on Static Friction. 41 



'discontinuous function of the thickness. When the layer is 



about 1 micron thick the function changes its sign. There 



... 

 is thus a region of instability, or regions of instability, which 



definitely mark off the composite surface from the true 

 double surface. 



In static lubrication a layer of fluid is interposed between 

 two solid faces. Now, though we know that the energy of a 

 composite surface is a discontinuous function of the depth of 

 the layer of fluid when the surface is bounded on the one 

 side by air or vapour, we know nothing directly of the form 

 of the function when it is bounded by another solid. Let us 

 assume that it is discontinuous also in this case, and consider 

 what must happen when the two solid faces are forced to- 

 gether by a normal pressure. The fluid will be squeezed 

 out the less rapidly the greater its viscosity until a certain 

 critical thickness is reached at which the. layer becomes 

 unstable. It will then collapse until the thickness is reached 

 at which the surface energy begins to increase as the 

 thickness decreases. The film now has gained tenacity and 

 lost fluidity. For a certain normal pressure therefore a 

 certain critical thickness of film will persist, and therefore 

 a certain definite resistance to slip. The critical thickness 

 may be expected to vary very little over a wide range of 

 pressure since the energy of thin films is a rapidly varying 

 function of their depth. 



The layer of fluid must have some tenacity to be able to 

 maintain itself, and as increase in tenacity and loss of fluidity 

 go together, a limit will be set to the lubrication. The 

 resistance to slip will never wholly vanish as it should do 

 if the surfaces were separated by true fluid. Thus, what 

 Osborne Reynolds calls "boundary conditions*' must always 

 operate in static friction, whereas they may be absent in 

 kinetic friction. The existence of a discontinuity in the 

 variation of energy with the thickness of the layer of 

 lubricant would tend to confine this maximum of lubrication 

 within narrow limits, and observation shows this to be the 



-case. 



As the facility for slinping increases the character of the 

 movement changes. When the surfaces are clean the pull 

 is 0"85 or 0'93 gramme per gramme normal pressure, and 

 steady slow sliding motion cannot occur owing to the violent 

 seizing. As the facility for slipping increases seizing de- 

 creases, and the motion assumes more and more a gliding 



•character. When the threshold value has fallen to 



