7. The Schrodinger Wave Equation and Quantum Mechanics - The Particle and Wave Characteristics of Matter



8. Nuclear Gravitation Field Theory Versus Accepted Strong Nuclear Force Overcoming Electrostatic Repulsion



9. Comparison of the Nuclear Gravitation Field to the Gravitational Field of the Sun and the Gravitational Field of a Neutron Star



10. Quantum Mechanics, General Relativity, and the Nuclear Gravitation Field Theory



11. Properties of the Strong Nuclear Force, Nuclear Properties of Bismuth, and the Nuclear Gravitation Field Theory



12. Conclusion



13. Appendix A:  References



14. Appendix B:  Background of the Author

Index and Direct Hyperlinks to the Other Web Pages on this Website:

1. Gravity Warp Drive Home Page



2. Nuclear Gravitation Field Theory  (Specific Chapter Links are Provided on this Web Page)



3. Purchase e-Books



4. History of My Research and Development of the Nuclear Gravitation Field Theory



5. “The Zeta Reticuli Incident” by Terence Dickinson



6. Supporting Information for the Nuclear Gravitation Field Theory



7. Government Scientist Goes Public



8. “Sport Model” Flying Disc Operational Specifications



9. Design and Operation of the “Sport Model” Flying Disc Anti-Matter Reactor



10. Element 115



11. Bob Lazar’s Gravity Generator



12. United States Patent Number 3,626,605:  “Method and Apparatus for Generating a Secondary Gravitational Force Field”



13. United States Patent Number 3,626,606:  “Method and Apparatus for Generating a Dynamic Force Field”



14. V. V. Roschin and S. M. Godin:  “Verification of the Searl Effect”



15. The Physics of Star Trek and Subspace Communication:  Science Fiction or Science Fact?



16. Constellation:  Reticulum



17. Reticulan Extraterrestrial Biological Entity



18. Zeta 2 Reticuli:  Home System of the Greys?



19. UFO Encounter and Time Backs Up



20. UFO Testimonies by Astronauts and Cosmonauts and UFO Comments by Presidents and Top U.S. Government Officials



21. Pushing the Limits of the Periodic Table



22. General Relativity



23. Rethinking Relativity



24. The Speed of Gravity - What the Experiments Say



25. Negative Gravity



26. The Bermuda Triangle:  Space-Time Warps



27. The Wright Brothers



28. Website Endorsements and Favorite Quotes



29. Sponsors of This Website



30. Romans Road to Eternal Life In Jesus Christ

© Copyright Kenneth F. Wright, April 10, 2000.
All rights reserved.  No portion of this document may be
reproduced in any form without written permission of the author.