INVESTIGATION OF STRUCTURE IN PLANT CELL WALLS 37 



that the wavelength of the radiation is much shorter, since the distance 

 between the diffracting points is much less. For the great bulk of the 

 work on cellulose an X-ray wavelength of 1-54 A. is employed as given 

 from copper bombarded with electrons at, say, 40,000 volts. Space will 

 not allow any reference here to the experimental methods used to 

 produce X-rays; reference must again be made to other texts (12, 8). 



Returning to the line lattice, suppose a beam of X-radiation is allowed 

 to fall on the lattice in the direction defined by d^ (Fig. 14). Most of the 

 radiation will pass straight through the specimen. Since, however, each 

 point on the lattice can be regarded as a point of secondary emission, 

 then there is a possibility of radiation in other directions. In fact, 



Fig. 14. Reradiation by a row of points. Radiation is incident on the row from the 

 left at angle Qi. Consider any direction on the right making an angle Q^ to the row 

 as shown. Take any two neighbouring points, A and B, and drop perpendiculars 

 AM and ^A^ as shown. Then A and M are "in step" and the perpendicular AM can 

 be taken to represent say a crest in the radiation. For reflection to occur at the 

 angle d^, N and B must also be "in step", so that 



MB-AN^nl, 

 where /j=0, 1, 2, 3 . . . i.e. 



a cos d^—a cos 62,—)}}., 



for rt=0, 61 = 62, i.e. a "reflection" occurs where the angle of incidence equals the 

 angle of reflection. Other reflections can be found for «=1, 2, 3, etc., but these 



progressively diminish in intensity. 



radiation will not be emitted in any particular direction only if the 

 individual radiations from each point cancel out, and this will normally 

 happen since a crest of the radiation from one point will meet a trough 

 from some other. The construction in the diagram shows, however, 

 that in one direction, making the same angle with the row of points as 

 the incident rays, reflection will in fact occur, i.e. the radiation can be 

 regarded geometrically as being reflected from the line of points. This 

 is the condition when the total path of the rays from any one point is of 

 the same length as that from a neighbouring point. Equally, of course, 

 there will be a "reflection" if the two path lengths diff"er by one wave- 

 length or, in fact, any whole number of wavelengths. There are, 

 therefore, a number of "reflections", decreasing in intensity as the path 

 difference increases from to 1 A, 2A, etc. Each of these "reflections" is 

 not, of course, a single ray, but rather a cone of rays making the same 



