254 TV. H. Finlay, M.A. — Approximate Tide- [Aug. 31, . 



2 "x 



* speed' of the tide (so that the function repeats itself in a time — )? • 



R, is the amplitude and t the epoch. Each such component is called a 

 tide. The actual height of the tide therefore at any time t is equated 

 to the expression 



Ao + Ri cos (??i ^ — n) + 1^2 cos (?72 ^ — «2) + &c. 



where A^ is the height of mean sea-level above some assumed datum- - 

 line ; and the solution of a large number of equations formed in this 

 way determines the most probable values of the constants involved. 



Prof. Gr. H. Darwin has shown that it is possible t® deduce very ' 

 approximate values of six of the most important tides from observ- 

 ations taken every hour for a month. These are the lunar, solar and 

 luni-solar semi-diurnal tides ; and the luni-solar, lunar and solar diurnal 

 tides : they will be referred to by the letters M2, S2, K2, Ki, O and 

 F respectively. Of these the two first are usually much the largest 

 and most important, and they are the only ones that can be taken into 

 account in forming a mean tide-table to apply approximately through- - 

 out the year. But it should be understood that such a table must 

 necessarily be rough : the diurnal tides are neglected and will have 

 the effect of making the predicted times of high water differ from the 

 observed times by about the same amount for the morning and 

 evening tides but in different directions, and there will be inequalities 

 depending on the moon's declination and distance from the earth. If 

 it be thought worth while to allow for these inequalities, the results of 

 the present investigation will allow of its being done : but as a 

 month's observations are not sufficient to determine the elliptic tides 

 and as the time and height of high water are to some extent depen- 

 dent on the meteorological conditions obtaining at the time, it is 

 perhaps scarcely worth while to incur the extra labour of the com- 

 putations. For Table Bay I have worked up two series, one in 1885, 

 November, and one in 1887, May : the results from the two series 

 showed a most satisfactory agreement. For Algoa Bay I have taken 

 one series in 1886, April. I have assumed that the height of the tide^^ 

 is affected to the extent of one foot by a change of one inch in the- 

 barometer reading, and corrections have been applied to reduce the- 

 readings to a mean height of the barometer of 30 inches. 



Putting H for the semi-range of a tide, and K for the constant 

 angle of retardation or * lag,' I find 



