The Crystalline Structure of Bismuth. 193 



At this stage we introduce the conditions at the surface 

 of discontinuity of the moving wave. These are 



<£ = constant, and ~dcj)/'dt= — cx)(p/~dr at r=(ct + a), 



the suiface of discontinuity being supposed to be moving 

 outward with velocity c. These two equations give only one 

 relation between (he constants 



Zc s = (11) 



1 



With the help of the third equation of (8) (with the right- 

 hand side zero) we can express all the B/s in u (10) in terms 

 of the A,'s, thus reducing the number of arbitrary constants 

 in u from six to three. Then the equation (8') or (8") gives 

 the ratios of C/s to A/s. which, taken with the relation (11), 

 would further reduce the number of arbitrary constants in u 

 from three to two ; so that, making use of all the conditions, 

 we can write both u and <p in terms of only two arbitrary 

 constants. These two are to be determined from the initial 

 conditions of motion of the shell, such as, for instance, the 

 position and velocity (u and "dufdt) of the shell at time zero. 



18 Mirzapore Street, 



Aerial Lodge, Calcutta. 



XXI. The Crystalline Structure of Bismuth. By R. W. 

 Jamem, M.A., Senior Lecturer in Physics in the University 

 of Manchester *. 



1. T>ISMUTH, like antimony, crystallizes in the di- 

 _D hexagonal alternating class of the hexagonal sysfem. 

 The crystalline symmetry is that of a rhombohedron the 

 edges of the rhombohedron which meet in the trigonal axis 

 being taken as the axes of the crystal. The angle between 

 any two of these edges is 87° 34', and the angle between the 

 rhombohedral faces 100 : 010 is 92° 20'. The crystals have 

 a perfect cleavage parallel to the (111) planes, and perpen- 

 dicular to the trigonal axis, and a fair cleavage parallel to 

 the (111) planes. Bismuth also crystallizes from fusion as a 

 skeleton rhombohedron of the form described above. 



The structure of antimony has already been determined |. 

 From the great similarity between the crystals of antimony 

 and bismuth, it was to be expected that their structures would 

 also be similar. The structure of bismuth has now been 

 determined, and this is found to be the case. 



* Communicated by Prof. W. L. Bragg. 



t James & Tunstall, Phil. Mag. vol. xl. p. 238 (Aug. L920), 



Phil. Mag. S. 6. Vol. 42. No. 217. July 1921. 



