[ 29 ] 
For, by the general law, a is to F, as the dif- 
ference of the fquares of z and z- i is to the fquare 
of z — i ; that is, as 2 z - 1 to z z - 2 z 1 • And 
the fame way b is to <p, as 2 d - 1 to d z - 2 d + 1 ; 
whence, halving the antecedents, and retaining only 
s; 2 , d z , in the cbnfequents, we have the ratio of a 
to b , as above. 
If the diftuibing force of B is exerted at v\ the 
oppofite vertex of C, b will now be to tp, as 2 1 # 
to d r q- 2 d -|- 1 ; and, in ftn&nefs, we ought to 
take a mean value of b : but this may be negleded as 
inconfiderable. 
Laftly, let the fun’s diftance be again expreffed in 
femidiameters of the lunar orbit j that is, if for z 
we write dx , and unity for cp, we have a : b :: 
F 1 
— : — , or as M to Q\ as before. 
(I x a 
VII. In Art. V. it was found that m denoting 
the denfity of the moon, and s that of the fun, y 3 
being triple the ratio of the fun’s mean femidiameter 
to the moon’s *, then will — =3 Whence it 
will eafilv follow, that the denfity of the earth is to 
that of the fun, as QJ_ X Ss to P 3 ; P being the 
moon’s horizontal parallax, and S the fun’s appa- 
rent femidiameter. 
*In the Principle, the femidiameters are i6\ 6", and 15'. 385" ; 
giving o 0379755 for the logarithm of q 3 . Others take a few 
feconds from each ; which does not much alter the value of q 3 . 
VIII. I 
