390 On the Variation of the Moon’s Motion. 
and its attraction on the moon at the 
mean distance as the unit by which to 
measure other attractive forces, the 
quantity of matter in the sun would A 
be 354936, (which number we call 8,) be 
and its mean attraction on the moon 
Sx EB? 
during a lunar revolution a 
vai 
) 
The whole attractive force of the 
sun upon the moon at any point M of 
its orbit was represented by the letter 
m, and was resolved into two others in 
the directions ME and ES. ‘The ex- 
pression for the disturbing force in the 
latter direction was shown to be ooeE mn, 8 
which was again resolved anit two others in the — EG 
and GS or MH. For the former of these, known in astronomy 
3EF? 
aul 
SM xME 
The latter, which we are now to examine, is called the tangential 
force, because it acts in the direction of a tangent to the moon’s 
orbit at the point M. 
The proportion for obtaining it will read ES : SG, or by 
similar triangles, CM; MF :; “a : the tangential force = 
EF x MF 
= ok ‘EM ME. By the principles of trigonometrical analysis, 
as the ablatitious force, we obtain the expression 
EF xMF=3EM xsin2MED. Substituting this value in the 
place of EF x MF, the expression for the tangential foree be 
13EM x sin2MED_ _ gsin2MED . 
~~ EMXSM sar or ORR ae 
great distance of the sun, all the terms in this expression are 
nearly constant, while the moon is passing through a quadrant, 
except sin2MED. Consequently the tangential force must be 
nearly proportional to this term, and the others may be taken at 
their mean value. The mean value of m we have given above 
SE 
vt A and that of SM is evidently SE. 
comes 
