NODAL POINTS 27 



tinctly thickened and appear darker. It is a consequence 

 of this that the froth appears with a low power, or with 

 cursory observation, to be composed of closely-packed fine 

 granules. The reason of this phenomenon must, be chiefly 

 as follows. If one investigates in macroscopic froths the 

 union of three lameUse at one edge, or the union of six 

 lamellae at a nodal point, as the case may be, it is found 

 that here the lameUffi do not simply meet one another, but 

 that the limiting surfaces of the neighbouring lamellae pass 

 into one another with a concave curvature (see Fig. 2). A 

 consequence of this must be, that the edges 

 are somewhat thicker than the rest of the 

 lamellae; but since the corresponding rela- 

 tions in the fine microscopic froths are 

 much too small for it to be possible to 

 make out distinctly the true form of these 

 nodal points, only a general appearance ^'°' ^' 



of a rounded thickening of the nodal points must arise. If 

 the nodal points of macroscopic froths are studied more 

 closely, it is further very often seen that they are occupied 

 by minute air-bubbles, which often bulge them out more or 

 less into a swelling. This is interesting at once for the 

 reason that it shows that such small vesicles or bodies in 

 the froths collect at the nodal points, and further, because 

 it proves the possibility that in the microscopic foams the 

 nodal points may in part be thickened by the inclusion of 

 very small foam vesicles, no longer recognisable as such, which 

 cause them to stand out more strongly. Pinally, yet a 

 third cause is to be mentioned, which produces the appear- 

 ance of dark nodal points in the framework of the meshes, 

 and to which I am now inclined to ascribe an essential 

 share in this effect. It has been already pointed out that 

 the optical appearance of the alveoli of the foam, i.e. bodies 

 of feebler refracting power enclosed in a more strongly 

 refractile medium, is of such a kind, that when focussed 



since, as has been set forth above, this distinction cannot be drawn in prac- 

 tice. In any case, the three lines that are actually to be observed, which 

 meet together in the nodal points, are, as a rule, sections through three 

 lamelloe, which meet at one edge. 



