OF THE TIDES IN THE PORT OP LONDON. 



29 



I proceed to discuss the variations of the heights of the London tides. 



2. The Semimenstrual Inequality, — The law of the heights is contained in the last 

 column of Mr. Lubbock's Table V., which gives the heights for every half-hour, mean 

 time, of the moon's transit, taking a mean of the months of the year. 



In order to obtain a formula expressing this series of quantities, we observe that the 

 maximum and minimum are nearly when the times of transit are 2^ and 8^ respectively; 

 that the mean of the extreme heights is 21*1 feet, and the difference of the extremes 

 3*4 feet. Hence the height may be expressed approximately by the formula 21'! -|- \'7 

 cos 2 (<p — 30°). It appears, however, that the maximum and minimum occur a little 

 earlier than 2^ and 8^. I shall therefore assume for the height the formula 21-1 + 1*7 

 cos (2^ — 51°) ; we shall then have the following comparison with observations. 



It is evident that this is a first approximation. Also the difference, which is always 

 positive, follows the law of a sine. To show this, subtract from this difference -23, 

 as is done in th6 last column. 



The difference in the last column will be when <p is 0^ 30«^ and 6^ 30™ nearly, and 

 will, in the course of 6 hours of <p, go through all the values of sin (p. Hence it may be 

 represented by — c sin (4 ^ — 30°), and it is evident that c is nearly '23. 



Comparison of the residual Phenomenon of the Semimenstrual Series of Heights, freed 

 of the Terms 21 •} + \'7 cos (29 — 51), with the Formula ^23 — -23 sin (4(p — 30). 



