266 The Rev. S. Haugbton on the Solar and Lunar 



Section XL Diurnal Tide at Courtown. 

 On proceediug to calculate tlie diurnal tide constants at Cour- 

 townj I found that it was impossible to construct satisfactorily 

 the diurnal tide at low water. The equinoctial lunar tide at low 

 water was + 25 ft. And this value was the same for the spring 

 and autumnal equinoctial tides ; but on constructing the tides 

 from the spring equinoctial tide, I could not reconcile it with 

 the autumnal tide, and vice versa. I therefore abandoned the 

 attempt to reconcile theory and observation with respect to the 

 tide at low water at this station, and have only used the lunar 

 equinoctial tide in height, which was found to be accurately the 

 same in amount for both equinoxes. 



I. Diurnal tide at high ivater. 



1. Maximum value of lunar tide for positive heights = 0"40 ft. 



2. Maximum value of lunar tide for negative heights = 0*40 ft. 



3. Maximum value of solar tide =0'30 ft. 



4. Diurnal solitidal interval =5l* l*"^. 



5. Age of lunar tide =6*1 22^^. 



II. Diurnal tide at low water. 



1. Maximum value of lunar tide for positive heights = 0'25 ft. 



3. Maximum value of lunar tide for negative heights = 0-25 ft. 



3. Maximum value of solar tide =0*30 ft. ? 



4. Diurnal solitidal interval = 5^ I"". ? 



5. Age of lunar tide =3'1 12i^. ? 



Adding together the first two of each of the preceding results, 

 we find — 



Range of lunar tide at high water =0'80 ft. 



Range of lunar tide at low water =0'50 ft. 

 Hence by equation (3), 



cot ('"-^«)= Q^ - ^^^ (^^°) > 

 or, converting the arc into time, 



Tw — f„, = 2i» 12""; 

 but since m, the moon's hour-angle at high water expressed in 

 Courtown time, is 7^ 40™, we obtain 

 f,„ = 5i» 28". 

 By equation (4), we have 



max. value of 2M sin 2/i= \/ (O-SO)^ + (O-oO)^ = 0-943 ft; 

 from which we find M = 0"719 ft 



Also, since the mean value of the solar tide is 0'30 feet, we have 



max. value of 2S sin 2c7 = 0-600 ft., 

 and therefore S = 0-410ft. 



