338 POLARISATION. 



With flat membranes, as indeed with all objects which can be 

 cut in every direction, the problem is much simplified. If, with 

 an object of this nature, two out of the three axes are known, their 

 ratio to the third axis is directly determined by transverse sections 

 cut parallel to the corresponding principal planes. If, for instance, 

 , b, c, d (Fig. 193) is the ellipse of elasticity of a flat piece of 

 membrane, and if a transverse section parallel to 

 e d shows that the third axis is less than c d, 

 then it is of course the minor axis of the ellipsoid ; 

 if it is greater than c d the ratio to a I decides 

 whether it is the major or the mean axis. 



Together with the relative magnitude of the 

 axes of elasticity the plane of the optic axes, as 

 already stated, is given, since it always passes 

 through the major and the minor axes of elas- 

 ticity. A very thin plate cut parallel to the 

 FIG. 193. mean axis must therefore, on rotation upon 

 this axis, come twice into such a position that 

 the rays incident from below enter it in the direction of an 

 optic axis ; it must consequently act as a single-refracting 

 medium, and must appear black with crossed Nicols. Hence 

 it is only necessary to measure the inclinations of the plate 

 corresponding to these positions, and also to take into account 

 the deviation at the bounding surfaces of the plate, in order to 

 determine approximately the angle which the optic axes make. 

 Such determinations are not absolutely accurate, yet it is generally 

 possible to distinguish whether the object is positive or negative. 

 In order to avoid erroneous interpretation of the interference 

 colours, it is always advisable to compare the positions of 

 acceleration and retardation accurately witli one another. If the 

 interpretation has been made correctly, retardation must yield 

 a colour which stands above, as regards the higher of the two corn- 

 results of observation appear too vague for a more detailed investigation to 

 be justifiable upon these and similar theoretical inferences. 



It is moreover sufficiently clear from the above that the deductions which 

 Valentin (" Die Untersuchung der Pflanzen- und der Thiergewebe im polarisirten 

 Licht," p. 144) makes from this rise and fall of colour in selenite plates are 

 entirely incorrect. Thus, he states that the plane of the optic axes corresponds, 

 "therefore," to the diagonal direction -f 45 (which in our figure is denoted 

 by c c), whilst in reality it coincides with the plane of the plate. 



