326 OF TIDES. 



moon, and opposed at the quadratures, or first and last quarters. 

 The high tides at the times of tiie equinoxes are produced by the 

 joint operation of the sun and moon, when botli of them are so si. 

 tuated as to act more powerfully than elsewhere. 



The lunar tide being much larger than the solar tide, it must al. 

 ways determine the time of high and low water, which, in the spring 

 and neap tides, remains unaltered by the effect of the sun ; so that 

 in the neap tides, the actual time of low water is lhat of the solar 

 high water; but at the intermediate times, the lunar high water is 

 more or less accelerated or retarded. The progress of this altera. 

 tion 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 shew 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 respec. 

 tively. Hence it appears that the greatest deviation of the joint 

 tide from the lunar tide amounts to 1 1 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 lumina- 

 ries diminish, as well as from other causes; and in order to deter- 

 mine their joint effects, the length of the sides of the triangle must 

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

 cumstances 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 na- 

 turally 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. 



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 



