REPORT ON PHYSICAL OPTICS. 375 



III. Double Refraction. 



The phenomeuon of double refraction was first discovered by 

 Erasmus Bartholinus, in Iceland spar. After a long series of 

 observations, he found that one of the rays vrithin the crystal 

 observed the known law of refraction discovered by Snellius, 

 while the other was bent according to a new and extraordinary 

 law. An account of these experiments was published at Copen- 

 hagen in the year 1669, under the title " Exjierimenta Crystalli 

 Islatidici Disdiaclastici, quibus mira et bisolita refractio de- 

 tegitw." 



The success of Huygens in deriving the laws of ordinary re- 

 fraction from the hypothesis of waves, naturally led him to 

 examine whether these new phenomena could be reconciled to 

 the same theory ; and in his desire to assimilate the two classes 

 of phenomena, he was happily led to assign the true law of 

 extraordinary refraction. Huygens had already shown that the 

 direction of the refracted ray, in glass and other uncrystallized 

 substances, could be deduced from the supposition, that the ethe- 

 real wave within the substance was a sphere ; or, in other words, 

 that the velocity of undulatory propagation was the same in all 

 directions. One of the rays in Iceland crystal, too, was found 

 to obey the same law ; and judging that the law which governed 

 the other, though not so simple, was yet next in simplicity, he 

 assumed the form of its wave to be the spheroid of revolution, 

 the greater and lesser axis of the generating ellipse being in the 

 ratio of the greatest and least index of refraction. The form of 

 the wave being known, the law of refraction is derived from the 

 principle of the superposition of small motions. Conceive three 

 surfaces having their common centre at the point of incidence, 

 and representing respectively the simidtaneous positions of three 

 waves diverging from that point, — the first in air, the other 

 two within the crystal. Let the incident ray be produced to 

 meet the air tvave, and at the point of intersection let a tangent 

 plane be drawn : through the line of intersection of this plane 

 with the refracting surface, let planes be drawn touching the 

 two refracted waves ; — the lines connecting the centre with the 

 points of contact are the directions of the two refracted rays. 

 This beautiful construction, and the other speculations of Huy- 

 gens on the subject of extraordinary refraction, are contained 

 in the fifth chapter of his Traite de la Lurni^re. 



Huygens was unable to reconcile the existence of a double 

 wave within the crystal with the supposition of a single vibrating 

 medium ; and he was accordingly forced to assume the existence 

 of two such media, the spherical wave being propagated by the 



