352 POLARISATION. 



the other two axes lie in a tangential plane. It is, therefore, 

 only necessary to determine the ellipse of elasticity of one 

 tangential section as, for instance, of the segments A A 

 of the cylinder (Fig. 202) in order to fix not only the 

 directions of the axes in question, but also their relative 

 magnitudes. 



We have not, however, yet arrived at the ratio of the two 

 tangential axes to the radial axes except only in the case 

 where the former correspond to the longitudinal and latitudinal 

 directions of the cylinder. In every other case the observer 

 is compelled to discover this ratio in sections which are 

 made through the axes to be compared, or, if they do not lead 

 to a result, by inclination of the cylinder, to which we shall refer 

 later on. 



If it should appear that sections, which have been made per- 

 pendicular to one of the three axes, act as single-refracting 

 media, then the two other axes are equal that is, the double- 

 refracting elements are optically uniaxiaL If, on the other hand, 

 each section made through two axes produces colour, the elements 

 of the cylinder are optically biaxial. Whether an object belongs 

 to the one or the other category, cannot, as a rule, be determined 

 until the direction of one optic axis is discovered experi- 

 mentally, by sections or by rotation. It would indicate a very 

 superficial knowledge of the phenomena if one imagined that 

 the optical properties of an object can be discovered in every 

 given section. 1 



1 The differences observed in such sections have been denoted by some 

 authors by expressions which have a totally different significance in crystallo- 

 graphic Optics. Mohl and Valentin, for instance, speak of negative and. positive 

 colour or composition of an object, according as the ellipse of elasticity, which 

 comes into play in transverse sections, is situated radially or tangentially. 

 In other places the major or the minor axis of the ellipse is briefly called the 

 optic axis, and it is therefore tacitly assumed that it lies in the plane of 

 the field of view, and so on. It is hardly necessary for us to point out the 

 inaccuracy of these and similar explanations, such as are found in the 

 literature of the subject; the reader who has followed our explanations will 

 be able to exercise the needful criticism. 



As an example we may, however, mention briefly a few results of Valentin 

 on the action of cylindrical structures (" Die Untersuchung der Pflanzen- und 

 Thiergewebe im polar. Licht," p. 161). Valentin assumes the uniaxial com- 



