THE ACTION OF CYLINDRICAL OBJECTS. 361 



action of the margins on inclination, are contained in the following- 

 paragraphs : 



(1.) If it is possible to discover the direction of the optic axes in 

 the tangential plane, the angle which they make with the axes 

 of elasticity, and consequently the inclination of the latter to 

 the axis of the cylinder, are likewise determined. Example : The 

 middle of the horizontal cylinder gives a colour which corresponds 

 to the position I ; on inclination to the one side, whereby the 

 end furthest from the observer falls and the near one rises, the 

 right margin becomes neutral after a rotation of 40, on rotation 

 to the opposite side, however, at 20 ; the left margin acts con- 

 versely. The elements of the cylinder are therefore negative, the 

 axial angle is 60, and the longitudinal axis L of the ellipsoid 

 is inclined in the direction of a left-handed spiral (in botanical 

 terminology) 10 to the axis of the cylinder. 



(2.) If the middle of the horizontal cylinder gives the same 

 colour as in the preceding example, and then neither margin 

 becomes neutral on inclination to 45, the elements of the 

 cylinder are optically positive. 



(3.) If the middle of the horizontal cylinder gives the colour 

 of the position q, and then neither margin becomes neutral on 

 inclination to 45, the elements of the cylinder are optically 

 negative. 



In two special cases the middle also of the horizontal cylinder 

 must act neutrally on a definite inclination. The one case 

 occurs when the horizontal position produces a colour corre- 

 sponding to the position I, and when, moreover, the radial axis 

 of the ellipsoid is the minor one. Then the inclination of the 

 cylinder implies a gradual approximation of the effective ellipses 

 of elasticity to the crossed position which they would also attain 

 after a revolution of 90. These ellipses must therefore, at a 

 definite inclination, deviate exactly 45 from the longitudinal 

 direction, and hence intersect at right angles. Their effects conse- 

 quently counteract each other ; the centre behaves neutrally. The 

 second case is analogous to this first one ; it occurs when the 

 colour of the horizontal position corresponds to the position gr, and 

 when, moreover, the radial axis of the ellipsoid is the major one. 

 Then the two ellipses approach each other on inclination of the 

 cylinder to the longitudinal position, and hence attain also a 

 position in which they intersect at right angles and counteract each 



