OF THE TIDES IN THE PORT OF LONDON. 43 



the line of the mean moon, to produce the inequality which arises from parallax ; 

 another auxiliary moon, by moving north and south in the meridian of the moon 

 to produce the inequality which arises from declination. Now the tides produced 

 by all these moons will require some time for the operation of the forces to take 

 effect ; that is, they will correspond to positions of the moon at a time anterior to 

 the actual time. But there seems not to be the smallest reason to conclude that 

 these anterior times will all be anterior by the same interval : the contrary, rather, is 

 obvious. It is clear, for instance, that a tide oscillating- in a north and south 

 direction in the Atlantic and Pacific Oceans, will take a different portion of time to 

 obey the forces which produce it, from the general tide which travels from east to west 

 round the earth in virtue of the diurnal motion, and impinges against the broad sides 

 of the great continents. We may therefore expect to find the epochs of all these 

 partial tides different ; and as eveiy separate term in the expression of an inequality 

 may be considered as representing a different tide, there will be nothing inconsistent 

 with the best physical notions we can yet form on the subject in finding the epochs 

 of the arguments of every separate term of our formulae different from one another. 



It appears, then, that though the equilibrium theory, taken in combination with 

 the preceding considerations, may very probably give us the general form of the 

 terms, and the variable part of the arcs on which they depend, the constant epoch 

 which occurs in each of these arcs, and which determines when the inequality 

 vanishes and reaches its maximum, will probably have to be determined in all cases 

 by observation. 



I will observe further, that not only the epochs, but the coefficients of each of these 

 terms will probably have to be determined for the most part from observation. For 

 the tides, though in the theory to which we refer considered as representing positions 

 of equilibrium of a fluid, are in fact the results of its motion ; and it is not at all clear 

 that the elevation which results from the motion will be equal to the elevation which 

 would be requisite for equilibrium. It is true that there must be always a tendency 

 to this equilibrium-elevation so long as the actual elevation is greater or less than 

 that ; but this tendency may never fully appear in the circumstance of the tide ; since 

 the tide-producing forces have to supply also a residue of force which must be em- 

 ployed in producing the motion of the fluid. 



Moreover, the motion of the fluid is of the nature of an oscillation, so that series 

 of increasing and diminishing oscillations at intervals of a half-day, a day, and other 

 intervals, pass through any given part of the ocean. Now it is physically, not only 

 possible but certain, that each oscillation in each series is affected by those which 

 precede it in the same series, and affects those which succeed it, so that their relative 

 magnitude is different from what it would otherwise be. And the effects thus pro- 

 duced will depend upon the depth of the ocean, the form of its shores, and other 

 causes, of which it is impossible to estimate the result a priori. 



Even in the case of the semimenstrual inequality, which in its form agrees so 



g2 



