242 THE 'FORMS OF CELLS [ch. 



Our full formula of equilibrium, or equation to an elastic 

 surface, is P = 'p^+ {TIE + T'/R'), where P is the internal 

 pressure, fg any extraneous pressure normal to the surface, R, R' 

 the radii of curvature at a point, and T, T' , the corresponding 

 tensions, normal to one another, of the envelope. 



Now in any given form which we are seeking to account for, 

 R, R' are known quantities ; but all the other factors of the equation 

 are unknown and subject to enquiry. And somehow or other, by 

 this formula, we must account for the form of any solitary cell 

 whatsoever (provided always that it be not formed by successive 

 stages of solidification), the cylindrical cell of Spirogyra, the 

 ellipsoidal yeast-cell, or (as we shall see in another chapter) the 

 shape of the egg of any bird. In using this formula hitherto, we 

 have taken it in a simplified form, that is to say Ave have made 

 several limiting assumptions. We have assumed that P was 

 simply the uniform hydrostatic pressure, equal in all directions, 

 of a body of liquid ; we have assumed that the tension T was 

 simply due to surface-tension in a homogeneous liquid film, and 

 was therefore equal in all directions, so that T = T' ; and we have 

 only dealt with surfaces, or parts of a surface, where extraneous 

 pressure, 2^„, was non-existent. Now in the case of a bird's egg, 

 the external pressure 2>nj that is to say the pressure exercised by 

 the walls of the oviduct, will be found to be a very important 

 factor ; but in the case of the yeast-cell or the Spirogyra, wholly 

 immersed in water, no such external pressure comes into play. 

 We are accordingly left, in such cases as these last, with two 

 hypotheses, namely that the departure from a spherical form is due 

 to inequalities in the internal pressure P, or else to inequalities in 

 the tension T, that is to say to a difference between T and T' . 

 In other words, it is theoretically possible that the oval form of 

 a yeast-cell is due to a greater internal pressure, a greater 

 "tendency to grow," in the direction of the longer axis of the 

 ellipse, or alternatively, that with equal and symmetrical tendencies 

 to growth there is associated a difference of external resistance in 



maximum surface-curvature lying at the level where the densities of the drop 

 and the surrounding liquid are just equal. The sectional outline of the drop has 

 been shewn to be not a true oval or ellipse, but a somewhat complicated quartic 

 curve. (Rice, Phil. Mag. Jan. 1915.) 



