286 H. K. SCHACHMAN AND R. C. WILLIAMS 



been derived, as well as some details of their packing arrangement within 

 crystals, but this is about all at the present. 



' g. Diffraction Patterns of Oriented Fibers. The preceding discussion has 

 been concerned with X-ray diffraction analysis of ttree-dimensional crystal- 

 line arrays, such as a crystal of rock salt. There is another general type of 

 oriented structure, however, than can be described as a fiber, or paracrystal. 

 It consists of a closely packed array of elongated particles with the fiber 

 axis parallel to the axes of the individual particles. Such paracrystals can 

 be formed, for example, by drawing out fibers of deoxyribonucleic acid 

 (DNA) or by orienting the rods of tobacco mosaic virus by rolling or by 

 controlled evaporation. 



An X-ray pattern of a fiber is usually obtained by directing the X-ray 

 beam perpendicular to the fiber axis. Two directions in the X-ray pattern 

 are then distinguishable: the "meridional" direction that is parallel to the 

 fiber axis, and the "equatorial" direction that is perpendicular to the axis. 

 If the fiber contains repeating structures, the X-ray pattern will consist of 

 a set of spots, or short arcs, that has symmetry about its center. In general 

 the spots will be arrayed along "layer lines"; these are linear groupings that 

 run perpendicular to the direction of the fiber axis and represent successive 

 orders of constructive interference of the X-rays scattered from some axial 

 periodicity of structure. From the spacing of the layer lines a determination 

 can be made of the size of this repeating structural miit. The spacing and 

 intensities of the X-ray Spots in the equatorial direction give information 

 about the interparticle spacing in the oriented array, and may disclose some- 

 thing about the intraparticle radial distribution of electron density. 



X-ray diffraction patterns of paracrystals made up of particles of a helical 

 configuration have recently assumed great importance owing to the ubiqui- 

 tous presence of elongated molecules of this type in biological systems. 

 Examples of helical configurations are the polymers of DNA and the rods of 

 tobacco mosaic virus. The theory of the X-ray analysis of helical structures 

 has been developed (Cochran et al., 1952), and predicts certain distmctive 

 aspects that allow such structures to be recognized and analyzed. The most 

 striking aspect of the diffraction patterns of helices is seen along the meridian, 

 where a region of emptiness prevails. The innermost spots of the layer lines 

 are off-meridian, with the distance from the meridian increasing with the 

 number of the layer line. To a first approximation, for example, the inner- 

 most spot of the fifth layer line will be five times as far off-meridian as will 

 the corresponding spot of the first layer line. As a consequence the pattern 

 appears at first glance to have an X-like shape. Meridional spots do appear, 

 however; if the structural unit within the helical particles repeats n times in 

 m turns of the helix (where n and m are integers) a meridional spot will be 

 found on the n^^ layer line. For example, in DNA there are 10 nucleotides in 



