404 NEWTON S PRINCIPIA. 



the effect of which is to vitiate his results, and, therefore, 

 also, all the numerical calculations founded on them. 



This theory is certainly a wonderful step in advance. 

 The only defects are those that the imperfection of our 

 mathematical knowledge renders imperative. The results 

 show how false that assumption is on which the equili 

 brium theory is built. That theory could never lead to 

 the result that there must be, under certain circumstances, 

 low water directly under the luminary. The theory of 

 Laplace is, indeed, founded on suppositions as to the depth 

 of the sea ; but still we may expect these results to bear 

 some analogy to the phenomena we actually meet with. 

 Further, only the principal terms are considered, and thus 

 the effects on the tides caused by the difference of the 

 motions of the sun and moon are not calculated. 



(3.) The third theory may be called the wave theory. It 

 is most successful exactly where all the other theories become 

 so inapplicable as evidently to be quite useless. Its pecu 

 liar merit is the discussion of river tides and the expla 

 nation of the various phenomena produced by barriers, 

 changes of depth and breadth in the various channels 

 through which the tide has to pass. It is not altogether 

 inadequate to the discussion of certain cases of ocean tides. 

 The problems considered are of two kinds. First, the tides 

 formed in very long canals, the waters of which are acted 

 on by the forces of the sun and moon. These results will 

 be afterwards found to bear some analogy to the case of 

 certain oceans as they exist in nature, bounded by their 

 continental shores. Secondly, the tides formed in rivers 

 which are so short that the action of the disturbing bodies 

 on their waters may be neglected, and the tide may be 

 considered to be freely propagated up the river from the 

 disturbance caused at its mouth by a tidal sea. 



This theory is not to be considered as contradictory of 

 that of Laplace. Two truths cannot be opposed to each 

 other. On the contrary, Laplace s equations are required 

 in some of the investigations of this theory. The dif- 



