1903.] On the Variation of Angles observed in Crystals. 439 



The volatile iron carbonyl has been made the subject of a number of 

 similar observations, dealing with its physical properties and chemical 

 stability, which will be discussed in another communication. 



"An Enquiry into the Variation of Angles observed in Crystals, 

 especially of Potassium-Alum and Ammonium-Alum." By 

 Professor H. A Miers, M.A., D.Sc., F.E.S. Eeceived 

 March 10 —Read March 26 : 1903. 



(Abstract.) 



Corresponding angles measured on different crystals of the same 

 substance usually differ slightly. On cubic crystals the theoretical 

 angles are known. Pfalf professed to have established that only 

 those cubic crystals which display birefringence exhibit divergence 

 from the theoretical angles, but Brauns showed that in lead nitrate, 

 ammonia-alum, and spinel, for both isotropic and birefringent crystals 

 alike, the octahedron angle may differ by as much as 20' from that of 

 the regular octahedron. 



The author has endeavoured to trace the changes of angle upon one 

 and the same crystal during its growth by measuring it at intervals 

 without moviiig it from the solution in which it is growing. This is 

 accomplished by means of a new telescope-goniometer in which the 

 crystal is observed through one side of a rectangular glass trough, 

 and the changes in the inclination of each face are followed by watch- 

 ing the displacements of the image of a collimator slit viewed by 

 reflection in it. The crystal is held by a platinum clip which it 

 envelopes as it grows. Small movements of the image are followed 

 by means of a special micrometer-eyepiece which accurately measures 

 the magnitude and direction of the displacement. 



Examined in this way an octahedron of alum (ammonium or 

 potassium) is found to yield not one but three images from each face ; 

 and closer inspection shows that the crystal is not really an octahe- 

 dron, but has the form of a very flat triakis octahedron. It often 

 happens that of the three faces which nearly coincide, one is large 

 and the remaining two very small, so that of the three images one is 

 bright and the others are very faint, and can only be discerned with 

 difficulty ; in such a case the crystal as measured in the ordinary way 

 would appear to be an octahedron whose angle differs from the theo- 

 retical value by a few minutes. 



When a growing crystal of alum is watched for several hours or 

 days, it is found that the three images yielded by an apparent 

 •octahedron face continually change their position ; one set fades away 

 and is replaced by another set, which are generally more widely 



