Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait.
- Date:
- 1883
Licence: Public Domain Mark
Credit: Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait. Source: Wellcome Collection.
Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.
533/594 page 503
![(G.)—On Tidal Friction, by G. H. Darwin, F.RS. (a.) The retardation of the earth's rotation, as deduced from the secular acceleration of the Moon’s mean motion. Iu my paper on the precession of a viscous spheroid [Phil. Trans. Pt. II., 1879], all the data are giveivwhich are requisite for making the calculations for Professor Adams’ result in § 830, viz. : that if there is an unexplained part in the coefficient of the secular acceleration of the moon’s mean motion amounting to 6, and if this be due to tidal friction, then in a century the earth gets 22 seconds behind time, when compared with an ideal clock, going perfectly for a century, and perfectly rated at the beginning of the century. In the paper referred to however the earth is treated as homogeneous, and the tides are supposed to consist in a bodily deformation of the mass. The numerical results there given require some modification on this account. If E, E', E be the heights of the semidiurnal, diurnal and fortnightly tides, expressed as fractions of the equilibrium tides of the same denominations ; and if e, e', e be the corresponding retardations of phase of these tides due to friction; it is shown on p. 476 and in equation (48), that in consequence of lunar and solar tides, at the end of a century, the earth, as a time-keeper, is behind the time indicated by the ideal perfect clock 1900'27 E sin 2e + 423'49 Er sine7 seconds of time (a), and that if the motion of the moon were unaffected by the tides, an observer, taking the earth as his clock, would note that at the end of the century the moon was in advance of her place in her orbit by 1043,'-28 E sin 2e + 232*50 E' sin e' (b). This is of course merely the expression of the same fact as (a), in a different form. Lastly it is shown in equation (60) that from these causes in a century, the moon actually lags behind her place 630-7 E sin 2e + 108-6 E' sin e' - 7'042 E sin 2e (c). In adapting these results to the hypothesis of oceanic tides on a heterogeneous earth, we observe in the first place that, if the Retardation of earth's rotation. Numerical estimates.](https://iiif.wellcomecollection.org/image/b21987312_0533.jp2/full/800%2C/0/default.jpg)
