and Longitude of the "Royal Obfervatory at Greenwich 157 
<( Rad. : tan. ZD :: f \m. ... . Rad. : tan. ZD — m : : refr. at 45°3 / : r 
“ [the refraction required].” It is eafy to fee that this rule 
agrees with the other: for putting /== 50, and barometer 
= 29,6, the firft analogy, putting the barometer down in 
tenths of an inch, is 350 + 50 = 400 : 296 :: 77" : 5 6 7/ ,9 8 for 
the refraCtion at 45 0 3", or 57" within T 4--th of a fecond. 
The fecond analogy ferves to give the treble refraCtion nearly, 
called m. Whence it is evident, the laft analogy coincides 
with the rule above given. 
This valuable rule was firft communicated by myfelf to the 
public in vol. LIV. of the Philofophical TranfaCtions, p. 265. 
and in p. 49. and 129. of the firft edition of Tables requifite to 
be ufed with the Nautical Almanac, together with a Table of 
the mean RefraCtions deduced from it, with the firft Nautical 
Almanac, that of 1767, publfthed by order of the Commif- 
fioners of Longitude in 1766 ; and again, at page the <;th of 
the Explanation and Ufe of the Aftronomical Tables, annexed 
to the firft volume of my Obfervations made at the Royal 
Obfervatory from 1765 to 1774, publilhed by order of the 
Prefident and Council of the Royal Society, with two tables 
in that work, containing the mean refraCtions and decimal 
multipliers for reducing them to any given temperature of the 
air indicated by the barometer and thermometer. The words 
in page the 5th of the faid preface are as follows. “ The 
“ aftronomical refraCtions and latitude of the Obfervatory were 
“ fettled with the greateft accuracy by Dr. Bradley, from his 
“ obfervations of the circumpolar ftars, with the brafs mural 
“ quadrant, during the three years that it was turned to the north, 
“ and of the fun and ftars in the fubfequent years after it was 
removed to point to the fouth. The following elegant rule 
“ was 
