HORIZONTAL FORCE OE THE EARTH’S MAGNETISM. 
391 
twice the sum of the lunar synodical variation as deduced from 17 successive means at 
intervals of 3|- days. In the same way the sums for 21 periods of the 3rd term in each 
day gives 
tlrsLT—a, 
the sum of the lunar tropical variations derived from 21 successive means at intervals 
of 1*3 day. If we employ, as in the following investigation, instead of the daily mean 
horizontal force the variations of these values from their mean, the constants C, C' will 
become equal to zero. On taking then the means of the three terms for each day 
in 14 periods, we obtain 
1st day. . . 
2nd day . . 
26 th day . . 
ll" + 8" + 4" 
10 r " + 9"' + 8'" + 6'" + S'" + 4"' + 2'" 
14 
14 
12" + 9" + 5" 
11"'+ 10'" + 9'" + 7"' + 6'" + 5'" + 3'" 
14 
14 
6" + 3" + 29" 
8'" + 7'" + 5'" + 4'" + 3'" + 1'" + O'" 
14 “ 
14 
The corrections of the means for the 1st, 2nd, 26th days of the solar rotation 
derived from 14 periods are the quantities given in the 2nd and 3rd terms, with the 
signs changed. 
In a similar manner the corrections of the lunar synodical and tropical variations 
derived from 12 and 13 periods respectively on account of the solar action uneliminated 
are for the lunar synodical period — 
1st day 
17' + 21' + 24' 
“f" 12 : 
and for the lunar tropical period — 
A _ , 18'+19' + 20' + 22' + 23' + 24' + 26' 
1st day . . . + * > 
„ , , , 19' + 20' + 21' + 23' + 24' + 25' + 1' 
2nd day . . . + ^ * 
The preceding expressions represent the corrections when all the periods are supposed 
to commence with the same day; this, however, was not the case in the following 
calculations : — 
For 1844, the solar period commences .... 1 January. 
„ „ the lunar synodical period commences . 5 ,, (full moon). 
„ „ the lunar tropical period commences . 3 „ (moon furthest north). 
For 1845, the solar period commences .... 30 December, 1844. 
„ „ the lunar synodical period commences . 24 „ „ 
„ „ the lunar tropical period commences .23 „ „ 
