528 Royal Society. 



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. Fig- 3. 



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 be=oT7v7j7j, while its 



attraction at A will be only i of this, 

 and the difference of its attraction on the 



two stations will therefore be po?^, 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 r4 ; and this would 



produce a difference of effect on A and B amounting to TTTTwTT)' ^'^^ 



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), i\\o\\^ possible, is not likely ; the same effect 

 might be produced by a smaller rate of change through a greater 

 space ; thus an addition of about 0'5 to the specific gravity of a 

 sphere of 1 mile in diameter, or of 0-33 to one of 10 miles diameter, 

 would have nearly the same effect, and it cannot be contended that 

 these are improbably large. 



Should the experiment ever be repeated, it would be desirable to 

 swing the pendulum at one (at least) intermediate station between 

 the top and bottom of the shaft, by which means any error of this 

 kind might be approximately eliminated. In the mean time I think 

 there are hardly sufficient grounds for impugning the correctness of 

 the value of E (5-ti7) deduced by the late Francis Baily from his 

 carefully conducted re[)ctition of the Cavendish experiment. 



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

 t Earth's mean density. 



