Sie Mr. Ivory on the Theory of the Astronomical Refractions. 



A = l-A+^--^ =-82193 



B=X-2A^+2A* =-134.23 



C = — A- - — A^ = -02377 



2 2 



D = — A^ = -02007 



For the horizontal refraction, when cos fl = 0, A = \/ 2is, 

 we obtain by the usual integrations, 



83= iiX^x |a + B/"2 + CV's'+DVT'X: 

 V 2i {_ ^ J 



or in seconds, 8 S = 2024-2 instead of 2025" as in Halley's 

 table. This proves the exactness of Kramp's elements. 



With respect to the other numbers in the table a distinc- 

 tion must be made. In every table of refractions, whatever 

 be the constitution of the atmosphere on which it is founded, 

 the numbers answering to altitudes greater than 16°, depend 

 only upon one element, namely, the refractive power of the 

 air. Reckoning from the zenith as far as 74°, any table may 

 be deduced from any other, provided both are accurately cal- 

 culated, merely by a proportion. In the table published an- 

 nually in the Con. des Temps^ the refraction at 4-5° is 58"-2 : 

 and, if Halley's table has been accurately computed, the 

 numbers in it, between the limits mentioned, will be equal 



540 

 to the like numbers in the French table multiplied by — 



_^ The calculation being made, the results will be 



97 

 found to agree almost exactly with the short table inserted 

 by M. Biot in the additions to the Con. des Tcmjps for 1 839, 

 p. 105, the greatest difference between the computed quan- 

 tities and the numbers in Halley's table, being about 2". 



But this gives no intimation with respect to the particular 

 constitution of the atmosphere assumed in the calculation 

 of the table. What is peculiar to a table in this respect has 

 no sensible influence on the refractions it contains except at 

 altitudes less than 16°. No definitive opinion can therefore 

 be formed on the question, whether Halley's table is the same 

 which Newton computed and communicated to Flamsteed on 

 the principle that the densities are proportional to the press- 

 ures, without comparing it with a sufficient number of re- 



