52 MR. AIRY ON THE LAWS OF THE TIDES 



water or low water, on the supposition that the fluctuation depends entirely on the 

 argument (phase +?>i). Since the Theory of Waves, as applied to Tides, leads us to 

 refer every angle to that argument, and induces us to suppose that the term connected 

 with that argument is the only one which is immediately created by the tidal 

 forces (the others depending numerically on it almost in the same way in which the 

 coefficients of successive multiples of anomaly depend on that of the simple anomaly)^ 

 it appears to be proper to consider the times of high and low water thus found as the 

 genuine times of high and low water. For the sake of distinction I call them the 

 Analysed Times. 



As it is convenient to use the time of one phase only, I have, when the analysis 

 gave the Analysed Times of two low waters, taken their mean for the Analysed Time 

 of High Water. 



Now if we put phase -l-(pj=/?, ^2"~2^i=^2> ^3 — S^^^Cg, ^4 — 4^1=04, our expression 

 for the height at every instant will be 



Ao+CiSinp+C2sin(2;? + C2)4-C3sin(3jo-fc3)+C4sin(4;?+<?4), 



and this, with a statement of the time at which the argument p has the value of 90° 

 (or the Analysed Time of Higli Water), gives a complete knowledge of the form of 

 every tide. 



I annex a specimen of the printed skeleton form in which the calculations described 

 in this section were made (the figures, and the words in italics, being inserted for 

 each special tide). And I subjoin the whole of the results for the twenty-one stations. 

 Each line is the digested result of about 170 observations. 



