448 LECTURE XLVII. 



retarded. The progress of this alteration may easily be traced by means of 

 a simple construction. If we make a triangle of which two of the sides are 

 two feet and five feet in length, the external angle which they form being 

 equal to twice the distance of the luminaries, the third side will show pre- 

 cisely the magnitude of the compound tide, and the halves of the two 

 angles opposite to the first two sides the acceleration, or retardation, of the 

 times of high water belonging to the separate tides respectively. Hence it 

 appears that the greatest deviation of the joint tide from the lunar tide 

 amounts to 11 48' in longitude, and the time corresponding, to 47 minutes, 

 supposing the proportion of the forces to remain always the same ; but in 

 fact the forces increase in proportion as the cubes of the distances of their 

 respective luminaries diminish, as well as from other causes ; and in order 

 to determine their joint effects, the lengths of the sides of the triangle must 

 be varied accordingly. In some ports, from a combination of circum- 

 stances in the channel, by which the tides reach them, or in the seas, in 

 which they originate, the influence of the sun and moon may acquire 

 a proportion somewhat different from that which naturally belongs to 

 them : thus at Brest, the influence of the moon appears to be three times as 

 great as that of the sun ; when it is usually only twice and a half as great. 

 (Plate XXXVIII. Fig. 522.) 



The greatest and least tides do not happen immediately at the times of the 

 new and full moon, but at least two, and commonly three tides after, even 

 at those places which are most immediately exposed to the effects of the 

 general tide of the ocean. The theory which has been advanced will 

 afford us a very satisfactory reason for this circumstance ; the resistance 

 of fluids in general is as the square of the velocity, consequently it must 

 be much greater for the lunar than for the solar tide, in proportion to the 

 magnitude of the force, and the acceleration of the lunar tide produced 

 by this cause must be greater than that of the solar ; hence it may happen 

 that when the lunar tide occurs two or three hours after the transit of the 

 moon, the solar tide may be three or four hours after that of the sun, 

 so as to be about an hour later, at the times of conjunction and opposition, 

 and the tides will be highest when the moon passes the meridian about an 

 hour after the sun ; while at the precise time of the new and full moon, the 

 lunar tide will be retarded about a quarter of an hour by the effect of the 

 solar tide. 



The particular forms of the channels, through which the tides arrive at 

 different places, produce in them a great variety of local modifications ; 

 of which the most usual is, that from the convergence of the shores of the 

 channels, the tides rise to a much greater height than in the open sea. 

 Thus at Brest the height of the tides is about 20 feet, at Bristol 30, at 

 Chepstow 40, at St. Maloes 50 ; and at Annapolis Royal, in the Bay of 

 Fundy, as much sometimes as 100 feet ; although perhaps in some of these 

 cases a partial oscillation of a limited portion of the sea may be an imme- 

 diate effect of the attraction of the luminary. In the Mediterranean the 

 tides are generally inconsiderable, but they are still perceptible ; at Naples 

 they sometimes amount to a foot, at Venice to more than two feet, and in 

 the Euripus, for a certain number of days in each lunation, they are very 



