MR. IVORY ON THE THEORY OP ASTRONOMICAL REFRACTIONS. 187 



fact. He returned to the subject in his Tahulce Regiomontance, published in 1830. 

 In this last work he retains only that part of the table of 1818 which extends to 85° 

 from the zenith, many corrections being applied from recent observations made with 

 improved instruments. In order to supply what is wanting in the new table, Bessel 

 has added a supplemental one containing the refractions at every half degree for 

 altitudes less than 15°: which supplemental table is independent of theory, being 

 deduced from observations alone. These two tables form together a real table of 

 mean refractions, independent of all suppositions respecting the constitution of the 

 atmosphere ; and no other similar table of nearly equal authority is to be found in 

 the astronomy of the present day. What Bessel has accomplished on the subject of 

 the refractions is not the least important part of his labours for the advancement of 

 astronomical science : it is precious to the practical astronomer ; and it is necessary 

 to the theoretical inquirer, for enabling him to confront his speculations with the 

 phenomena to be accounted for. 



6. In the paper published in the Philosophical Transactions for 1823, the refrac- 

 tions are deduced entirely from this very simple formula, 



[^=l-/(l-c-), (4.) 



in which |3 stands for the dilatation of air, or a gas, by heat ; r' is the temperature at 

 the earth's surface, and r the temperature at any height above the earth's surface ; at 

 the same height c~" is the density of the air in parts of its density at the surface. 



In order to understand the application of the formula, it is necessary to premise 

 that in the remaining part of this paper we do not consider a variable atmosphere 

 subject to continual fluctuations, as is the case of the real atmosphere: we contem- 

 plate an atmosphere fixed in its condition at any given place or observatory, being 

 supposed a mean between all the variations that actually take place in an indefinite 

 time. In such an atmosphere the temperature and pressure at the earth's surface 

 will be mean quantities deduced from observation : the air at all elevations will have 

 an elastic force equal to the incumbent weight which it supports, as an equilibrium 

 requires : and, whether the air be dry or moist, its refractive power will be equal to 

 the refractive power of dry air subjected to the same pressure and temperature*. 

 These properties of the mean atmosphere rest upon experiment and demonstration : 

 in other respects its nature is not directly known to us : and the laws of its action 

 can only be discovered, not by hypothesis, but by observation. 



The consideration of a mean atmosphere, invariable at any given observatory, is a 

 necessary consequence of the notion we attach to the mean refractions ; for these 

 would be realized in such an atmosphere : but they are different in any other state 

 of the air. 



These observations being premised, if the formula (4.) be verified at the earth's 



* Additions ^ la Conn, des Temps, 1839, p. 36. 

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