ON THE COASTS OF IRELAND. 41 



The only remaining result of the table in page 39 which deserves attention here, is 

 the difference of the times occupied by the rise of the water and by the fall of the 

 water. Jn the river stations (Limerick and New Ross) the fall of the water occupies 

 a longer time than the rise. This, as a consequence of theory, is explained in Art. 206 

 of the Tides and IVaves. At most of the other stations, the rise appears to occupy a 

 very little longer time than the fall. This, however, as it depends on the estimation of 

 the times of high and low water, is subject to great doubt : the terms upon which such 

 difference depends will be investigated with great accuracy in Sections X. and XVI. 



Section VIII. — Semimenstrual inequality in time, proportion of solar and lunar effects 

 as shown hy times, and apparent age of tide as shown hy times ; from high ivater 

 and from low water. 



The interval from the moon's transit over the meridian to high water (and similarly 

 from the moon's transit over the six-hour meridian to low water) is theoretically ex- 



M 

 pressed by E-f F, where E is a constant, and tan2F= g— — ? & being the hour- 



l + j^cos2d 



angle of the moon from the sun. The declinations, &c. are supposed here to have their 

 mean values. Investigating from this the expression for F, integrating from ^=0 to 



f>=2' and dividing by g' we obtain the value of the mean of large intervals ; performing 



If 

 the same operation from ^^^ to ^=t, we obtain the value of the mean of small in- 



tervals. The difference which will be found =~'m'( I+oIm/ /' ^^ the difference be- 



tween the 2nd and 3rd columns or between the 5th and 6th columns in page 39, ex- 

 pressed in arc ; or, as 2'r of arc in the estimation of & and F correspond to a tidal day 

 of 1488°*, if we put i for the number of minutes in that difference, the equation is 



7r*M*V+9 AM/ /— '^1488' 

 From this we obtain 



S 



^x{i-Kn^)'}"^^''^y' 



M~"1488 



S 

 and then the maximum value of F in arc will be found *by making sin2F'=j^j and 



converting F' into time by the proportion stated above. Thus the following Table is 

 formed. 



MDCCCXLV. 



