146 



effect is still more restricted. For only at a few characteristic glancing 

 angles (p lt $ 2 > $s> etc., can reflections take place, these all being 

 determined by the equation: 2dsinty = nh. 



The crystal in this case must be held at exactly the characteristic 

 angle, and even then it can only give a spectrum of one order at 

 the same time ; in this respect it differs principally from an ordinary 

 line-grating which may give at any angle of incidence spectra of 

 different orders simultaneously. It follows from this that in the 

 patterns previously considered, where the crystal-plate remained 

 in a fixed position during the experiment, each spot on the photo- 

 graphic plate corresponds to a single, definite wave-length. If we 

 could distinguish the "colours" of a R on t gen-radiation with 

 continuous spectrum, as we do in visible light, we should see that 

 the pattern would be a multi-coloured one, every spot having its 

 own colour, wholly depending on the direction of the set of net-planes 

 in the crystal from which the ray which produced that spot, took 

 its origin. 



23. For our purpose the facts referred to in the preceding 

 paragraphs may be considered sufficient. Indeed, if Rontgen- 

 radition of known wave-length A be used, observation of the angles 

 of reflection on a definite set of net-planes will give us a relation 

 between A and d, and by doing this for various known directions 

 of a crystal, for instance for the three pinacoides {100}, {010}, and 

 {001}, etc., we shall gain an important insight into the dimensions 

 d lf d z , d s , etc., related to them. 



The equation deduced in the above includes all we have to know 

 for the study of the special arrangement of the net-planes in such 

 a crystalline medium with respect to each other, and it was in this 

 way, that W. H. and W. L. Bragg made their successful investi- 

 gations of the internal structure of a number of crystals. Without 

 considering their special methods of experimenting x ) in detail, 

 we shall only discuss here some of their results, in so far as they 



!) The directions in which, on turning the crystal about an axis, real inter- 

 ference-maxima occur, can be found by several methods. The English investigators 

 mentioned used for this purpose the ionising effect R on t gen-rays have on gas- 

 molecules. The "indicator" of their X-ray-spectrometer was an ionisation-chamber, 

 filled with a suitable gas, as for instance sulphur -dioxide. However it is equally 

 possible to make use of other effects produced bij Ron t gen-rays, when these 

 effects can be measured or observed even if they be very feeble. Many investigators 

 have in recent times made use of the photographic plate (De Broglie, Friman 

 and Siegbahn, Debije, and others), especially for the study of wave-lengths. 



