﻿of the common Surface of two Liquids. 475 



2. The tension of the surface or capillary constant ct x<i of the 

 common bounding surface of two liquids, multiplied by the sum of 

 the inverse principal radii of curvature of a point of the bounding 

 plane, gives the capillary pressure in the direction of the perpendi- 

 culars to the surface. 



3. The magnitude of this capillary constant ot n does not admit 

 of being directly determined from the capillary constants a x and a 2 

 of the free surface of the two liquids, but must be found by special 

 experiments. It may have all possible values between and 



4. y/*a 12 = 0, then the liquids 1 and 2 are miscible in all pro- 

 portions, and no drop or bubble of one liquid is formed in the in- 

 terior of the other. Moreover a 12 appears smaller the more 

 miscible the liquids are, and is always less than u x — a 2 . 



5. If three capillary surfaces meet together in a point, then the 

 exterior angles of a triangle whose sides are proportional to the 

 capillary constants of the three capillary surfaces are the marginal 

 angles of tlie surfaces of the liquids. 



6. A liquid 3 spreads out on the common bounding surface of 

 two liquids 1 and 2 when « ]2 <a 31 — «23- 



7. A liquid 2 spreads out on the free surface of a liquid 1 

 when a l2 '<a l — oc 2 . 



8. If liquids which are miscible in all proportions, for which 

 therefore ot iq =0,be arranged so that each following one spreads out 

 on the free surface of the foregoing, the same series will be ob- 

 tained as if the liquids had been arranged according to the magni- 

 tude of the capillary constant of their free surface. 



9. If a lens-shaped drop of a liquid 2 remains on the free sur- 

 face of a liquid 1 without spreading itself out, then it is certain 

 that in most, and probable that in all cases the free surface of 

 liquid 1 is rendered impure by a thin layer of a foreign liquid 3. 

 The effect of this foreign layer increases with its thickness up to a 

 certain limit, which is equal to twice the radius of the sphere of 

 action. 



10. If a liquid 2 spreads out in a thin layer upon a flat drop of a 

 liquid 1 in air or upon aflat air-bubble in the interior of the same 

 liquid \, then the vertical distance K — k of the horizontal and ver- 

 tical parts of the capillary surface diminishes. The new shape of 

 the flat drops and bubbles may be calculated when a 12 and a. 2 are 

 known. 



11. If a liquid 3 spreads out on tlie surface of a flat drop of a 

 liquid 2 in a liquid 1, it can only be said that the height K — k of 

 the drop of the liquid 2 diminishes. The change of form in this 

 case cannot always be calculated beforehand. 



12. The capillary constants of free liquid surfaces, determined 

 on flat drops or bubbles, are greater than if calculated from the 



