208 ON TIDES AND TIDAL ACTION IX HARBORS. 



occurrence and magnitude for any place, is encompassed with difficul- 

 ties, from causes to which we shall hereafter revert. 



If we conceive the earth to be wholly, or for the greater part, covered 

 ■with water and subject to the attraction of the sun, the force of which 

 varies inversely as the square of the distance, it will be obvious, that 

 while the whole earth will fall toward the sun with a velocity proportioned 

 to the aggregate attraction upon its solid portions,.(\vhich is the same as 

 if all the matter were collected at its center,) the water nearest to the 

 sun being accelerated by a greater force, and being fluid, will approach 

 the sun more rapidly than the solid core. It will thus run from all sides 

 iuto a protuberance beyond the forni of equilibrium of the earth's attrac- 

 tion and rotation, until the pressure of the elevated mass equals the dif- 

 ference in the attraction of the sun. Moreover, a similar protuberance 

 will be formed on the side opposite to the sun, since the particles of 

 water, being solicited by a less force than the solid core, will fall more 

 slowly toward the sun, and as it were remain behind. Nor does the fact 

 that on the average the earth does not lessen its distance from the sun, in 

 the least invalidate the force of this reasoning ; for the deviations from 

 the tangential motion of the earth in its orbit are precisely those which 

 the earth would niove through if falling toward the sun unaflected by 

 any other impulse. 



The same considerations hold good in regard to the attraction of the 

 moon upon the earth and the waters surrounding it ; for although we are 

 in the habit of considering the moon as simply revolving about the earth, 

 it must be remembered that the attraction is mutual, that both bodies 

 describe orbits about their common center of gravity, and that while the 

 moon obeys the attractive force of the earth, the latter equally follows 

 that of the lormer, by which it is at every instant of time drawn from the 

 path which it would pursue if that influence did not exist by an amount 

 precisely equal to the fall corresponding to the moon's attractive force. 



As a necessary consequence of the elevation of the water in the 

 regions nearest to and most remote from the attracting body, there 

 must be a correspondiug depression below the mean level of the sea 

 at points distant ninety degrees from the vertices of the protuberances, 

 or at the sides of the earth, as seen from the sun or moon. If the latter 

 bodies maintained a constant position with respect to the earth, the 

 effect would therefore be to produce a distortion of figure in the ocean- 

 surface, (assumed to cover the whole earth,) having the form of a slightly 

 elongated ellipsoid, the two vertices of which would be the one pre- 

 cisely under, the other precisely opposite to, the points at which the 

 disturbing body is vertical. This, however, is not the case ; for by the 

 rotation of the earth, and the motion of earth and moon in their orbits, 

 the direction of the disturbing forces is constantly changing with respect 

 to any point on the earth's surface. New points arrive at every instant, 

 under the zenith and nadir of either luminary, and thus it is that waves 

 ore produced which follow them round the globe. The highest i)oints 



