ON THE COASTS OF IRELAND. HI 



mula in Section X. undergoes when the magnitude of the range is altered. Thus, the 

 maximum and minimum intervals of sea-tide (which are the objects of our search) 

 occur at the times (corrected forage of tide) when the moon's hour-angle from the 

 sun is 3^, 9^, &c. But from hour-angle 9^> to hour-angle 12^^ the range of tide is in- 

 creasing: the modification of time of station-tide as related to time of sea-tide is 

 therefore increasing; a second inequality of time is therefore combined with the first, 

 having a different time of vanishing: the time of vanishing of the compound in- 

 equality is therefore different from that of the first inequality, and the maximum mag- 

 nitude of the compound inequality is different from that of the first. And this pro- 

 duces its full effect if we make our divisions of groups with reference to the time of 

 vanishing of the compound inequality. But if we make our divisions strictly at the 

 times when the first inequality ought to vanish_, then^ though every individual time 

 be affected by the second inequality, yet there are the same number of instances 

 affected in the same way on opposite sides of our places of division, and their effect 

 disappears in the final result. But as the full compound effect is not used for our 

 final result, conversely we cannot from our final result infer the maximum magni- 

 tude of the full compound effect, or the maximum value of the semimenstrual in- 

 equality in time. 



These considerations appear to be deserving of the utmost attention in investi- 

 gating the most important single result which can be deduced from the tides, namely 

 the proportion of the hydrodynamical effects of the sun and the moon. 



S 



The mean of all the values of rj in page 108 is 0*38. It is probable that, on at- 

 tending more scrupulously to the age of the tide at the different stations, results 

 would have been found agreeing more closely with each other : but I think it likely 

 that the mean would scarcely have been altered. 



With regard to the apparent age of tide obtained from times, we must com- 

 pare the numbers in page 108 with those in page 44. The general result of the com- 

 parison is, that the mean of the opposite ages deduced from high and low water 

 agrees with that deduced from the analysis as nearly as can be expected (where a 

 small error in the estimated time of high or low water would produce a great effect 

 on the resulting age). They agree in giving a small apparent age at Port Rush and 

 Ballycastle. The ages deduced from range agree also in this. Now this result* is 

 exactly that which would follow from the supposition that a tidal wave with a large 

 range travels more quickly over the shallow bottom than one with a small range : 

 and that this holds not for the phase of high water or low water only, but for the 

 zero of the angle p. Or it would follow from the supposition that a wave of short 

 period travels more quickly than one of long period (the tidal day near conjunction 

 being shorter than that near quadrature). Neither of these points has been esta- 

 blished by theory ; but the former appears to be very probable. 



* Tides and Waves, Art. 463. 



