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For instance, if a sphere of uniform density, radius r, be expanded into a spheroid of uniform density, the radius of the equatoreal circular section being r'.

Since Mk is the same for the spheroid, and for a sphere, the radius of which is equal to the equatoreal radius of the spheroid, we shall still have

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If we suppose a small portion, n, to be detached from the surface of the equator of the revolving mass, M; and to continue to revolve uniformly with the angular velocity a, at the distance r; either in the manner of a planet, or as a thin ring; and that the remaining matter N is condensed into an interior mass, revolving with the angular velocity a;

let Mk moment of inertia of the whole mass:

NK =

.contracted mass.

Then, by the principle of conservation of areas,

Mka Nka + nr2a;

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For instance, suppose the Earth to be at present a sphere, or a spheroid, of uniform density; the mass of which is N. And that it had once been expanded so as to form together with the matter of the Moon, n, another sphere or spheroid, of uniform density, the radius of which at the equator, was equal to that of the Moon's orbit.

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the number of days, in which the Earth would have revolved together with the Moon, upon this supposition.

If we suppose the Earth, when so expanded, to have assumed the form of a cylindrical plate, of uniform density, the radius of which was equal to that of the Moon's orbit;

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We may assume such an arbitrary arrangement of the particles, as would render true the equation

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Thus, assuming the present form of the Earth to be a

sphere of uniform density, the radius of which =

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;

60

N=685, n = 10, m = 27.3,

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If the original form of the mass were nearly spherical, this would require a nucleus of much greater density towards the center, than near the surface.

But it surpasses all probability to suppose that there could have existed, without design, the precise arrangement of the particles of a vortex of this nature, which would have been necessary, in order that the surface of the Sun's equator should have had the angular velocity with which the respective planets now move, when it was expanded so as successively to have been in contact with them.

NOTE B. LECTURE IV. p. 75.

On the Chronology and Astronomy of the Hindus.

It would be difficult to mention a subject upon which there exist more various, and indeed contradictory, opinions, than the Chronology of the Hindus. Sir William Jones treats their pretensions to extraordinary antiquity, as altogether chimerical. "The aggregate of the four first ages constitutes the extravagant sum of four million three hundred and twenty thousand years: which aggregate multiplied by seventy-one is the period, in which every Menu is believed to preside over the world. Such a period one might conceive would have satisfied Archytas, the measurer of the sea and earth, and the numberer of the sands; or Archimedes, who invented a notation that was capable of expressing the number of them. But the compre

hensive mind of an Indian chronologer has no limits: and the reigns of fourteen Menus are only a single day of Brahma: fifty of which days have already elapsed, according to the Hindus, from the time of the Creation. All this puerility may be an astronomical riddle." Sir William Jones's Works, vol. 11. p. 345.

Halhed, in his Preface to the Translation of the Gentoo Laws, p. 36, after describing the four ages, and assigning

their respective durations, and the corresponding alteration in the length of human life, from 100,000 years, to 10,000, 1,000, and finally 100 years, thus expresses himself. "Computation is lost, and conjecture overwhelmed, in the attempt to adjust such astonishing spaces of time to our own confined notions of the world's epoch. To such antiquity the Mosaic creation is but as yesterday; and to such ages the life of Methuselah is no more than à span." Still Halhed seems inclined to give some credit to this extravagant tale; observing that the duration of life in the third period corresponds nearly with the longevity of the patriarchal age. It must be remembered that Halhed was a most credulous man; and himself furnished a touchstone of his sagacity. On March 31, 1795, and April 21, of the same year, he made a speech, in the House of Commons, in favour of Brothers, a pretended prophet, who was to restore the Jews. And in a tract which he published as a Testimony of the Authenticity of the Prophecies of Richard Brothers." London, 1795, p. 14, are found these words; "I affirm, from my own discoveries, that the prophet Daniel positively and particularly denounces annihilation to the British navy, in this war. And on proof of this proposition, in the course of my Essay, I am content to rest my whole pretensions to penetration."

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All accounts of Hindu chronology agree in dividing time into four Yugas, or ages. The first, as such, is styled Satya Yuga; and when it is regarded as the age of purity, it is styled the Krita Yuga. The second, in which one-third of mankind are considered to have been reprobate, is called the Treta Yuga. The third, in which one half of the human race became depraved, is denominated the Dwapar Yuga. And the fourth, in which all mankind are corrupted, or lessened, as the term implies, has the name of Kali Yuga. These divisions are evidently analogous to the mythological golden, silver, brazen, and

iron ages.

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