The quantity of the refraction at every altitude, from the horizon, where it is greatest, to the zenith'where it is nothing, has been determined by observations by many astronomers ; those of Dr. Bradley and Mr. Mayer are esteemed the most correct of any, being nearly alike, and are now chiefly used by astronomers. Dr. Bradley, from his observations, deduced this general rule for the refraction, r, at any altitude, a, whatever ; viz. as rad. 1: cotang. a + 3 r : : 57" : r" the refraction in seconds. This rule is adapted to these states of the barometer and thermometer, viz. either 29.6 inch barometer and 50° thermometer, or 30 inch barometer and 550 thermometer, for both which states it answers equally the same. But for any other states of the barometer and thermo meter, the refraction above found is to he corrected in this manner ; viz. if b denote any other height of the barometer in inches, and t the degrees of the thermo meter, r being the refraction incorrected, as found in the manner above. Then as 29.6: b: : r : It the refraction corrected on account of the barometer, and 400 : 450 t:: It the refraction corrected both on account of the barometer and thermome ter; which final corrected refraction is therefore = 450— br. Or, to correct 11840 the same refraction, r, by means of the latter state, viz. barometer 30 and
mometer 55, it will be as 30 : b : : It = br 455 — t and 400: 455 —t R : 400 R 455 — t b r the correct refraction.
1'z000 Mr. Simpson has determined, by theo ry, the astronomical refractions, from which he brings out this rule, viz. as 1 to .9986, or as radius to sine of 86° 58' 30", so is the sine of any given zenith distance, to the sine of an arc ; the difference between this arc and the zenith distance, is the refraction sought for that zenith distance. And by this rule Mr. Simpson computed a table of the mean refrac tions, which are not much different from those of Dr. Bradley and Mr. Mayer, and are as in the following table. See Simp son's Dissertations.
It is evident that all observed altitudes of the heavenly bodies ought to be dimi nished by the numbers taken out of the foregoing table. It is also evident that the refraction diminishes the right and oblique ascensions of a star, and increases the descensions ; it increases the north. ern declination and latitude, but decreas es the southern ; in the eastern part of the heavens it diminishes the longitude of a star, but in the western parts of the heavens it increases the same. See QUA. DRANT.