METEOROLOGICAL PARADOXES — HUMPHREYS. 197 



change of direction by the time the surface of the earth is reached 

 depends upon the wave length, or color, of the light; the slope at 

 which it enters, or zenith distance of the luminous object; the tem- 

 perature and barometric pressure at the place of observation; the 

 humidity; and several other minor factors. On the average, how- 

 ever, light from a star for instance, that appears to be 90° from the 

 zenith, and, therefore, on the horizon — just rising, say — has been 

 bent out of its original course by about 34.5'. That is, it comes into 

 view (rises) while actually more than half a degree below the hori- 

 zon. And as the angular diameter of the sun and the moon are each 

 less than this horizon refraction, it follows that when the sky is 

 sufficiently clear the whole of either luminary may be seen before 

 even its topmost portion is up; that is, before it is geometrically 

 above the horizon, or actually within 90° or less of the zenith. 



THE SUN SETS AFTER IT IS DOWN. 



Since the virtual wave length of a given radiation of celestial 

 origin and, therefore, the value of its astronomical refraction is modi- 

 fied by the rotation of the earth, as are also certain scintillation phe- 

 nomena, it follows that the above paradox is not identical with the 

 one just explained. Nevertheless, as the spectra of the stars and 

 other celestial objects all overreach the visible portion at each end 

 it follows that the Doppler effect produces no appreciable altera- 

 tion in the ensemble of the light from any one — merely a minute 

 shift of its entire spectrum that can be detected only in the positions 

 of definite lines. 



But even this displacement of the spectral lines, due to the rota- 

 tion of the earth, is far too small, roughly one three-hundredth the 

 distance between the sodium D's, to affect detect-ably astronomical 

 refraction. Hence as the sun, the moon, and the stars all rise before 

 they are up, so too they must all set only after they have gone down. 



