176 Prof. W. L. Bragg on the 



position, was found by the author to be approximately 

 0*30/1, corresponding to a distance between oxygen and 

 carbon centres of 1*47 A. This distance is the same for all 

 compounds of the series. 



In the diamond the o distance between the centres of the 

 carbon atoms is 1'54 A. Taking the diameter of the carbon 

 atom as 1*54 A., and that of the oxygen atom as 1"30 A., the 

 distance between oxygen and carbon centres should be 

 1*42 A. This is in agreement with the distance of 1*47 A. 

 deduced from the X-ray measurements. 



The distance between the centres of the metallic atom and 

 the oxygen atom may be compared with the distance in the 

 metallic oxide. In the carbonates the atom of the metal is 

 surrounded by six oxygen atoms. In zinc carbonate the 

 distance between zinc and oxygen centres is 1*99 A, in zinc 

 oxide it is 1*97 A. The agreement is not so good in other 

 cases. o The distance between calcium and oxygen centres is 

 2*40 A. in OaO, 2*30 A. in CaC0 3 . The corresponding figures 

 for MgO and MgC0 3 are 2*10 and 2-00 A. In FeC0 3 the 

 distance between the iron and oxygen centres is 2*04 A., 

 in Fe 3 4 * (magnetite) it is 2*00 A. This leads to a value 

 2*74 A for the diameter of iron, greater than the value 2'47 A 

 calculated from pyrites and metallic iron. Although this is 

 the case, it will be seen that the conception of the crystal 

 as a number of spheres packed tightly together leads to a 

 determination of the parameter which is near the true one. 



8. Two other examples will be taken as affording a cross- 

 check on these measurements. In fluorspar, CaF 2 , the 

 distance between calcium and fluorine centres is 234 A. 

 In sodium nitrate, NaN0 3 , the arrangement of the sodium 

 and nitrogen atoms is that of the calcium and carbon atoms 

 in calcite. The ratio x/d determining the position of the 

 oxygen atoms is approximately 0*25. This gives the distance 

 between oxygen and nitrogen centre o s as 1*30 A., between 

 oxygen and sodium centres as 2*33 A. We thus have the 

 relations — 



Na— O ... 2-33 A. (NaN0 3 ) Ca— 2-30 A. (CaC0 3 ). 



Na— F ... 2-39 A. (NaF). Ca-F 2'34 A. (CaF 2 ). 



The space occupied by calcium in a crystal is much the 

 same as that occupied by sodium; that occupied by oxygen is 

 much the same as that occupied by fluorine, 



9. These examples will indicate the manner in which the 

 results shown in fig. 3 have been calculated. Fo o r instance, 

 the diameter of oxygen has been taken to be 1*30 A., and that 



* W. H. Bragg, Phil. Mag. vol xxx. (Aug. 1915). 



