382 
MESSES. C. AND E. CHAMBERS — PLANETARY INFLUENCE 
lated difference is less than three days, or of the period of Venus ; we shall there- 
fore, in the first place, find (in accordance with what has preceded) the coefficients of 
Bessel’s series expressing the variation of aggregate disturbance of Magnetic Declina- 
tion, Easterly and Westerly, and the variation of aggregate disturbance of Horizontal 
Force (increasing and decreasing) with variation of the position of Mercury in its orbit, 
just as if the observations were wholly due to the action of that planet, and so for each 
planet in turn; and we shall afterwards examine to what extent the values of the 
coefficients thus found are affected by the influence of the other planets. 
18. The ninety-nine periods of Mercury extend over 23 years and 10 months, and 
the observations treated commence with the aggregates of March 1847, and end with 
those of December 1870. The thirty-nine periods of Venus and twenty-four periods of 
the Earth extend over 24 years, the observations treated being those for January 1847 
to December 1870. 
The application of Bessel’s process to these observations, taken from Tables I. and 
II., gives the values of the coefficients for the sidereal periods of Mercury, Venus, and 
the Earth as shown below*. 
Table III. — Values of the coefficients q„ &c. for the sidereal periods of Mercury, 
Venus, and the Earth. 
Declination. 
Coefficients 
Easterly Disturbance. 
Pv 
Si- 
Pv 
Sv 
Pv 
Sv 
Mercury 
Venus 
The Earth 
-0-523 
-4-591 
+1146 
-1-190 
-1-199 
-4-054 
+3-604 
+ 1-428 
-4-812 
+3-435 
+ 1 055 
+7-217 
+3-781 
+3-422 
+0558 
+2-707 
-2-786 
-0-700 
Coefficients 
Westerly Disturbance. 
Pi- 
Si- 
Pv 
Sv 
Pv 
Sv 
Mercury 
Venus 
The Earth 
-4-302 
-1-516 
-7253 
-1-802 
+ 1-497 
-1-168 
— 1-314 
+ 1-156 
+0131 
+ 1-796 
- 1 -965 
+2-584 
+4-533 
+2-440 
+3-274 
-2-495 
+2-083 
+0-684 
Horizontal Force. 
Coefficients 
Increasing Disturbance. 
Pv 
Si- 
Pv 
Sv 
Pv 
Sv 
Mercury 
Venus 
The Earth 
- 00702 
— 00493 
-00112 
+•0003 7 
+ 00438 
- -00524 
+ -00080 
- 00203 
-■00442 
+ -00326 
+ 00111 
+ -00967 
+ 00322 
- -00190 
+ -00056 
- -00428 
+ 00004 
+ -00779 
Coefficients 
Decreasing Disturbance. 
Pi- 
Si- 
Pv 
Sv 
Pv 
Sv 
Mercury 
Venus 
The Earth 
- -00928 
- -02002 
+•03 189 
- -01847 
— -00659 
- 06212 
+ -02370 
- 00353 
- 07347 
+ -03871 
- -00730 
+ •04314 
+ 05141 
+■01617 
+-02711 
+ 00490 
- -02442 
+ 01362 
* An example of the calculations of one of these sets of coefficients is given at the end of the Appendix. 
