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LIII. On the atmospherical Refraction. By Mr. J. Ivory. 

 To the Editor. 



Sir, — J.N some researches on astronomical refraction I found 

 the subjoined formula, which is not unworthy of the attention of 

 astronomers on account of its exactness, its convenience for cal- 

 culation, and because it comprehends all the refractions from the 

 zenith to the horizon in one expression. It is not an empirical 

 formula, or one obtained by altering the coefficients till they re- 

 present with sufficient accuracy a certain number of observed 

 places. It is entirely theoretical, and, in fact, borrows nothing 

 from astronomical observations. The only elements that enter 

 into its construction are the numbers that denote the refractive 

 force of tiie air; the mean pressure of the atmosphere ; and the 

 mean horizontal refraction; quantities which have been taken as 

 they are laid down in the Mccanique Celeste, In its original 

 state, the formula would therefore give the refractions for the 

 mean height of the barometer adopted by the French astrono- 

 mers, and for the temperature of melting ice; but, in order to 

 facilitate a comparison with the Table pul)lished in the Connais- 

 sance des Terns, it has been reduced to the temperature of 10° of 

 the centigrade thermometer, or 50^ of Fahrenheit, by applying 

 the correction directed to be used with the Tal)le. It would oc- 

 cupy too many of your pages, sir, to enter on a detail of the 

 analysis ; but I shall attempt below to point out the principles 

 on which the investigation proceeds. I put A for the zenith 

 distance, and R for the refraction : then, having found the sub^ 

 sidiary angle ^ by means of the formula. 



Log. tan (|)- 18-9873149- log. cos A, 



we have Log. of the coefficients. 



R = sin A X -|^1200-"93 tan i ^ .... 3-0795 170 



+ 637-88 tan' | ^ .... 2-S0473S3 



+ 163-78 tan' |^ 2-2142677 



-1- 19-51 tan''!^ .... 1-2903704 



+ 3-95 tan'^i^ 05967129 



+ 0-64 tan" i^ .. -1-8037929 



The comparison of this formula with the refractions in the 

 Connuissunce des Terns, is contained in the following Table: 



Vol.57. No. 277. iVioy 1821. Ss A. 



