ON THE COASTS OF IRELAND. 117 



town (as at other stations) from the observations themselves, it was necessary to take 

 them from another station. The station selected for this purpose was Ardglass. 

 The limits and the divisions into twelfths and sixteenths for Ardglass were therefore 

 adopted for Courtown, as far as the continuity of observations permitted. Where 

 (as is just mentioned) it was necessary to change the limits, this was done if possible 

 by altering the limits and all the divisions by three or six of the twelfths (correspond- 

 ing to four or eight of the sixteenths) ; in other cases they were all altered by a defi- 

 nite time. Then the means of the heights in these observations were treated in the 

 usual way. 



A correction for diurnal tide was indispensable (the diurnal tide being, at some 

 times, as large as the semidiurnal). For obtaining this from the observations there 

 were two means. One was, by means of the investigations connected with tertio- 

 diurnal tide to be detailed in the next section. These gave the diurnal tide for the 

 beginning and the fourth parts of each of the whole day's group used there. These 

 were the diurnal coefficients proper to be used in the semidiurnal groups composing 

 each day's group. But the corresponding diurnal coefficient applicable at the times 

 of any Ardglass high or low water was easily deduced from them by taking the sum 

 of the products of the coefficients next it by the cosines of their respective distances 

 from it (considering 360° as corresponding to a tidal day). Another method was, to 

 select from the observed heights those which corresponded to the times of Ardglass 

 high water and Ardglass low water, and to treat them by the method of fourth differ- 

 ences explained in Section III. ; as these heights ought (in relation to each other) to 

 be perfectly free from the effect of semidiurnal tide and of all tides occurring at por- 

 tions of a semidiurnal tide. Using then these two methods, and adopting the mean 

 of their results when both could be applied, a number of diurnal coefficients were 

 obtained from the observations themselves. On comparing these with the diurnal 

 coefficients at the neighbouring stations, it was found that the coefficients at Courtown 

 might very well be represented by the mean of those for Kingstown and Dunmore 

 East at the same time. Accordingly, for all the times for which no diurnal tide 

 could be safely extracted from the observations, the mean of coefficients for Kings- 

 town and Dunmore East was used ; and from these, when necessary, the coefficients 

 for other times were deduced by the operation described above. The process then 

 pursued was exactly the same as in other cases, except that no correction was at- 

 tempted for rise of water. The results are the following, which differ in form from 

 preceding results only in this circumstance, that the origin of phase is the time of 

 mean water at Ardglass preceding high water, and that therefore an angle expressed 

 by a number of degrees must be added to the phase to form the argutnent of the 

 first variable term. 



