Diurnal Tides on the Coasts of Ireland. 41 



Fourth Difference • . ,^o , „,> ^ ^„„. , . 



i-^-j .,qo Q7/X = sm< (6 18') = 0000145. 



\&A cosn (12 37 ) ^ ' 



a quantity which is perfectly insensible. 



The slow changes of level due to the slow changes of atmospheric pressure 

 will in like manner disappear from the Fourth Difference of the heights at High 

 and Low Water, and there remains, therefore, nothing to consider but the Diur- 

 nal Tide, and the accidental changes due to sudden variations of wind. The 

 latter cannot be eliminated by any process of calculation, as they simply pro- 

 duce the effect of making a particular height, or two or three successive heights, 

 differ from their true values ; they are to be considered as in the same category 

 as errors of observation, and so far as they occur they vitiate the observations 

 which they affect. 



In the Diurnal Tide, on the contrary, the value of </> is nearly 180^, and, 

 therefore, sin* ^0 is nearly unity ; and consequently, the whole effect of the 

 Diurnal Tide remains in the Fourth Difference of the successive heights, or, 



■n- 1 rp-j hi-4h2 + Qh3-4h, + fis ,,^ 



Diurnal Tide = r-^ . (1) 



Having arranged the High and Low Waters for the ten stations in regular 

 order, I employed two calculators, who were unconnected with each other, 

 to calculate the Diurnal Tide for the High and Low Waters following the 

 Moon's southing, from equation (1). These independent calculations were 

 then compared, and wherever they differed I repeated the calculation myself, 

 and in this manner secured the perfect accuracy of the figures which will be 

 given in the Tables of this Memoir. Notwithstanding the accuracy of obser- 

 vation obtained by the form of tide-gauge used by us, and the evident care 

 of the observers, there are occasional irregularities in these figures, which must 

 be attributed to the fifth cause, mentioned in p. 40; and such irregularities 

 happened principally during the stormy part of the year, and occasionally on 

 the occurrence of isolated storms ; but, on the whole, I believe the observa- 

 tions of the Diurnal Tide now presented to the Academy are the most perfect 

 that have been ever made on so large a scale, and for such a length of time. 



Having thus eliminated the Diurnal Tide from the observed heights, I con- 

 structed the Diurnal Tide at High and Low Water following the Moon's south- 



VOL. xxiu. G 



