168 THE PHILOSOPHY OF BIOLOGY 



as are partially the result of a very great number of 

 small and unco-ordinated causes : the form of an 

 island or a mountain suffering erosion, or the shape 

 of a river valley or delta, or the arrangement of the 

 stones forming a moraine at the side of a glacier. 

 Essential forms are such as are assumed as the result 

 of the operation of one or a few co-ordinated causes, 

 and such are the forms of crystals. They are invari- 

 able, or they vary within very small limits about an 

 invariable mean form. 



The form of a crystal depends on the structure of 

 the molecules of the chemical substance from which 

 it is produced. We cannot, of course, speak of the 

 shape of a molecule, but we know that the atoms of 

 which it is composed have certain positions in space 

 relative to each other — positions which are con- 

 ceptualised in the structural formulae of the chemists. 

 In the solution, or mother-liquor, these molecules 

 move freely among each other, but in the crystal they 

 become locked together and their motions are re- 

 stricted. The shape of the crystal depends on the 

 way in which the molecules are locked together, or on 

 the way in which they are arranged. A cube may 

 be built up by the arrangement of a number of very 

 small cubes : obviously we could not make a cube from 

 a number of very small hexagonal prisms if the latter 

 were to be packed together in such a way as to occupy 

 the minimum of space. An infinitely great number 

 of cubes might also be formed by adding single layers 

 of very small cubes to the faces of an already existing 

 one — that is, by the accretion of elements of essentially 

 similar form. In every cube (or crystal) of this infinite 

 number the geometrical form would be the same, 

 and if we were to measure any one side of any cube 

 of this series we should find that the total surface 



