110 . MR. AIRY Om THE LAWS OF THE TIDES 



is greater than 2 Cj in the formulae of Section X. ; and that in the river-stations the 

 difference is considerable. Without accounting for the two exceptions, I may remark 

 that this shows that the departure from the pure form of tide depending on a single 

 sine is, at all the other stations, similar in some important points of its character to 

 that in a river tide. The nature of the tide at each station will be examined more 

 accurately in Section XVI. 



With regard to the semimenstrual inequality in height and the apparent value of 



yF, we have to compcire the two last columns of the Table on page 105 with the two 



similar columns of the Table on page 35. The numbers are so nearly equal that we 



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 cannot assert that there is any certain difference. The large value of i^ at Port Rush, 



the small value at Glenarm, and the general smallness from Donaghadee to Castle 

 Townsend (like that in the river station Limerick) are equally marked in both. 



With regard to the age of the tide as obtained from heights or ranges (which, as I 

 have stated before, is the true age of the tide), we must compare the results on page 

 105 with those on page 38. They agree, on the whole, very well; though the ages 

 deduced from the analysis appear to be somewhat smaller than those deduced from 

 high and low waters. The ages deduced from the analysis also agree better among 

 themselves. The diminution however from Port Rush to Ballycastle is remarkable. 

 The general result seems to be that on the south-western coast of Ireland the age of 

 the tide is about one day twenty hours. 



For the establishment, we must compare the Table of page 106 with that of page 

 39. Only at Limerick and New Ross is the difference considerable : at these sta- 

 tions it amounts to about twenty minutes. 



For the semimenstrual inequality in time, we must compare the numbers in page 

 107 with those of page 42. And here it will at once be remarked that a great and 



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 important change has been made in the resulting values of tt by the new mode of 



treating them. The values at Old Head and Glenarm and the following stations are 

 increased, and those at Port Rush and Ballycastle are diminished, till they agree suf- 

 ficiently well with the others. This change arises from two causes. First, the deter- 

 mination of times from the analysis is vastly more accurate than that from the esti- 

 mation of the times of high and low water. Secondly, in Section VIII. the groups 

 for large intervals and small intervals were divided at each station from a consideration 

 of the magnitudes of the intervals themselves, whereas in Section XIV. they were di- 

 vided from consideration of a totally different circumstance, namely the age of the tide 

 as shown by the time of occurrence of the mean value of range. Strange as it may 

 appear, the former method was incorrect, and the latter is correct. The former method 

 is affected by a circumstance which ought not to enter into the formation of this result 

 at all, namely the change in the time of station-tide, not depending on the change in 

 the time of sea-tide, but depending on the change which the character of the tidal for- 



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