Saturated bodies 355 



Now consider a body containing M grammes of matter and F units of the 

 electric fluid. The repulsion between this body and a unit of the electric fluid 



at distance unity is 



F - Ma. (i) 



If this expression is zero, the body will neither repel nor attract the electric 

 fluid. In this case the body is said to be saturated with the electric fluid, and 

 the condition of saturation is that every gramme of matter contains a units 

 of the electric fluid. From what we have already said, it is plain that a must 

 be a number reckoned by thousands of millions at least. The definition of 

 saturation as given by Cavendish is somewhat different from this, although on 

 his own hypothesis it leads to identical results. He makes the condition of 

 saturation to be (in Art. 6) " that the attraction of the electric fluid in any small 

 part of the body on a given particle of matter shall be equal to the repulsion of 

 the matter in the same small part on the same particle." Hence this condition 



is expressed by the equation 



Fa = Mr. (2) 



But as the essential property of a saturated body is that it does not disturb 

 the distribution of electricity in neighbouring conductors, we must consider 

 the true definition of saturation to be that there is no action on the electric fluid. 



Now [following Cavendish's ideas] consider two bodies of different kinds of 

 matter M l and M 2 , and let each of them be saturated. 



The quantity of electric fluid in the first will be 



F! = Mja lt (3) 



and that in the second F 2 = M 2 a 2 . (4) 



The repulsion between the two bodies will be 



F I F * ~ F iM z a 2 - F 2 Af ^ + MjMfu , (5) 



or, substituting the values of F l and F 2 , and changing the signs, it will be an 



attraction equal to 



AfjAf.teaj-fu). (6) 



Now we know that the action between two saturated bodies is an attraction 



equal to 



M^Jt, (7) 



where k is the constant of gravitation. 



Hence we must make 



A - u "" * ( 8 ) 



for every two kinds of matter, k being the same for all kinds of matter. 



According to Baily's repetition of Cavendish's experiment for determining 

 the mean density of the earth*, 



(centimetre) 3 



k = 6-506 x io-* - 3 . (9) 



gramme . second 



* Baily's adopted mean for the earth's density is 5-6604, which, with the values 

 of the earth's dimensions and of the intensity of gravity at the earth's surface used 

 by Baily himself, gives the above value of k as the direct result of his experiments. 

 [Cavendish's value 5-45 has been shown by modern determinations to be too small 

 by less than two per cent.] 



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