INVESTIGATION OF STRUCTURE IN PLANT CELL WALLS 41 



along the surface of the cone. If, now, the reflected radiation is received 

 on a photographic film formed into a cylinder with the rotating crystal 

 axis as centre, then the reflections will lie along a series of straight lines 

 at right angles to the rotation axis. If, on the other hand, a flat film is 

 used, then the reflections lie on a series of hyperbolae, as in Plate II 

 (Fig. 1), since the intersection of a cone with a plane is a hyperbola. 



Fig. 17. The rotation diagram. For construction, see text. The radiations at A and 

 B are "in step". Reflection will occur along AP if 



BN=id, 



where AN is perpendicular to ^A'^, i.e. if 



b sin ai — fi?., 

 where « is an integer. 



For the direction AP, «= 1, so that 



sin ai=A/Z>. 



The angle of the reflected ray to the line AB is therefore fixed. Its direction is other- 

 wise not specified, so that reflection can occur anywhere from A along the conical 

 surface APP'. Similarly for AQ (/2=2) and AR 07=3). The condition n=0 corre- 

 sponds to the horizontal plane containing the primary beam. 



These hyperbolae are called the layer lines. This latter procedure is the 

 one usually adopted with fibres. There is now an easy method for 

 calculation of the primitive translation b. Thus, if r is the distance on 

 the plate between the apex of the hyperbola (or the line in cylindrical 

 films) and the centre of the photograph (or, better, one-half the distance 



