214 Dr. H. Chatley on Cohesion. 



effective is the whole section of the bar, and the actual size 

 of the atoms, independent of the space they occupy, has 

 nothing whatever to do with it. 



One can scarcely conceive how Kelvin overlooked the fact 

 that the mass of the atom is a function of the spacing, so 

 that in the molecular realm the gravitational stresses still 

 remain minute. If we consider two 1-centimetre cubes 

 of a substance of density three and an atomic interval of one 

 Angstrom unit, the mass of a bar of atoms of the type 

 postulated is 10" 16 gram. 



The mutual attraction of two collinear bars of unit length 

 end to end is 



/=M a VM 2 .log,[|^], 



where M 1? M 2 are the masses per unit length and 8 the 

 distance between the ends (Earnshaw, ' Dynamics,' p. 327). 

 In this case, when M X = M 2 and 1/8 is very large, we can 

 write 



/= 2-3026 M 2 ;log 10 (^). 



If 8 = 10~ 8 and M=10~ 16 , 



/= about 2 x 10~ 31 dyne. 



If the number of bars, " n," is (10 8 ) 2 , then 



'F 1 = nf=2 x 10 -15 dyne on a square centimetre. 



The additive effect of the various bars on those other than 

 their own partners must also be considered. Even if we 

 assume that each bar of the cube acts on all those of the 

 second cube other than its own mate with the same force as 

 on its own mate, then the total attraction, due to the 

 longitudinal bars only, is but 



F 2 < n 2 f= 20 dynes per sq. cm. 



[Note. — Taking the cubes as wholes, we have for the whole 

 attraction (of all the masses across the interface) about 

 20 dynes.] 



In actual fact, most solids have a tensile strength of more 

 than 1 kilogram per sq. cm. or 10 6 dynes per sq. cm., and 

 certain steels (with atomic intervals certainly larger than 

 10~ 8 cm.) have tensile strengths as great as 25 tonnes per 

 sq. cm. or 2*5 x 10 10 dynes per cm. 2 It is to be presumed 



that Kelvin had in mind the fact that l g]o(p^) becomes 



