from Bradley to FresneL 131 



such close relations between the different elements of the 

 phenomenon are conclusive in favour of the hypothesis on 

 which they are based." 



The question as to the correctness of Fresnel's construction 

 was discussed for many years afterwards. A striking conse- 

 quence of it was pointed out in 1832 by William Kowan 

 Hamilton (b. 1805, d. 1865), Royal Astronomer of Ireland, who 

 remarked* that the surface defined by Fresnel's equation has 

 four conical points, at each of which there is an infinite number 

 of tangent planes ; consequently, a single ray, proceeding from 

 a point within the crystal in the direction of one of these 

 points, must be divided on emergence into an infinite number of 

 rays, constituting a conical surface. Hamilton also showed 

 that there are four planes, each of which touches the wave- 

 surface in an infinite number of points, constituting a circle of 

 contact : so that a corresponding ray incident externally should 

 be divided within the crystal into an infinite number of refracted 

 rays, again constituting a conical surface. 



These singular and unexpected consequences of the theory 

 were shortly afterwards verified experimentally by Humphrey 

 Lloyd,f and helped greatly to confirm belief in Fresnel's theory. 

 It should, however, be observed that conical refraction only 

 shows his form of the wave- surf ace to be correct in its general 

 features, and is no test of its accuracy in all details. But it 

 was shown experimentally by Stokes in 1872J Glazebrook in 

 1879, and Hastings in 1887,1 1 that the construction of Huygens 

 and Fresnel is certainly correct to a very high degree of 

 approximation; and Fresnel's final formulae have since been 

 regarded as unassailable. The dynamical substructure on 

 which he based them is, as we have seen, open to objection ; 



* Trans. Roy. Irish Acad., xvii (1833), p. 1. 



t Trans. Roy. Irish Acad., xvii (1833), p. 145. Strictly speaking, the bright 

 oone which is usually observed arises from rays adjacent to the singular ray : 

 the latter can, however, be observed, its enfeeblement by dispersion into the 

 conical form causing it to appear dark. 



I Proc. R. S., xx, p. 443. 



Phil. Trans., clxxi, p. 421. 



|| Am. Jour. Sci. (3), xxxv, p. 60. 



K 2 



