58. 



NOTE ON SIR WILLIAM THOMSON'S CORRECTION OF THE ORDINARY 

 EQUILIBRIUM THEORY OF THE TIDES. 



[From the Report of the British Association, 1886, p. 541.] 



IN Art. 806 of Thomson and Tait's Treatise on Natural Philosophy it 

 is pointed out that if the Earth's surface is supposed to be only partially 

 covered by the Ocean, the rise and fall of the water at any place, according 

 to the equilibrium theory, would be falsely estimated, if, as is usually done, 

 it were taken to be the same as the rise and fall of the spheroidal surface 

 that would bound the water were there no dry land. 



In the articles which immediately follow the above, it is shewn that 

 in order to satisfy the condition that the volume of the water remains 

 unchanged, the expression for the radius vector of the spheroid bounding 

 the water must contain, in addition to the terms which would be sufficient 

 if there were no land, a quantity a which depends on the positions of the 

 Sun and Moon at the time considered, and which is the same for all 

 points of the sea at the same time. 



This quantity a contains five constant coefficients which depend merely 

 on the configuration of land and water. The values of these coefficients 

 in the case of the actual oceans of our globe have been carefully deter- 

 mined very recently by Mr H. H. Turner of Trinity College, in a joint paper 

 by Professor G. H. Darwin and himself, which is published in Vol. XL. of 

 the Proceedings of the Royal Society. 



