Bisectrix

Mittel-lauf, m. (in distillation) middle fraction, -lauge, /. weak lye. -Unie, /. median line center line bisectrix axis equator, mittel-los, a. without means, -mitssig, a. middling, mediocre, average. 

Fig. 52. Convergent light figures, a. Uniaxial crystal with optic axis parallel (left) and slightly inclined (right) to line of vision. 6. Biaxial crystal with acute bisectrix parallel (left) and inclined (right) to fine of vision.

Biaxial crystals under similar optical conditions produce convergent light figures like that shown in Fig. 52 6, when the acute bisectrix of the optic axes lies along the line of vision and the vibration directions... 

The observation of convergent light figures may often provide confirmation of the orientation of the indicatrix. The plane of the optic axes is the ay plane, while the normal to this plane is the j8 vibration direction. For a positive crystal the acute bisectrix is the y vibration direction, while for a negative crystal it is the a vibration direction. 

Fedorov complex symbol = (4d)59( - ) trans. llO/TlO/OOl. Cleavage c perf. and showing pearly lustre. Acute positive bisectrix (with medium angle) perpendicular to 6 axial plane c(001). 

From the crystallographic point of view selenium benzoylacetone crystallises in elongated, six-sided plates, with a dome termination of 64°. The extinction is straight and a positive bisectrix emerges normal to the plate, whether acute or obtuse has not been determined with certainty. In any case, the optic axial plane contains the morphological direction of elongation. 

The optic axial plane is (010) and the negative acute bisectrix is inclined at about 10° to the vertical in the acute angle j8. An optic axis is visible through c(001). The dispersion is abnormally strong, p > v. 

The Fedorov complex symbol is 4a(45° 36 ) 0. Optically the crystals are biaxial the acute bisectrix is negative. 

Dispersion v>r very slight Sign of Double Refraction Negative Acute Bisectrix Almost 001 Extinction yAa = 13° on 001 Molecular Refraction (R) (5893 A 25°C). 

This factor can be evaluated exactly for many geometries. It is usually an advantage to perform the integration using lamella parallel to the bisectrix, x", defined by... 

Figure 4.9 Construction of the bisectrix to produce points having the same phase.

A sphere of radius a is pictured in Figure 4.10. The bisectrix disk shown in this figure has... 

The differential volume of the bisectrix disk is Jt a -b ) db and the form factor is... 

Fig. 3. Evolution of the binding energies of NHj or HjO along the approach in different positions as indicated, (dir. = approach to NH bis. = along bisectrix).

The case of SO2 offers a more complex situation. As for the two other ligands the electrostatic results point to three areas of favorable interaction the inner bisectrix region, the external bisectrix region and... 

Fig. 8. a) The preferred orientation of the plane of SO2 in the mutual perpendicular arrangement when the S atom moves around the periphery of the nitrite ion (values of the electrostatic interaction as indicated, in kcal/mole Oj. .. S or N. .. S = 2.6 A), b) Angles defining the position of SOj with its sulfur atom in the plane of the nitrite ion. 0 is the angle of the bisectrix of SOj with N. .. S for bisecting positions, with the direction of the bisectrix of ONO for the more general case. 3 is the NOS angle. 

Fig. 9. Location of the minima of the energies of interaction (S02 perpendicular to the plane with its bisectrix oriented as indicated).

The assignment to the monoclinic system was based not so much on the uncertain measures on the inclined facets of the laminae but on the accurate corrosion-figures (Baumhauer, 1874, 1875) measured on both light and dark micas and, above all, on the final ascertainment by Hintze in 1875 of minimal deviation of the perpendicularity of the acute bisectrix with respect to the lamina, that had been suspected previously (Rose 1844, Marignac 1847, Kenngott 1848, Miller 1852). After the studies of Baumhauer and of Hintze, the last word was written by Bauer in 1877 and by Tschermak in 1875-1877 who performed a series of measures on numerous specimens from various locations. 

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