344- The Rev. Brice Bronwin on the Theory of the Tides. 



planet to raise the water; we see from what has been done in 

 these papers that the passage of the planet over the meridian 

 and the time of high water will not necessarily coincide, and 

 that the retardation or acceleration of the tide is a necessary 

 consequence of the mathematical theory itself. Moreover, we 

 see tliat the retardation or acceleration is not a constant quan- 

 tity ; but the variable part of it is small, and may be insensible. 



The four arbitraries flg' ^n ^^2» ^v which have been intro- 

 duced by integration, depend upon the depth of the sea, and 

 the form of the shores ; or, in other words, they depend upon 

 the closed surface of the water, and must be determined for 

 each particular place by observation. Hence the theory and 

 observation will not be at variance, as heretofore, with regard 

 to the height of the tide at any particular place, or in any 

 particular latitude, when these arbitraries are properly deter- 

 mined. 



The variation Sco has been made a complete variation rela- 

 tive to the quantities 9, ot, and r; but the terms depending on 

 V have been neglected ; not necessarily, but for the sake of 

 simplicity. It is possible, Itowever, small as this quantity is, 

 that it might make a sensible alteration in the form at least of 

 the coefficients as functions of 5 ; but this is a matter of no 

 practical importance. 



Heretofore the direct action of the planet has alone been 

 considered in this theory ; whereas the simple consideration 

 that the water will turn round an island or headland, and 

 (juite change or even reverse its course, and this perhaps in a 

 very short time, and with little or no variation in the velocity, 

 in despite of the action of the planet, shows how very small a 

 part of the cause its direct action is. 'J'he height of the tide, 

 therefore, in particular places has been made to depend on a 

 cause which produces directly scarcely any part of it ; and the 

 horizontal displacements and velocities, which ought chiefly 

 to be considered, have been entirely neglected. This has no 

 doubt been owing to the extreme difficulty of taking account 

 of them. 



The difficulty experienced in putting the coefficient of 

 cos ((p— jS,) under a suitable form, owing to our not being able 

 to estimate with sufficient precision fche relative magnitudes 

 of the quantities which it contains, renders it very difficult to 

 say what alteration this theory will make in the height of the 

 tide as it depends on the declinations of the planets, and it is 

 possible that the coefficient may vary greatly in different 

 places. 



It will be seen that in the coefficients of both cos2((p— /Sj) 

 and cos (f — /3,) this theory makes a considerable alteration as 



