202 Professor W. Lawrence Bragg [May 28, 



crystal structure receives a natural explanation on this theory. The 

 valency of the ion of either sign is due to an electrostatic attraction 

 and can be subdivided to any extent. 



The other type of chemical compound is that of two electro- 

 negative elements. Each element in this case has a smaller number 

 of electrons than is necessary for complete stability. In order that 

 the empty spaces in the outer shell may be completely filled, the 

 atoms share electrons, the valency bonds corresponding to a pair of 

 electrons held in common by both atoms. It is in this way of 

 regarding the combination of electronegative elements that the 

 Langmuir theory finds one of its strongest supports ; the complicated 

 valencies of elements such as nitrogen and phosphorus are readily 

 explained by a consideration of the ways in which these atoms can 

 fill up their outer shells by holding electrons in common with other 

 atoms. 



10. It has been seen that the potassium chloride crystal consists of 

 alternate ions. The structure of calcite (Plate I, fig. b) presents 

 the same alternation of ions, only in this case one of the ions, the 

 C0 3 group, is complex. The calcium atom has lost two electrons in 

 reverting to the argon arrangement of electrons, and it is therefore 

 a doubly charged positive ion. The C0 3 group has absorbed into its 

 system two additional electrons, and the four atoms in the group are 

 surrounded by the total complement of electrons for stability, some 

 of the electrons being held in common. In this crystal both types 

 of chemical combination are illustrated : the calcium and C0 3 ions 

 are held together by their charges ; the carbon and oxygen atoms are 

 bound together into the C0 3 group by holding electrons in common. 

 The crystal is therefore divisible into units, each unit having a 

 continuous outer electron shell. One unit is the calcium nucleus 

 surrounded by its proper electron cloud, the other is the C0 3 group 

 again surrounded by its electron cloud. Some repulsive force must 

 be supposed to exist between the outer electrons which keeps the ions 

 apart, opposing their electrostatic attractions for each other. The 

 arrangement of the ions in potassium chloride and calcite is the same, 

 except that in the latter case the substitution of the complex C0 3 ion 

 for the CI ion distorts the cube into a rhombohedron (cp. figure). 



11, The empirical relations summarized by Fig. 3 can readily be 

 interpreted on this theory. In calcium carbonate, for example, the 

 proximity of the carbon and oxygen centres leads to a small diameter 

 being assigned to the spheres representing these atoms, while the 

 comparative isolation of the calcium atoms leads to a large diameter 

 being taken for the corresponding sphere. We now see that the 

 carbon and oxygen atoms are close together because they share 

 electrons ; the calcium atom is isolated because it has no electrons in 

 common with the other atoms. The large diameter assigned to the 

 electropositive elements does not therefore indicate that the outer 

 electrons are anv further from the nucleus than thev are in the 



