14 MR. AIRY ON THE LAWS OF THE TIDES 



sea (as Limerick or New Ross), where the law of the height of semidiurnal tide, as 

 depending on the time, differs sensibly from that of cos 2^. 



Upon investigating the magnitude of the diurnal tides, by the method detailed a 

 short time since, it appears that, at most stations, the diurnal tide in height was given 

 with great regularity ; but that, at the greater number of stations, the diurnal tide in 

 time was not very regular. In order to compare the diurnal tides by means of the 

 theory above, as well as for the purpose of ascertaining their magnitudes with some 

 accuracy, it was necessary so to combine them that a mean of many determinations 

 could be made available. This was done in the following manner : — 



First, it is to be remarked that in this and all the following investigations the high 

 and low waters of the jfirst division only are used ; these being evidently sufficient 

 for the complete solution of any problem of diurnal tides. 



Next, it is well known, or may be anticipated from the investigations of the next 

 section, that on examining successively the diurnal tides at high water (first division) 

 on successive days, they increase, diminish, change sign, and increase and diminish 

 with the changed sign, in nearly the same manner as the sine of an arc increasing 

 proportionally to the time ; and that the same remark applies to the diurnal tides at 

 low water. 



The first thing to be done in investigation was therefore to ascertain when the 

 diurnal tide vanishes. This was done by taking the five diurnal tides nearest to the 

 estimated place of evanescence and combining them by the method of minimum 

 squares, on the supposition that the diurnal tide ought there to alter by uniform steps ; 

 an assumption sensibly correct. 



The next thing was, to take the mean of all the diurnal tides between two vanishing 



points. Supposing them to be expressed by the law a.sin^, the mean of all these 



, . Sum of the values of asin d , . , . . , i , 1 /* . 2a 



values IS Number of values ' which IS approximately expressed by -«/, sm^=-. 



and hence the coefficient a, or the maximum diurnal tide, must =0^. the mean of 



the diurnal tides between two vanishing points. 



The following results have been obtained by these methods ; — 



