92 THEORY OF THE TIDES. SECT. XIII. 



which are diametrically opposite to her, in both instances pro- 

 ducing an elevation of the ocean of nearly the same height above 

 the surface of equilibrium ; for the diminution of the gravitation 

 of the particles in each position is almost the same, on account 

 of the distance of the moon being great in comparison of the 

 radius of the earth. Were the earth entirely covered by the sea, 

 the waters thus attracted by the moon would assume the form of 

 an oblong spheroid whose greater axis would point towards the 

 moon ; since the columns of water under the moon, and in the 

 direction diametrically opposite to her, are rendered lighter in 

 consequence of the diminution of their gravitation ; and, in 

 order to preserve the equilibrium, the axes 90 distant would be 

 shortened. The elevation, on account of the smaller space to 

 which it is confined, is twice as great as the depression, because 

 the contents of the spheroid always remain the same. If the 

 waters were capable of assuming the form of equilibrium instan- 

 taneously, that is, the form of the spheroid, its summit would 

 always point to the moon notwithstanding the earth's rotation. 

 But, on account of their resistance, the rapid motion produced 

 in them by rotation prevents them from assuming at every 

 instant the form which the equilibrium of the forces acting upon 

 them requires. Hence, on account of the inertia of the waters, 

 if the tides be considered relatively to the whole earth and open 

 seas, there is a meridian about 30 eastward of the moon, where 

 it is always high water both in the hemisphere where the moon 

 is and in that which is opposite. On the west side of this circle 

 the tide is flowing, on the east it is ebbing, and on every part of 

 the meridian at 90 distant it is low water. This great wave, 

 which follows all the motions of the moon as far as the rotation 

 of the earth will permit, is modified by the action of the sun, the 

 effects of whose attraction are in every respect like those pro- 

 duced by the moon, though greatly less in degree. Consequently 

 a similar wave, but much smaller, raised by the sun, tends to 

 follow his motions, which at times combines with the lunar 

 wave, and at others opposes it, according to the relative positions 

 of the two luminaries ; but as the lunar wave is only modified a 

 little by the solar, the tides must necessarily happen twice in a 

 day, since the rotation of the earth brings the same point twice 

 under the meridian of the moon in that time, once under the 

 superior and once under the inferior meridian. 



