Surface Forces in Fluids, 341 



constant, or diminishing more slowly than E, were to begin to 

 diminish more rapidly. 



4. The significance of this result may be exhibited graphi- 

 cally with great advantage*. 



Let X and Y be rectangular axes of coordinates, and 

 along X let distances be taken proportional to the distance 

 between adjacent layers of molecules for different states of 

 extension of the solid, and parallel to Y let lines be drawn 

 proportional to the attractive and repulsive forces in the inte- 

 rior of the liquid per unit area respectively at some given 

 temperature. In this way we should obtain curves of attrac- 

 tion and of repulsion, the latter of which, from what we have 

 seen, will slope downwards towards the axis of X; while the 

 former may be represented by a curve such as that shown in 

 fig. 1, which, after sloping less rapidly than the curve of repul- 

 sion, cuts that curve, and finally has the more rapid slope of 

 the two. Let P be the point of intersection, P M the ordinate 

 at P, and let N be the foot of the ordinate which cuts the 

 curves where their tangents are parallel to one another. 



If the intramolecular distance is less than M, repulsion 

 exceeds attraction, and equilibrium is only possible when 

 there is an external pressure equal to the difference of the 

 ordinates to the two curves. If the intramolecular distance 

 exceed M, then equilibrium demands an external tension. 

 At the extension indicated by ON this tension reaches its 

 maximum value; and it is evident that the equilibrium is 

 unstable, for beyond this distance a diminution of volume 

 will mean an increase of attraction. The breaking-stress is 

 therefore proportional to the difference of the ordinates at 

 N. We shall afterwards return to this point when we come 

 to consider the equilibrium of a liquid in contact with its 

 vapour. 



5. It is here only necessary to remark that the argument 

 from the existence of the breaking-stress may be extended to 

 liquids. For though we are prevented from determining the 

 breaking-stress of a liquid in the same way as that of a solid 

 by difficulties depending on the conditions of stability of 

 liquid figures, yet there are many indications, derived partly 

 from the adhesion to the top of a barometer-tube of a column 

 of liquid more than barometric height, partly from the mag- 

 nitude of the elastic resistance to compression, partly from the 

 difficulty of starting ebullition in the interior of a liquid, and 

 partly from capillary phenomena themselves, that the breaking- 

 stress, if it could be determined, would in many cases be a 



* I owe to my friend Prof. Riicker the first suggestion of the graphical 

 illustrations made use of in this paper. 



