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force which is a function of the distance ; and in the case of 

 crystalline structure, also of the direction of the line joining 

 the molecules. 



The general equation of equilibrium of a system is, 



555(xg5 + Yg*, + zdZ) dm - %E\dxd7jdz. (1) 



Mr. Haughton shows from the definition of the medium, that 

 V = Vo + v„ 

 where Vq is a homogeneous function of the first degree of 

 the six quantities, 



dl <h d^ ^ , ^ ^ . ^ ^ . ^ 

 dx' dy dz' dz dxf dx "^ dz' dy "*" dx 



and Vi a homogeneous function of the second order of the same 

 quantities. The function Vq is zero in a solid body, and not in 

 a fluid ; which is equivalent to saying that in a solid body the 

 molecular forces equilibrate each other without the aid of ex- 

 ternal forces, but that in fluids this is not the case, and that 

 consequently a fluid left to itself would be dissipated by the 

 action of its own molecular forces ; this Mr. Haughton con- 

 ceives to be true of all fluids, whether gaseous or liquid. It 

 should be understood that the mutual gravitations of the par- 

 ticles are not included among the molecular forces, but among 

 the external forces. 



The values of Vq and v, are shewn to be finally 



^ \ dy dz dx dz' dx dy) 



i f d^ ^dn dZ,\ f d^ dn dZ\ 



+ 'X-^Tx-^(^'Ty'^'^'d-z)f 



