116 MR. AIRY ON THE LAWS OF THE TIDES 



In regard to the river stations, I may remark that the Shannon does, in conse- 

 quence of the barriers to the tide at Limerick, resemble a gulf in its tidal character ; 

 and the second of the formulae above ought therefore to apply to it ; and, as will 

 easily be seen, it does apply with considerable approximation. The river Barrow, 

 upon which New Ross is situated, is not obstructed in the same manner, and there- 

 fore we might expect the third formula to apply, and it does apply very nearly. 



I omit discussion of the third and fourth terms, because theory, in a shape appli- 

 cable to cases of nature, has not yet been extended sufficiently far. I may however 

 observe that, as I have shown with regard to the tide at Deptford*, and to those at 

 Southampton and Ipswich -f, so also at Limerick, and in some measure at Foynes 

 Island and New Ross, the third term is almost as important as the second, and the 

 fourth is one of considerable magnitude. 



I may also call the attention of the wave-theorist to this circumstance, that the 

 difference between the coefficients for large tides and for small tides does not appear 

 sufficiently great in relation to the difference between the coefficients of the first term 

 for large tides and small tides. The coefficient of the first term being considered as 

 of the first order, that of the second term would consist of a series whose leading 

 term was of the second order, &c. The departure from the proportions given by 

 this consideration may depend upon the succeeding terms of the series. 



It is also to be remarked that there is an undoubted difference between the argu- 

 ments for large tides and for small tides. This seems to show that each sine is ac- 

 companied by a cosine, and that their coefficients have, for their leading terms, terms 

 of different orders in respect of the first coefficient of semi-range. 



Section XVII. — Separate discussion of the tidal observations made at Courtown. 



The observers at Courtown soon discovered that it was impossible to adhere to the 

 instructions sketched in Section I. The tide was sometimes apparent as a semi- 

 diurnal tide, but with considerable irregularity ; at other times, the character of 

 semidiurnal tide was (to common observation) completely lost, and in its stead Uiere 

 was a small tide four times a day ; in all cases the tide was small. In this state of 

 things, the course which they adopted was, to observe continuously whenever the 

 semidiurnal tide was not distinctly marked, and to follow the usual rule (with some 

 extension of observations) when it was well-marked. In this manner a tolerably 

 complete and very important set of observations has been secured. In several cases 

 the observations have been interrupted by the discharge of water from the sluices 

 for scouring the harbour of Courtown ; in some instances there has been no difficulty 

 in filling up the observations by conjecture, in others I have been obliged to adopt 

 the limits of the tide (in the form of analysis) to these interruptions. 



In order to apply the method of analysis explained in Section X., it was necessary 

 to fix upon precise limits for each tide. But as no limits could be obtained at Cour- 

 ♦ Philosophical Transactions, 1842, p. 4. f Ibid. 1843, pp. 49 and 53. 



