PROBLEMS OF BIOLOGY 317 



a few of its physical manifestations or laws. Of these 

 the most essential facts for us are as follows: Surface- 

 tension is manifested only in fluid or semi-fluid bodies, 

 and only at the surface of these : though we may have to 

 interpret surface in a liberal sense in cases where the interior 

 of the mass is other than homogeneous. Secondly, a fluid 

 may, according to the nature of the substance with which 

 it is in contact, or (more strictly speaking) according to the 

 distribution of energy in the system to which it belongs, 

 tend either to spread itself out in a film, or, conversely, to 

 contract into a drop, striving in the latter case to reduce 

 its surface to a minimal area. Thirdly, when three sub- 

 stances are in contact (and subject to surface-tension) as 

 when water surrounds a drop of protoplasm in contact with 

 a solid, then at any and every point of contact, certain 

 definite angles of equilibrium are set up and maintained 

 between the three bodies, which angles are proportionate to 

 the magnitudes of the surface-tensions existing between the 

 three. Fourthly, a fluid film can only remain in equilibrium 

 when its curvature is everywhere constant. Fifthly, the 

 only surfaces of revolution which meet this condition are six 

 in number, of which the plane, the sphere, the cylinder, and 

 the so-called unduloid and catenoid are important for us. 

 Sixthly, the cylinder cannot remain in free equilibrium if 

 prolonged beyond a length equal to its own circumference, 

 but, passing through the unduloid, tends to break up into 

 spheres : though this limitation may be counteracted or 

 relaxed, for instance by viscosity. Finally, we have the 

 curious fact that, in a complex system of films, such as a 

 homogeneous froth of bubbles, three partition walls and no 

 more always meet at a crest, at equal angles, as for instance 

 in the very simple case of a layer of uniform hexagonal cells ; 

 and (in a solid system) the crests, which may be straight or 

 curved, always meet, also at equal angles, four by four, in 

 a common point. From these physical facts, or laws, the 



