DISCUSSION OF TIDES IN BOSTON HARBOR. 45 
A is the mean time of the moon’s upper transit over the meridian preceding the Washington 
meridian 2.4 hours, and is obtained from page 332 of the American Ephemeris by interpo- 
lation by means of the hourly differences. 
ais the equation of time to be subtracted from mean time. 
B contains the hours and minutes of the apparent time of the moon’s transit over the meridian 
above stated. 
Cis the moon’s horizontal parallax for a time 18 hours before the time of the Washington 
transit, or about 6 hours after the preceding upper transit, taken from page 339 of the 
American Ephemeris, by interpolation by means of the hourly differences. 
c is the corresponding hourly difference. 
D is the moon’s declination 7 hours preceding the time of Washington transit, or 2 hours pre- 
ceding the time of the Greenwich transit, taken from page 6 of the American Hphemeris. 
dis the corresponding hourly difference of declination, 
I’ is the part of L (99) depending upon /’, or upon the solar tide, plus a constant of 30 minutes. 
The part independent of the constant, and also Q, can be readily obtained, with sufficient accu- 
racy for practical purposes, by construction or by trigonometry, as has been explained in ($47). 
But the method by trigonometry does not answer well near the times of the conjunctions or quad- 
ratures, where the angles are very small, unless these angles are determined with great accuracy. 
If L/ and Q are determined by computation it is best to compute Q and f’, (97) and (98), directly 
from the expressions, as in the last part of the example at the end, in which 
M is taken from Table I, with the arguments C and D, and 
S from Table II, with the date as the argument. 
Log sin 2 B and log cos 2 B are taken from Table VII, which is so arranged, with the sine and 
cosine adjacent to each other, that they can be taken out at the same time, using B instead of 2B 
as an argument. The remaining steps in the example, to obtain tan /’, need no explanation. With 
tan #’ as an argument, the variable part of L’ is taken from Table VI, to which the constant, 30 
minutes, is added to make all the values positive. 
eis equal to three times ¢ with the sign changed, calling seconds of are minutes of time, plus a 
constant of 10 minutes. 
J is taken from Table V, with D and d as arguments, a constant of 10 minutes being also 
added. 
g is taken from Table III, with the time of transit, B, as an argument. 
his taken from the same, with the parallax, C, as an argument. 
i is also taken from the same, with the declination, D, as an argument. 
j is taken from the last part of Table IV, using the declination, D, one day in advance, as taken 
out above. 
By is taken from Table I, with the date as the argument, the day and hours not being written 
in the example, but borne in mind. 
H=A+L/-te+f+g+h+itj+By 
The value of A being taken from the ephemeris in astronomical time, the constant, Bo, in the 
table has been increased 12 hours in order to give E in civil time. When the apparent time of 
high water is required, B should be used instead of A in the preceding expression of E. 
4’ and 4? are the first and second differences of E belonging to the upper transits, used as a 
check, and also for interpolating the intermediate numbers belonging to the lower transits. 
The minutes only of 4' are written in the example, the 24 hours being understood. The 
intermediate numbers, in smaller type, are $ 4! and £4’, used in the interpolation. 
o' are the differences after interpofition, used as a check, and also in interpolating to low water, 
the 12 hours understood not being written. 
k is taken from the last part of Table IV, with D as an argument taken one day in advance. 
U is the effect of the solar diurnal tide upon the time of high water, taken from Table VIII, with 
B and the day of the year as arguments. 
m=k-+1 is the effect of the whole diurnal tide upon the time of high water. The values belong- 
ing to the lower transit are readily obtained by interpolation, and must be used with a 
contrary sign. 
