THE TIDES. (A PP. D.} 211 



ties depending on the varying declinations of the 

 two bodies. Each such inequality of any one of 

 the chief tides may be regarded as a smaller super- 

 imposed tide of period approximately equal ; pro- 

 ducing, with the chief tide, a compound effect 

 which corresponds precisely to the discord of two 

 simple harmonic notes in music approximately in 

 unison with one another. These constituents may 

 be called for brevity elliptic and declinational tides. 

 But two of the solar elliptic diurnal tides thus 

 indicated have the same period, being twenty-four 

 mean solar hours. Thus we have in all twenty- 

 three tidal constituents : 



Coefficients of / in arguments. 

 Lunar. Solar. 



The lunar monthly ana solar \ 

 annual (elliptic) . . . . / : 



The lunar fortnightly and ") 



solar semiannual (decli- > 2 20- 2/7 



national) ....... J 



The lunar and solar diurnal \ 

 (declinational) J 



The lunar and solar semi- 

 diurnal 



The lunar and solar elliptic "I 

 diurnal J 



The lunar and solar elliptic 1 / 27 o--5> (27 T? 



semidiurnal J '" (27 3o--}-> (27 3/1 



The lunar and solar decli- ) 



national semidiurnal . . j 2 2y 2 ^ 



3. Here 7 denotes the angular velocity of the 

 earth's rotation, and a, rj, & those of the moon's 



P 2 



