578 LECTURE XLYII. 



the line passing througli the attracting body, either in the nearer, or in the re- 

 moter hemisphere; but to urge them towards the centre, although with a smaller 

 force, in the remaining part. Hence, in order that there may be an equi- 

 librium, the depth of the fluid must be greatest where its gravitation, thu» 

 composed, is least ; that is, in' the line directed towards the attracting body, 

 and it may be shown that it must assume the form of an oblong elliptic spheroid. 



If the earth were wholly fluid, and the same part of its surface were 

 always turned towards the moon, the pole of the spheroid being immediately 

 under the moon, the lunar tide would remain stationary, the greatest eleva- 

 tion being at the points nearest to the moon and furthest from her, and the 

 greatest depression in the circle equally distant from these points; the eleva- 

 tion being, however, on account of the smaller surface to which it is confined 

 twice as great as the depression. The actual height of this elevation would 

 probably be about 40 inches, and the depression 20, making together a tide 

 of 5 feet. If also the waters were capable of assuming instantly such a form 

 as the equilibrium would require, the summit of a spheroid equally elevated 

 would still be directed towards the moon, notwithstanding the earth's rota- 

 tion. This may be called the primitive tide of the ocean: but on account of 

 the perpetual change of place which is required for the accommodation of the 

 surface to a similar position with respect to the moon, as the earth revolves, 

 the form must be materially different from that of such a spheroid of equili- 

 brium. The force employed in producing this accommodation may be esti- 

 mated by considering the actual surface of the sea as that of a wave moving 

 on the spheroid of equilibrium, and producing in the water a sufficient 

 velocity to preserve the actual form. We may deduce, from this mode of consi- 

 dering the subject, a theory of the tides which appears to be more simple and 

 satisfactory than any which has yet been published: and by comparing the 

 tides oi' narrower seas and lakes with the motions of pendulums suspended on 

 vibrating centres, we may extend the theory to all possible cases. 



If the centre of a pendulum be made to vibrate, the vibrations of the pen- 

 dulum itself, when they have arrived at a state of permanence, will be perform- 

 ed in the same time with those of the centre; but the motion of the pendulum 

 will be either in the same direction with that of the centre, or in a contrary 

 direction, accordingly as the time of this forced vibration is longer or sliortcf!- 



