324 Prof. G. Quincke on the Edge-angle and 



surfaces of the solid and of the fluids, constant for all points of 

 the intersecting line of the three bounding surfaces, and deter- 

 mined only by the nature of the solid and of the fluids. 



Therefore the surface common to mercury and water or air, 

 for example, makes the same edge-angle with the solid wall 

 of a cylindrical glass tube as the surface of a drop of mercury 

 in water or air makes with a flat glass plate on which it rests. 



The second known axiom of the capillary theory concerning 

 the constancy of the edge-angle is only a special case of that 

 just mentioned (viz. the case when fluid 3 is air), and was first 

 deduced, we may remark in passing, by Dr. Thomas Young*, 

 from considerations similar to the foregoing. 



If the fluids are brought, as is repeatedly the case, into con- 

 tact with solids which have a continuously curved surface 

 without sharp corners or edges, as, for example, into a glass 

 tube or onto a flat plate, then the surface-tensions of the sur- 

 faces common to the solid and to the fluids 2 and 3 act in op- 

 position to each other. 



Let normals be drawn to the surface of the solid 1 and to 

 the free surface of the fluid 2, and let the acute edge-angle 

 which is included between the normals be called 6 Z ; then 

 there is equilibrium as soon as the following equation is ful- 

 filled :— 



ai 3 = a 12 + a 2 3COS0 3 ; (4) 



or, omitting the index 3, 



COSC7= (5) 



(see Plate XII. fig. 6). 



The edge-angle 6 becomes 0°, and the fluid spreads over 

 the wall of the tube and moistens it, as soon as 



«1 — a 12>«2 • ' . . • , • . • • (6) 



For the case where the air is replaced by a fluid 3, the con- 

 dition of spread is 



«13 — «12>«23 (6 A) 



The theory developed in the preceding paragraphs will, in 

 the sequel, be compared with experience. 



2. The edge-angle of the free surface of a fluid must be the 

 same for flat air-bubbles under a level plate of glass as for fluids 

 which ascend capillary tubes of the same material. 



From the whole height K, and from the vertical distance 

 (K — k) between the horizontal and vertical elements of the 



* Lectures on Natural Philosophy, ii. p. 658 (1807), aud Young's 

 Works, i. p. 459 seqq, {Encyclop. Brit. 1816). 



