[ 107 ] 



XVlII. Comparison of Mr. Ivory's Table of Refractions, 

 Philosophical Transactions 1824, 'with Dr. Bradley's Ob- 

 servations published in M. Bessel's FuyidavientaAstronomicey 

 pp. 53, 54. By J. Ivory, Esq. F.R.S. 



[In the paper on the Least Squares, the words " relatively to every error, 

 and an absolute maximum relatively to all the errors " occur in the be- 

 ginning of No. 2 ; for which read "relatively to every variable in the errors, 

 and an absolute maximum relatively to all the variables." And the same 

 words must be corrected in the same manner when they occur immediately 

 below in speaking of the minima of \p.] 



THE annexed table shows the errors of my refractions 

 when compared with the observations of Dr. Bradley 

 cited above. In the six last stars the mean of the observa- 

 tions recorded by M. Bessel is taken. In the calculations the 

 temperature of the air is estimated by the exterior thermome- 

 ter, and the barometer is reduced to the standard by means 

 of the interior thermometer. When the interior thermome- 

 ter is not set down in M. Bessel's table, it is taken 5° higher 

 than the exterior one. 



It appears from this comparison that the errors of my table 

 are very small when the zenith-distance does not exceed 88°^: 

 but when the altitude is less than 1°^, the errors increase sud- 

 denly, and are all in defect. The same conclusion is con- 

 firmed by other computations which I have seen. 



It must be observed, that in the construction of my table 

 no assumption has been made for the horizontal refraction. 

 The theory requires us to know only the quantity that mea- 

 sures the refractive power of air, and the gradation of heat in 

 the atmosphere. The horizontal refraction obtained in this 

 manner from theory alone is 26" greater than vvhat the French 

 astronomers make it, and much less than the magnitude which 

 the observations of M. Bessel seem to indicate. As my re- 

 fractions agree with nature to so great an extent from the 

 zenith, it seems reasonable to infer that the mean condition of 

 the atmosphere, beyond the influent* of the earth and while 

 the aerial fluid is at liberty to arrange itself in equilibria by 

 its own inherent powers, is represented with tolerable accu- 

 racy. But in the neighbourhood of the horizon the ex- 

 traneous heat and moisture emanating from the earth must 

 derange the regular disposition which the strata of air would 

 otherwise assume ; and to this cause, for which no allowance 

 is miide in the theory, we must ascribe the sudden deviation 

 of tlic theoretical retractions from those observed. 



I have no other intention in publishing this comparison, 



O 2 than 



