On the Tidal Retardation of the Earth's Rotation. 533 



Not so with the ice-sheet. The ice-sheet is rigidly attached to 

 the earth, which the moon is not. It may produce a strain in 

 the solid materials of the earth by its attraction, but cannot draw 

 the earth's centre to it. Hence the ice-sheet will have its whole 

 effect on the ocean, which must not be diminished by theoreti- 

 cally applying a force equal to the attraction on the centre in 

 the opposite direction. 



It may be said, But the moon does not actually draw the 

 earth's centre to it. If this be true, it is because the earth-and- 

 moon's revolving round their common centre of gravity produces 

 a centrifugal force in each, so as to keep each in its place ; and 

 this centrifugal force affects not only the centre, but the ocean too. 



It is not, however, strictly true that the moon does not draw 

 the earth's centre to it. This would be the case if the orbit 

 were a circle ; but it is more like an ellipse, the moon sometimes 

 receding, sometimes approaching the earth's centre. This of 

 itself might perhaps be a sufficient answer to the writer who says 

 that the moon's action on the earth and ocean would not be 

 affected if it were rigidly connected with the earth, and there- 

 fore why may not the ice-sheet be considered to be like the moon 

 in its effect in raising the water opposite to it as well as under and 

 near it ? But the proper answer is, that the ice-sheet's being 

 rigidly connected with the earth's centre produces a force which 

 keeps them at the same distance from each other, and that force 

 has no effect whatever (as the centrifugal force between the 

 moon and earth has) on the ocean. In fact, to return to what I 

 said at first, the moon is a free body with reference to the earth, 

 but the ice-sheet is a fixed body. 



J. H. Pratt. 

 Calcutta, April 20, 1866. 



LXXVII. On the Observations and Calculations required to find 

 the Tidal Retardation of the Earth's Rotation. By Professor 

 W. Thomson, F.R.S.* 



THE first publication of any definite estimate of the possible 

 amount of the diminution of rotatory velocity experienced 

 by the earth through tidal friction is due, I believe, to Mr. Wil- 

 liam Ferrel, and is to be found in the Number for December 8, 

 1853, of the Astronomical Journal of Cambridge, United States. 

 It is founded on calculating the moment round the earth's centre 

 of the attraction of the moon, on a regular spheroidal shell of 

 water symmetrical about its longest axis, this being (through the 

 influence of fluid friction) kept in a position inclined backwards 



* From the Rede Lecture, Cambridge, May 23, 1866, " On the Dissi- 

 pation of Energy." Communicated by the Author. 



Phil. May. S. 4. No. 212. Suppl. Vol. 31. 2 N 



