Dr. Nagy I. Zoltán szerk.: Fragmenta Mineralogica Et Palaentologica 4. 1973. (Budapest, 1973)

Kjj and include and angle of 90.31°. From these two vectors Z_JJ is obtained by vectorial multiplication. -II o 5n x MII o o = - 0.69964 i + 0.00795 A + 0.71443 k The adequate optical vibration directions of the twin members B and D are close to each other, accordingly in case of all of them the problem is the same than in case of the[n^| vibration directions of the Carlsbad twinning law. The bisectrixes between the neighbouring points show the measurement error in form of the multiplicated error. Thus the following procedure was performed : the acute bisectrixes were computed and the following facts were obtained:the bisectrixes of the vibration directions [n

a

] and[n

y

] include 89. 97°, [nj and[n^[ include 90.32° and£n

ß

"Jand [n

Y

] include 89.97°. T = - 0.63660 i + O.53252 d + 0.55782 k ™Q ~~ — o T, = + 0.71117 i + O.12550 A + 0.69173 k 0 T

c = - 0.29826 i - 0.83687 A + 0.45902 k o On the basis of the optical directions the twinning axis cannot be determined and the right bisectrix cannot be choosen. Out of the bisectrixes of the (OlO) face pole of the two complexes one coincides with the acute bisectrix of the optical symmetry axis of the two^np^J within a small limit of error. This direction is finally unambiguously the wanted twinning axis. T

M = + 0.71569 1 + 0.12517 A + 0.68709 k o In this case the twinning axis obtained from the crystallographic directions is the basis of the further computions. This will be transformed to the system of co-ordinates in which the following conditions are valid for the axes: X» = K Y» = - My Z» = Zj