392 
MESSES. C. AND F. CHAMBERS — PLANETARY INFLUENCE 
25. Similarly, to find the effects of the Earth’s period upon the coefficients for the 
sidereal period of Mercury, we have in lieu of (37), 
Vi=^k cos m 30°) ] — ^ [P, cos sm 30°+(+ sin sm 30°] cos ^y| m 30°^ 
= ^ X 7 [ ' a m cos ^ m 30°) ] + ~ % [P # cos sm 30° + Q, sin sm 30°] cos m 30°) ; 
calculating which for Easterly disturbance, we obtain 
i>,=ihy 1 'T“" cos (il m30 °)]- 0 ' 0i6; ' 
also 
»,=+2 l: [“*» sin (f|» SO*)] +0-004, 
P,= + 2 " [«. cos 2 (|| m 30°) ] - 0 - 022 , 
2s=+ s "[«. sin 2 (g m 30°)] +0-022, 
^ = i 4 ij_ 0 [«*cos3f||w80°j] -0-031, 
^ 3 = li 4 ^ [« TO sin3 30°^ J— 0*014 ; 
and for Westerly disturbance 
-P I = Ii4 J~7[““ C0S (ll m300 )] -°' 084 ’ 
^ 1 = li 4 \ f [ a >» sin (if ™ 30°)] +0-000, 
P* = fii j J 7 [« m cos 2 (ffm 30°)] +0*063, 
^=iii£‘ 8 / [a ni sin2 (jfm30°)] -0-032, 
1 ”L=287 r /54 \ 
^ = i4ij _ 0 cos 3 (t^ 3°°)] -°-°25, 
J to= 287 r- /C 4 N 
f h — 144 [a* sin 3 30°jJ +0*046, 
26. To make a similar estimate of the reciprocal actions of Venus and Mercury would, 
with a month as the interval between successive observations, be extremely trouble- 
some, but what has been done shows sufficiently the practicableness of the process, and 
we do not consider it necessary to apply it at present to this or any of the other cases 
we are dealing with. 
in all of which also the last 
terms are small enough to be 
neglected, in comparison with 
J>the range of each component 
variation, as may be seen from 
the values of the several coeffi- 
cients given in paragraph 18. 
