by Means of two Altitudes of the Sun. 
107 
EXAMPLE III. 
Let os suppose the true lat. to be 54 0 27 7 50", and two obser- 
vations to be made in the afternoon — one when the sun's dis- 
tance from the meridian is y 30' o", the other when his distance 
is 45 0 10' 15" — the declin. in the former case being 8° 7' 35", 
and in the latter 8° 5' 3", on the same side of the equator with 
the latitude TllSii 'will tlic greatest amtuue De iouna equal to 
43 0 31' 19", and the least to 31 0 20' 23". 
Observation i st. Observation 2d. Observation 1st. Observation 2d. 
Lat 54 0 1 o' o" Lat 54 0 10' o" Lat. 54 0 u' o" Lat. 54 0 n' o" 
Log. of a — 9,8379894 
9,7161022 
d — 9,1503179 
9,1480707 
1 — 9,9088727 
- 9,9088727 
^ = 20,7787988 
- 20,6591588 
Incr. of log. of / — 912 
912 
^ = IO >3 8 93994 
- io , 3295794 
log. secant — 456 
456 
Log. tang. = 10,3498734 
10,2758492 
tang. = 545 
5 8 4 
2 x incr. of log, - — ■ 

2 X log- tang, = 20,6997468 
20,5516984 
tang. - = 1090 
1 16s 
Log. of r — 9,1547009 
9,1524081 
11 
O 
OA 
; VO 
1 2? 
- 10,1413981 
Incr. of log. of s — 2662 
2662 
Computed log. of yzz . 9>995 8 45 8 
- 9,8455046 
Area gc — 1572 ..gc: 
= J 494 
True = 9,9 986590 
9,8481862 
Area gb — 28132 
Area gb — 26816 
Now, by diminishing gb and gb, till 
the ratio of gc to gc 
be- 
comes equal to the ratio of g b to gb, we should get gb = 28126, 
and gc = 26735. Hence — 17' 53" the correc- 
tion, and the latitude = 54 0 27' 53". 
But the same conclusion would have been obtained indepen- 
P 2 
