334 ON THE INTERNAL FORM [ch. 



If the cell be homogeneous, taking in and giving out at a constant 

 rate in a uniform way, its shape will be spherical, the concentration- 

 field of force, or concentration-field, will likewise have a spherical 

 symmetry, and the resultant force will be zero. But if the symmetry 

 be ever so little disturbed, and the shape be ever so little deformed, 

 then there will be forces at work tending to increase the deformation, 

 and others tending to equalise the surface-tension and restore the 

 spherical symmetry, and it can be shewn that such agencies are 

 within the range of the chemistry of the- cell. Since surface- 

 tension becomes more and more potent as the size of the drop 

 diminishes, it follows that (under fluid conditions) the smallest 

 solitary cells are least likely to depart from a spherical shape, and 

 that cell-division is only likely to occur in cells above a certain 

 critical order of magnitude; and using such physical constants 

 as are available, Rashevsky finds that this critical magnitude 

 tallies fairly well with the average size of a living cell. The more 

 important lesson to learn, however, is this, that, merely by virtue 

 of its metabolism, every cell contains within itself factors which may 

 lead to its division after it reaches a certain critical size. 



There are simple corollaries to this simple setting of the case. 

 Since unequal concentration-gradients are the chief cause which 

 renders non-spherical shapes of cell possible, and these last only so 

 long as the cell lives and metabolises, it follows that, as soon as the 

 gradients disappear, whether in death or in a "resting-stage", the 

 cell reverts to a spherical shape and symmetry. Again, not only is 

 there a critical size above which cell-division becomes possible,, 

 and more and more probable, but there must also be a size beyond 

 which the cell is not likely to grow. For the "specific surface" 

 decreases, the metabolic exchanges diminish, the gradients become 

 less steep, and the rate of growth decreases too ; there must come 

 a stage where anabolism just balances katabolism, and growth 

 ceases though life goes on. When streaming currents are visible 

 within the cell, they seem to complicate the problem; but after all, 

 they are part of the result, and proof of the existence, of the gradients 

 •we have described. In any further account of Rashevsky 's theories 

 the mathematical difficulties very soon begin. But it is well to 

 realise that pure theory often carries the mathematical physicist a 

 long way ; and that higher and higher powers of the microscope, and 



