Diurnal Tides of the Coasts of Ireland. 53 



Taking the fourth difference, we have, after some transforma- 

 tions, 



4th cliff. = ^,-4//2 + 6/?3-4//4 + /?g= 16A cos n<^ single/). 



The right-hand member of this equation disappears for all the 

 terms except the diurnal tide. For, in the semidiurnal tide, the 

 value of is nearly 3G0°, and consequently sin''^<^ is evanescent ; 

 for the tides of long period, such as those under the third and 

 fourth heads, ^ is a very small angle ; for example, in the semi- 

 uienstrual tide, ^ is about 12° 37', and therefore 



4th difference ■ 4/ro i dm nnr^MA" 



16Acos?i(12 3/') ^ 



a quantity which is perfectly insensible. 



The slow changes of level due to the slow changes of atmo- 

 spheric pressure will in like manner disappear from the 4th dif- 

 ference of the heights at higK and low water, and there remains 

 therefore nothing to consider but the diurnal tide, and the acci- 

 dental changes due to sudden variations of wind; the latter 

 cannot be eliminated by any process of calculation, as they sim- 

 ply produce 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 siu'*^^ is nearly unity ; and there- 

 fore the whole effect of the diurnal tide remains in the 4th dif- 

 ference of the successive heights, or 



-p.. ,,.1 /?!— 4^2 + 6^3— 4^4 -f/ig ,.^ 



Diurnal tide = -^ — ^ 3 ?, . . . (1) 



Having arranged the high and low waters for the ten stations 

 in regular order, I employed two calculators, who were unac- 

 quainted with each other's name and address, to calculate the 

 diurnal tide for the high and low waters following the moon's 

 southing, from equation (1). I then compared these independ- 

 ent calculations, and whenever they differed, I repeated the calcu- 

 lation myself, and in this manner secured the perfect accuracy 

 of the Tables, from which the results of this paper are calculated. 

 Notwithstanding the accuracy of observation obtained by the 

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

 servers, there arc occasional irregularities in these figures which 

 must be attributed to the fifth cause mentioned in p. 52. And 

 such irregularities occur principally during the stormy part of 

 the year, and occasionally on the occurrence of isolated storms; 

 but, on the whole, I believe tlie present observations of the 



