SEQUEL TO THE EPOCH OF NEW1OX. 457 



Sect, 9. Application of the Newtonian Theory to the Tides. 



WE come, finally, to that result, in which most remains to be done 

 'or the verification of the general law of attraction the subject of the 

 Tides. Yet, even here, the verification is striking, as far as observa- 

 tions have been carried. Newton's theory explained, with singular 

 felicity, all the prominent circumstances of the tides then known ; 

 the difference of spring and neap tides ; the effect of the moon's and 

 sun's declination and parallax; even the difference of morning and 

 evening tides, and the anomalous tides of particular places. About, 

 and after, this time, attempts were made both by the Royal Society of 

 England, and by the French Academy, to collect numerous observa- 

 tions ; but these were not followed up with sufficient perseverance. 

 Perhaps, indeed, the theory had not been at that time sufficiently de- 

 veloped ; but the admirable prize-essays of Euler, Bernoulli, and 

 D'Alembert, in 1740, removed, in a great measure, this deficiency 

 These dissertations supplied the means of bringing this subject to the 

 same test to which all the other consequences of gravitation had been 

 subjected ; namely, the calculation of tables, and the continued and 

 orderly comparison of these with observation. Laplace has attempted 

 this verification in another way, by calculating the results of the the- 

 ory (which he has done with an extraordinary command of analysis), 

 and then by comparing these, in supposed critical cases, with the Brest 

 observations. This method has confirmed the theory as far as it could 

 do so ; but such a process cannot supersede the necessity of applying 

 the proper criterion of truth in such cases, the construction and verifi- 

 cation of Tables. Bernoulli's theory, on the other hand, has been used 

 for the construction of Tide-tables ; but these have not been properly 

 compared with experiment ; and when the comparison has been made, 

 having been executed for purposes of gain rather than of science, it 

 has not been published, and cannot be quoted as a verification of the 

 theory. 



Thus we have, as yet, no sufficient comparison of fact with theory, 

 for Laplace's is far from a complete comparison. In this, as in other 

 parts of physical astronomy, our theory ought not only to agree with 

 observations selected and grouped in a particular manner, but with the 

 whole course of observation, and with every part of the phenomena. 

 In this, as in other cases, the true theory should be verified by its giv- 

 ing us the best Tables; but Tide-tables were never, I believe, calcula- 



