INVESTIGATION OF STRUCTURE IN PLANT CELL WALLS 39 



It should be noted that the angle between the primary beam and the 

 first order reflection is 26. 



Suppose, therefore, that a crystal is set up in the path of a parallel 

 beam of X-rays and a photographic plate is placed some distance D 

 behind it (Fig. 16), then the position of the plate 



primary beam will be recorded as a spot on 

 the plate. This is usually so intense as to 

 cause serious fogging of a large area of 

 plate, so that usually a small lead cup is 

 inserted to intercept the beam, as in Fig. 16. 

 The first order reflection will be recorded F'°- ^^- see'ext'^"^^'°"' 

 at R, say, so that the distance RO=r can 

 be measured. The value of 6 can then be calculated from the relation 



rlD=tan2d. ..(2) 



Substitution of this value of 6 in equation (1) will then give the corre- 

 sponding value of d, the interplanar spacing responsible for the reflec- 

 tion. In general, of course, the crystal will not be in such a position as 

 to give any particular reflection, but rotation around an axis normal to 

 the beam wiU cause the reflection to appear; further rotation until the 

 same reflection occurs on the other side of the central spot makes for 

 more accurate measurement since the value of 2r can then be deter- 

 mined without attempting to define the position of the primary beam. 

 This in brief, then, is the method used to determine a whole series of 

 interplanar spacings. If, now, these reflections can be "indexed", i.e. if 

 the indices of the planes producing the reflections can be found, then 

 the validity of any proposed unit cell can be tested. From this point of 

 view it should be noted that, though for simplicity attention has been 

 confined so far to first order reflections, in the photographs to be dis- 

 cussed second and even third order reflections occur and this is liable 

 to lead to confusion. For this reason it has become standard to include 

 the order of the reflection in the index. Thus, if we take for simplicity 

 planes parallel to the basal plane of the unit cell (Fig. 21), then reflec- 

 tion occurs from the 010 planes as a first order reflection when there is 

 a path difference of one wavelength between waves from successive 

 planes spaced b A. apart. The second order reflection from these planes, 

 when there is a path diff'erence of two wavelengths between successive 

 planes, can be considered as first order reflections from planes spaced 

 half the distance b apart, i.e. from planes with index 020, and the 

 reflection can be so recorded. Similarly, for any combination of indices, 

 the third order reflection from planes with indices 21 1, for instance, can 



