86 FUNDAMENTALS OF SUBMI C ROSCOPI C MORPHOLOGY I 



is inserted into the polarizing microscope. It is in the form of a sliding 

 wedo-e, or a flat plate which can be tilted so that its thickness d is variable. 

 Since the light oscillating parallel to the direction of the minor refractive 

 index of a double refracting specimen passes faster through the object than 

 the beam oscillating in the perpendicular direction parallel to the major 

 refractive index, a path difference of these two beams results, which causes 

 the interference colours observed in the polarizing microscope. This 

 retardation can be diminished if the direction of the major refractive index 

 of the specimen is oriented parallel to the minor index of the compensator. 

 By varying the thickness of the compensator, the retardation of the specimen 

 can be counterbalanced, until the colours disappear completely. Then the 

 double refraction is compensated and the value of F can be read from the 

 compensator. For delicate measurements there are compensators which 

 permit determination of the phase difference y of the two beams. Then the 

 readings must be multiplied by the wavelength A of the monochromatic 

 light used, or by A = 550 m/x for white light. 



The formula mentioned above applies to objects bounded by two 

 parallel planes as, e.g., in microtome sections, where d corresponds to 

 the thickness of the section. Many biological objects, however, 

 (myelin tubes, myelin sheath of the nerves, fibres with narrow lumen, 

 etc.) occur in the form of hollow cylinders. In this case the thickness 

 becomes greater with increasing distance from the edge, and according- 

 ly the path difference increases. The phenomena are particularly com- 

 plicated when the optical axis is not parallel to the axis of the cylinders 

 as in fibres, but perpendicular to the cylinder axis, as is the case of 

 myelin objects. The birefringence An. may then be calculated from 

 a formula of Bear and Schmitt (1936) if the largest possible path 

 difference /^(max) is measured. This formula runs : 



(d, + zda) arc cos [(d^ + 2d2)/3di] 



where d^ represents the diameter and d., the inner diameter of the 

 hollow cylinder. 



A similar problem occurs in the determination of the double re- 

 fraction of objects with spherite texture and radially oriented optical 

 axis Ce.g., grains of starch). In this case the double refraction is 



1 (max) 



An 



1. 122 r 



where r is the radius of the spherites (Frey-Wyssling, 1940b). Bear 

 and Schmitt's formula should yield this value for a solid cvHnder, 



