of the Problem of Ainiospherical Refraction. 37 



exploring the manner of its construction. What are the em- 

 pirical modifications in this instance? Are they derived from 

 original observaticms ? Or must we seek for them in the tables 

 already known to astronomers ? 



Entertaining a curiosity to understand something of the 

 real nature of the table of refractions in the Nautical Al- 

 manack ; and suspecting that original observations were not 

 much employed ; I thought of comparing it with the tables in 

 the best repute at the time of its publication. I found that 

 it perfectly coincided with M. Bessel's table in the Fundamenta 

 Astronomice, as far as 45" from the zenith. Hence there is 

 a great probability that the one table was used in the con- 

 struction of the other. If there be 10 chances to 1 that two 

 languages are in some way connected which have three names 

 in common, as the author has determined in another place *, 

 how great must be the chance of connexion in two short tables 

 that perfectly agree in 45 consecutive numbers. At greater 

 zenith-distances the refractions in the Nautical Almanack fall 

 between M. Bessel's table and that of the French astronomers ; 

 and they ultimately become identical with the latter at the 

 horizon. We can now form some idea of the nature of the 

 empirical modifications of the formula. The table in the 

 \Nautical Almanack is a melange of the tables of M. Bessel 

 ard the French astronomers ; and the numerical coefficients 

 are adjusted accordingly. What I have now said is not to 

 be considered as mere conjecture ; it is the result of calcula- 

 tions that are easily verified. 



The table of refractions in the Nautical Almanack is a sin- 

 gular instance of a set of practical calculations seemingly de- 

 chiced from a deep theory ; and yet, when we fully reach into 

 the truth, having a slight, or even no, coimexion with the 

 theory. For it is not the formula which produces the table; 

 it is the table, after the choice is fixed to make it consist of 

 numbers taken from the tables of M. Bessel and the French 

 astronomers, which determines the formula. 



In finally retiring from so long and teasing a controversy, 

 allow me, gentlemen, to thank you for the attention you have 

 paid to the various papers I have addressed to you in the 

 course of it. I remain, &c. 



January 14, 1825. JamES Ivory. 



• Philosophical Transactions 1819, pp. 81, 82. 



VII. On 



