iO MR. AiaY ON THE LAWS OF THE TIDES 



evident to all who inspected the collected heights at high and low water, that irregn- 

 larities in the heights at any one station were sensible with no important difference 

 of magnitude at the neighbouring stations. This will be abundantly shown in Sec- 

 tion XI. On this assumption, a comparison of the height or time at one station 

 with that at each of the neighbouring stations, for a few tides near to that at which 

 the observation was deficient, would give the means of supplying the omitted height 

 or time. But it was necessary to bear in mind that all the observations were affected 

 by diurnal tide, and that the diurnal tide might vary sufficiently from port to port 

 to render it unsafe to use comparisons of evening tides for the correction of morn- 

 ing tides, &c. The process adopted therefore was the following:— The results, 

 both for times and for heights, were divided into four groups. One comprehended 

 the high waters which next followed the moon's transit; these were called High 

 Waters of the First Division. Another comprehended the low waters which next 

 followed those high waters ; these were called Low Waters of the First Division. 

 The remaining high waters and low waters were called respectively High Waters and 

 Low Waters of the Second Division. Each of these groups was treated separately. 

 When a height or time of high or low water at any station was to be supplied, the 

 observed height, &c. at that station was compared with the mean of the observed 

 heights, &c. for at least two neighbouring stations, in at least two tides preceding 

 and two tides following, in the same group; and the mean difference thus found was 

 applied to the mean of the observed heights, &c. at the stations compared, on that 

 day for which the tide was deficient. I have no doubt that the results thus supplied 

 are sensibly as accurate as those which were actually observed. 



On consideration of the difficulty of determining the times of high and low water, 

 which has been already explained, it appeared necessary to endeavour to smooth 

 down some of their irregularities, without at the same time endangering the conclu- 

 sions as affected by difference of diurnal tides and of semidiurnal tides at the different 

 stations. The following is the method employed : — Each of the groups already men- 

 tioned was separated into four subdivisions, determined by the proximity of stations. 

 One included Kilbaha, Kilrush, Foynes Island, Limerick, Casleh Bay, Galway, and 

 Old Head. The second included Mullaghmore, Buncrana, Port Rush, Carrowkeel, 

 and Ballycastle. The third contained Glenarm, Donaghadee, Ardglass, Clogher Head, 

 and Kingstown. The fourth contained Dunmore East, New Ross, Passage West, and 

 Castle Townsend. [Courtown was omitted, because, as will be hereafter seen, no 

 times of high or low water could be fixed for it.] Then each subdivision was treated 

 separately. For each tide the mean of the times for all the different stations was 

 taken (Buncrana, Ballycastle, and Glenarm, being excepted ; as, from the smalt 

 range of tide at thiese places, the determinations were more uncertain than at others). 

 Then for every station (including those already named) the difference of the time from 

 the mean of times was formed. Thus, for any one station, a difference from mean 

 was obtained for each day. Let these differences for successive days be called 



