Bia* 



THE ACTION OF CYLINDRICAL AND SPHERICAL OBJECTS. 349 



The possible positions of the ellipses of elasticity are now limited 

 to the space which the acute angle leaves vacant. In order to 

 determine this angle we may endeavour to observe separately the 

 colours of the two lamellae in sections cut perpendicularly to the 

 surface, so as to draw further conclusions from their rise and fall 

 on rotation in different directions. In the majority of cases, how- 

 ever, we shall arrive at the conviction that this part of the problem 

 does not admit of solution. 



IY. 



THE ACTION OF CYLINDEICAL AND SPHEEICAL 



OBJECTS COMPOSED OF CONCENTEICALLY GEOUPED 



ANISOTEOPIC ELEMENTS. 



A FURTHER problem, frequently occurring in practice, is the 

 determination of the axes of elasticity in spherical and cylindrical 

 structures, whose component parts lie in radial series round the 

 axis or the centre, as in starch-grains, cylindrical fibres and 

 tubes, &c. The difficulties to be surmounted are similar in 

 nature to those of the previous case ; they consist in the inequality 

 of the positions of the double-refracting elements to the 

 transmitted light, and in the different hypotheses which may 

 be based thereon. The process of investigation is therefore pre- 

 scribed : we must endeavour to clearly grasp all the conceivable 

 possibilities, and then by observation reduce them to the narrowest 

 circle. 



1. CYLINDRICAL OBJECTS. 



The term cylinder, or hollow cylinder, does not of course refer 

 merely to the outward form, but rather to the inner structure 

 that is, to the arrangement of the double-refracting elements. 

 We will assume that the elements of equal radius agree with 

 reference to the position of their planes of vibration and to the 

 effective elasticities ; that all radii lying in a plane through the 

 axis are equal ; and that all the radii, upon a section at right 

 angles to the axis, act as if the said radius were carried round in a 

 circle. 



