Captain Jacob on the Earth's Mean Density. 527 



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

 would displace the centre of gravity to a sensible extent, which 

 would become perceptible in the measurements of latitude ; but a 

 local deviation might produce a smaUer but yet sensible amount of 

 error; thus if AC (fig. 2) represent a sphere of 100 miles dia- 

 Fig- 1. Fig. 2. 



\ 



meter, the attraction of this on tlie point A will=-jjr -^ ; where 



D is the earth's mean density, d that of the small sphere, and^ 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 



d' — d 

 proportion of 1:1+ „ , ; which might be a sensible quantity 



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

 on the position of the ceiitre of gravity, since the bulk of AC would 

 be only about j,,,,;^ 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 api)roach 1 per mille. The Cavendish 

 experiment may tlierefore be considered as practically free from error 

 of this kind; and as regards errors arising from manij)ulation 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 lluttonian experiment equally be considered free 

 from error I Because in the former we arc dealing with disturbing 

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

 wc may approximately measure the mass of the mountain abore the 

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

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

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



