MR. LUBBOCK ON THE TIDES. 
101 
C and G being constant for any given place. Probably the amount depends also 
upon the moon’s parallax, and then the expression for d h will be 
pin 
C X Jjj ’jiyi sin 2 }>' (for a given transit a.m. or p.m.). 
But this expression will not afford results agreeing with those which I have obtained 
from the observations at Liverpool if the declination of the moon be employed be- 
longing to the time of the transit A ; and it is necessary to employ the moon’s decli- 
nation at some time previous ; that is, several days before the high water under 
consideration. This is not at variance with what is stated in the Exposition , except 
that, although Laplace considers the two waves separately*', he has not, I think, 
referred distinctly to the change in the epoch for different places, or to the difference 
between the epoch of the original diurnal and semidiurnal waves, which produce the 
derived tides observed on our coasts. If, however, the diurnal inequality- wave 
travels more slowly than the semidiurnal inequality-wave, the epoch also will be 
different, and thus it may depend upon the moon’s declination several days earlier. 
If this view be correct, the diurnal inequality of high water has a maximum (geo- 
graphically) at those places on the coast at which the diurnal inequality-wave and 
the semidiurnal inequality-wave arrive simultaneously, and there will be places inter- 
mediate at which the diurnal inequality of high water is imperceptible, but where the 
diurnal inequality of low water is a maximum. This theory agrees with observation 
in giving no difference in the diurnal inequality for upper or lower transits. 
The diurnal inequality in the interval at Liverpool is inappreciable ; the diurnal in- 
equality in the height has been laid down in Plate III. from the approximate expression 
d h = B [A sin 2 cos — <p) - j- sin 2 h' cos (for transits A.) 
The moon’s declination W was taken from Table X., where it is given for the time of 
the moon’s transit A, but the curve evidently requires to be shifted more to the right; 
it is difficult to decide exactly how much. In the observations of the height at Liver- 
pool in May 1836 (see Plate IV.) the diurnal inequality vanishes on the 15th, the 
moon having crossed the equator on the 11th. If we consider that the theory curve 
requires to be shifted to the right about two hours, this would amount to referring 
the diurnal inequality at Liverpool to the moon’s declination about four days pre- 
viously. 
Mr. Russell has extended the discussion of the London observations given in my 
last paper by employing those made between 1802 and 1807, and those between 1827 
and 1835, omitted before, so that we have now obtained tables similar to those con- 
tained in my last paper from the concurrence of no less than 24,592 observations. 
* J’ai determine la grandeur de ce flux et l’heure de son maximum dans le port de Brest. J’ai trouve un 
cinquieme de metre [7 ’4 inches] a fort peu pr&s pour sa grandeur ; et un dixieme de jour environ, pour le temps 
dont il precede a Brest, l’heure du maximum de la maree semidiurne. (Exposition du Systeme du Monde, 5 e ed., 
p. 286.) 
