Account of pendulum experiments undertaken in the Harton Colliery, for the purpose of determining the mean density of the earth, by G. B. Airy
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."
Please login to transcribe
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
Please login to comment