486 



Sir G. B. Airy on the Tides at Malta. 



[Dec. 6, 



plained. The object is to express every height on each separate day by 

 the following formulae, in which is the tidal angle, increasing from at 

 the beginning to 2tt, or 24 h , at the end of the tidal day : — 



For mean height, M ; 



For semidiurnal tide, P . sin 26 + Q • cos 20 ; 

 For diurnal tide, p . sin 0+ q . cos 6. 



The mathematical process is investigated, and an easy practical rule is 

 found for its application. Thus the numerical values of M, P, Q,_p, q are 

 found for every day. The two tidal expressions are without difficulty 

 converted into the following — 



Half semidiurnal range x cosine of (26 — 2 retard of semidiurnal high- 

 water on the zero of tidal time), 



Half diurnal range X cosine of (6 — retard of diurnal high-water on the 

 zero of tidal time), 



By the formulae, 



Half -range = V(P 2 + Q 2 ) or= V(p 2 + ? 2 ) f° r the two tides respectively, 



P 



Tan 2 retard for semidiurnal tide=— , 



Tan retard for diurnal tide=^. 



% 



Thus the retard of each tide on the zero of tidal time is found for every 

 day. The adopted zero of tidal time, for a reason given in the paper, is 16 m 

 earlier than the tabular time of London high-water : and thus the real 

 time of each of the Malta high waters for every day is found. This is 

 then compared with the time of moon's transit in the Nautical Almanac ; 

 and thus the retard of each high water on the moon's transit is found. 

 Por more distinct view of the changes the lunation is divided into eight 

 equal parts, and the means of the several classes of results are taken for 

 each eighth part, by a process explained in the paper. 



The following are the principal results : — 



1. The value of M, the mean height for each day, has a regular and 

 well-defined luni-menstrual change connected with the moon's declina- 

 tion. It is suggested that, viewing the extreme slowness of the change, 

 it is probable that this inequality differs little in magnitude and epoch from 

 the corresponding inequality on the oceanic shores of Spain and Morocco, 

 and that perhaps it gives the best measure of that inequality. 



2. The semimenstrual inequality in time of the semidiurnal tides is 

 very well marked. In magnitude it is sensibly the same as that at London, 

 but its epoch is about three days earlier. 



3. The semimenstrual inequality in height of the semidiurnal tides is 

 also very well marked. Its epoch is earlier than that for London by 

 about three days ; but the proportion of its coefficient in height to the 

 coefficient of semidiurnal tide in height is greater than at London. 



(It is curious that these results should be deduced with such certainty 



