472 THE FORMS OF TISSUES [ch. 



(9) Statically though not dynamically, that is to say as a line or 

 surface of continuity in Plateau's sense, our bourrelet is analogous 

 to the accumulation of sand seen where two nodal lines cross in a 

 Chladni figure: "Vers les endroits oii des lignes nodales se coupent, 

 elles s'elargissent toujours, de sorte que la forme des parties vibrantes 

 pres de ces endroits n'est pas angulaire mais plus ou moins arrondie, 

 sou vent en forme d'hyperbole*." And in somewhat remoter analogy, 

 we may look on the three corpora Arantii as so many bourrelets, 

 helping to fill the angles where three semilunar valves meet at the 

 base of the great arteries. 



We may now illustrate some of the foregoing principles, con- 

 stantly bearing in mind the principles set forth in our chapter on 

 the Forms of Cells, and especially those relating to the\pressure 

 exercised by a curved film. 



Fig. 157. 



Let us look for a moment at the case presented by the partition- 

 wall in a double soap-bubble. As we have just seen, the three films 

 in contact (viz. the outer walls of the two bubbles and the partition- 

 wall between) being all composed of the same substance and being 

 all ahke in contact with air, the three tensions must be equal, and 

 the three films must, in all cases, meet at co-equal angles of 120°. But 

 unless the two bubbles be of precisely equal size, and therefore of 

 equal curvature, the tangents to the spheres will not meet the plane 

 of their circle of contact at equal angles, and the partition-wall will 

 of necessity be a curved, and indeed a spherical, surface; it is only 

 plane when it divides two equal and symmetrical cells. It is 

 obvious, from the symmetry of the figure, that the centres of the 

 two bubbles and of the partition between are all on one and the 

 same straight line. 



The two bubbles exert a pressure inwards which is inversely 



♦ E. F. F. Chladni, Traite d'acoustique, 1809, p. 127. 



