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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                                52. In figure 2 then, conceive that for some distance
on each side of I (say twenty or thirty times the depth of I)
the external surface is sensibly spherical: and conceive that
at A, B, C, &c there are local irregularities, perhaps
large in extent as compared with the depth of I, but
very small as compared with AB in Figure 1. <s>[?]</s> Trace the
inner surface DEF by making AD = Ia, BE = Ib,
CF = Ic, &c. These <s>[?]</s> lines however
are to be made geometrically equal only when the density
of the matter is the same as that above I: if the
density about A is less than that above I, take the
geometrical length AD greater than Ia in the same
proportion. Then the attraction of the shell on the point
I will be strictly equal to 0. Moreover its attraction
on the point U will be sensibly the same as if its
form were free from irregularities. For, the attractions
on U are all <u>added</u> together: the irregularities are
local and numerous, and are partly additive and
partly subtractive: and by hypothesis we have
excluded all the irregularities near I <s>[?]</s> or U
which, individually, can be important. And it may
be accepted as a universal principle than when a
result is produced by the <u>addition</u> of a great number
of small components which are liable individually to 
                            
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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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