The London, Edinburgh and Dublin philosophical magazine and journal of science . n R. 5. Regarding these four quantities it must here suffice tostate four propositions which, though only qualitative, areeasily understood and extremely helpful towards an explan-ation of the effects considered. These propositions followfrom the equations (5) and (6). In order to arrive at them,consider once more all the directions as passing through thecentre of a sphere, and defined by their intersections withthe spherical surface. The region surrounding an optic axisAx may then be approximately represented by
The London, Edinburgh and Dublin philosophical magazine and journal of science . n R. 5. Regarding these four quantities it must here suffice tostate four propositions which, though only qualitative, areeasily understood and extremely helpful towards an explan-ation of the effects considered. These propositions followfrom the equations (5) and (6). In order to arrive at them,consider once more all the directions as passing through thecentre of a sphere, and defined by their intersections withthe spherical surface. The region surrounding an optic axisAx may then be approximately represented by a plane, asshown in fig. 2. We here have, besides the direction of theoptic axis, represented by the point A,, and that of the wavenormal, represented by the point Z, also the plane A1A2 ofthe optic axes ; A2 being inclosed in brackets in order to Crystals in the Neighbourhood of an Optic Axis. 93 indicate the fact that the direction A2 is not capable o£ beingrepresented in the figure itself. The straight line Aj Qfurther represents a plane through the optic axis A1 obtained. as follows :—Let a plane be drawn through the axes A! Bl5 andanother through the axes A1 B2; let the angle between thembe J\. Then Ax Q is the trace of the plane bisecting theangle J\ ; let the angle made by this plane with the directionAi A2 be denoted by K. 6. From the formulae (5) and (6) it follows that thephenomena under consideration in the neighbourhood of theaxis A! are symmetrical with respect to the trj system ofcoordinates (also shown in the figure), the angle made bythe — f-axis with the direction A{ A2 being equal to 2K. Such being the case, the plane A^ contains two directions,Ci and C/ (see fig. 3), making the same angle 6 with Al5 andwhich are highly characteristic of the behaviour of thecrystal, and may be termed singular axes. The angle 6 isdeter mined by the tensors al5 a2. a3 and Z>l5 b2, b-s which arecharacteristic of the crystal, and is most simply expressed inthe form e_(bi-h
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
