OF THE TIDES IN THE PORT OF LONDON. 19 



bodies were referred to their true causes. Indeed, I believe the instances are compa- 

 ratively few in the history of philosophy, in which the general laws of the phenomena 

 have been pointed out by the theory before they had been gathered by observation. 

 The laws of the tides, thus empirically obtained, may be used either as tests of the 

 extant theories, or as suggestions for the improvement of those portions of mathema- 

 tical hydraulics on which the true theory must depend. And this is the way in which 

 we are most likely to discover how the theory must be applied. The problems 

 regarding the motion of fluids, which we are unable to solve directly, are far too 

 numerous to allow us to be surprised that we should be obliged to desert the a priori 

 road in this case. The phenomena of waves, the motions of water in tubes, in canals, 

 in rivers, the motion of winds, the resistance of fluids to bodies in motion, are all 

 cases in which we are yet far from having drawn our analytical mechanics into a 

 coincidence with experiment, or even a tolerable proximity to it. The theoretical 

 aralysis of the tides is, at present, in an equally imperfect state. It is not at all im- 

 probable that, as in many other cases, this problem in the mechanism of the solar 

 system (for such it is) may be found in the end less complex and difficult than similar 

 problems concerning the motions of smaller masses ; but the problem remains still 

 to be solved, or at least it remains still to be shown that the solution has been approxi- 

 mated to. I shall therefore here proceed to examine the empirical laws of the tides 

 of the port of London, as they appear from the records of the nineteen years of 

 observations above mentioned. 



Chap. I. On the Empirical Laws of the Time of High Water. 



The point which I have first to determine is, the manner in which the time of high wa- 

 ter is affected by the right ascensions, declinations, and parallaxes of the sun and moon. 

 For this purpose I shall have to consider the establishment, the semimenstrual inequality, 

 the corrections for lunar parallax, lunar declination, oxi^ solar parallax and declination. 



1. The Establishment. — The vulgar establishment of any port is the interval of time 

 by which the time of high water follows the moon's transit on the day of the new and 



full moon. But it is the mean value of this interval of time which we must here employ, 

 in order to simplify our discussion. This is what Laplace calls t\\Q fundamental hour of 

 the port : I have termed it, in a former paper on this subject, the corrected establishment, 

 since it is the lunar hour of high water, freed from the semimenstrual inequality. Its 

 value at the London Docks is I*' 26™, by the mean of all the observations. 



2. The Semimenstrual Inequality. — The interval of tide and moon's transit is affected 

 by a considerable inequality, which goes through its period twice in the space of one 

 month : it may be considered as depending upon the moon's distance from the sun in 

 right ascension ; or, which is the same thing, on the solar time of the moon's transit. 

 It has been examined by Mr. Lubbock, and shown to agree, with remarkable exact- 

 ness, with the formula, 



, , // sin 2 (<p — a) 



tan 2 (^ — X) = — ^/ + ^cos2(f-«)» 



d2 



