827 
never produce a completely asymmetrical diffraction-pattern; and 
that there is an appreciably fair chance that the symmetry of it 
will be diagonally-symmetrical, as found in the case of fig. 2; it 
is no wonder, that we just now met with ts symmetry in the 
case of the preparation investigated in the above, 
In the same way it is possible to deduce the possibilities to be 
expected, if the composing lamellae cross at 45°. However, 
because in such mica-piles there are always lamellae present per- 
pendicular to, or coinciding with the geometrical symmetry-plane in 
one of the eight lamellae, the case of fig. 36 will never result 
from the reversion of a single lamella but only a lamellar symmetry 
L of the intensities can be produced thereby. A general review 
of the possible cases can be given as follows *): 
A Review of the Possible Types of Intensity-Distribution in the Diffraction-Patterns, 
Obtained by Mica-Complexes with Lamellae Crossing at 45°. 
| If one lamella Iftwolamellae If three lamel-| If four lamel- 
| | be turned: be turned: | lae be turned:| lae be turned: 
| 
| Number of possible 
| Combinations: 8 28 56 10 
Normal images: 0. 4 (octogon.). 0. 6 (octogon.). 
Asymmetrical Images: 0. 0. 16. 0. 
Diag. Symm. Images: 0. 16. 0. 48, 
Lamell. Symm. Images: 8. 8. 40. 16. 
If only two lamellae be turned, there is an appreciable chance of 
a diagonally-symmetrical image, as found in fig: 36; but if four 
lamellae be accidentally reversed, this chance is extremely great. 
For the rest, there are about equal probabilities for the bilaterally- 
symmetrical images D and L, both of which were observed formerly 
in the case of natural pseudo-symmetrical crystals. 
§ 6. A number of mica-piles were, moreover, prepared, in which 
the right orientation of the muscovite-lamellae was rigorously checked 
by comparison with their true position in a single muscovite-crystal *). 
First a dextro-, and a laevogyratory combination, in which the 
) My assistant Dr. A. Simex was kind enough to check the number of these 
possible combinations systematically. | wish to express my best thanks to him 
here once more for the trouble he has given himself in this matter. 
2) This erystal my colleague Prof. Bonnema most kindly gave me for this purpose 
from the mineralogical collection of the University. 
