OX IMPACT WITH A l.lyPH) SPRFACK. 187 



/.-lie of surface which enters is more nearly parallel to the direction of motion of the 

 .sphere, the displacement of liquid is most rapid at the lowest point, from the neigh- 

 Ixmrhood of which fresh liquid in supplied to flow along the surface. Whether the 

 rising sheath shall leave the surface of the sphere or shall follow it depends ujx>n the 

 efficiency of the adhesion to the sphere. If the sphere is smooth, the molecular forces 

 of cohesion will guide the nearest layers of the advancing edge of the sheath, and will 

 thus cause the initial flow to be along the surface of the sphere. 



To pull any portion of the advancing liquid out of its rectilineal path the sphere 

 must have rigidity. If the advancing liquid meets loosely attached particles, e.g., 

 of dust, these will constitute places of departure from the surface of the sphere ; 

 the dust will be swept away by the momentum of the liquid which, being no longer 

 in contact with the sphere, perseveres in its rectilineal motion. If the dust particles 

 are few and far between, the cohesion of the neighbouring liquid will bring back the 

 deserting parts, but if the places of departure are many, then the momentum of the 

 deserters will prevail. Thus at every instant there is a struggle between the 

 momentum of the advancing edge of the sheath and the cohesion of the sphere ; 

 the greater the height of fall the greater will be the momentum of the rising liquid, 

 and the less likely is the cohesion to prevail, and the presence or al>sence of dust 

 [articles may determine the issue of the struggle. 



Roughness of the surface will be equally efficient in causing the liquid to leave the 

 sphere. For the momentum will readily carry the liquid past the mouth of any 

 cavities (see fig. 3), into which it can only enter with a very sharp curvature of its 



Fig. 3. 



path. It is to be observed that the surface tension of the air-liquid surface of the 

 sheath will act at all times in favour of the cohesion of the sphere, and even if the 

 film has left the sphere the surface tension will tend to make it close in again, 

 but we should not be right in attributing much importance to this capillary 

 pressure which, with finite curvatures, is a force of a lowor order of magnitude* 



* This point may lx> made clearer by a numerical statement of the case. The particles of the liquid 

 sheath on the shoulders of the sphere (itself defending) in figs. 5 and 6 of Series XIII., Plate 3, must be 

 describing paths whose centres of curvature lie on the side of the sphere, and on every element of the 

 film there must be an inwardly directed force. (We speak of the film as a whole, and ignore any minute 

 vortical motion.) With a sphere of 1 centim. radius, and water as the liquid, the surface-tensional 

 pressure would be about 0'075 gramme per sq. centim., which is quite insignificant as compared with the 



2 B 2 



