W. Harkness—The Solar Parallax. 881 
If 7 is the length of a simple pendulum which makes. one 
vibration in ¢ seconds of mean time, the observed force of grav- 
ity will be 
2 
L : 
Gas (1) 
: t 
The attraction of the earth at a point upon its surface in geo- 
centric latitude ¢ is 
RE 
; 2 
7 (2) 
The observed force of gravity is the earth’s attractive force 
diminished by the resolved value of its centrifugal force. t 
the equator the centrifugal force is G+289-24, while in any 
other latitude it is G cos y+ 289-24; and the resolved part of this 
force acting in the direction of the vertical is G cos’ g+289°24. 
Equating the earth’s attraction to the force of gravity augmented 
by the centrifugal force, we have 
RE _ cos’ p 
Ari G (1 +) (3) 
Whence, by (1) 
Fis Bll yi SO 
ao FE. (: + 389-24 (4) 
If T is the length of the sidereal year, expressed in seconds 
of mean time, and a, is that value of the semi-major axis ot the 
earth’s orbit which would satisfy Kepler’s third law, we have 
a 8 
+ ole 5 
(S+E) ©) 
_ Le Verrier has shown that a=1:000141a,, (OPM, ii, 60, and 
lv, 103). Substituting this value in (5), and transposing 
T 
(6) 
k 
a 'T?(S+E) (1:000141)’ 
Eliminating & and z between (4) and (6), and rearranging the 
terms 
S+E 400° 
E 
Toke. fy. 08 (7) 
UT’ p,*(1°000141) ( +) 
Owing to the equatorial bulging of the earth, the points 
which have + for the sine of their geocentric latitude are the 
only ones upon the surface of the earth at which a pendulum 
will vibrate as it would if the whole mass of the earth were 
concentrated at its center. For that reason we take sin’p=}4, 
and consequently cos*g=%. We also put p,=cp, and a sin p 
=p. Substituting these values in (7), it becomes 
