[ 65 ] 
3* Let 5 reprefent the fan, at an immenfe diftance, 
*T the earth (fuppofed, for the prefent, at reft) P the 
moon’s place in her orbit ADBC , in which C, D, 
are the quadratures, A, B , the fyzygies : then if PIC, 
parallel to AB , and cutting 2 C in Z\, be produced 
till KL is double of PK ; and LAZ parallel to P7 
meet AB produced in M L M and APT will rcpre- 
fent the difturbing forces of the fun, by which the 
moon is urged in the directions PZ, MT. See Prin- 
cipe lib. i. prop. 66. and lib. iii. p op. 25, 26. 
And if PR is made perpendicular to LM, the 
force MT (hall be refolved into two forces as RT 
and MR ; whereof the latter, AIR, taken from LAI, 
reduces the difturbing force, in the direction P'J, 
to their difference LR. 
4. Put now P T (z=zLM)= 1 PK, tlie fine of the 
arc PC—s : and then TM (=PP= 3 s) : MR :: 1 : r; 
that is MR = 3 f , an 1 LR, the difturbing force in 
the direction PP, is as 1 — 3 j\ 
When Cp, the moon’s diftance from the quadra- 
ture, is an arc of 3 5-° 15' 52 v , in which cafe 1 — 
33 z =o, l and r coincide j and the difturbing force 
vanifhing, the line of the apfids becomes ftationary. 
But if the moon’s diftance from her quadrature is 
ff ill greater, as at 7 r, then ^ exceeds ^A s and their 
difference A^ is a force represented by — 7—' act- 
ing in the direction Ttt. This force, at the fyzygies, 
is double of TC. 
5. Whence, and from §1, it follows ; that c be- 
ing the fun’s disturbing force, in the direction CT, at 
the quadrature ; at any other point, as P, it will 
be -f z x 1 — 3 7 . And that writing for c the variable 
quantity cxi — 3P, and A for the fluxion of the 
I arc 
