Parallel to an Optic Axis. 433 



Aragonite 



( 



Mcite 



a = 



1-5301 



to = 



1-6585 



P = 



1-6816 



e — 



1-4863 



7 — 



1-6859 



(o>- € ) = 



0-1722 



2V = 



17°50' 



log k = 



7-46201 



(y-a) = 



0-1558 







log k = 



7-58012 







Eadii of 



Kfcdii of 



Radii of 



Eadii of 



bright 



dark 



bright 



dark 



rings 



rings 



rings 



rings 



0° 36' 





3° 37' 







1°12' 





5° 07' 



1 48 





6 17 







2 24 





7 15 



3 00 





8 07 







3 36 





8 54 



§4. The maximum divergence of so-called parallel light is 

 often considerable, as a simple calculation will show. The 

 lowest power objective (No. 0) that is furnished with the Fuess 

 No. 3 microscope has a focal length of about 42 mm ; its work- 

 ing distance was found to be 38'2 mm , its aperture, 6'8 mm , and 

 its field, 4*8 mm in diameter. From this, its angular aperture is 

 17° 30' approximately, and when the low power lens that is fur- 

 nished with the polarizer is in place, the objective works at 

 this full angle. By removing this condensing lens, the effective 

 aperture is considerably diminished, becoming approximately 

 7° 30' ; this may be reduced to 6° 30' by the substage diaphragm. 

 Only by decreasing the size of the source of light, or by in- 

 creasing its distance, can we obtain light that has less divergence 

 than this. A source l cm in diameter, at a distance of 1 meter, 

 for example, gives with the above objective a pencil whose 

 angle is roughly 1°. 



By comparing these values with the diameter of the first 

 bright ring for aragonite, the reason is apparent for the bright- 

 ness of a section of this substance, cut normal to an axis, of 

 appreciable thickness. It is evident that a basal section of 

 uniaxial calcite, l mm thick, should also be bright when exam- 

 ined with the above objective, even without the substage con- 

 densing lens ; experiment verifies this. 



The dark brushes of the interference figure, that mark the 

 points for which the factor sin 2 20 (in (1) ) approaches zero, 

 widen out as the distance from the axis increases. At an 

 appreciable distance from the axis, a small circle, centrally 

 located in a brush, has an average intensity that is practically 

 zero. This is the reason why a biaxial crystal, placed so that its 

 axial plane coincides with the plane of one of the nicols, and 

 rotated in this plane, is dark except in those positions in which 

 an axis is approximately vertical. 



Am. Jour. Sci.— Fourth Series, Vol. XXIX, No. 173.— May, 1910. 

 29 



