New views of Mr. George H. Darwin's theory of the evolution of the Earth-Moon system : considered as to its bearing on the question of the duration of geological time / by Samuel Haughton.

  • Haughton, Samuel.
Date:
1882
Catalogue details

Licence: Public Domain Mark

Credit: New views of Mr. George H. Darwin's theory of the evolution of the Earth-Moon system : considered as to its bearing on the question of the duration of geological time / by Samuel Haughton. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    body such as the moon), Mr. Darwin has found a remarkable equa- tion of condition, which may be thus expressed : (1) where y — distance between centres of earth and moon. t — time elapsed from a fixed epoch. p{n—Q) {n— (2) n = angular velocity of earth’s rotation. a =z angular velocity of moon’s orbital revolution. p = quantity varying inversely as the viscosity of the planet. The extreme interest of equation (1) consists in the appearance of the inverse sixth power of the distance. As the function If' varies very slowly, we find by integration, for any portion of time during which If' may be regarded as con- stant t = (3) a most unexpected and remarkable result. Upon reading Mr. Darwin’s papers, my mind turned to a prob- lem with which I was familiar, viz.: the retardation of the earth’s rotation produced by the lunisolar tide exerted upon the ocean supposed collected in an equatorial canal, the moon and sun hav- ing no declination, and I readily found an equation to express the evolution of the earth-moon system, on the foregoing hypothesis as to friction. This equation is the following: ^(l/r) (4) where i4V;(n-fl)“-/c^j V4(n-i2y+/ (5) f = coefficient of friction supposed proportional to relative velocity. k varies inversely as r\ = velocity at earth’s equator. This leads, as in Mr. Darwin’s hj^pothesis of viscous earth, to the integral (6)-