98 LIFE AND WORKS OF KEPLER. 



simply concludes that one of these observations is erroneous ; but the 

 same singularity presented itself on different occasions to Ty{;ho, who, 

 certain of his own skill and of the precision of his instruments, could 

 not admit such an ox])lanation. He pointed out the true cause in the 

 refraction of the luminous rays, which, null at the zenith, acquires at 

 tlie horizon its greatest value ; consequently, when the sun is, in the morn- 

 ing, a little below the equator, the refraction, by elevating its rays, may 

 produce the impression of the observation of the equinox. Some hours 

 later, when the sun is uearing the zenith, the refraction is less, and this 

 cause of depression, compensating for the distance which the sun has 

 traversed in its orbit, may cause it to be observed anew in the eqnator. 



Pliny cites another contradiction not less i)alpable, which, wliile 

 equally showing theimi)ortance of the phenomenon of refraction, should 

 have led the ancient astronomers to make it the subject of their study. 

 "An eclipse of the moon," he says, "has been observed at the moment 

 when the sun was still visible above the horizon." The moon conse- 

 <iuently disappeared although the right line which joins its center with 

 that of the sun appeared not to encounter the earth. 1'he fact is a con- 

 stant one ; it was observed particularly by Mcestlin and by Tycho ; yet 

 there is e^ idently a necessity that the earth, in order to eclipse the moon 

 by its shadow, must be placed in a right line between the moon and sun. 

 It is undeniable, therefore, that the three bodies are really in a right 

 line at the moment of the eclipse, and the phenomenon must be ex- 

 plained by the refraction which brings the two luminaries into an appar- 

 ently simultaneous opposition above the horizon. It will be seen from 

 these instances how important it is that this cause of error should be 

 taken into account in the discussion of observations. The Arabian as- 

 tronomer Alhazen and the Polonese Yitellion were the tirst to call at- 

 tention to this point, and Tycho, who thoroughly felt its importance, gave 

 still later a table of refractions relative to different inclinations. 



The difiliculty of such an investigation is readily perceived, not to 

 say that any direct determination is impossible. Refraction is the angle 

 formed by the right line which really connects the luminous body with 

 our eye, and the line resulting from the direction iu wdiich it is per- 

 ceived. Now, of these two directions the second alone is open to actual 

 observation 5 the angle which it forms with the other cannot be meas- 

 ured, and it is necessary to calculate it by an indirect process. The con- 

 tinuous observation of a star followed from the zenith to the horizon 

 might give it; the diurnal movement, the laws of which are not contested, 

 causes the star, in eifect, to describe a i^erfect circle in the heavens, and 

 knowing at every instant where it ought to be, we may i)lace to thie ac 

 count of refraction the observed irregularities. 



The process followed by Tycho is a little different, but he was far from 

 attaining the object in view ; according to him, the refraction of the 

 light of the stars completely ceases at 20° from the horizon ; that of the 

 sun, being more considerable, becomes null only at 45°. This is alto- 

 gether inexact, refraction follows the same laws for all these luminaries, 

 and becomes null only at the zenith. Kepler, therefore, took up the 

 question from the beginning, and composed, under the modest title of 

 Paralipomena ad VitaUionem, a complete treatise of optics. This work, 

 though containing serious errors, is truly remarkable for the time when 

 it was composed. We find therein the correct theory of telescopes, ex- 

 act rules for determining the focal distance of lenses and the augment- 

 ative power of an instrument. Here, for the first time, was given an exact 

 description of the eye and the explanation of its mechanism ; it is here, 

 finally, that we find an explanation of the cinereous light of the moon, at- 



