GEOGRAPHICAL LATITUDE. 773 



quantity decreases from the horizon to the zenith, where it disap- 

 pears.^ However, though he had a better idea of the subject than the 

 earliest of modern astronomers, he failed to discover any of the laws of 

 its action.'^ The subject was merely mentioned by Sextus Empiricus, 

 in a work entitled Ad versus Astrologus (in the third century);^ was taken 

 up by Alhazen about 1100, in his work on optics ; then remained un- 

 noticed till the Nuremberger astronomer, Walther, about 1500, com- 

 menced to estimate, at least near the horizon, the effects of refraction.'' 

 He was probably the first who ever really observed astronomical re- 

 fraction, which he had done before becoming acquainted with the an- 

 cient works wherein it is mentioned.^ About a century later Tycho 

 Brahe was lead to a re-discovery of the phenomenon while trying to de- 

 termine the latitude of his observatory. For greater accuracy he made 

 observations of a circumpolar star and of the sun at the solstices, and 

 found a difference of four minutes in the results. In a new instrument, 

 built with more care for similar observations, showing the same diver- 

 gence, he believed the difference to be caused by refraction, and fell to 

 making a special study of the subject, from the results of which he con- 

 structed the first table of astronomical refractions ; but he not only 

 missed an important truth, which had been already guessed by Ptol- 

 emy, viz, that refraction ceases only at the zenith, but he believed 

 that refraction for the sun and the stars ceases at different altitudes, and 

 found the latter at an end of 26 degrees above the horizon, while at 45 

 degrees the sun's rays still suffered a refraction of five seconds.^ Here 

 was indeed a valuable beginning, but the whole matter rested upon an 

 empirical basis ; for as yet there was no conception of the laws of the 

 action of light. The first of these, that of the relation of the angle of 

 incidence to the angle of refraction, was first published by Descartes 

 in his Dioptrice, though the honor of precedent discovery belongs to 

 Suellius, who unfortunately died before he could publish his work.' 

 Tycho himself remarked that refraction is not always the same, but of- 

 tered no explanation of the fact. Cassini and Picard found that it was 

 greater in winter than in summer, by night than by day, and by a happy 

 chance the latter was led to the true explanation of this irregularity ; 

 for, observing once at sunrise, he found the horizontal refraction sud- 

 denly change twenty-five seconds, which could have no other cause 

 than the increased warmth of the air,^ caused by the appearance of 

 the sun. Two other laws of nature discovered about the same time 

 aided materially in increasing the knowledge of astronomical refrac- 

 tion, the first being the one discovered by Edmund Mariotte, that the 



1 Delambre, Astron. du xviii™"^ si^cle, 774. 

 -'Bruhus, 8. UMd. 



^Delambre, Astron. du xviii'"S si^cle, 775. 

 * Delambre, Astron. du luoyen-Age, 33i>. 

 8 Delambre, Astron. dn xviii""' si^cle, 775. 

 ^Bruhns, 24, '25. «Ihid.,^\. 



