of the Cry stallo graphic Law of Valency Volumes. 519 



constitution are but imperfectly understood. One of the 

 generalizations in this connexion which has gained wide 

 support, and is commonly accepted, is the ^theory due to 

 Pope and Barlow, known as the Law of Valency Volumes. 

 According to this theory *, the entire space occupied by a 

 crystal can be regarded as a close-packed assemblage of 

 approximately spherical cells of various sizes, representing 

 by their relative volumes the spheres of influence of the 

 component atoms of any particular crystalline structure. 

 The volumes of the cellular domains allotted as above 

 are further supposed to be approximately in the ratio of 

 the integers which respectively express the fundamental 

 chemical valencies of their contained atoms. 



There is a certain amount of indirect evidence f against 

 the truth of this theory ; but the application of the X-ray 

 method of investigating crystal structure now furnishes us, 

 for the first time, with incontrovertible evidence of its failure 

 in a typical case. 



In the present paper the results of an investigation of 

 the crystalline structure of the sulphates of potassium, 

 rubidium, ammonium, and csesium are set forth and dis- 

 cussed in reference to the Law of Valency Volumes. 



These crystals all belong to the orthorhombic system, 

 and form one of the best-known examples of an isomorphous 

 series. 



The crystals were examined in a Bragg X-ray spectro- 

 meter, using an X-ray bulb with a palladium anticathode. 



It was soon evident that the elementary cell, or unit 

 rhomb, of each of these crystals contained four molecules. 



Thus it was found that the glancing angle in the second- 

 order spectrum reflected from the (100) face of potassium 

 sulphate was 5° 51'. Substituting this value, and that of 

 the appropriate wave-length of the X -radiation used, in the 

 usual formula 



rik = 2 d sin 0, 

 we find 



d m = 5-73 xl0"\ 8 cm. 



Now the molecular weight of K 2 S0 4 is 173'04, its density 

 is 2*666 gms./cm. 3 , and its axial ratios 



a:6:c=0«5727: 1:0-7418 f. 



* Vide ' Annual Reports on the Progress of Chemistry,' vol. v. (1908) 

 pp. 268 et seqq. ; also ' Mineralogical Magazine,' vol. xvii. (April, 1916) 

 pp. 314-323. 



+ Tutton, ' Crystalline Structure and Chemical Constitution ' 

 (Macmillan & Co.', 1910), pp. 123 et seqq. 



X Tutton, ' Crystalline Structure and Chemical Constitution,' p. 119. 



