80 On the supposed Tides in the 



" 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 elevation 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 elevation 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 forty inches, and the depression twenty, 

 making together a tide of five feet. If also the waters were 

 capable of assuming, instantly, such a form as the equilibri- 

 um would require, the summit of a spheroid equally elevated 

 would still be directed towards the moon, notwithstanding 

 the earth's rotation. 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 sur- 

 face, to a similar position with respect to the moon, as the 

 earth revolves, the form must be materially diflferent, from 

 that of such a spheroid of equilibrium. The force employed, 

 in producing this accommodation, may be estimated, by con- 

 sidering 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 considering 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 of narrow seas and lakes, with the mo- 

 tions 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 vi- 

 brations of the pendulum itself, when they have arrived at a 

 state of permanence, will be performed 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 for- 

 ced vibration is longer or shorter, than that of the natural 

 vibration of the pendulum ; and in the same manner it may 

 be shown that the tides either of an open ocean, or of a con- 

 fined lake, may be either direct or inverted, with respect to 

 the primitive tide, which would be produced, if the waters 

 always assumed the form of the spheroid of equilibrium, ac- ' 

 cording to the depth of the ocean, and to the breadth as well 



