297 



Fig. 2. 



Now it is quite true that we need not fear any great deviation of 

 density extending through so large a portion of the earth, for that 

 would displace the centre of gra- 

 vity to a sensible extent, which 

 would become perceptible in the 

 measurements of latitude ; but a 

 local deviation might produce a 

 smaller but yet sensible amount of 

 error ; thus if AC' (fig. 2) repre- 

 sent a sphere of 100 miles dia- 

 meter, the attraction of this on 



the point A will =7^ jy 



where 



D is the earth's mean density, d 

 that of the small sphere, and g the 

 total attraction at A. If, therefore, 

 d should be changed to d' } the 

 attraction at A, or the apparent mean density, will be altered in the 



proportion of 1:1 + -o/rr ; which might be a sensible quantity 



without producing any sensible effect on the true mean density, or 

 on the position of the centre of gravity, since the bulk of AC' would 

 be only about - 5 - 00>000 of that of the earth. Now we know little or 

 nothing of the density of the matter a few miles below the surface ; 

 only we are sure, from the discordant lengths of the pendulum in 

 different latitudes, and even in the same latitude under different 

 meridians, that the local deviations are indeed sensible, yet of so 

 small an amount as hardly to affect this inquiry, and that the error 

 from this cause can never even approach 1 per mille. The Cavendish 

 experiment may therefore be considered as practically free from error 

 of this kind; and as regards errors arising from manipulation or instru- 

 mental causes, their probable amount may be determined in the 

 ordinary way from the variation of the results. But if the Cavendish, 

 why may not the Huttonian experiment equally be considered free 

 from error ? Because in the former we are dealing with disturbing 

 masses whose amount is exactly known, whereas in the latter, while 

 we may approximately measure the mass of the mountain above the 

 surface, we do not know how much may be added or abstracted 



