ELASTICITY AND CRYSTALLINE FORMS. 
283 
luminiferous force is, that under no conceivable system of tasinomic coefficients in a 
homogeneous solid, would the plane of distortion in a wave be rotated continuously 
round the direction of propagation. 
Much has been written, both recently and in former times, concerning an alleged 
difficulty in the theories of waves, both of sound and of light, arising from the 
physical impossibility of the actual divergence of waves from, or their convergenc<" 
to, a mathematical point. This impossibility must be admitted; but the supposed 
difficulty to which it gives rise in the theories of waves is completely overcome in 
Mr. Stokes’s paper on the Dynamical Theory of Diffraction*, in which that author 
proves, that waves spreading from a focal space, or origin of disturbance, of finite 
magnitude, and of any figure, sensibly agree in all respects with waves spreading 
from an imaginary focal point, so soon as they have attained a distance from the 
focal space, which is large as compared with the dimensions of that space ; so that 
the equations of the propagation of waves spreading from imaginary focal points may 
be applied without sensible error to all those cases of actual waves to which it is usual 
to apply them. 
The physical impossibility of focal points applies to light independently of all 
hypotheses ; for at such points the intensity would be infinite. It appears to be 
worthy of consideration, whether this impossibility may not be connected with the 
appearance of spurious disks of fixed stars in the foci of telescopes. 
32. On the Action of Crystals on Light. 
If we set aside those actions on light to which there is nothing analogous in the 
phenomena of the elasticity of homogeneous solids, the laws of the refractive action 
of a crystal on light are in general of a more symmetrical kind, or depend on fewer 
quantities than those of its elasticity. 
Thus, the elasticity of a homogeneous solid depends on twenty-one quantities ; its 
crystalline form, on fifteen (the Homotatic Coefficients), while its refractive action 
on homogeneous light in most cases is expressible by means of the magnitudes and 
directions of the Orthogonal axes of Fresnel’s Wave-Surface, making in all six 
quantities. Crystals which possess only Rhombic or Hexagonal Symmetry in their 
Eiithytatic Axes, are usually Monaxally Isotropic in their action on light ; while 
crystals which possess only Cyboi'd Symmetry in their euthytatic axes, are completely 
isotropic in their action on light. 
From these remarks, however, there are exceptions, as in the case of the extra- 
ordinary optical properties discovered by Sir David Brewster in Analcime, which, 
in its refraction as well as in its form, is Cyboi'dally Symmetrical without being Iso- 
tropic. 
* Cambridge Transactions, vol. ix. part 1. 
Glasgow^ June 1855. 
