28 Lieut. Hunt on Cohesion of Fluids, 



layers. This is equal to the resultant of all the forces acting 

 from cither direction against this unit of surface, these forces 

 being held hi equilibrio by the equally opposing forces. To 

 obtain an expression for this cohesion, let the fluid mass be 

 conceived as divided into elementary layers relative to three 

 perpendicular co-ordinate axes. Let the layers above the 

 plane X, Y, be called 1, 2, 3, &c, those below being called 

 «, b, c, &c. Take the unit of surface in the plane X, Y, be- 

 tween layers 1 and a. Then the force with which the unit 

 in layer 1 presses against layer a is composed of all the at- 

 tractions which the entire layers a, b, c, &c, exert on the 



I I 



I I i_ 



1 1 3 



I I 2 



3 L_L, 



a 



c 



units in layers 1, 2, 3, &c, which make up the prism 

 basing on the unit of surfaces. Or, making the cohesion -v[/, 

 and designating the elementary forces by the layers between 

 which they are exerted, we have 



-l = a, 1 + b, 1 4 c, 1 + d, 1 + &c. 



+ a, 2 + b, 2 + c, 2 + &c 



4- a, 3 + 6, 3 + &c. 



+ <2, 4 + &C 



in which the terms arranged above each other have equal 

 values. This series would require to be extended so as to 

 include all terms corresponding to distances at which cohe- 

 sive forces may not be regarded as evanescent. By assuming 

 some law of connection between this force and the distance, 

 an integration of effect could be attained ; but this is not noyv 

 necessary. An inspection of the formula gives the main fea- 

 tures in the mechanism of cohesion within masses, either solid 

 or fluid. 



In order now to study the peculiarities of constitution be- 

 longing to surfaces, let us, in this formula, introduce the hy- 

 pothesis that layer 1 becomes a surface layer. All terms 

 containing 2, 3, 4, &c., are thus struck out, and we 



