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

All the three optical vibration directions can be rarely measured in the single twins, the third one is computed from the two measured directions by vectorial multiplication, in general,The twinning axes can be obtained by computing the bisectrix of the adequate vibration directions, i.e. by the addition of the vectors. In case of determining the new twinning laws the twinning axis was computed separatedly from the optical and crystal-morphological directions, the only requirement being the coincidence of the components within a rather small limit of error. Further the fact should have been determined that what crystallographic direction corresponds with the computed twinning axis. For this reason the system of co-ordinates determined by the plane and position of the slide should be transformed into such a right-angular clock-wise system of co-ordinates which has been accepted for plagioclases in general and to which all the existing crystallographic directions were referred. This is the system of co-ordinates initiated by C. Burri in 1956, its X axis is Roc Tourné twinning axis, it s Y axis is the Albite and Z axis the Carlsbad twinning axis.These three directions are known in the plagioclase grains in question, since all the three laws do not exist the third can be computed from the two twinning axes by vectorial multiplication. The position of the wanted twinning axis is determined by coordinate transformation known from vector geometry; from its Ç' and n ' values the $> and p values of Goldschmidt are computed taking into consideration that the system of co-ordinates of Goldschmidt is left-handed. In this way the wanted crystallographic direction, i.e. the face normal is obtained. When the starting data were of the required accuracy, nearly the same <p and p values are obtained in the system of co-ordinates of both complexes. The transformed values of the optical vibration directions are converted into the Euler angles initiated by C. Burri: 0 = 90° - rj 0 = 270° -£