224 
MR. LUBBOCK ON THE TIDES. 
log tan 21° = log {A) = 9-5841774. 
(T) = 2 ’ 605 - 
When the discussion was instituted with reference to the transit immediately pre- 
ceding the time of high water, the value of log (A) came out 9-5784858. 
I find, moreover. 
D — 16 f ‘-69 (E) = 4-43 log (E) = -6468993. 
The semimenstrual inequality calculated from Bernoulli’s expression is very similar 
to the inequality deduced from observation. See Table XXVIII. and Plate XVIII. 
The mean interval in the former discussion corresponded to the moon’s transit at 
2 h ; now it corresponds to the moon’s transit at 26 m . The constants now obtained 
differ so little from those obtained before, that the tables calculated by Mr. Jones, 
and given in my last paper*, are applicable, making the moon’s transit at 30 m corre- 
spond to <p = 0, for the moon’s transit at l h 30 m <p = 15°, &c. 
The calendar-month inequality is complicated in its nature ; it results from the va- 
riations in the declinations of the luminaries, and in the sun’s parallax. Table XXIX., 
calculated by Mr. Jones, offers a comparison in this respect between theory and ob- 
servation 'f v . The results in this table have been laid down in diagrams (see Plate XIX.), 
in order that the nature of the agreement may be better understood. The terms 
{ 
fcos n 
3m R P 3 
1VI 
sin 2 h -j- 
3 m 1 R P 13 
sTm 
sin 2 h' 
}> 
occur in the expression for the height (see p. 222.), substituting of course for 
1 — cos 2 l 
a certain constant, to be determined from the observations, which amounts to intro- 
ducing an inequality in the height 
= C {{A) sin 2 h + sin 2 S'}, 
C being a constant ; but these terms appear to be insensible. 
The calendar month inequality in the height may also result partly from the fluc- 
tuations in the barometer. According to Mr. Daniell^, the following are the heights 
of the barometer in the different months of the year: 
inches. 
January 29-921 
February 30-067 
March 29-843 
inches. 
April 29-881 
May 29-898 
June 30-020 
inches. 
July 29-874 
August 29-891 
Sept. 29-931 
inches. 
October 29774 
November 29 7/6 
December 29"693 
Hence, in order to arrive at the utmost precision in the comparison, it might, per- 
* Philosophical Transactions, 1836, p. 58. 
t The sun’s declination is that for the middle of the month, and the moon’s declination is given for each 
category in Table I. 
1 Meteorological Essays. 
