224 POPULAR LECTURES AND ADDRESSES. 



APPENDIX E. 



EQUILIBRIUM THEORY OF THE TIDES. 

 {Thomson and Taifs " Natural Philosophy? 804870.] 



IF we suppose the moon to be divided into two 

 halves, and these to be fixed on opposite sides of 

 the earth, at distances each equal to the true moon's 

 mean distance : the ellipticity of the disturbed 

 terrestrial water-level would be 3/(2 x 60 x 300000) 

 or 1/12,000,000; and the whole difference of levels 

 from highest to lowest would be about if feet. 



The rise and fall of water at any point of the 

 earth's surface we may now imagine to be produced 

 by making these two disturbing bodies (moon and 

 anti-moon, as we may call them for brevity) revolve 

 round the earth's axis once in the lunar twenty-four 

 hours, with the line joining them always inclined to 

 the earth's equator at an angle equal to the moon's 

 declination. If we assume that at each moment 

 the condition of hydrostatic equilibrium is fulfilled, 

 that is, that the free liquid surface is perpendicular 

 to the resultant force, we have what is called the 

 " equilibrium theory of the tides." 



But even on this equilibrium theory, the rise and 

 fall at any place would be most falsely estimated if 

 we were to take it, as we believe it is generally 



