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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                                to the small inequalities of the ground at any great
distance from the pendulum stations.

57. The inequalities which we have to consider
are entirely at the surface and do not in any case
exceed in vertical <s>ordinate</s>measure one-tenth of the
depth of the mine. They may therefore be considered as
being actually at the surface, and, if their horizontal
extent is not very great, <s>they</s> each may be considered as
collected at its center of gravity. Its effect on the
upper station will be 0: its effect on the lower
station will be c/(p<sup>2</sup> + c<sup>2</sup>)<sup>3/2</sup> x d x volume: where p is the horizontal distance of the center of gravity. An eminence
will increase the attraction upwards, and a depression will
diminish it. But as our only object is to find the difference of
attractions on the two stations, we may estimate the whole, with changed sign, as an
effect on the upper station: then an eminence will increase the attraction downwards, and a
depression will diminish it.
    There is however one depression which it is
desirable to consider in a different way, namely
that of the sea. The depth of the sea itself is less
important than the depression below the table land which
continues with little change of level to the edge of the
cliffs: and a sufficiently accurate estimate may be
                            
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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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