ON THE COASTS OF IRELAND. 43 



But the value in page 35 is deduced from the comparison of high and low tides, in 

 which the stream of tides, &c. is different. The second apparent alteration can take 

 place only where the tide has arrived at such localities that the second order of the 

 vertical oscillation produces sensible terms. I was at first misled by the plausibility 

 of this reasoning. 



Its fallacy, or rather its error, will appear from the following considerations. The 

 semimenstrual inequality in time which theoretically is proper for giving the value 



S 

 of j^ is that which depends only upon those differences of time which are caused by 



difference in the relative positions of the sun and moon, when the magnitudes of the 

 tides are exactly the same. But when there also exists a difference of time caused 

 by the difference of magnitude of the tide (having its maximum nearly at the time 

 of evanescence of the proper semimenstrual inequality), then these two differences or 

 inequalities are combined, forming a single inequality whose time of evanescence is 

 different from those of both the original inequalities, and whose magnitude is greater 

 than the magnitude of either. Thus it appears that the gross semimenstrual ine- 



S 

 quality in time must not be used for estimation of j^- A correct application of these 



principles, and a consequent harmony of results, will be seen in Section XIV. 



S 

 At every station except MuUaghmore, the value of ^ in the table above appears 



greater at low water than at high water. This evidently depends upon the difference 

 in times (as affected by magnitude of tide) for low water and for high water, which 

 is combined as above stated with the proper semimenstrual inequality. 



Mr. Whewell, in his invaluable memoirs on cotidal lines, stated that there were 

 great contradictions in the accounts of the establishment of Ballycastle. The num- 

 bers above serve in some degree to explain this. The semimenstrual inequality alone, 

 comparing observations taken when its value was maximum positive with those taken 

 when its value was maximum negative, would produce nearly four hours of uncer- 

 tainty. More than half an hour (see the table in page 19) might be added by the 

 diurnal tide. 



I shall now proceed with the age of tide as shown by the times. The method em- 

 ployed was the same as for the heights, in forming the table in page 38. The times 

 were ascertained at which the interval from moon's transit over the meridian to high 

 water (and similarly the interval from moon's transit over the 6-hour meridian to 

 low water), corrected for diurnal tide, agreed with the mean interval for high water 

 (or for low water) in page 39. These times were then compared with the times at 

 which the moon's hour-angle from the sun was 0^ 6^ 12*^ 18^ ; namely, June, 22*^9^, 

 30^ 20^; July, 7^ 19^ 14'' 21^ 2^ 23^ 30^ 16^ August, 6^ 4^ 13*^ 5^^ 20^1 16^ 

 The high and low waters were treated separately. At Ballycastle low water six re- 

 sults only were obtained ; for all the other determinations seven or eight results were 

 compared. Thus the following Table was formed. 



G 2 



