224- Royal Society. 



teen years of observations which have been discussed by Mr. Dessiou, 

 under the direction of Mr. Lubbock, and which include 13,073 ob- 

 servations. His first object is to determine the manner in which the 

 time of high-water is affected by the following conditions, namely, the 

 right ascensions, declinations and parallaxes of the sun and moon ; 

 for which purpose he considers at some length, first, the establish- 

 ment ; secondly, the semimenstrual inequality ; thirdly, the correc- 

 tions for lunar parallax ; fourthly, the lunar declination ; and lastly, 

 the solar parallax and declination. He next discusses the empirical 

 laws of the height of high-water ; which he observes will be affected 

 in the same manner as the periods of the tides, by a semimenstrual 

 inequality, by corrections for lunar parallax and declination, and by 

 a solar correction ; and concludes by giving a formula for computa- 

 tion which comprehends all these elements. He then enters into a 

 comparison of the results thus obtained with the theory of Daniel 

 Bernoulli, according to which the waters of the ocean assume nearly 

 the form in which they would be in equilibrium under the actions of 

 the sun and moon, on the supposition that the pole of the fluid sphe- 

 roid follows the pole of the spheroid of equilibrium at a certain angular 

 distance ; and that the equilibrium corresponds to the configuration 

 of the sun and moon, not at the moment of the tide, but at a previous 

 moment, at which the right ascension of the moon was less by a 

 constant quantity. The author thinks, however, that it would not be 

 safe to attempt to deduce from the preceding investigations any ge- 

 neral views concerning the laws of the tides, for it is not likely that the 

 discussion of observations at any one place should exhibit clearly the 

 true principles of the theory, especially as, in the present case, it so 

 happens that the phenomena of the tides at London are in some 

 measure masked by a curious combination of circumstances, namely, 

 by the mouth of its river being on the side of an island, turned away 

 from that on which the tide comes, and so situated that the path of 

 the tide round one end of the island is just twelve hours longer than 

 round the other. 



In consequence of the time required to transmit to any port the 

 general effect of the tide-producing forces being different from the 

 time required to transmit to the same port the effects of particular 

 changes in these forces ; or, in other words, from the epochs of the 

 changes due to parallax and declination being different from the epoch 

 of the semimenstrual inequality, it follows that although the general 

 form of the terms, and the variable part of the arcs on which they de- 

 pend, may be deduced from the theory of equilibrium, yet 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. 



In conclusion, the author gives a statement of what appears to 

 him to be the most important steps from which any great improve- 

 ment to our knowledge on the subject of the tides may be hoped ; 

 and recommends the discussion of extensive collections of observa- 

 tions made at a variety of places, in a manner similar to what has 

 been done by Mr. Dessiou with regard to those at London ; and the 



