352 Mr. Potter oji Conical Refraction. 



of light from .a closed lamp, and when the incident pencil is 

 very small ; for then, when we desire to obtain the ring with 

 maximum distinctness, we can see, that as one portion of it 

 becomes more distinct the other becomes less so, on varying 

 slowly the distance of the eye-lens. 



A popular explanation of the formation of the ring, and 

 consequently of the two series of cones, may be thus given : 

 any physical point being taken in the small hole on the first 

 surface of the crystal, it will have two images polarized in 

 planes at right angles to each other; these are two points at 

 the extremities of some diameter of the ring; and every other 

 point having similarly two images, the locus of all these images 

 forms the ring. Speaking more correctly, if we call Ej 

 and E.2 the two images of any physical point, then the locus 

 of El forms one ring and the locus of E.^ the other, as before 

 described. 



The conclusion we come to, from the preceding discussions, 

 is that the phasnomena of conical refraction were not adequately 

 examined by Professor Lloyd. It may be that Sir William 

 Hamilton and Professor Lloyd have exjiected results from 

 their experiments for which Fresnel's expression for the wave- 

 surface in biaxal crystals gives no warrant. The cylindrical 

 refraction in air, being merely the transition from a series of 

 converging cones to a series of diverging ones, may not be 

 separable from them by any mode of experimenting. My 

 present impression is that no such cylindrical refraction ex- 

 ists, but it is a point for future careful experimental re-ex- 

 amination, accompanied by an attentive comparison with the 

 properties of Fresnel's expression. The angle of the cone 

 which has its vertex at the second surface of the crystal, I 

 find to be about 3° 30', or something less than this, consider- 

 inc a point outside the crystal as the vertex ; for a series of 

 careful micrometrical measures with a compound microscope 

 of a magnifying power of twenty-six times, and a minute in- 

 cident pencil of lamp light, gave the diameter of ihe ring 

 l-53'4th of an inch, and by finding the apparent position of 

 the ring, within the crystal, we have the angle of the cone as 

 above. Now the angle from Sir William Hamilton's calcu- 

 lations should be about 3°, a sufficiently near coincidence to 

 produce an impression in the mind in favour of Fresnel's ex- 

 pression. 



We saw, however, that one image of the sun, on the se- 

 cond surface, in the first-mentioned experiment with sun-light, 

 on approaching the position of the optic axis, expanded into 

 a ring, whilst the other image became an ill-defined point in 

 its centre : it is seen also that the two images leave the optic 



