222 PHILOSOPHICAL TRANSACTIONS. [aNNO 1787. 



But it may be proper to confirm this rule for refractions also from the same 



■ manuscript of Dr. Bradley, which I before cited for confirming the latitude, by 



the following passage, which immediately follows the other. " Suppose the 



mean refraction at 45° 3' = bT', and y = 350; then y -^ t\ bar. :: T]" : refr. at 



45° 3". .... Rad. : tan. zd :: 3' : w rad. : tan. zd — m :: refr. at 45° Z' : r 



the refraction required." It is easy to see that this rule agrees with the other; 

 for putting t = 50, and barometer = 29.6, the first analogy, putting the baro- 

 meter down in tenths of an inch, is 350 + 50 = 400: 296 :: "JT" -. 56^^98 for 

 the refraction at 45° 3', or 57'^ within -^\^ of a second. The second analogy 

 serves to give the treble refraction nearly, called m. Whence it is evident that 

 the last analogy coincides with the rule above given. 



This valuable rule was first communicated by myself to the public in vol. 54 

 of the Philos. Trans., p. 265, and in p. 49 and 129 of the first edition of tables 

 requisite to be used with the Nautical Almanac, together with a table of the 

 mean refractions deduced from it, with the first Nautical Almanac, that of 1767, 

 published by order of the commissioners of longitude in 1766; and again, at 

 page the 5th of the Explanation and Use of the Astronomical Tables, annexed 

 to the first volume of my Observations made at the Royal Observatory from 

 1765 to 1774, published by order of the president and council of the r. s., with 

 two tables in that work, containing the mean refractions and decimal multipliers 

 for reducing them to ainy given temperature of the air indicated by the barometer 

 and thermometer. The words in page the 5th of the said preface are as follow. 

 " The astronomical refractions and latitude of the observatory were settled with 

 the greatest accuracy by Dr. Bradley, from his observations of the circumpolar 

 Stars, with the brass mural quadrant, during the 3 years that it was turned to 

 the north, and of the sun and stars in the subsequent years after it was removed 

 to point to the south. The following elegant rule was the result of his observa- 

 tions, that the refraction at any altitude is to 57 seconds, in the direct com- 

 pound ratio of the tangent of the apparent zenith distance lessened by 3 times 

 the refraction, to the radius, and of the altitude of the barometer in inches to 

 29.6 inches, and in the reciprocal ratio of the height of Fahrenheit's thermo- 

 meter increased by the number 350, to the number 400. Tables 22 and 23 

 were adapted to this rule; the first containing the mean refractions answering to 

 .29.6 inches height of the barometer and 50 degrees height of the thermometer; 

 and the 2d table containing decimals for multiplying the mean refraction in order 

 to find the correction, which applied to it will give the actual refraction, the 

 same as would have been produced by the rule with somewhat more trouble. 

 Dr. Bradley supposed the horizontal parallax of the sun 10^ seconds, in the cal- 

 culations from which he inferred the refractions; and I have been informed, that 

 he determined the latitude of the Observatory 51° 28' 39^^ But, had he made 



