E 47 ° 3 
XL VI* Calculations in Spherical trigonometry abridged. 
By Ifrael Lyons, hi a Letter to Sir John Pringle, 
Bart. P. R. S. 
TO SIP^ JOHN PRINGLE, BART. P. R. S. 
SIR, 
Redde, July 6 , j N" c E aftronomical obfervations have 
1775* 
S 
been made with much greater precilion 
than formerly, it became requifite that the calculations 
correfponding to them fliould likewife be made to much 
greater degrees of exa61:nefs. The ancient aftronomers 
defired only to make their obfervations and computations 
agree within a part of a degree ; fucceeding ones were fa- 
tisfied when they correfponded within a minute ; but no 
lefs exadlnefs than feconds will content the moderns. 
The rules in fpherical trigonometry being reduced to 
operations by logarithms, it is necelTary to ufe fuch a 
number of figures in the tables as will produce the re- 
quired precifion ; this is very different in the various parts 
:of the quadrant, infomuch that if the arc is only one de- 
gree, four places of decimals in the logarithm of a fine 
are fufficient to determine the arc to which it belongs 
within a fecond: whereas if the arc is 89 °, there is a 
neceffity 
