On the Mean Density of the Earth. 325 



invention of particular contrivances to simplify it, and to render 

 it very correct. All this was executed in the most satisfactory 

 manner by Dr. Hutton, an illustrious geometrician, to whom 

 the mathematical sciences are indebted for numerous other im- 

 portant researches. His labours on the subject in question were 

 rewarded by the Royal Society of London, who had appointed 

 him to the undertaking. The result is, that the density of the 

 earth is to that of the mountain, in the ratio of 9 to 5. In or- 

 der to obtain the proportion between the density of the mouu- 

 tain and that of water, Mr. Playfair made a lithological exa- 

 mination of this mountain, and found it to be composed of rocks, 

 the specific or relative density of which to that of water, varies 

 from 2-5 to 3-2 ; and he judged that of the mountain to be be- 

 tween 2-7 and 2-8, which gives 5 very nearly as the mean spe- 

 cific density of the earth. 



Mr. Michell, of the Royal Society of London, planned an ap- 

 paratus calcuhited to measure the attraction of very small bodies, 

 such as leaden spheres of one or two decimetres' radius ; but he 

 did not live long enough to put it in practice. This apparatus 

 was transmitted to Mr. Cavendish, who made considerable al- 

 terations in it, to obviate all causes of error in the measurement 

 of such slight attractions. The fundamental piece of the appa- 

 ratus is the balance delorsion, which my learned colleague Cou- 

 lomb invented and was the first to publish, and which he has so 

 successfully ap])lied to the measurement of electric and magnetic 

 forces. Having examined with scrupulous attention the appa- 

 ratus of Mr. Cavendish, and all his experiments, which are made 

 with that precision and sagacity which distinguish this excellent 

 philosopher, I see no objection to his result, which gives 5 -48 for 

 the mean density of the earth: it is the mean of 29 experiments, 

 the extremes of which are 4'88 and .5*79. If to this result we 

 appiv the formulae of my T/ieorie Jlnahjllque des ProbaljilUcs, 

 it will be found that there is a very great probability tTiat the 

 error is very inconsiderable. Thus, according to these experi- 

 ments, which are confirmed by the observations made on Mount 

 •Schihallien, we may consider the mean specific density of the 

 earth as well known, and very nearly equal to 5-48, which con- 

 firms the supposition of Newton. 



These experiments and observations evince tlie reciprocal at- 

 traction of the smallest particles of matter, in the ratio of their 

 masses divided by the square of the distances. Newton had 

 concluded it from the |)rincip!e of the ecinality of action to re- 

 action, and horn his experiments on the weight of bodies, which 

 he found, i)y the oscillations of the pendulum, to be in propor- 

 tion t(» their mass. Notwithstanchng this proof, Ilnyghens, who 

 was belter able than anv other contemporary of Newton properly 



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