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



electroscope was increased by the deposited drop of liquid. 

 This would indicate that a thin film of liquid already previously 

 existing upon the glass (probably moisture from the atmo- 

 sphere) was driven away by the deposited drop of solution 

 and repelled from the surface of the glass. 



15. Breath-figures. — Finally a series of long-known phe- 

 nomena, which I have included in a treatise * " On the Con- 

 densation of Gases and Vapours on the Surface of Solid 

 Bodies/' find their natural explanation in the influence which 

 imperceptibly thin films of liquid on the surface of a solid 

 body exercise upon the spread and edge-angle of a liquid. 



The edge-angle which lenticular drops of water, alcohol, or 

 other liquids make with the surface of a liquid or solid body 

 differs in magnitude with the substance, and the thickness of 

 the imperceptibly thin film with which the surface is covered. 

 I established this formerly f for mercury and other liquids, 

 and have now proved it for solid substances such as glass, 

 mica, silver, &c, in the earlier part of this communication 



(§§4-7). 



Suppose the thickness of this film of substance 2 upon the 

 solid body 1 to increase from to a maximum value D, then 

 the value of the edge-angle will vary continuously from the 

 value #!, corresponding to the clean surface of the substance 

 1, up to the value 6 2 , corresponding to the clean surface of 

 the liquid 2, and will then remain constant for any further 

 increase of the thickness. 



This maximum value D of the thickness, from which on- 

 wards the edge-angle acquires the constant magnitude 2 , must 

 in general depend upon the radius of the sphere of sensible 

 action of the molecular forces. If no change of density occur 

 in the interior of the substance 2 (as was amply set forth above 

 in § 12), then of necessity D = l. 



This last is the case if the substance 2 consist not of liquid, 

 but of some solid body whose particles admit only of a slowly 

 occurring shifting, so that the density may be regarded as 

 constant during the period of the experiment. This relation 

 has indeed been employed by me J for a determination of the 

 magnitude I ; and at the same time it was proved that with 

 an increasing thickness of the solid substance 2 the edge-angle 

 did in fact approach a constant value 6 2 . By this means, 

 the edge-angles formed by mercury against films of iodide 



* Pogg. Ann. cviii. p. 339 (1859), " Ueber Verdichtung von Gasen 

 und Dampfen an der Oberflache fester Korper." 



t Pogg. Ann. cxxxix. p. 64 (1870) ; and Phil. Mag. June 1871. 

 X Pogg. Ann. cxxxvii. p. 402 (1869). 



