132 The Rev. S. Haughton on a Classification of Elastic Media, 



the equations of liquid motion, including friction, which have been deduced 

 by various writers from different considerations. 



A liquid need not be supposed to be exactly in this state at all times ; a 

 slight cohesive or a slight repulsive force may be supposed to exist among 

 its molecules, according to the quantity of caloric contained in it, or other phy- 

 sical circumstances, which may modify the intensity of the molecular actions. 

 If such cohesive or repulsive forces be considered very small, as compared with 

 the cohesive forces in a perfect soUd, or the repulsive forces in a perfect gas, 

 the equations deduced from the hypothesis, that these forces are zero, may still 

 be used. 



We obtain from equation (36) the following: 



dV dV 



da du 



fiV dV 



dp ^ ^' dv 



-^- = .4«) - 2P(a) - 7), -^i- = Pw. 



dy \ lyi ^i^, 



It is necessary and sufficient for stable equilibriimi that these six forces 

 should have signs contrary to the signs of (la, cji, cy, hu, Zv, oiv). If these be 

 made positive, then the forces must have negative signs, and vice versa. 



Hence, for stable equilibrium, it is necessary that A and P be both negative, 

 which will reduce the function (36) to the following, 



-2V^Ao,-+P(\ + fi + >^). (36, a) 



Also the first three equations (changing the signs of A and P), added together, 

 must be negative ; hence the condition, 



(_ 3^4 + 4P) «, < 0. (36, b) 



4P 



If the equilibrium be stable, A cannot be less than — ; and if it be exactly 



equal to this value, we shall obtain the equations peculiar to liquids, because a 



4P 

 displacement will produce no molecular force ; and if .4 < -^-, a molecular force 



