[ a6 + ] 
imperfection lying in the firSt rule derived from the 
fluxions of a Spherical triangle. To the rules I have 
here fubjoined their demonstrations. 
With refpeCt to the ufefulnefs of thefe rules, I 
cannot but entertain hopes that they will appear more 
Ample and eafy than any yet propofed for the fame 
purpofe : the lait rule, for computing the diftance of 
the Moon from a ftar, though only an approximation, 
being fo very exaCt, feems particularly adapted for the 
conftruCtion of a nautical Ephemeris, containing the 
distances of the Moon from the Sun and proper fixed 
Stars ready calculated for the purpofe of finding the 
longitude from obfervations of the Moon at lea ; an 
affiftance which, in an age abounding with fo many 
able computers, mariners need not doubt they will 
be provided with, as Soon as they manifelt a proper 
difpofition to make ufe of it. 
A RULE 
To compute the contraction of the apparent distance 
of any two heavenly bodipc by rpfraCtion • the ze- 
nith distances of both, and their distance from each 
other being given nearly. 
Add together the tangents of half the fum, and 
half the difference of the zenith distances ; their fum, 
abating io from the index, is the tangent of arc the 
firSt. To the tangent of arc the firft, juft found, 
add the co-tangent of half the distance of the Stars ; 
the fum, abating io from the index, is the tangent 
of arc the Second. Then add together the tangent 
of double the firSt arc, the co-fecant of double the 
fecond 
