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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                                as the only quantities in this equation liable to sensible
numerical error, δ(d/D) = R/3c . δ(g/G). As the
density of the shell, or d, may be ascertained
by actual examination, δ(d/D) = -d/D . δD/D : and
therefore δD/D = -D/d . R/3c . δg/G.
3. In order to give a numerical value<s>s</s> to the error of
result, suppose that D/d = 2 nearly (a <s>result</s> proportion
rather higher than Maskelyne's): that R/c = 16000
(which supposes the thickness of the shell, or the depth
of the mine, to be a quarter of a mile nearly):
and that δ(g/G) = 1/432000 (which corresponds to
an error of 0.1 per day in the vibrations of a seconds
pendulum). The δD/D = -2.16000/3 . 1/432000 = -2/81:
or the mean density would be determined with an
error not exceeding 1/40 part of the whole. <s>Such a</s> This error,
I apprehend, is far less than those to which Cavendish's
experiments were liable (Reich's and Baily's experiments had not been made at the date of this investigation, but I do not except them from the same remark). <s>[?]</s> It is also quite as
small as that to which the more astronomical
determination in the Schehallien experiment was

                            
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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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