THE ACTION OF SPHERICAL AND OVAL OBJECTS. 363 



as spheres with equal diameters, or as bodies with a particular 

 axial direction. 



A. Objects witli Equal Diameters. 



The position of the neutral cross to the polarising prisms at 

 once decides the question, whether one of the three axes of 

 elasticity of the double-refracting elements is situated radially or 

 stands in a definite relation to the radius or not ; for in the former 

 case the neutral lines correspond to the polarising planes of the 

 prisms, whereas in the latter they cut them obliquely. Strictly 

 speaking, indeed, this latter case cannot be combined with the 

 equality of the diameters and with the constant position of 

 the neutral cross thereby conditioned. For as soon as the axes of 

 elasticity are situated obliquely to the layers or to the radius, 

 the equality of the diameters demands all possible positions in 

 the tangential plane i.e., the double-refracting elements must 

 assume all the positions which a single element takes up, one 

 after another, by rotation upon a radial diameter; the neutral 

 line therefore lies in the same vertical plane with the axis of the 

 cone which the element describes during rotation. If the axes of 

 elasticity were situated in every direction in space, and if there- 

 fore the different positions were equally often represented, then 

 the sphere would act as a single-refracting substance, and any 

 further investigation would be purposeless. 



A definite relation of the axes of elasticity to the radius is 

 therefore already indicated by the mere presence of interference 

 colours; the one of the axes having the preponderant number 

 of elements must coincide with the radius, or, at any rate, 

 form an angle of less than 45 with it. For our further 

 consideration we will completely exclude this latter case, and 

 assume here, just as we did with the cylinder and the 

 single membrane-lamellae, that the double-refracting elements 

 are regularly situated throughout, and that consequently the 

 axes of elasticity are so situated at all points of the 

 object that one of them coincides with the radius, whilst the 

 other two lie in a tangential plane i.e., in the plane of the 

 surface of the layers. 



