TIDAL OBSEUVATIONS. 369 



23. The values A^, B, in columns S and H express the mean solar semi- 

 diurnal and mean lunar semidiurnal tides. 



A^, Bj of column K express the luni-solar declinational semidiurnal tide. 



A^, B., of columns L and IS express two constituents of the lunar elliptic 

 semidiurnal tide. 



A^, B^ of column express zero tolerably well *. 



A^, Bj of columns K and express the two constituents of the lunar 

 diurnal tide. 



Aj, Bj of column S express one constituent of the solar elliptic diurnal 

 tide. 



A,, Bj of column M express one constituent of the lunar elliptic diurnal 

 tidef. 



Aj, Bj of columns L and N possibly depend on the elliptic lunar diurnal 

 tides, but will no doubt be found a better approximation to zero when cal- 

 culated by the average of several years. There is no tide corresponding 

 strictly to them. 



A3, B3 are, as they ought to be, very good approximations to zero in all 

 the columns except M. Their values in this column constitute, probably, a 

 genuine expression of the terdiurual lunar tide [not included in the pre- 

 ceding general schedule (§ 3) but referred to in § 4], investigated by 

 Laplace as depending on the fourth power of the moon's parallax. 



A^, B^ express shallow-Avater tides J derived from the lunar semidiurnal 

 tide, according to precisely the same dynamical principle as that by -which 

 Helmholtz has explained the overtones generated in very loud sounds, even 

 when the source of the sound is a simple harmonic motion. There ought to 

 be no sensible tide expressed by A^ and Bj in column L ; and the comparative 

 largeness of these numbers is probably an accident, owing either to errors of 

 observation or the imperfection of the system of combination adopted, or a 

 chance concurrence of disturbance due to wind &c. 



A., Bj in almost every column axjproximate remai-kably well to zero ; and 

 even their greatest values (those of column S) express merely a deviation 

 of ^ of a foot (or 0-3 of an inch) on each side of the mean level. 



A^., B^, may be considered as insensible for every column except M, for 

 which they express, as they ought to do, an undoubtedly genuine shallow- 

 water tide, being the second harmonic (as it were overtone) of the lunar 

 semidiurnal tide. 



A^, B^ are very good approximations to zero in all the columns. 



A^, Bjj in column M express probably a genuine, though very small, 

 shallow-water tide, the third harmonic of the lunar semidiurnal tide. There 

 is a very good approximation to zero in all of the other columns. 



It is interesting, with reference to the mode of reduction which has been 

 adopted, to remark to how nearly zero the comparatively large values of 

 A., B. in column and A^, B^ in column L of the first approximation are re- 

 duced by the corrections found in the second approximation explained above. 



24. Selecting from the preceding Table the coefficients, which are each 

 probably a genuine tide, and applying the proper corrections (Everett, Roy. 

 Soc. Edin. Trans. I860), which are the following : — 



* There being no theoretical tide of tlic period corresponding to them. 



t Being tlie resultant of the two whose speeds are y — (r+-w and y — cr — vr, inasmuch 

 as for a single year tlie effect of the +-nr may be neglected. 



J It is this term that mates the whole resultant tide rise foster than it falls, as is 

 generally observed in estuaries and other localities separated from the oceans by consider- 

 able spaces of shallow water. 



1872. 2 C 



