354 
MR. AIRY’S ACCOUNT OF THE HARTON EXPERIMENT 
value of the fraction g^^v-ty abo^^ (which I will call F), calculated on the supposition 
that all the attracting mass is internal to both stations, 
F=l — 
9 dv 
where, after differentiation, r is to be put equal to the radius vector of the surface, 
namely a(l— scos^^). Now the value of V (Article 5 of the paper referred to) is 
E 
Es 1 
2 
a — COS^^— 
which is true, independently of any particular hypothesis respecting the distribution 
of matter in the interior of the Earth ; so that 
E /Es 1 
E=— — — 7i^ 
i \ CO 
cos^ d— ^ sin^ ^ 
and 
S' 
dr 
= 72 — 3 ^^yV^^^cos"* &— —ai^r sin" 
whence 
dv dr 
2E ,^/Es 2*2/1 
12 -5(^cos" ^-3 j +&»" Sin" 0 . 
Putting now r=a(l — s cos" d), we find 
1+22 cos" -^(e— f) (cos" - ^ ^( 1 —cos" &) 
Ef /5m \ 2 Sot) 
12E/ m\ / _ 1\ , mE.^ „ /.x 
(e-2)(cos=^-3j+-^(l-cos i) 
dg 2E 
Whence 
=^|l + (^— 3 £)cos’^+ 26— ij- 
g' dv a 
1 + (^— 3£^C0s"^+22 — ^ 
— S^COS"^— £ + 
(bm 
IT 
3m 
T 
=-{l— 2gcos"^+s+^} ; 
F=l+— {1— 2s cos"^+e+^}* 
and therefore 
