320 OF TIDES. 



ed : 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 per- 

 manence, will be performed in the same time with those of the 

 centre ; but the motion of the pendulum will be either in the same 

 direclion with that of the centre, or in a contrary direction, accord, 

 ingly 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 coincide 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 synchronous, its depth must be greater than thirteen miles, and 

 for the solar tides than fourteen. The less the depth exceeded 

 these limits, the greater the tides would be, and in all cases they 

 would be greater than the primitive tides. But in fact the height 

 of the tides in the open ocean is always far short of that which 

 would be produced in this manner; it is therefore improbable that 

 the tides are ever direct in the open ocean, and that the depth of 

 the sea is so great as thirteen miles. 



In order tliat the height of the inverted or remote lunar tides 

 may be five feet, or eqifcil to that of the primitive tides, the depth 

 of the open sea must be 6% miles ; and if the height is only two 

 feet, which is perhaps not far from the truth, the depth must be 

 three miles and five-sevenths. 



The tides of a lake or narrow sea differ materially from those of 

 the open ocean, since the height of the water scarcely undergoes 

 any variation in the middle of the lake ; it must always be high 

 water at the eastern extremity when it is low water at the western : 

 and this must happen at the time when the places of high and low 



