Don J. Rodriguez’s Observations on the 
84$ 
of the triangles, considered as spherical, the logarithmic sines 
of the sides in the series were next computed, and then 
reduced to logarithms of the arcs themselves by the formula 
i K.sin. a £ 
log. £ = log. sm. 6 -f - Tk - a - . 
For the purpose of making this last reduction, it is sufficient 
to take a single value of R, corresponding to the mean lati- 
tude of the entire arc 5s 0 2' 20". It was thus that the table 
was formed of logarithmic sides considered as arcs. 
Let m be one of these arcs, and let us represent by Sip and 
Sip" its value reduced to the meridian, the one in toises, the 
other in seconds of a degree, and we shall have the following 
formulas ; 
= m ■ cos - 5 ~ (— — ) • tan S' + - ( 2R J • (—Jr — ) 
. (1 +3 .tan. *4/) 
W = (dsb>) + (1 + ') • 
( 3 T^ ) • (|f) } : the superior sign being taken when the 
latitude 4'" is greater than t]/, and the inferior when it is less. 
The correction dependent on the convergence of the meri- 
sin. 2 (4- -f ip) 
[ m 
. sin. 
6 1 
\Ri 
. sin. 
i"J ‘ 
t cos. ip • cos. | c)\j/" j 
Hence the azimuth of the first station seen from the second 
and reckoned westward from the north, is 6' = 180* -f- 0 
-f S9. 
If P" be put for the difference of longitude between two 
points distant by an arc which measures m, we have sin. P" 
— — oTJ— > lo S- Sln - * = lo S- I 
= lo s- (ct) + r • ( sin - p ")- 
\ 
K 
/ 171 V 
) “ 
6 * 
(r») 
