218 
MR. LUBBOCK ON THE TIDES. 
for 1 834, Part I. The nature of this inequality, which has not been yet understood, is 
clearly shown in this paper. When the moons transit immediately preceding the 
time of high water is taken as the argument , this inequality arises chiefly from the 
variation in the interval between successive transits of the moon*. 
I shall now endeavour to explain Bernoulli’s solution of the problem, in order to 
render intelligible the comparisons between theory and observation which accompany 
this paper. Let us allow for an instant, that were the earth a perfect sphere covered 
throughout by a fluid, the fluid would assume the same form at any given instant as 
it would do if the forces then acting upon each particle were invariable in magnitude 
and direction. The actual approximation to this state of things is greater in the 
southern hemisphere than in northern latitudes, and on our coasts. Moreover, 
let us suppose that the tide-wave is subject to this law at the Cape of Good Hope, or 
in some region still more remote, and that it is propagated along the Atlantic Ocean 
and round our island, “ according to the stamp first set upon it by the moon’s pres- 
sure.” Upon these suppositions, which are virtually those of Bernoulli, and which 
may be said to constitute the equilibrium-theory, it is easy to calculate the variations 
in the time and height of high water at any given place, if the time in which the 
tide-wave is propagated does not vary. The results which are contained in this paper 
are intended to assist in determining how far the phenomena accord with these sup- 
positions. 
The tide-wave travels from the Cape of Good Hope to Gibraltar in about twelve 
hours, from Gibraltar to Edinburgh in about twelve hours, and from Edinburgh to 
London in about the same time. I have shown that the retard at Brest is consider- 
ably less than at London ; and there can be no doubt that at the Cape of Good Hope 
it is less than at Brest. 
Bernoulli’s theory may be considered as proceeding upon these principles. Ber- 
noulli calculated tables for some of the corrections, but he did not explain with 
sufficient precision the manner in which these tables must be used. I allude here 
particularly to Bernoulli’s parallax correction for the interval, p. 165. He says, 
“ Pour se servir de cette table, il ne faudra plus qu’ajouter aux nombres des six der- 
nieres colonnes l’heure moyenne du port.” But it is not sufficient to increase the argu- 
ment of the table, which is the angular distance between the luminaries, by twenty 
degrees, as Bernoulli supposes, in order to accommodate the table to the reasoning 
in ]>. 161, where he says, “ Et enfin on trouve une conformite exacte entre les deux 
points en question, en donnant un jour et dcmi au retardement des marges, c’est-^-dire, 
cn supposant que l’6tat des marges est tel qu’il devroit etre naturellement, un jour 
et demi plutot.” Although this supposition is admissible, at Brest, for example, 
and although Bernoulli’s table would I think afford the true correction in the in- 
terval between the moon’s transit and the time of high water, in the case of a perfect 
sphere covered by an ocean, by applying it to the transit of the moon immediately 
* See Table XXIII. 
