Royal Society. 217 



of the world, and to account for their varieties and seeming anoma- 

 lies. The first scientific attempt that was made to compare the de- 

 veloped theory with any extensive range of observations, was that of 

 Daniel Bernouilli in 1740: the subject has since been pursued by 

 Laplace and Bouvard, and still more recently by Mr. Lubbock. But 

 the comparison of contemporaneous tides has hitherto been unac- 

 countably neglected : and to this particular branch of the subject the 

 researches of the author are in this paper especially directed j the 

 principal object of his inquiry being to ascertain the position of what 

 may be called cotidal lines, that is, lines drawn through all the adja- 

 cent parts of the ocean where it is high water at the same time ; as, 

 for instance, at a particular hour on a given day. These lines may 

 be considered as representing the summit or ridge of the tide-wave 

 existing at that time, and which advances progressively along the 

 sea, bringing high water to every place where it passes. Hence the 

 cotidal lines for successive hours represent the successive positions of 

 the summit of the tide-wave, which in the open sea travels round the 

 earth once in twenty-four hours, accompanied by another at twelve 

 hours' distance from it, and both sending branches into the narrower 

 seas. Thus a map of cotidal lines may be constructed, at once ex- 

 hibiting to the eye the manner and the velocity of all these motions. 



Although the observations on the periods of the tides at different 

 places on the coast and different parts of the ocean, which have been 

 at various times recorded, are exceedingly numerous, yet they are 

 unfortunately for the most part too deficient in point of accuracy, or 

 possess too little uniformity of connexion to afford very satisfactory 

 results, or to admit of any extended comparison with theory. With a 

 view to arrive at more correct conclusions, the author begins his in- 

 quiry by endeavouring to determine what may be expected to be the 

 forms of the cotidal lines, as deduced from the laws which regulate the 

 motions of water : and he proceeds afterwards to examine what are 

 their real forms, as shown by the comparison of all the tide observa- 

 tions which we at present possess. 



The paper is divided into five sections. In the first the author 

 treats of cotidal lines as deduced theoretically from the known laws 

 of the motion of fluids. On the supposition that the whole surface of 

 the globe is covered with water, the cotidal lines would coincide with 

 the meridians, and would revolve round the earth from east to west 

 in something more than twenty-four hours, with a velocity of nearly 

 1000 miles an hour at the equator. The form and the regularity of 

 these lines would be materially affected by the interposition of land 

 in different parts of this ocean, whether in detached islands, or 

 groups of islands, or large continents, occupying a considerable por- 

 tion of the surface. In these cases the primary wave will be broken, 

 deflected and variously modified, so as to give rise to secondary or 

 derivative tides, sometimes separating into branches, and producing 

 points of divergence ; sometimes uniting at various places, or points 

 of convergence j and at other times producing, by more complex 

 combinations, various phenomena of interference, and other appa- 

 rently anomalous results. Such is the general character of the tide- 

 Third Series. Vol. 3. No. 15. Sept. 1833. 2F 



