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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                                be infinite, this expression becomes 4πcd. Now the
attraction of a shell whose thickness is c, computed
as in article 2, is 0 for the <s>[?]</s> point at the
inner surface of the shell and 4πc.d for the point
at the outer surface, and therefore the difference is
4πcd. Hence it is indifferent whether we consider
the difference of attractions at the upper and lower
stations (independent of the change in the attraction of
the nucleus <s>produced</s> caused by the change of distance from
it), as produced by a shell of matter, or as produced
by the matter between two parallel planes of unlimited
extent.
    If the extent of the planes be limited, their form
being circular, let p = nc: then the difference of
attractions is <s>[?]</s> 4πcd{n + 1 - (n+ 1/2n - θ<sub>n</sub>)}
=  4πcd.{1- 1/2n} nearly. If (as in the Harton experiment), r = 1/4 mile, p = 3 miles = 12<s>p</s>c
nearly, this = 4πcd{1- 1/24} nearly. Thus it
appears that 23/24 of the effect is produced by the matter
within 3 miles of the pendulum stations. It is
evident therefore that it is not necessary to give attraction
                            
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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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