OF THE TIDES IN THE PORT OP LONDON. 17 



established, it would then, no doubt, become highly probable that the simplifications 

 hypothetically introduced into the natural state of things were not such as materially 

 to alter the general course of the phenomena. 



But this has not been done by any of the theoretical writers above referred to. Un- 

 doubtedly most of them have undertaken to show that some of the known laws of 

 the facts are accounted for by the theory, and that the measures of some of the phe- 

 nomena agree with those which theoretical calculations give. But this has been 

 executed only with respect to a few of the circumstances of the case. It has not been 

 shown, by any writer, that the general course of the effects produced upon the tides, 

 by the changes of position and distance of the heavenly bodies, is such as, according 

 to the mathematical reasoning, it ought to be. In short, the mathematicians who 

 have treated this subject have not completed their task by giving rules for the calcu- 

 lation of tide tables, and showing that the tables so produced agree with the general 

 course of the observations in all essential circumstances. 



The task just mentioned would consist of two parts ; the theoretical deduction of 

 the effects produced in the tides by changes of distance and position of the sun and 

 moon ; and the examination of the laws which such changes appear to follow in tlie 

 observations ; with a comparison of the two sets of results. The latter part of the task 

 had not been executed, so far as 1 am aware, by any one, previously to Mr. Lubbock's 

 discussion of the Tides of the Port of London, inserted in the Philosophical Transactions 

 for 1831 ; and that memoir is hitherto the only published record of such an examina- 

 tion. The establishment, on theoretical grounds, of rules for the calculation of tide 

 tables, has been attempted by Bernoulli and by Laplace. The methods recommended 

 by the former are probably the foundation of those at present used by the calculators of 

 such tables. The method of Laplace is complicated, and would be very laborious in 

 practice. He has unfortunately, as appears to me, not put his process in such a form 

 as to give a principal term, with smaller corrections for declination, parallax, and 

 other circumstances if necessary, to be combined with the principal term. When the 

 results of such an investigation are not made to assume this shape, the comparison of 

 the formula with observation becomes a work of very repulsive labour and trouble. 



It has already been stated, that some of the published tide tables are found to be 

 not very incorrect when compared with observation. If any tide tables were so good 

 that they might be considered as representing the general laws of the actual pheno- 

 mena, we might discuss such tables, and compare them with theory, in the same 

 manner as if they were the records of observation ; and with this additional advan- 

 tage, that they would be free from the effect of the accidental causes, as wind and 

 other circumstances, which produce irregularities in the actual tide. Nor would it be 

 difficult, by such a discussion, to discover the rules which are followed in the con- 

 struction of such tables. 



It mayj however, be doubted whether there are any tables which are worth this 

 trouble. Original tide tables are very few : I know of none except those which are 

 published for Liverpool, and those for London. The former are remarkably exact ; they 



MDCCCXXXIV. D 



