DISCO VEKY OF THE LAW OF EEFRACTIONS. 55 



The assertion, that the angles of refraction are not proportional to 

 the angles of incidence, was an important remark ; and if it had beer, 

 steadily kept in mind, the next thing to be done with regard to refrac- 

 tion was to go on experimenting and conjecturing till the true law of 

 refraction was discovered ; and in the mean time to apply the prin- 

 ciple as far as it was known. Alhazen, though he gives directions for 

 making experimental measures of refraction, does not give any Table 

 of the results of such experiments, as Ptolemy had done. Vitello, a 

 Pole, who in the 13th century published an extensive work upon Op- 

 tics, does give such a table ; and asserts it to be deduced from experi- 

 men , as I have already said (vol. i.). But this assertion is still liable 

 to doubt in consequence of the table containing impossible observations. 



[2nd Ed.] [As I have already stated, Vitello asserts that his Ta- 

 bles were derived from his own observations. Their near agreement 

 with those of Ptolemy does not make this improbable : for where the 

 observations were only made to half a degree, there was not much 

 room for observers to differ. It is not unlikely that the observations 

 of refraction out of air into water and glass, and out of water into 

 glass, were actually made ; while the impossible values which accom- 

 pany them, of the refraction out of water and glass into air, and out 

 of glass into water, were calculated, and calculated from an erroneous 

 rule.] 



The principle that a ray refracted in glass or water is turned to- 

 wards the perpendicular, without knowing the exact law of refraction, 

 enabled mathematicians to trace the effects of transparent bodies in 

 various cases. Thus in Roger Bacon's works we find a tolerably dis- 

 tinct explanation of the effect of a convex glass ; and in the work 01 

 Vitello the effect of refraction at the two surfaces of a glass globe is 

 clearly traceable. 



Notwithstanding Alhazen's assertion of the contrary, the opinion 

 was still current among mathematicians that the angle of refraction 

 was proportional to the angle of incidence. But when Kepler's atten- 

 tion was drawn to the subject, he saw that this was plainly inconsistent 

 with the observations of Vitello for large angles ; and he convinced 

 himself by his own experiments that the true law was something 

 different from the one commonly supposed. The discovery of this 

 true law excited in him an eager curiosity ; and this point had the 

 more interest for him in consequence of the introduction of a correc- 

 tion for atmospheric refraction into astronomical calculations, which 

 had been made by Tycho, and of the invention of the telescope. In 



