Diurnal Tides on the Coasts of Ireland. 49 



kind of certainty into a Solar and Lunar Tide. I, therefore, supposed the tide 

 to be due to the Moon only, and made the following inferences, which I do not 

 however, consider as of high value. 



The mean of all the maximum values of the tide at High Water was found 

 to be + 0-0885 and - 00835, giving an average range at High Water of 0-1720. 



The mean of all the maximum values at Low Water was found to be 

 + 0-0820 and -0-0906, giving an average range at Low Water of 0-1726. 



If, therefore, h and I represent the ranges of Diurnal Tide at fLgh and Low 

 Water respectively, we have by equation (2) 



h = 2Msin (2 Max. Declination) x cos (?n -?,„), 

 ^= 2J/sin (2 Max. Declination) x cos (90°+ tw - /'„), 

 and consequently, by equation (3), 



J = - cot {m-i^). 



Substituting for h and I their values we find, 



0-1720 



^q-^ = cot {m - ?„) = cot (45° 6'), 



and converting 45° 6' into time, we have 



m-i„,= i" e*"; 

 but 7», at the time of High Water, is the Establishment at Castletownsend ex- 

 pressed in local time, and is equal to 4'' 17"' ; therefore 4=1" 11"". 

 Equation (4) also gives us the relation 



2Ms\n (2 Max. Declination) =: \/F+7l 



Hence, 



sm42° 0-669 



If, therefore, the Diurnal Tide at Castletownsend be supposed wholly due to 

 the Moon, it may be expressed by the formula 



-O = 0-181 sin 27< cos (m- 1*1 1"). (g) 



In this equation, ^, the Moon's declination, is to be assumed for a period preceding 

 the time of observation; but the length of this period or Age of the Tide could 

 not be ascertamed in consequence of the irregularity of the times of vanishing 



VOL. XXIII. g ^ 



