92 SCIENCE PROGRESS 



fundamental forms, and demonstrated that difference in chemical 

 composition is accompanied by difference of crystalline form. 

 Moreover, he discovered the all-important law of rational indices — 

 that is, the fact that the lengths cut off along the three principal 

 axes of the crystal by the various faces, other than the primary 

 ones parallel to the axes, are relatively expressed by very simple 

 whole numbers, usually only i, 2, 3, or 4. Haiiy further 

 elucidated the simple relation between crystalline form and 

 cleavage, which had been discovered in 1780 by Bergmann 

 and Gahn, and laid the foundation of the idea of the molecular 

 structure of crystals at a time when chemistry was in its 

 infancy. 



Many of Haiiy's conclusions, however, were exposed for 

 years to grave doubt, and even open scepticism, owing to the 

 remarkable discoveries of Mitscherlich, and their but partial 

 comprehension. In the year 1819, Mitscherlich, a young student 

 of Berlin, pursuing his first research, made the accidental dis- 

 covery that two different substances, acid ammonium phosphate 

 and acid ammonium arsenate, possessed apparently the same 

 crystalline form. To be on safe ground, he studied crystallo- 

 graphy under Gustav Rose, and was subsequently able to 

 carry out the necessary crystal measurements. He then found 

 that two further substances, the two corresponding potassium 

 salts of phosphoric and arsenic acids, were likewise apparently 

 identical in crystalline form. Later, under the guidance of 

 Berzelius at Stockholm, he illustrated his new principle of 

 "isomorphism" by many further examples. Moreover, in 1821, 

 he demonstrated that the same substance, sodium dihydrogen 

 phosphate, crystallises in two distinct forms; and in 1823 followed 

 this up by discovering the much better known case of sulphur, 

 which crystallises from fusion in monoclinic prisms, while the 

 natural form and that deposited from solution is rhombic. 



These striking results appeared to demolish at once the 

 theory that any one substance of definite chemical composition 

 is characterised by a specific crystalline form. During the 

 period which followed, new isomorphous series of salts and 

 dimorphous, or even polymorphous, substances were discovered, 

 one after the other, at a rate which was only commensurable 

 with the rapid advance of chemistry. The use of the reflecting 

 goniometer, which had been invented in 1809 by Wollaston > 

 who had thereby placed an infinitely more accurate measuring 



