ON THE TIDES. 443 



distance of 79 from the line passing through the attracting body, either 

 in the nearer or in the remoter hemisphere ; but to urge them to- 

 wards the centre, although with a smaller force, in the remaining part. 

 Hence, in order that there may be an equilibrium, the depth of the fluid 

 must be greatest where its gravitation, thus 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 imme- 

 diately 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 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 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 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 equilibrium. The 

 force employed in producing this accommodation may be estimated 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 considering 

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

 factory than any which has yet been published ; and by comparing the 

 tides of 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 

 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 forced 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 confined 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 according to the depth of the ocean, 

 and to the breadth as well as the depth of the lake. In the case of a direct 

 tide the time of the passage of the luminary over the meridian must coin- 

 cide with that of high water, and in the case of an inverted tide with that 

 of low water. 



In order that the lunar tides of an open ocean may be direct, or synchro- 



' nous, its depth must be greater than 13 miles, and for the solar tides than 



14. The less the depth exceeded these limits, the greater the tides would 



