100 
MR. LUBBOCK ON THE TIDES. 
in sign, and I have taken the mean of the whole for the result, as in the following 
example. 
Moon’s transit A. — Liverpool, Jan. 
July 
h m ft. 
0 30 A.M. — -631 
. . . P.M. +'57 
substituting 
mean of all 
a.m. +'60 with proper 
p.m. — '42 J 
sign 
ft. 
-'56 
+ '56 
+ '56 
-'56 
4)2-22 
•56 
In the comparison of the heights in Plates I. II. and III. the London corrections 
have been multiplied by 1*7, that being the ratio of the quantities (E) for London 
and Liverpool, agreeably to the remark made in my last paper, p. 223. As the Lon- 
don discussion contained in my last paper was instituted with reference to transit B, 
and this discussion of the Liverpool observations has been made with reference to 
transit A, and as the tides which correspond to P.M. transits B correspond to A.M. 
transits A about twenty-five minutes less, in comparing our London and Liverpool 
results in all the Plates it was necessary to change the epoch, or to place the London 
corrections more to the left by half an hour, and to substitute in Plate III. for the 
London results corresponding to transits P.M. those corresponding to transits A.M. 
The diurnal inequality therefore, as it is laid down in Plate III. for London and 
Liverpool, has reference to the same tide or semidiurnal wave, making high water at 
London about fifteen hours later than at Liverpool. 
I have already remarked that the laws to which the wave producing the semi- 
diurnal inequality is subject, agree remarkably with Bernoulli’s theory. The equi- 
librium theory also implies the existence of another wave producing a diurnal in- 
equality. 2 ip — 2 <p and 2 -p are the arguments of the semidiurnal inequality, p — <p 
and p °f the diurnal inequality. If we suppose the diurnal inequality- wave to move 
with a different velocity from the other, the diurnal inequality in the height may still 
be represented by the expression 
d h = B {A sin 2 cS cos (+ — <p) + sin 2 V cos p}, 
and may be calculated by means of Tables X. and XL, h being the sun’s declina- 
tion, and cf that of the moon, but the constants which accompany p and <p will be 
different from those which accompany 2 p and 2 <p ; and if we consider the constants 
to be included in the quantities p and <p, at high water, cos p may no longer be nearly 
equal to + 1 in the last expression, but it will nearly equal + some other constant, 
supposing the angle p still to increase by 180° in passing from one high water to the 
next ; and the diurnal inequality, if the smaller term due to the sun’s declination be 
neglected, may be represented approximately by 
G tan S' 
d p = y + A CQS 77 . d h— Csin 2 S' (for a given transit a.m. or p.m.), 
