Diurnal Tides of the Coasts of Ireland. 55 



remaining six, thi-ee belonging to the solar, and three to the 

 lunar diurnal tide, are to be determined, and being found, the 

 values of D calculated from (2) are to be compared with its 

 values deduced from observation in the way already described. 



The unknown quantities of the diurnal tide are therefore, — 



1st. The coefficients of solar and lunar tides. 



2nd. The diurnal solitidal, and lunitidal intervals. 



3rd. The ages of the solar and lunar tides. 



Of these quantities, one, viz. the age of the solar diurnal tide, 

 cannot be found from observation, because the sun's place or 

 declination changes so slowly that it is a matter of indifference 

 what place we assign to the sun (within a limit of some days) in 

 estimating the amount of the solar tide. The other five quan- 

 tities may and have been found from the observations, as I 

 shall presently show. 



The constants of equation (2) were found as follows for each 

 of the ten tidal stations. An inspection of equation (2) shows 

 that the solar diurnal tide disappears at the equinoxes (because 

 o-=0, or is very small), hence the equinoctial diui'nal tide ob- 

 served at high and low water is altogether due to the moon. The 

 lunar diurnal tide was thus found appi'oximately from the equi- 

 noctial tides, and was constructed on the same abscissae as the 

 observed diurnal tide. This lunar tide, constructed from calcu- 

 lation, differs considerably from the observed diurnal tide at the 

 solstices, the difference being due to the solar diurnal tide. In 

 this way the solar diurnal tide was in its turn calculated approxi- 

 mately from the solstitial tides, and the calculated solar tide 

 carefully superposed upon the lunar tide. 



The observed and calculated tides, constructed as just de- 

 scribed, were then compared, both with reference to the maximum 

 heights at high and low water, both positive and negative ; and 

 with reference to the times of vanishing of the diurnal tide at 

 high and low water ; and from this comparison the constants 

 used in the construction were corrected, and the heights and 

 times again compared, until the agreement was as close as the 

 obsei"vations would allow. 



The constants thus successively corrected are those given for 

 each locality, and the comparison of the observed and calculated 

 tides is also given, so as to afford a very good idea of the degree 

 of agreement between the observations and theory. 



The unknown constants of equation (2) are — 



Lunar Diurnal Tide. 



1. Age of tide. 



2. ?'„= lunitidal interval. 



3. M= coefficient of lunar tide. 



