KERATIN AND MOLECULAR BIOLOGY 13 



The equation which must be satisfied by the angle 6 between the incident 

 radiation and a given set of planes is the Bragg law: 



nX = 2d sin d 



Where n is any whole number (the order of the reflection), d is the spacing 

 between the set of planes and A the wavelength of the X-rays. Thus, 

 from the photographic plate, the angle 6 is determined from the distance 

 of any reflection (" spot ") from the central spot due to the undeflected 

 beam, A is known from the target used (in biological work it is often copper 



/ 



itHrHf. 



i' 1 [ !' 

 _-ff-f-4-+4-4^ 



<i i l \ T 



A ' * V 



Fig. 5. Idealized diagram of a typical " X-ray fibre photograph " taken 

 with the X-ray beam perpendicular to the fibre-axis and to the photo- 

 graphic film (fibre axis vertical). The reflections are seen to lie along a 

 series of hyperbolae referred to as layer lines. Redrawn from Astbury 

 and Bell (1939). 



giving a wavelength of 1-54 A for copper K a- rays) and thus the distance d 

 between the planes can be calculated. Notice that the smaller d is, the 

 greater the distance the reflection occurs from the centre. For this reason 

 the smaller spacings < 10 A, arising from close-packed atoms and 

 characteristic of the molecular level of organization, are found at wide 

 angles ( > 10°) and constitute the characteristic " wide-angle patterns" '. 



With single crystals of pure substances the practice is to rotate the 

 crystal in the beam to give all sets of planes in it a chance to pass through 

 the Bragg angle and thus register themselves photographically. In natural 

 high-polymeric materials in the fibrous form, this is not necessary because 

 these consist of innumerable small crystals (or crystallites) with one 

 principal direction parallel to the fibre axis, but randomly arranged in 



