INVESTIGATION OF STRUCTURE IN PLANT CELL WALLS 43 



must therefore be made to more indirect methods. These involve a 

 trial and error method; in principle, reasonable values are assumed for 

 a, c and /?, followed by a calculation, from the unit cell thus determined, 

 of the spacings d and the indices hkl for all possible planes, and a com- 

 parison of these with the spots on the diagram. The method is nowadays 

 rendered much more workable by the use of the concept of a reciprocal 

 lattice which enables the spots on a rotation diagram to be indexed 



Fig. 18. Diagrammatic representation of the investigation of a plate of cellulose as 

 it occurs in, for instance, the tunicates. Six unit cells are drawn (cp. Fig. 19) with 

 the b axis horizontal and the spacings 10-3, 6-1, 5-4 A. are indicated. When an X-ray 

 beam is directed along 1, reflections are observed from planes spaced 5-4 A. apart 

 (since there is in a natural specimen some angular dispersion around the axis) but 

 not from the 6-1 planes (since these stand at right angles to the beam). 

 When the beam lies along the direction 2, then reflection is observed from the 

 6-1 A. planes only. Hence by rotating the specimen about the b axis, the angle of 

 rotation between the positions of maximum reflection from 5-4 A. planes and from 

 6-1 A. planes, after a correction for the (small) difference in glancing angle, gives a 



rough measure of the angle yS. 



(see e.g. 13). In order to choose reason- 

 able values for a and c, it should be noted 

 that along the horizontal line of the 

 diagram of ramie fibres (Plate II, Fig. 2 

 {a)) there are three principal arcs on each 

 side of the centre; these, counting from 

 the outer arc to the inner, correspond to 

 planes spaced 3-9, 5-4, 6-1 A. apart and 

 lying parallel to the b axis. This makes it 

 reasonable to suppose that the unit cell 

 is at least monoclinic and, as a first trial, 

 any two of these three spacings could be 

 equated to the two unknown sides of the 

 unit cell. The first suggestion, made by 

 Sponsler (14), was that fl=6-l, c=5-4 

 when it was found that if /3=88° then 



Fig. 19. The unit cell proposed 

 by Sponsler. 



