ON THE EARTH’S MAGNETISM. 
389 
Table VIII. — The calculated values of Aggregate Disturbance of Horizontal Force for 
the synodic periods of Mercury, Venus, and Jupiter are as follows : — 
Aggregates of Disturbances increasing the Horizontal Force, diminished by the constant value shown in the 
last column of the Table. 
Twenty-fourths of the period... 
0 
1 
2 
3 
4 
5 
6 
7 
8 
Mercury 
Venus 
Jupiter 
-•00761 
+ 01134 
—•00552 
-•00661 
+ 00483 
-■00387 
- 00530 
-■00228 
■00000 
- 00533 
-■00686 
+•00493 
- 00732 
- 0071 8 
+ •00895 
-01037 
-•00384 
+•01013 
-01251 
+■00051 
+■00763 
-•01189 
+ •00282 
+•00207 
- 00786 
+ 00126 
- 00451 
Twenty-fourths of the period... 
9 
10 
11 
12 
13 
14 
15 
16 
17 
Mercury 
Venus 
Jupiter 
-•00151 
-■00366 
- 00969 
+ 00492 
-•00950 
-•01164 
+ •00917 
-01321 
- 00993 
+•01015 
-01284 
- 00560 
+ 00845 
- 00867 
- 00053 
+•00592 
- 00288 
+ ■00348 
+ •00459 
+ •00176 
+ 00551 
+ 00542 
+■00350 
+ •00565 
+■00781 
+•00260 
+•00471 
Twenty-fourths of the period... 
18 
19 
20 
21 
22 
23 
Pa- 
Mercury 
Venus.. 
Jupiter 
+ •00997 
+ 00099 
+ 00349 
+ 01005 
+ •00102 
+ •00233 
+•00724 
+ ■00390 
+ •00103 
+•00225 
+•00876 
-•00075 
-•00302 
+ 01318 
-•00296 
- 00661 
+•01445 
- 00491 
•05000 
•04611 
•04611 
Aggregates of Disturbances decreasing the Horizontal Force, diminished by the constant value shown in the 
last column of the Table. 
Twenty-fourths of the period... 
0 
1 
2 
3 
4 
5 
6 
7 
8 
Mercury 
Venus 
Jupiter 
-•02137 
+•03025 
+•00081 
-■01791 
-•00489 
- 00674 
- 00763 
-01960 
-01886 
+ 00111 
-•02085 
-•04842 
+ 00056 
- 02311 
-•06853 
-01155 
-•03690 
- 06680 
-•02997 
-•06040 
- 04410 
- 04459 
-•07984 
-01360 
- 04592 
- 07831 
+ ■00771 
Twenty-fourths of the period... 
9 
10 
11 
12 
13 
14 
15 
16 
17 
Mercury 
Venus 
Jupiter 
- 03053 
- 04779 
+ ■00986 
—•00335 
+ •00342 
- 00374 
+ •02469 
+ •05291 
-•01808 
+ 04231 
+ 07543 
-01583 
+ •04375 
+•05705 
+ 01150 
+ 03145 
+ 00426 
+•05702 
+ 01431 
- 05787 
+ •10114 
+ 00234 
- 09791 
+ •12169 
+ 00111 
- 09398 
+•10616 
Twenty-fourths of the period... 
18 
19 
20 
21 
22 
23 
Pa- 
Mercury 
Venus 
Jupiter 
+•00903 
-•04528 
+•05912 
+•01875 
+ 02768 
+•00024 
+ •02210 
+ •09365 
-•04587 
+ 01511 
+•12651 
-•06258 
+•00045 
+ 11760 
-•04942 
-•01425 
+ •07797 
-•02128 
•29213 
•27529 
■27529 
22. Let us now estimate the errors in the coefficients for the Earth due to the 
sidereal period of Venus, and those of the coefficients for the sidereal period of Venus 
due to the Earth’s period. The periods have the ratio of 13 to 8, so that in equations 
(7) /=13, ^=8, and r=96; that is, in 96 months eight periods of the Earth and 
thirteen of Venus have been just completed. The least value of s for which (sipi)y 
or (s+1) 8 is a multiple of r or 96 is 11*, and therefore p n or q u is the first coefficient 
(after p x or q x ) that affects the value of a x or b x ; the least value of s for which (s+2) 8 
is a multiple of 96 is 10, and therefore or q 10 is the first coefficient (after p 2 or q 2 ) 
that affects the value of a 2 or b 2 ; and similarly q? 7 or q 7 is the first coefficient (after p 5 
or q b ) that affects the value of a 5 or b b . Hence if we may disregard as small those 
terms in the expression for the Earth’s period which repeat themselves six or more 
times in a year, or whose period is less than two months, a x , b x , a. 2 , b 2> a 3 , b 3 , &c. will 
* See second set of demonstrations in the Appendix. 
