ON THE TIDES. 585 



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 precisely 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 aj)pears 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 lu- 

 minaries 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 ac- 

 cordingly. In some ports, from a combination of circumstances in the chan- 

 nel, by which the tides reach them, or in the seas, in which they originate, 

 the influence of the sun and moon may acquire a propartion somewhat dif- 

 ferent from that which naturally belongs to them: thus at Brest, the in- 

 fluence 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 XXXVIIL 

 Fig. 5^22.) 



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

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

 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 mucli 

 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 

 title may be tju-ee 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^ wilt 

 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. 



