444 LECTURE XLVII. 



be, and in all cases they would be greater than the primitive tides. But m 

 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 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, the depth of the open sea must 

 be 6 1 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 deep, in order that the time of high water might coincide with 

 that of the moon's southing. 



Hitherto we have considered the motion of the water as free from all 

 resistance ; but where the tides are direct, they must be retarded by the 

 effect of a resistance of any kind ; and where they are inverted, they must 

 be accelerated ; a small resistance producing, in both cases, a considerable 

 difference in the time of high water. 



Where a considerable tide is observed in the middle of a limited portion 

 of the sea, it must be derived from the effect of the elevation or depression 

 of the ocean in its neighbourhood ; and such derivative tides are probably 

 combined in almost all cases with the oscillations belonging to each parti- 

 cular branch of the sea. Mr. Laplace supposes that the tides, which are 

 observed in the most exposed European harbours, are produced almost 

 entirely by the transmission of the effect of the main ocean, in about a day 

 and a half ; but this opinion does not appear to be justified by observation ; 

 for the interval between the times of the high water belonging to the same tide, 

 in any two places between Brest and the Cape of Good Hope, has not been 

 observed to exceed about twelve hours at most ; nor can we trace a greater 

 difference by comparing the state of the tides at the more exposed situations 

 of St. Helena, the Cape Verd Islands, the Canaries, the Madeiras, and the 

 Azores, which constitute such a succession as might be expected to have 

 indicated the progress of the principal tide, if it had been such as Mr. 

 Laplace supposes. The only part of the ocean which we can consider as 

 completely open, lies to the south of the two great continents, chiefly 

 between the latitudes 30 and 70 south, and the original tide, which hap- 

 pens in this widely extended ocean, where its depth is sufficiently uniform, 

 must take place, according to the theory which has been advanced, at some ' 

 time before the sixth lunar hour. It sends a wave into the Atlantic, which 



