10 
THE REV. W. WHEWELL ON THE EMPIRICAL LAWS 
Effect of the Moons Parallax. 
15. In Mr. Lubbock’s Table VII., which contains the effect of lunar parallax, and 
has a column for each minute of parallax, we have, in Art. 13, taken the mean of 
each column, and subtracted it from every number in the column. In this way, it 
is evident that the mean contains the non-periodical part of the effect, and the re- 
mainder contains the part which goes through its period in a semi-lunation. 
The non-periodical part of the interval stands in the uppermost line of Table VII. 
(a) Art. 13. ; and its variations are manifestly nearly or exactly proportional to the 
variations of the parallax. If we take 57' as the mean parallax, we may express 
these means very nearly by the formula 
ll h 6 m -5 — 2-5 ( p — 57'), 
p being the II. P. The agreement of the formula with observation is as follows, and 
is a near approximation. 
H. P 
54'. 
55'. 
56'. 
57'. 
58'. 
* 
60'. 
61'. 
Obs 
h m 
11 12*7 
11 13 
h m 
11 11-5 
11 11-5 
h m 
1 1 8-3 
11 9 
h m 
1 1 6*5 
11 6-5 
h m 
11 3-7 
11 4 
h m 
11 0-3 
11 1-5 
h m 
10 5-85 
10 5-9 
h m 
10 54-5 
10 56-5 
Formula .... 
The column for II. P. 60' is completed by interpolation, and the column for H. P. 61' 
is omitted. The latter is defective in half the hours of moon’s transit, which arises from 
the effect of the Moon’s Variation on the parallax. The parallax has a term depending 
on the sine of twice the distance of the moon from the sun, and cannot be so great as 
61' except near syzygy. The “ observed” mean for 61' is that which makes the num- 
bers in that column follow nearly the same law as the rest. 
The periodical part of the effect of lunar parallax is shown in the lower part of Ta- 
ble VII. (a). It appears there that the intervals for all the values of H. P. follow 
nearly the same law as the mean interval already considered, but with a difference in 
the maximum value of the inequality. If we add together the greatest positive and 
negative numbers in each column, we obtain the double of the maximum inequality 
nearly, but not exactly, since the maximum does not correspond exactly to times 
of moon’s transit contained in the Table. Making a slight addition on this account, 
we have, 
H. P 
54'. 
55'. 
56'. 
57'. 
58'. 
59'. 
60'. 
61'. 
Sum 
Double Max. 
Formula. . . . 
m 
99-9 
101 
101 
m 
95-1 
96*1 
97 
m 
91*9 
92-8 
93 
m 
88*2 
89 
89 
m 
84- 5 
85- 2 
85 
m 
80-1 
80-7 
81 
m 
78-5 
79 
77 
Now in the expression 
tan 2 (6 - VI - - c sin 2 L(f ~ u) 
tXX\2{0 /.) — 1 -t-c cos 2 (<p — a) 
+ c cos 2 (<p — a) 
the maximum value occurs when cos 2 (<p — cc) = — c, and is equal to 
v' I - c 
s' 
If 
