Popular lectures and addresses / by William Thomson.

  • William Thomson, 1st Baron Kelvin
Date:
1889-
Catalogue details

Licence: Public Domain Mark

Credit: Popular lectures and addresses / by William Thomson. Source: Wellcome Collection.

    119/486 page 101
    The semi-period of an infinitesimal satellite revolving round the earth, close to its surface,1 is equal to the semi-period of an ideal simple pendulum of length equal to the earth's radius, and having its weighted end infinitely near to the earth's surface ; and therefore, when reckoned in seconds, is approximately equal to the square root of the number of metres (6,370,000) in the earth's radius ; because the length of a seconds pendulum (or the pendulum whose semi-period is a second) is very approximately one metre. Thus we find 2,524 mean solar seconds for the semi-period of the satellite, and its angular velocity in radians per second is therefore (77/2524=) 0*001244: hence the earth's mean density, reck- oned on the universal-gravitation system, with the mean solar second for the unit of time, is [(0-001244)2 X 3/(47r) = ] 370 X io~7 ; and, if we take (from Bailey's repetition of Cavendish's experiment),2 the earth's mean density as 5-67 1 Thomson and Tait's Natural Philosophy, 2nd edition, vol. i., parti., § 223. 2 M. Cornu has criticised Bailey's method of reducing his observa- tions, in respect to allowance for viscous diminution of the oscilla-
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