3oG 



llEfOHT — 1873. 



tiJo a compound effect which corresponds precisely to the discord of two 

 simple harmonic notes in music approximately in unison with one anotlier. 

 These constituents may be called, for brevity, elliptic and decliuational tides. 

 Thus we have the following schedule of tidal constituents : — • 



Speeds. 



The lunar monthly and solar annual (elliptic). 2 



The lunar fortnightly and solar semiannual 1 ^^ 



(decliuational) J '^ 



The lunar and solar diurnal (decliuational) . 4 



The lunar and solar semidiurnal .... 2 



The lunar and solar elliptic diurnal 



The lunar and solar elliptic semidiurnal 



i 



The lunar 

 diurnal 



and solar decliuational semi- 



}^ 



4. Hero y denotes the angular velocity of the earth's rotation, and a, rj, nr 

 those of the moon's revolution round the earth, of the earth's round the sun, 

 and of the progression of the moon's perigee. The motion of the first point 

 of Aries and of the earth's perihelion are neglected. The slow variation of 

 the lunar declinational tides due to the retrogression of the nodes of the 

 moon's orbit may be dealt with, probably with sufBcient accuracy, according 

 to the equilibrium method. The inequalities produced by perturbations of 

 the moon's motion, other than of erection and variation, are insensible. 

 These perturbations give tidal constituents, which must be included in the 

 analysis for all places at which the range of tide is considerable. The follow- 

 ing are the speeds of these perturbing elements for semidiurnal tides : — 



r-\- OT— 2;j 



Lunar wnvVfi/on semidiurnal J "^ -ta-r-ij 



Lunar evection semidiurnal 



f2y- a 

 t2y-3^ 

 f2y-4(7 + 2 



I 2y-2,, 



There are also evection and variation diurnal tides, but which, from their 

 nature, must be necessarily very small, and consequently have not hitherto 

 been included in the analj'sis. 



5. There are besides, as Laplace has shown, very sensible tides depending 

 on the fourth power of the moon's parallax*, the investigation of which 

 must be included in the complete analysis now suggested, although for 

 simplicity they have been left out of the preceding schedule. The amplitude 

 and the epoch of each tidal constituent for any part of the sea is to be deter- 

 mined by observation, and cannot be determined except by observation. But 

 it is to be remarked that two of the solar elliptic diurnal tides thus indicated 

 have the same period, being twenty-four mean solar hours, and also the 

 period of one of the lunar diurnal tides agrees with that of one of the solar 

 diurnal tides, being twenty-four sidereal hours, and that the period of one 



[* The chief effect of this at any one station is a ferdiurnal lunar tide, or one whose 

 rjeriod is eight lunar hours. Values of this have been determined from the tidal observa- 

 tions at Liverpool, Ramsgate, Portland Breakwater, &c.] 



