V] OF ASYMMETRY AND ANISOTROPY 401 



Our formula of equilibrium, or equation to an elastic surface, is 

 P = jDg + (TjR + T' jR), where P is the internal pressure, jo^ 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 seek to account for, R, R' are 

 known quantities; but all the other factors of the equation are 

 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 sohdification), 

 the cyhndrical cell of Spirogyra^ the elhpsoidal yeast-cell, or (as 

 we shall see in another chapter) even the egg of any bird. In 

 using this formula hitherto we have taken it in a simphfied form, 

 that is to say we have made several limiting assumptions. We have 

 assumed that P was the uniform hydrostatic pressure, equal in all 

 directions, of a body of hquid; we have assumed likewise that the 

 tension T was due to surface-tension in a homogeneous hquid 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, jo„, was non-existent. Now in the case of a bird's egg 

 the external pressure p^, 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 Spirogym, 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 inequahties in the internal pressure P, or else to inequahties 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 respect of 

 the tension, and implicitly the molecular structure, of the cell- wall. 

 Now' the former hypothesis is not impossible. Protoplasm is far 

 from being a perfect fluid; it is the seat of various internal forces, 

 sometimes manifestly polar, and it is quite possible that the forces, 

 osmotic and other, which lead to an increase of the content of the 



