[ a6 5 ] 
double the fecond arch, and the conftant logarithm 
of ii 4" or 2,0569: the fum abating 20 from the 
index, is the logarithm of the number of feconds 
required, by which the diftance of the liars is con- 
tracted by refraCiion: which therefore added to the 
obferved diftance gives the true diftance cleared from 
the effeCt of refraction. 
Explication of the foundation of the preceding rule. 
This rule is founded upon an hypothecs that the 
refraCtion in altitude is as the tangent of the zenith 
diftance : and the refraCtion at the altitude of 45 
degrees being 57" , according to Dr. Bradley’s ob- 
fervations, therefore the refraCtion at any altitude, 
calling the radius unity is = 57" x tangent of the 
zenith diftance. This rule is exaCt enough for the 
purpofe of the calculation of the longitude from 
obfervations of the diftance of the Moon from ftars 
at fea as low down as the altitude of io°, for there 
the error is only 10" from the truth. But, if the 
altitude of the Moon or ftar be lefs than io°, the rule 
may be ftill made to anfwer fufticiently, by only firft 
correcting the obferved zenith diftances by fubftraCt- 
ing from them three times the refraCtion correfpond- 
ing to them taken out of any common table of re- 
fraCtion, and making the computation with the zenith 
diftances thus corrected. This correction depends 
upon Dr. Bradley’s rule for refraCtion, which he found 
to anfwer, in a manner exactly, from the zenith 
quite down to the horifon, namely that the refraCtion 
is = 57" x tangent of the apparent zenith diftance 
Vol. LIV. M m leffened 
