OF THE TIDES IN THE PORT OF LONDON. 41 



and (sin- S — sin^ A) C,) which term is not given by the theory; besides giving another 

 term which coincides with the one given by the theory. The latter term depends on 

 the hour of the moon's transit, and vanishes twice in the course of a semilunation ; 

 the former term in each case is independent of the time of the moon's transit, and 

 depends only on the parallax and on the declination. 



Now F and Q' are the corrections to which & — a' is subject, where ^ is the hour- 

 angle of the tide from the moon. In the theory, ?i' is supposed to be constant, so that 

 the variation of & — X' alone affects ^. 



But since ^' = x' + ip — ^0? if ^' were affected by an inequality arising from pa- 

 rallax equal to (P — p) A, we should have, taking the theoretical value of the variation 

 of &' — K due to this cause, and adding it to the value resulting from the common 

 theory, the whole variation of ^ = (P — 7?) (h. -f B sin 2 (^ — y) Y 



In like manner, if ?l' were affected by an inequality equal to (sin' S — sin- A) C, and 

 ^ — ?^' by the inequality resulting from the theory, we should have for the whole ine- 

 quality in & arising from declination, (sin^^^ — sin* A) {C -}- D sin 2 ((p — y)}. 



Now these expressions agree with those which we have obtained from observation, 

 excepting that we have other arcs in the place of the arc a. It appears, therefore, 

 that the empirical laws will be verified by supposing X' to be affected by inequalities 

 depending upon the parallax and declination of the moon, but having an epoch differ- 

 ent from that of the semimenstrual inequality. 



The quantity X' is the hour-angle by which the lunar tide follows the high water of 

 the lunar spheroid of equilibrium. It appears, therefore, that the physical statement 

 of the result just obtained is this, that the distance at which the actual elevation of 

 the waters follows the position of equilibrium, varies as the parallax and declination 

 of the disturbing luminary vary. 



This distance was, in the theory, assumed to be constant ; but there is no obvious 

 physical reason why it may not change with changes of the force by which the fluid 

 spheroid of equilibrium is determined. This distance, or lagging, of the pole of the 

 watery spheroid behind the place which it would occupy if the earth and luminary 

 wer^ at rest, is owing to the resistance of the shores and of the parts of the water 

 amongst each other ; and its amount is determined by the amount of these resistances. 

 But we are very far from being able to trace the mode in which these causes operate, 

 so as to be entitled to affirm that changes, and even small changes, in the force or 

 velocity of the disturbing body, may not produce corresponding changes in the extent 

 of this lagging. 



In fact, there seems to be good reason to suppose, from other circumstances, that the 

 force and velocity of the disturbing body do affect the distance by which the actual 

 elevation lags behind the elevation of equilibrium. For X and a', the lagging in the 

 case of the solar and of the lunar tide, are quite different ; the former (for the London 

 Docks) being 3^ 25'", the latter 1^ 25" *=. It is true that this difference of 2^' is, in the 



* See Mr. Lubbock's Memoir, Philosophical Transactions, 1831, p. 387. 

 MDCCCXXXIV. G 



