Diurnal Tides of the Coasts of Ireland. 429 



The meau ratio of S to M here found, shows that the sun's 

 effect on the diurnal tide is somewhat more than half the moon's 

 effect. In Mr. Airy's discussion of the semidiurnal tides of 

 Ireland, the following mean ratios of S to M are found* : — 



Page 35 . . 0-33 deduced from Heights. 



... 106 . . 0-34 



... 42 . . 0*35 deduced from Times. 



... 108 . . 0-38 



Mean . . 0-35 

 According to the statical theory of the tides, the ratio of the 

 solar to the lunar effect should be the same for the diurnal and 

 for the semidiurnal tides; but according to the dynamical theories 

 of the tides, the coefficients in the solar and lunar tides depend in 

 a different manner on the depth of the sea, and therefore the 

 ratios deduced from the diurnal and semidiurnal tides should 

 be different. 



According to Mr. Airy's theory of tides with friction, the 

 ratios of the solar to the lunar coefficients in the semidiurnal 

 and diurnal tides are given by the following equations : — 



n'^Z> k 



Diurnal solar coefficient _ ^ (P_ _g b ,r>^ 



Diurnal lunar coefficient" M ^ D^ ^ -^^ '•'■ * ^^ 



Semidiurnal solar coefficient _ ^ (P_ ^ ^ ,^^ 



Semidiurnal lunar coefficient ~ M D^ ^ _ A " 



9 b 

 In these equations — 



S, M are the masses of the sun and moon ; 

 d, D are the distances of the moon and sun ; 

 n, 7i' are the angular velocities of the sun and moon ; 

 k is the mean depth of the sea ; 

 b is the mean radius of the earth ; 

 ff is the force of gravity. 

 Substituting the known values of all the quantities, excepting 

 k, we find, — 



orv , ^- 000323-4^ 



Solidiurual coefficient _«.^« ^. /iq\ 



Lunidiurnal coefficient n-nnS4.i" —4. — ' 



b 



* Transactions of Royal Society, 1845. 



