9 o SCIENCE PROGRESS 



usually the case, they are small— are in the simple ratio i, 2, 3, 

 etc. With the same X-rays another face of the crystal with 

 a different spacing d' between the planes will reflect at another 

 set of angles 0' u 6' 2 , 6' 3 , etc. Nothing else is required to determine 

 directly the ratio djd' of the spacing in different planes. This 

 is generally known from crystallographic considerations, arid 

 the direct verification of the latter is easy to carry out, and 

 furnished one of the first proofs of the theory. 



On the other hand, if different X-rays but the same face of 

 the crystal be used, the ratio of the wave-lengths of the two 

 X-rays at once follows. But the absolute determination of 

 both X and d is possible when a complete knowledge of the 

 structure of any one simple crystal is obtained. 



For isomorphous crystals and for similar planes the spacing 

 d should vary from crystal to crystal proportionately to the 

 cube root of the molecular volume, and this was found to be 

 the case for a whole range of cubic crystals. From this 

 molecular volume and the mass of the hydrogen atom, these 

 distances d can be computed, and consequently X also. Thus, 

 in rock salt, the distance between the successive planes parallel 

 to the (100) face was found to be 2 8 x io~ s cm., and the wave- 

 lengths of the two strong characteristic X-rays of rhodium, for 

 example, 0*607 and 0*533 x io~ s cm., i.e. 0*607 and 0*533 Angstrom 

 units. Compare this with the wave-lengths of the visible 

 spectrum, from 7,000 to 3,500 Angstrom units, and this again 

 with the waves used in wireless telegraphy, half a kilometre or 

 more in length, and ponder for a moment on the incalculable 

 service this extension of the scale of radiations has incidentally 

 rendered to humanity. What unexplored stretches in this vast 

 gamut yet remain blank ! What secrets may still lie hidden 

 within so vast a range ! 



It has been too often the reproach of the otherwise well- 

 trained scientific man that crystallography remains to him a 

 sealed book, a science with the meaning even of its nomen- 

 clature he is unfamiliar, a science of one too many dimensions 

 to be easily pictured in what, owing to the fatal facility of 

 scribbling upon paper, is in danger of becoming a two-dimen- 

 sional mind. The authors have met this difficulty frankly and 

 well, and it would be difficult to find anything of the kind more 

 excellent than Chapter V., dealing with the rudiments of 

 crystallographic principles. The labour of assimilation is 



