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XIV. Account of Pendulum Experiments undertaken in the Harton Colliery, for the 
purpose of determining the Mean Density of the Earth. 
By G. B. Airy, Esq., Astronomer Royal. 
Received December 26, 1855, — Read January 24 and 31, 1856. 
Section Introductory and Historical. 
1. In the spring' of the year 1826, the idea occurred to me of attempting a deter- 
mination of the Mean Density of the Earth by means of pendulum-experiments at 
the top and the bottom of a deep mine; and rough preliminary calculations, which 
seemed to show that the effect of accidental errors of observation on the ultimate 
result would probably be less than in the methods which up to that time had been 
used, confirmed me in the wish to try it. The nature of these preliminary calculations 
was nearly the following. 
2. Conceive the earth to be a sphere of radius R and mean density D, surrounded 
by a spherical shell of thickness c and density d, so that the radius of the external 
surface is R-f-c. As the attraction of the spherical shell upon a point at or within 
its inner surface is nothing, the attraction at the confines of the inner sphere and 
shell is represented by _ and the attraction at the external surface of 
the shell is represented by y which to the first power of ~ is 
y RD^l Calling the gravity at those two points respectively G and g, 
:D=rcG~(i~l)- considering the fractions ^ 
and ^ as the only quantities in this equation liable to sensible numerical error, 
i density of the shell, or d, may be ascertained by actual 
examination, = 5 therefore ^ 
\D/ D D ’ D d G 
3. In order to give a numerical value to the error of result, suppose that ^=2 
R 
nearly (a proportion rather higher than Maskelyne’s) ; that— =16000 (which sup- 
poses the thickness of the shell, or the depth of the mine, to be a quarter of a mile 
nearly) ; and that ”43^00 corresponds to an error of 0‘1 per day in the 
2 R 
MDCCCLVI. 
