358 POLARISATION. 



It is a simple task to deduce the conclusions shown in the 

 above table from the positions determined by observation, or 

 to render them perceptible through models or figures, and no 

 further explanation will be required by readers who clearly 

 grasp the given ratios in their minds. It will amply 

 suffice if we show by an example the course that has to be 

 pursued. 



Let the observed combination be / II (the first in our series), and 

 let the longitudinal axis L of the ellipsoid be placed obliquely to 

 the axis of the cylinder. Then the limiting value of the angle 

 which the axis L forms with the axis of the cylinder is determined 



by the intersecting ellipses, which affect 

 the middle of the horizontal cylinder 

 i.e., it is in this case less than 45, 

 These ellipses are consequently situated 

 as represented in Fig. 205 that is, if 

 C C is parallel to the axis of the cylin- 

 der. We get, therefore, s t > m n, and 

 L L greater than T T. The diameters 

 m n and s t, however, which correspond 

 to the latitudinal and longitudinal 

 directions of the cylinder, represent re- 

 spectively an axis of the ellipses which- 



affect the transverse section and the margin of the horizontal 

 cylinder ; m n is the tangential axis of the ellipse of the section, 

 s t the longitudinally situated one of the marginal view. But, from 

 the form of these ellipses, as it is fixed by the combination 1 1 1, it 

 is clear that the radial axis R of the ellipsoid is greater than m n r 

 and less than s t ; it must therefore be the mean axis of the ellip- 

 soid. Hence the elements are biaxial, and the optic axes lie in a 

 tangential plane. The ratio of the axis R to the two others, and 

 the situation of the segments dependent thereon, still remain un- 

 determined, and the positive or negative character of the elements 

 is therefore doubtful. 



A few simple combinations, of the thirteen above-mentioned, 

 deserve additional special consideration on account of the optical 

 effect they produce. We will, first, emphasize the case given in 

 the combinations 5 and 6 of our series, where the margin and 

 the middle of the horizontal cylinder produce colours of opposite 

 character. Its characteristic feature is that on observing with 



