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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                                54. To illustrate in some degree the difference in the
attractions and changes of attraction depending on different
slices of the sphere, I have supposed a homogeneous sphere divided into
20 slices by equidistant planes parallel to the tangent
at I, and have computed (by formulae easily
investigated) the attraction of each slice upon the point
I at the surface, and upon a point raised above the
surface by 1/10 part of the radius.
The results are as follows:

No.of   Attraction on point     Attraction on point     Decrease by the
slice     at the surface          elevated 1/10 radius    elevation of the point
1      .17019     .10401    .06618
2      .14548     .11404    .03144
3      .12941     .10644    .02297
4      .11640     .09811    .01829
5      .10519*    .09002    .01517
6      .09515     .08231    .01284
7      .08600     .07501    .01099
8      .07756     .06808    .00948
9      .06963     .06144    .00819
10     .06217     .05509    .00708
11     .05512     .04901    .00611
12     .04833     .04315    .00518
13     .04191     .03745    .00446
14     .03568     .03207    .00361
15     .02973     .02666    .00307
16     .02391     .02161    .00230
17     .01836     .01655    .00181
18     .01295     .01165    .00130
19     .00766     .00693    .00073
20     .00249     .00232    .00017
______________________________________
* I was not aware till I made the calculation that the plane which bisects the
radius drawn to I divides the sphere into two segments whose attractions on I are equal.
                            
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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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