FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
355 
Now the method adopted in the " Account of Experiments/ &c., article 57, gives 
1 dg 2c 2c 
— — =— (1 +2 COS 
g dr r 
whence 
2c 
F= 1 +“(1 + £ cos* ^). 
Therefore, if R be the ratio of the value of F — 1 given above, to F— 1 as ealculated 
by the method of the ‘Account of Experiments/ 
-P, 1 — 2scos^fl + e + OT 
R= 1 + j cos^ 9 =1 — 3ecos 
If / be the geocentric latitude of the place, we may in the small term replace ^ 
by 90°—/; and since cos* sin*/=^(l — cos 2/), we find 
6 3b 
R=l~j-m— 5+- 2 cos 2/. 
Now 
m=. =0’00346 
■ 300-8 
:0-00333 
/, for Harton, =54° 48' ; 
R=1 4-0-00346 — 0-00334= 1-00012. 
That R should have been so very nearly equal to unity, depends upon an accidental 
numerical relation between the values of m, g, and /. At the equator, R— 1 would 
have been as great as 0-00679. 
In article 60 of the ‘Account/ F— 1 was found =-00012032; whence 
R.(F— 1) = -00012033 ; which only alters the final value of the mean density in 
the ratio of 6836 to 6835, giving for result 
6-565. 
At the equator, the correction to the deduced value 6-566 would have been — -077-” 
