1914] on X-Rays and Crystalline Structure 201 



It is easily seen that the question of fit depends on how much 

 distance a wave reflected at one plane loses in comparison with the 

 wave which was reflected at the preceding plane : the fit will be 

 perfect if the loss amounts to one, two, three, or more wave-lengths 

 exactly. In its turn the distance lost depends on the spacing of the 

 planes, that is to say, the distance from plane to plane, on the wave- 

 length and on the angle at which the rays meet the set of planes. 



The question is formally not a new one. Many years ago Lord 

 Rayleigh discussed it in this room, illustrating his point by aid of a 

 set of muslm sheets stretched on parallel frames. The short sound 

 waves of a high-pitched bird-call were reflected from the set of frames 

 and affected a sensitive flame ; and he showed how the spacing of 

 the planes must be carefully adjusted to the proper value in relation 

 to the length of wave and the angle of incidence. Eayleigh used the 

 illustration to explain the beautiful colours of chlorate of potash 

 crystals. He ascribed them to the reflection of light by a series of 

 parallel and regularly spaced twinning planes within the crystal, 

 the distance between successive planes bearing roughly the same 

 proportion to the length of the reflected wave of light as the distance 

 between the muslin sheets to the length of the wave of sound. 



Our present phenomenon is exactly the same thing on a minute 

 scale : thousands of times smaller than in the case of light, and 

 many millions of times smaller than in the case of sound. 



By the kindness of Prof. R. W. Wood I am able to show you some 

 fine examples of the chlorate of potash crystals. If white light is 

 allowed to fall upon one of them, the whole of it is not reflected. Only 

 that part is reflected which has a definite wave-length or something 

 very near to it, and the reflected ray is therefore highly coloured. 

 The wave-length is defined by the relation already referred to. If 

 the angle of incidence is altered, the wave-length which can be 

 reflected is altered, and so the colour changes. 



It is not diflicult to see the analogy between tliese cases and the 

 reflection of X-rays by a crystal. Suppose, for example, that a pencil 

 of homogeneous X-rays meets the cube face of such a crystal as rock- 

 salt. The atoms of the crystal can be taken to be arranged in planes 

 parallel to that face, and regularly spaced. If the rays meet the face 

 at the proper angle, and only at Ihe proper angle, there is a reflected 

 pencil. It is to be remembered that the reflection is caused by the 

 joint action of a series of planes, which, in this case, are parallel lo 

 the face ; it is not a reflection by the face itself. The face need not 

 even be cut truly : it may be unpolished ov dehberately roughened. 

 The reflection takes place in the body of the crystal, and the condition 

 of the surface is of little account. 



The allotment of the atoms to a series of planes parallel to the 

 surface is not of course the only one possible. For example, in the 

 case of a cubic crystal, parallel planes containing all the atoms of 

 the crystal may also be drawn perpendicular to a face diagonal of the 



