614 Mr. Eankine on the Centrifugal Theory of Elasticity, 



which is equivalent to 



lz=sJ^du{u^^|ru) (2) 



(11.) So far as our experimental knowledge goes, the more 

 substances are rarefied, that is to say, the more the forces which 

 interfere with the operation of the elasticity of the atomic atmo- 

 spheres are weakened, the more nearly do they approach to a 

 condition called that of perfect gas, in which the elasticity is 

 simply proportional to the density. I therefore assume the elas- 

 ticity of the atomic atmosphere at any given point to he repre- 

 sented by multiplying its density at that point by a constant 

 coefficient b, which may vary for different substances, but, as I 

 have already stated, without deciding whether that elasticity is a 

 primary quality or the result of the repulsion of particles. Con- 

 sequently the superficial atomic elasticity 



p = b ^J)f{l), (3) 



1/^(1) being the value of yjru which corresponds to the bounding 

 surface of the atom, where u=l, 



(12.) Let an oscillatory movement have been propagated from 

 the nuclei to every part of their atmospheres, the size of the 

 orbits of oscillation being everywhere very small as compared 

 with the radii of the atoms, and let this movement have attained 

 a pei-manent state, which will be the case when every part of 

 each atmosphere, as well as each nucleus, moves with the same 

 mean velocity v ; mean velocity signifying that part of the velocity 

 which is independent of periodic changes. It is necessaiy to 

 suppose that the propagation of this movement to all parts of a 

 molecular atmosphere is so rapid as to be practically instan- 

 taneous. 



We shall conceive all the masses and densities referred to, to 

 be measured by weight. Then taking g to represent the velocity 

 generated by the force of gravity at the earth's surface in unit of 

 time, the whole mechanical power to which the oscillatory move- 

 ment in question is equivalent in one atom will be represented 

 in terms of gravity by 



^=^' (^^ 



that is to say, the weight of the atom, M, falling through the 



v^ 

 height ^r- due to the velocity v ; and this is the mechanical 



measure of the quantity of heat in one atom in terms of gravity. 



