the relation of Pressure to Density. 403 



the amount of accelerative force irrespective of its sign is H . Q, 



or H . — ^, H being a certain constant. 



Let lis now suppose that each atom of the medium is also 

 acted upon by an extraneous force, as the earth's gravitation, 

 and that this force just counteracts the resulting molecular force. 

 If the extraneous force be G, since there is equilibrium of the 

 insulated atom, we must have 



G = H.^. 



But the pressure being p, and being due to the action of the 

 force G, we shall have by hydrodynamics. 



Hence 



and by integration. 





We have thus been conducted to a law connecting the pres- 

 sure and the density, different from that of Mariotte, by a pro- 

 cess which assumes only that media are molecularly constituted, 

 and that molecular action is insensible except at insensible di- 

 stances. To account for this difference is a matter of some sci- 

 entific interest. Since experiment has shown that for the earth's 

 atmosphere, the temperature being given, dp = Gpdz=Kdp, K 



being constant, it follows that ■—- varies as p ; that is, the differ- 

 ence of the mean densities of two contiguous atmospheric strata 

 of given small thickness is greater as the density is greater. And 

 yet the resulting molecular action of the strata on a given insu- 

 lated atom is everywhere equal to the force of gravity. Not 

 having met with any explanation of this fact, I proceed to apply 

 to it the theory of molecular action T have proposed above. 



According to this theory, besides the repulsive action of in- 

 dividual neighbouring atoms on a given atom, varying invei-sely 

 as the fourth power of the distance, there may be a repulsion 

 due to the condensation of waves propagated from an aggregation 

 of atoms, varying cateris j)aribus according to the distribution of 

 the incident condensation about the surface of the given atom. 

 This repulsion will be less as the density of the medium, and 

 consequently the condensation of the aggregate waves, is greater, 

 because, as the condensation increases, the pressure on the 

 hemisphere of the atom on which tlie waves are incident dif- 



2 vrz 



