470 Lord Rayleigh on the 



The case of Young's experiment, in which oil stands upon 

 water in a glass tube, is not covered by the foregoing reason- 

 ing. The oil must be supposed to wet the glass, that is to 

 insinuate itself between the glass and air, so that the upper 

 part of the tube is covered to a great height with a very thin 

 layer of oil. The displacement here takes place under con- 

 ditions very different from before. As the column rises, no 

 new surface of glass is touched by oil, while below water 

 replaces oil. The properties of the oil are thus brought into 

 play, and Laplace's theorem does not apply. 



That theory indicates the almost indefinite rise of a liquid 

 like oil in contact with a vertical wall of glass is often over- 

 looked, in spite of Young's explicit statement quoted above. 

 It may be of interest to look into the question more narrowly 

 on the basis of Laplace's hypothesis. 



If we include gravity in our calculations, the hydrostatic 

 equation of equilibrium is 



p = const. + aY—gpz, (56) 



where z is measured upwards, and V denotes as before the 

 potential of the cohesive forces. Along the free surface of 

 the liquid the pressure is constant, so that 



o -V = <7 2 K + ^, (57) 



z being reckoned from a place where the liquid is deep and 

 the surface plane. 



At a point upon the surface, whose distance from the wall 

 exceeds the range of the forces, 



° Y = K+T (k + %) ; ■-'■•■ (58) 



or, if we take the problem in two dimensions, 



<-V=K+|, (59) 



where R is the radius of curvature, and K, T denote the in- 

 trinsic pressure and tension proper to the liquid and pro- 

 portional to <7 2 . Upon this equation is founded the usual 

 calculation of the form of the surface. 



When the point under consideration is nearer to the wall 

 than the range of the forces, the above expression no longer 

 applies. The variation of V on the surface of the thin layer 

 which rises above the meniscus is due not to variations of 

 curvature, for the curvature is here practically evanescent, 

 but to the inclusion within the sphere of influence of the 

 more dense matter constituting the wall. If the attraction 



