Results of Crystal Analysis. 411 



real tetrahedron with all sides of equal length. Then we 

 should have 



^ = ^ 2=0 . 707 . . . ; . ( i 66 ) 



On account of the particular value of the ratio c/a, we get 

 that, if condition (15) is fulfilled, the atoms are placed at 

 the corners of a sphenoid, which has very nearly the form 

 of a tetrahedron. 



The Arrangement of the Hydrogen Atoms. 



§ 6. We saw that the positions of the hydrogen atoms were 

 not necessarily fixed by symmetry ; but when all require- 

 ments of symmetry were fulfilled, there would generally be 

 at least five parameters left undetermined. As the reflecting 

 power of the hydrogen atoms is very small as compared with 

 that of the other atoms, a direct determination of the para- 

 meters would be very difficult, if at all possible. 



On the other hand, the H atoms appear in such a great 

 number that their reflecting power is by no means negligible; 

 and if we have to choose between several quite different 

 arrangements, the reflecting power of the H atoms ma}^ be 

 great enough to enable us to make the right choice. 



Now we have seen that the carbon atoms appear in groups 

 of four, placed at the corners of a tetrahedron ; and there 

 is a comparatively small number of arrangements of the 

 H atoms which should naturally present themselves. We 

 shall consider the following three : — 



(1) The three H atoms belonging to a certain C atom are 

 placed on the three sides of the tetrahedron which pass 

 through the C atom. This arrangement is shown in fig. 6. 

 To fix the position of the H atoms on the lines, two para- 

 meters should be required, because the distance from the 

 atom to the one H atom placed on the line OP parallel 

 to the base plane may be different from the distance from the 

 same atom to one of its two other H atoms. In view of 

 the fact that all sides of the sphenoid are nearly equal, 

 we should expect that also the three H atoms were placed 

 at nearly equal distances from the C atom. 



If the sides are not equal, the simplest assumption to 

 make would be the following : — 



One C atom and its three H atoms are placed at the 

 corners of other sphenoids such as Op' q' r' , and we assume 

 that these sphenoids are similar in form to the central one 

 formed by the carbon atoms. In this way the positions 



