ox THE TIDES, 57!) 



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, Avhich 

 woukl be produced if the waters always assumed the form of the spheroid of 

 equilibrium, according to tlie depth of the ocean, and to the breadth as well 

 as tlie depth of the lai<e. In the case of a direct tide, the time of the passage 

 of the luminary over the meridian must coincide with that of high w ater, 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 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 maii|ier; 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 13 

 miles. 



In order that the height of the inverted or remote lunar tides may be five 

 feet, or equal to that of the primitive tides, tlie depth of the open sea must 

 be 64- miles ; and if the height is only two feet, which is perhaps not far from 

 the truth, the depth must be 3 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 water, with respect to the primitive tides> 

 are equally distant from the middle of the lake. (Plate XXXVIII. Fig. 

 520.) 



The tides may be direct in a lake 100 fathoms deep and less than 8 degrees 

 wide; but if it be much wider, they must be inverted. Supposing the depth 

 a mile, they will be direct when the breadth is less than 25'^; but if a sea, 

 like the Atlantic^ were 50 or 60 degrees wide, it must be at least four miles 



