390 
ME. J. A. BEOUN ON THE VAEIATIONS OE THE 
Lunar synodical period 15 x 29-53=442-95 days. 
Solar 17x26-0 =442-0 „ 
Lunar tropical 20x27-3 =546*0 „ 
Solar synodical 21x26-0 =546-0 „ 
Lunar synodical 12x29*53=354-36 „ 
Lunar tropical 13x27"3 =354*9 „ 
As the projected observed daily means of the horizontal force for 1845 show a more 
frequent action of irregular disturbing causes than those for 1844, the discussion has 
been made separately for the two years. 
In the calculations for the lunar synodical and tropical periods, 12 of the first and 
13 of the second were taken; as these occupy the same time, the effects due to the one 
are eliminated in the calculation for the other (constancy of law being always assumed). 
This is not the case, however, with reference to the solar period of 26 days, for which 
14 periods were taken. 
Since it requires 17 and 21 periods of 26 days for the elimination of the effects due 
to the lunar synodical and tropical periods respectively, if we seek the mean result for 
the solar rotation from 14 periods ( = 364 days) corrections must be applied on account 
of lunar actions not eliminated. Let 1', 2', 3' 26' represent the mean values of 
the horizontal force for the 1st, 2nd, 26th days in the solar period ; 1", 2", 3", 
29", 30" represent those corresponding to the days of the lunar synodical action, and 
V", 2"', 27"' those for the lunar tropical action. If we neglect the variations due 
to other causes, the mean horizontal force for each day, commencing all the periods with 
the 1st January 1844, may be represented as follows : — 
Number of 
solar period. 1st day. 2nd day. 26th day. 
1. 
l'+ 1" + 1"' 
2'_p 2" + 2'" 
...26' +26" +26"' 
2. 
l'+27" +27'" 
2' +2 8" + 0"'-7. . , 
. .. 26'+22"-5+24'"-7 
14. 
l' + 14"-5+ll'"-4 
2' + 15"-5+12"'-4. . . 
, . . 26'+10" + 9'"*1 
15. 
l'+ll" +10'"-1 
2' + 12" +11"'-L .. 
..26'+ 6" -5+ 7"'*8 
16. 
l'+ 7"-5+ 8"'-8 
2'+ 8"-5+ 9"'-8... 
..26'+ 3" + 6'"-5 
17. 
l'+ 4" + 7"'-5 
2'+ 5" + 8"'-5... 
. . 26' + 29"-5+ 5'"- 2 
20. 
l'+24" 3"'-6 
2' +2 5" + 4'"-6... 
. . 26' + 19"-5+ l"'-3 
21. 
r+20"*5+ 2'"- 3 
2' + 21"-5+ 3"'-3. . . 
. . 26'+ 16" + O'" 
If now we take the sums for 17 periods of the 2nd term in each day, we may repre- 
sent it in each case by 
2^ 9 . 5 L S ,=C, 
