their atomic motion toward each other.

Hence, we have this:

Their distances from the sun ought to be inversely proportional to their densities.

"The following shorter process of Kepler's Third Law gives the inverse ratio of velocities, which, when squared, gives the distances of the planets :

"If the earth's true distance, found from the above table, be divided by the distances of the other planets, the quotients will be the ratios of the densities, which very nearly coincide with the densities given by Laplace.

"In Biot's 'Astronomy' the density of Mercury, resulting from the diameter and mass there given, is 3.097; but the author (L. B. Francecur) from whom Olmsted copied, puts it down as 1.12; Laplace is between these authors. Olmsted put it 2.7820.

It has been shown that the square roots of the distances of the planets are inversely proportional to their velocity of revolution. Hence, the nearer a planet approaches the sun, its velocity is more and more increased. At the distance of one mile, therefore, from the sun, the velocity of the earth's revolution around it would be 19 miles per second, and this multiplied

by the square root of 92,890,000 miles (19 X 8638) 183,122 miles per second, and which is very nearly up to the estimated velocity of light. The atoms of terrestrial matter, therefore, if placed at the surface of the sun, would have a motion equal to the velocity of solar light.

"If the resistance of atoms of matter retards the velocity of light, and modifies the force of gravity, the amount of such retardation ought to be in some ratio with the number of atoms, or masses of the planets. It is found that the sixth root of the masses represent this retardation. Therefore, the times of the rotation of the planets should be in the ratio of the square roots of the cube roots, that is, the sixth root of the masses.

In the second table by Dr. Wm. S. Green, given to illustrate his stated law, it will be observed that about half of the results are wide of the mark; yet if his law obtains as to the masses other methods are at fault.

The following table gives the densities of the planets taken from several authorities as stated at the head of each column, each being on the basis that the Earth = 1: A comparison of these show quite a difference :

"The times of the rotation of the planets should be in the ratio of the square roots of the cube roots; that is, the sixth roots of the masses." W. S. Green.

The following table gives the masses as per the authorities stated at the head of each column:

Orson Pratt, in his work, "Key to the Universe, or a New Key of its Mechanism," Utah, 1879, published his new law which he developed August 14, 1855. It was first published in

a newspaper called The Mormon, October 27, 1857, New York.

"The cube roots of the densities of the planets are as the square roots of their periods of rotation.

Or, which amounts to the same thing:

"The squares of the cube roots of the densities of the planets are as the periods of rotation.

"But as the densities of globes are proportional to their masses or quantities of matter, divided by their volumes or by the cubes of their diameters, it follows that the rotations of the planets, considered as spheres, are proportional to their masses and diameters, as follows:

"The squares of the cube roots of the masses of the planets divided by the squares of their diameters are as their periods of rotation.

"If the masses be divided by the cubes of the diameters, the quotients will be the densities of the planets. If the density of the earth be taken as unity or 1, the densities of the other

planets, deduced from data given, will be as in second column:

Inasmuch as there is disagreement as to the densities and the masses, there is a nearer agreement among authorities as to the times of rotation of the planets. Now reverse Dr. Green's stated law and say:

"The masses of the planets should be the sixth power of the ratio of the times of rotation."

If the law is correct it will test the authorities as to the estimates ef the masses. We take the rotation periods from Chambers' "Descriptive Astronomy," page 40, Oxford, 1867. These nearly agree with Newcomb's, 1878; in Chambers', Uranus and Neptune are questioned (?), while in Newcomb's Mercury and Venus are questioned (?) and Uranus and Neptune are designated "unknown." Norton, in his "Numerical Basis of of the Solar System," London, 1890, gives Uranus as 9h, 30m., and Neptune Ioh, 16m, 23s.

Some of these results show by inspection quite a little contrast

in the masses with those tabulated above.

M. T. Singleton, in his "Gravitation and Cosmlogical Law," give the following law: "The velocity of rotation varies inversely as the square root of the distance from the center of motion."

"In a rotating fluid mass, the time or period of revolution of any point is equal to the space described divided by the velocity. "Therefore, the velocity equals ÷ by √x, and the space described in making a complete revolution is 27. Hence, c = 2π, and the distance. The Earth = 1.

The author of "The Cycle" (J. E. W.) constructed a table on the orbital velocity of the planets per hour based on the multiples of 7 and a connection of the value of . His formula may be expressed as follows: 2(3.14159) + 1 X multiples of 7. Planets. 7×2+1 Times.

Mercury, 7.28318 × 14} =

J. E. W.

Stearns.

Astro. Works.

105 331

Mars,

7 28318 X 7

= 57 62385

53.080

53.611

Pliny E. Chase, in his "Beginnings of Development," has investigated the various cosmological and analogical laws of the solar system with most remarkable perseverance, and has published results in tables culminating in several harmonic laws :

"The unit of rotation radius is the Sun's radius. The actual rotation-radius of each planet = (radius-vector 18). For