PROPERTIES OF FOAM 23 



strongest systems (Zeiss Apochr. 2 mm., Ap. 1'30 and 1'40), 

 and by employing strong oculars (comp. Oc. 12 and 18), is 

 it seen for certain that we are dealing here with a very fine 

 foam-like structure. Such a very fine microscopic froth 

 does not, as a rule, appear any different from a macroscopic 

 soap or beer-froth. There is this difference, however ; the 

 microscope only represents clearly an image that falls in 

 one plane, and therefore only brings into view a plane section 

 through a froth of this kind. Moreover, there are still a 

 number of relations to be taken into consideration in con- 

 nection with the peculiarities of microscopic vision ; they 

 will be further discussed below. As a result, the microscopic 

 image of such a froth will appear as a meshwork or network, 

 the meshes of which are formed of the most varied kinds of 

 polygonal figures. Very numerous transitions from triangular 

 meshes to those with many angles will be found. 



As is well known, a number of laws obtain for the 

 formation of microscopic froths which Plateau (1873 and 

 earlier) developed with exactitude, and which are chiefly 

 as follows. A froth represents a system of thin lamellae 

 of fluid, the arrangement of which is always such that 

 three lamellae meet at one edge, each making with its neigh- 

 bour an angle of 120. Since each lamella, in con- 

 sequence of its surface tension, exerts a pull upon the 

 common edge in which they meet, it is clear, a priori, that 

 as long as the three lamellae have equal tensions and this 

 is invariably the case in ordinary froths equilibrium can 

 only be established between the three lamellae under the con- 

 dition stated. The edges in which the lamellae of froth touch 

 one another are connected amongst themselves in such a way 

 that three edges meet in a nodal point, so that the lamellae 

 form the most varied polyhedral figures, in which the rule 

 obtains that the angle, which every two neighbouring edges 

 form in the nodal point, amounts to 109 28' 16" (see 

 Plateau, T. I. p. 315). If one attempts to build up a system 

 of lamellae under the conditions stated, and assumes an equal 

 length of edge in all lamellae that meet, a system is obtained 

 composed of nearly regular dodecahedra, a natural result, 

 since the dodecahedron comes nearest to the conditions to 



