Prof. A. D. Bache on Tidal Observations. 349 
TABLE No. IV. * 
Showing the effect of change of moon’s parallax on height. 
Nuwmbes Mean sine2 |M’nsine 2sun’s|M’n parallax|M’n parallax|Mean height] Mean height 
of results, |™00’S declina-| declination both| correct. for | correct. for | for lesser | for greater 
4 * tion both series, series. 1 ies i parallax. parallax, 
st series, 2d series, 
| wh | 594 | 485 |. 529 659 | 074 | 
The parallax correction is taken as the cube of the parallax mul- 
tiplied by the sine of twice the moon’s declination. 
These are the principal variable terms in the formula derived 
by Mr. Lubbock, from Bernouilli’s theory of the tides, for the 
diurnal inequality, namely,* 
dh=B[A . sin 20. cos(y—)-+ sin 2 0’. cos ¥]; 
in which dh is the difference in height of the morning and even- 
ing tide, B and A are constant coefficients, 6’ is the moon’s de- 
clination and 6 the sun’s; y is a small variable to be added to the 
mean lunitidal interval to give the interval corresponding to the 
moon’s age, and g is the hour angle of the moon at the time of 
transit. ‘The second term, introducing the parallax of the moon, 
would be : 
43 : 
mt. sin 20 ;t 
TABLE No. V. 
Showing the value of coefficients deduced fr 
and mi 
minimum of sw 
om maximum sine twice moon’s declination 
n’s, and vice versa; neglecting variations due to 
cos (\v—¢) and cos. 
First six months, lhceucees< 
Second six months, ...... 
e yea 
pe eee ee eee ee 
As each day’s results are referred to the mean level of the day, 
and the mean of the low and high waters 1s taken as giving the 
height of the diurnal tide, the constant from the mean level of 
the whole should not appear in the values. In beginning these 
* Transactions al Society of London, 1836, p. 223. 
+ Lubbock’s dbo x the Tides, London, 1839. 
Szoonp Sxrizs, Vol. XIV, No. 42,—Noy., 1852. 5 
