112 MR. AIRY ON THE LAWS OF THE TIDES 



Section XVI. — Remarks on the succeeding terms of the expressions for individual tides, 

 as related to the magnitude of the tide, to the position on the sea-coast, to the 

 position on the river, S^c. ; comparison with the terms given by the theory of waves ; 

 discussion of the quarto-diurnal tide. 



In order to reduce to a smaller number the numerous formulae of Section X., and 

 to render the relations of their coefficients and arguments at once accurate and di- 

 stinct, the formulae have been divided into groups corresponding to large tides and 

 small tides, the times of division being the same as those used in the discussions of 



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 the semimenstrual inequality of height. Then, for the large tides, the numbers — Ag 



have been collected and their mean has been taken ; similarly, the mean of the numbers 



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— B2 has been taken ; and from these, by the treatment described in Section X., a 



term similar to C2 sin (2 phase +<p2) is formed. The mean of all the angles <p^ is also 

 taken, and its double is subtracted from the number corresponding to <p2- A similar 

 process is used for 3 phase and 4 phase. As for some tides <pi is nearly equal to 90° 

 and for others is nearly equal to 270° ; the expressions in the latter case are made to 

 admit of combination with those in the former case by subtracting 180° from ^^ and 

 by changing the signs of A3 and B3. The small tides are treated in the same manner. 

 The following Table contains the result. 



