THE ACTION OF SPHERICAL AND OVAL OBJECTS. 



365 



only when the axes of the ellipses lie in the imaginary polarising 



planes. In every other position 



the neutral lines form oblique 



angles, and if the ratio of the 



axes does not remain constant, 



they appear, in general, more 



or less curved. If, for instance, 



P P and N N (Fig. 208) are 



the planes of vibration of the 



Xicols, and a I and c d the 



axes of the elliptical layers, 



the neutral lines must appear 



as represented * in the figure ; 



they connect the points of 



contact of the tangents, leaving P P and N N at right angles. 1 



B. Objects with One Axis. 



The double-refracting elements are here grouped round one 

 definite diameter, instead of round a centre. Assuming that the 

 grouping is uniform throughout, so that, for instance, the axes of 

 the ellipsoid of elasticity always form the same angles with the 

 radius and the meridian circle, which intersect in its centre, then 

 such an object acts essentially like a cylinder. With horizontal 

 position of the axis, at least in a middle latitudinal zone (which 

 may be denoted as an equatorial zone), it produces the colours of 

 the horizontal cylinder; and with perpendicular position of the 

 axis, even if only in the peripheral portion, it produces the colour 

 of the cylindrical transverse section. The effect may hence be 



1 The -fact that the neutral lines in a system of such ellipses are straight 

 lines where consequently the ratio of the minor axis to the major remains 

 the same follows immediately from the relatively equal magnitude of the 

 ordinates and abscissae for the points of contact of the tangents. It is, in 

 general, evident that the neutral lines in our figure with the diameters lying 

 in the planes of polarisation P P and N N represent two pairs of conjugate 

 diameters, and consequently intersect at angles which vary within certain 

 limits. The construction of the neutral lines for any system of oval layers is, 

 from what has been already shown, a matter of no difficulty ; it is only 

 necessary to draw the tangents, and to join their points of contact. 



