322 



On the atmospherical Refraction. 



It appears from this comparison that the formula is in perfect 

 agreement with tlie French Table, at least as far as 80' from tiie 

 zenith, which includes all the useful part of such a Table. At 

 85" from the zenith the difference amounts only to 1"; and the 

 greatest divergence at 0° 45' above the horizon is short of 

 12'. 



At 70° fiom the zenith the third term of the series is insensi- 

 ble ; and at 80', it only comes to 0"'19; so that, if we neglect 

 this small quantity, the two first terms of the series are suffi- 

 cient for all stars elevated 10° above the horizon. The three 

 first terms are sufficient as far as 85° from the zenith. 



Most physical problems are solved by a series of attempts in 

 which some of the conditions are either omitted entirely, or so 

 modified as to bring the investigation within the range of our 

 knowledge. The first attempt to solve the problem of the astro- 

 nomical refractions was made by Cassini, who neglected all 

 changes of density in the atmosphere, whether arising from un- 

 equal pressure or variation of temperature. In this view, the air 

 would constitute a uniform refracting medium surrounding the 

 earth to the height of about 4343 fathoms. The simple hypo- 

 thesis of Cassini seems hardly to have met from astronomers with 

 the attention it deserves : for, if we use accurate elementary 

 quantities in the computation, it will determine the refractions 

 to the extent of 74° from the zenith with the same degree of ex- 

 actness as any of the other methods, without even excepting the 

 formula of Laplace. In an atmosphere such as Cassini sup- 

 posed, 



