614 Dr. A. 0. Orehore on the Construction of • 



systems or" growth from the fields of force surrounding the 

 atoms when their axes are parallel, which agrees with those 

 of organic chemistry, seems to justify this view. 



Another important difference between a crystal and a 

 chemical molecule is the order of magnitude of the distances 

 between the atoms composing them. The edge of the tetra- 

 hedron forming the basis of the diamond has a length of 

 about 2*5xl0~ 8 cm., whereas 10~ lu cm. is the order of 

 magnitude of the distances between atoms in most of the 

 compound molecules. Roughly the distances are 100 times 

 greater in crystals, or we may say in crystal molecules, 

 thinking of a crystal as a single compound molecule built upon 

 a separate and distinctive system. Not only does the distance 

 differ, but the forces which hold the molecule together are 

 vastly greater in the case of the chemical compound molecule 

 due to this reduced distance. 



This latter fact has an important bearing upon crystal 

 formation. It becomes possible, on account of the small 

 distances between the atoms in a chemical compound, for a 

 molecule composed of a group of atoms to behave as though 

 it were a single atom; for example, in a cubic crystal like 

 sal ammoniac NH 4 CJ, the group NH 4 may act as a single 

 molecule taking the place, say, of Na in the compound NaCl, 

 the atoms of which are known to be in cubical army,, 

 alternating in three directions. 



Graphical Method of Constructing Molecules. 

 In some of the simpler molecules with a very small 

 number of atoms the equilibrium positions of the atoms may 

 be found hy means of the equations of the field, as has been 

 done in several cases ; but this method very soon becomes 

 impracticable because it requires the solution of simultaneous 

 equations of a high order with two or more unknown 

 quantities necessitating approximation to roots by trial, a 

 very laborious process. Were it not possible to get approxi- 

 mate results in any other w T ay little progress could be made. 

 By means of graphical charts of the fields of force between 

 two atoms, as measured by one of them, it has proved to be 

 possible to obtain approximate solutions for a sufficiently 

 large number of atoms to ascertain the different systems of 

 growth that are possible with such fields. On the theory 

 of probabilities it is very probable, on account of the com- 

 plexity and peculiarity of the known phenomena of organic 

 chemistry, that any theory which explains these things in 

 detail must contain premises that have certain elements of 

 the truth as to the theory of the atoms. 



