1208 
On the other hand, in the ease of the neutral ethylsulfates of the 
rare earth-metals *), which possess hexagonal-bipyramidal symmetry, 
the hemihedrical structure was found to be expressed quite clearly 
in the RörteeNogram, which is also in full accordance with the 
consequences of the theory, as this represents the case above mentioned 
sub 5). 
Further control of the exactness of these conclusions by experiment 
was finally only possible to me with the aid of the beautiful RÖNTGEN- 
ograms obtained at the Physical Laboratory of this University by 
my friend and colleague H. Haca with the erystallographieal material 
especially selected by me for this purpose. Without his aid and 
kindness this investigation would have been quite impossible, and I 
therefore wish to express to him here my sincere thanks once more. 
In fig. 1 the corresponding photo of the apatite: Ca,Cl(PO,), is 
reproduced in stereographical projection *). 
The plate used here was cut perpendicularly to the c-axis; it 
gave a very beautiful photographic image (Table I, fig. 3). The 
presence of a senary axis, but the absence of all vertical symmetry- 
planes is immediately recognisable here. 
§ 3. For the purpose of obtaining further data of this kind, 
plane-parallel plates were cut from crystals of ferric-ammonia-alum : 
Fe (SO), . NH), SO, . 24H,O, and of potassium-chromic-alum : 
K,SO,. Cr,SO,), .24H,O, — in both cases perpendicularly to a 
ternary axis. ; 
In fig. 2 and 3 the patterns obtained are reproduced in stereo- 
graphic projection. It is immediately evident that these images only 
show a ternary axis, but no planes of symmetry whatever. This is 
in full agreement with the theory: for the alums, just like pyrite, 
are dyacisdodecahedrical, and from the theoretical considerations 
mentioned above it follows, that they may eventually manifest their 
hemihedrical character in their RONTGENograms. But because these 
crystals do not possess any other planes of symmetry than those 
which are parallel to the faces of the cube, the image perpendicular 
to the ternary axis will in fact manifest no other symmetry-properties 
than those which follow from the mere presence of the ternary 
axis itself. 
1) F. M. Jaeger, these Proceed. 16. 1095. (1914); Receuil des Trav. des Chim. 
des Pays Bas et de la Belgique, T. 33, 343. (1914). 
2) In all these projections, d signifies the thickness of the crystalplate, A the 
distance between the frontal face of the crystal plate and the sensitive film of the 
photographic plate, 
