298 



below ; and we have no right to assume that the mountain is merely 

 a detached mass resting upon the general surface ; it will almost cer- 

 tainly have roots differing in density from the surrounding country, 

 as has been ably shown by Mr. Airy in the Philosophical Trans- 

 actions for 1855, page 101. 



In the case of the pendulum experiment the uncertainty is some- 

 what greater ; thus, let AB represent the Harton pit, and let BC be 

 a sphere of lead (supposed to lie at its 

 foot) of a diameter equal to AB (i. e. 

 about i mile) ; the density of this being 

 about double the mean density of the 

 earth and about quadruple that of the 

 neighbouring country, its excess of attrac- 



tion on B will b e= oiQQ( while its 



attraction at A will be only A of this, and the difference of its attrac- 



tion on the two stations will therefore be oogoy being only a little 



less than the whole quantity observed by Mr. Airy. We may indeed 

 be pretty sure that there is no such mass of lead, or mineral of nearly 

 equal density, at the foot of the Harton shaft, yet it is quite con- 

 ceivable that there should be, within the sphere BC, an excess of 

 density amounting to of that of lead, or about T4 ; and this would 



produce a difference of effect on A and B amounting to ^44 QQ^ afl d 



D* 



would alter the value of -j- to 2-384, and that of Ef to 5'96, 



approaching considerably nearer to Baily's determination. Further, 

 there must doubtless be a small latitude allowed to the assumed den- 

 sity of the upper strata, the average of which, within the limits that 

 would affect the pendulum, may not be exactly the same as in the 

 immediate vicinity of the pit ; supposing it to be 2'4 instead of 2'5, 

 E will be reduced to 5 '72, being nearly identical with Baily's value. 

 If it should be objected that so large a variation of density as that 

 assumed above (1*4), though possible, is not likely ; the same effect 



* Ratio of mean density of the earth to that at the surface, 

 f Earth's mean density. 



