302 DR. S. CHAPMAN ON THE LUNAR DIURNAL VARIATION OF THE 
Lunar phase. 
a\. 
Vi. 
a' 2 . 
b' 2 . 
a 3 . 
b\. 
CL 4. 
h\. 
1 
% 
hi 
a- 2 
h 2 
®3 
b 3 
CI4. 
hi 
2 
k + h) 
k ( — «i + h{) 
a 2 
h 2 
k (a 3 — b 3 ) 
k (a 3 + b 3 ) 
-b 4 
a 4 
3 
^1 
-ai 
a 2 
h 
- h 3 
a 3 
- a 4 
-hi 
4 
k (— + &i) 
k(-ai-bi) 
a 2 
h 2 
k(-a 3 - b 3 ) 
k {a 3 - b 3 ) 
hi 
-a 4 
5 
-«i 
- bi 
a 2 
h 2 
-«3 
- b 3 
CL4. 
hi 
6 
k (- % - h) 
k («i — b{) 
a 2 
b'2 
k ( — a 3 + b 3 ) 
k(-a 3 -b 3 ) 
-w 
CL 4 
7 
- hi 
Cli 
a 2 
b 2 
h 3 
— a 3 
- u 4 
-h 
8 
k («i - hi) 
k («i + bi) 
a 2 
h 2 
k (a 3 + b 3 ) 
k(-a 3 + b 3 ) 
hi 
- a 4 
variation for the particular season, over the period for which data- have been used, 
except for small corrections to be applied (i) to the amplitudes of the components, on 
account of the fact that the epochs are changing continuously, while we have treated 
the group of days corresponding to each lunar phase as though each of the days of the 
group was centred precisely at that phase (this makes the computed amplitude 
smaller than it should be); and (ii) to the epochs also, in case the civil times adopted 
for lunar hour 0 and the phases of new moon, &c., have been the times appropriate to 
the meridian of Greenwich instead of to the meridian of the observatory dealt with. 
The former correction, to the amplitudes, is effected by multiplying the computed 
amplitudes C l5 C 3 , C 4 , or the corresponding a, b coefficients, by 1 *02, 1*02, and I'll 
respectively.* 
§6. The correction to the epochs is found as follows : we consider a place in West 
longitude IT, for which the civil times of lunar hour 0 and of new moon first-eighth 
phases, &c., appropriate to Greenwich have been used instead of the local times. 
The error in the local civil time of lunar hour 0 is equal to the gain in longitude of 
the moon upon the sun during the time taken for the moon to traverse the angle L ; 
this time is, with accuracy sufficient for our purpose, equal to L°/29 in lunar time. 
On this account an angle wL°/29 must be subtracted from the deduced epoch 6 n . 
Next as regards the hour of new moon, &c., since these phenomena have no relation 
to any special meridian, the adopted times are in error by the full amount L° in solar 
time. This results in an error of amount (?i — 2)L°/29 in the reduction of the phases 
to the true epoch of new moon. Combining the two corrections it appears that the 
epochs of all the components must be corrected by the same amount, viz., — 2L°/29. 
This correction is so simple to apply, and the adoption of one set of times for all 
observatories is so convenient, that the plan can be recommended, certainly for all 
observatories for which no direct ephemeris is published. 
Having applied these corrections, it is desirable that the results from all 
observatories should be given in the following form: the elements should be 
transformed into the geographical components of force, to North, West, and the nadir, 
the unit being conveniently taken as 10 -7 C.G.S. ; the time zero should be the local 
* Cf. ‘ Util. Trans.,’ A, vol. 213, p. 309, for the deduction of these factors. 
