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ment, in which the earth's total attraction is compared, by means of 

 the torsion-balance, with that of a small mass of known dense material ; 

 and 3rd, the pendulum, or Airy's experiment, in which the total 

 attraction is compared with that at some distance below the surface, 

 or by means of differences, with that of the outer spheroidal shell, 

 whose density may be supposed, approximately at least, to be 

 known. 



Now none of these methods give the mean density as a direct 

 result ; for the result obtained, the earth's total attraction, is=<7 x the 

 sum of (all the particles divided respectively by the squares of their 

 distances) instead of g x (the total mass divided by the square of the 

 radius or mean distance) : and to assume the equality of these, is to 

 assume the earth to be a sphere, and to have its matter arranged in 

 concentric shells or layers of equal density throughout each layer, 

 both of which we know to be untrue. Mr. Airy has indeed shown 

 that, in the case of his experiment, it is sufficient if we know, as 

 regards the upper shell, the form and density of that portion which 

 is in the immediate neighbourhood of the place of observation, with- 

 out attending to irregularities of distant parts ; but he has not shown 

 that variations of density below and near to his lowest station would 

 not sensibly vitiate his results. 



In order to show the nature and amount of error that might 

 thus be introduced, let AB be 

 a section of the earth through Fi S- 1 



the centre, AC an inscribed 

 sphere of half the diameter ; 

 then it is evident that on the 

 supposition of a uniform den- 

 sity throughout, the attraction 

 of the small sphere on the 

 point A would be just half of 

 the total attraction of the earth, 

 although its mass would 

 amount to but \\ and if this 

 small sphere were to have its 

 density doubled, the total at- 

 traction at A would be increased by one-half, while the mean density 

 would be altered by only \. 



