42 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



between the apices of two corresponding hyperbolae, one in the upper 

 and one in the lower half of the diagram) then clearly 



/•/Z)=tan ai, 



hence a^ can be calculated and b determined from equation (3). 



For reasons into which we need not go, but will be obvious after a 

 little thought, there is never a reflection at the apex itself; hence the 

 calculation is usually made from other spots on the hyperbolae. This 

 complicates the mathematics, but the principle remains the same. 



Now this process applies strictly also to fibrous cells. If a bundle of 

 cells, say of ramie fibres, is prepared in such a way that the fibres lie 

 strictly parallel to each other and this bundle is mounted in the X-ray 

 beam as in Plate II (Fig. 1), then the "fibre diagram" obtained is essen- 

 tially a rotation diagram, as will be clear from the figure. The reason for 

 this is obvious. In the first place, this is a bundle of fibres in which the 

 fibres lie parallel but otherwise in random orientation about their 

 lengths. Hence the photograph will naturally be that of a single fibre 

 rotated about its length. More than this, however, each single fibre is 

 a hollow thread with an axis of symmetry parallel to its length. Hence 

 the diagram of a single fibre corresponds to that of any part of its wall 

 rotated about the cell axis. The pattern of spots in the diagram makes 

 it clear that one axis of the unit cell Hes almost parallel to the fibre length 

 and this makes calculation of one side of the unit cell a very simple 

 matter. 



The unit cell of cellulose 



The parameter b for cellulose turns out to be 10-3 A., or very nearly 

 that, for every type of cellulose examined. This is formally regarded as 

 the b axis. It will be noticed that a reflection corresponding to a spacing 

 of 10-3 A. does not actually appear in the diagrams of cellulose. This 

 must mean that, between planes passing through neighbouring lattice 

 points and parallel to the ac plane there must be at least one other plane 

 interleaved, spaced bjl A. apart (for then reflections from successive 

 planes spaced b A. apart with a path diff'erence of U will be obliterated 

 since the path diff'erence for the interleaved planes will be A/2. As a 

 matter of fact the first strong reflection to appear is often the fourth 

 order, indexed therefore 040, and corresponding to an interplanar 

 spacing of 2-56 A. (approximately 10-3 A). 



Determination of the other two axes of the unit cell is not so simple 

 since, in view of the cyhndrical nature of the cells, it is impossible to 

 obtain rotation diagrams about axes other than the b axis. Recourse 



