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is one of the rare instances of a successful theoretic prediction. You 

 know that the ordinary course of scientific discovery is, that a phe- 

 nomenon is first observed, and then accounted for. The experimen- 

 talist establishes its reality, and then the theorist endeavours to reduce 

 it under a general law. Thus Kepler discovered that the planetary 

 orbits are in fact elliptical, before I^Tewton established the mechanical 

 principles on which the form depends. The laws of reflexion and re- 

 fraction were known as facts before ISTewton and Huygens endeavoured 

 to reduce them under the more general laws of mechanics. But in the 

 case of conical refraction, this order was reversed. The mathematical 

 genius of Sir William Hamilton enabled him to predict this phenome- 

 non as a consequence of Tresnel's theory, before the experimental skill 

 of Dr. Lloyd established its reality. Sir William Hamilton saw that 

 the rule by which Fresnel determined the course of the two rays into 

 which a single incident ray is divided by crystalline refraction, appeared 

 to fail under certain circumstances. With a certain disposition of the 

 incident light, he found that not two, but an infinite number of direc- 

 tions might be found satisfying the laws of ]Fresnel, and from this in- 

 definiteness he rightly inferred that light would actually pass along 

 each of these directions ; and that therefore, instead of emerging in two 

 rays, the light would emerge in a hollow cone. With another dispo- 

 sition of the incident ray, he inferred, by similar reasoning, that the 

 light would emerge in a cylinder. The establishment of the reality of 

 these phenomena by Dr. Lloyd must be regarded as a great triumph 

 of experimental skill. The difficulties attending such an investigation 

 can, of course, be fully appreciated only by those who have been en- 

 gaged in similar labours; but there is in these experiments one pe- 

 culiar source of difficulty, which will be intelKgible to every one — 

 it is this, that they do not admit of approximation. Generally speak- 

 ing, in conducting an experiment, if the adjustment of the apparatus be 

 nearly, though not mathematically exact, the phenomenon produced 

 will be nearly, though not exactly, that which we are seeking ; and 

 the more nearly we approximate to perfect accuracy of adjustment, the 

 more nearly will the phenomenon actually produced approximate to that 

 which is required. And therefore, in ordinary experiments, an indif- 

 ferent observer, though he will not perfectly succeed, will not wholly 

 fail. He will make an approximation to the truth — an approximation 

 which, with increasing skill and greater attention, he will gradually 

 render more and more close. With conical refraction it is not so. That 

 phenomenon admits of no degrees. If the adjustment be not mathe- 

 matically accurate, the phenomenon is not produced, nor any thing like 

 it. The smallest deviation from the proper disposition of the incident 

 light will cause the cone or cylinder to disappear, and to be replaced by 

 the two rays which are seen under ordinary circumstances. Every one 

 can understand the difficulty of even conducting such an experiment 

 as this when the means of doing so have been already devised and put 

 into the hands of the observer — a difficulty, indeed, so great, that 

 observers have been found to deny the reality of the phenomenon. 



