Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy

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                                If L be the <s>eccentric</s> astronomical latitude of the place,
we may in the small term replace θ by 90<sup>o</sup> - L;
and since cos<sup>2</sup>θ = sin<sup>2</sup>L = 1/2 (1 - cos2L), we find
     R = 1 + m - ε/2 + 3ε/2cos 2L
     Now m = 1/289 = 0.00346
     ε = 1/300.8 = 0.00333
     L, <s>[?]</s>, for Harton, = 54sup>o</sup>.<s>4</s>58sup>'</sup>;
R = 1 + 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, ε, and L.
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."
                            
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Manuscript details

Author
George Biddell Airy
Reference
PT/54/5
Series
PT
Date
1855
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Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy, 1855. From The Royal Society, PT/54/5

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