DEGREE 
Let n= fins 3 % (1 +4) tang. £A = fin?  (H —d) 
cot. LA, 
any cor. x == 2, fec. H, fec. b. 
zen, diftances differ more than 2° or 3° from go%, 
I 
this nee may be rare a 
-i) (C442 2) 
— in ( ae 
Ne 5 ® — 
— fin. 
z being the angle reduced to Sale horizon, C the angle 
at os centre, 0 and 3’ the zen. diftances of the fignals, 
V'o facilitate this eae we have added the tabies 
calculated for this purpofe elambre. By thef 
tables we may at fame time reduce the horizontal angle 
to i formed by the chor 
ufe of thefe es will be eafily underftood by an 
exam i. 
H + 4 is the fum of = zenith diftances of the obferved 
objedts diminifhed by 1 
the fum fhould be ce than 5180" » H+ A is the re- 
mainder required to complete 180°. 
ae Ais always the iference between the two zenith 
dift 
(H 4 h) and (H — +4) are always confidered as pofitive 
oumbers. 
Q is the fum of the ee in French toifes be- 
tween the pea and each of the fignals. 
dis di fae between thefe diftances; (P — Q.) 
is slays sae 
With (P + Q) and (P - Q ) take in Tab. IL, two 
numbers, to which you always muit annex the ‘fen 
Wi e number, 
; y und 
the factors (P + Q ) and ( me, as in the aa 
Make the four dias liao 
The difference of the two firft produ i is the reduction 
to the beans et be denied according to its fign. 
The difference of the two laft products is the redu@ion 
to the chords, to be applied with its proper fign to the hori- 
zontal angle 
This lat redu@iion is almoft always fubtra&tive, but it 
fometimes becomes additive, by the fourth product exceed- 
ing the third. 
“In general, the fourth produét is nothing, and the third 
always very {mall; fo that in calculating the reduétion, 
which is pee area it is very little more trouble to re- 
duce t o the chords. Thefe tables are, in gene- 
ral, anes fafficient for the redudtion to the horizon; but 
for greater exactnefs, Table III. is added. ‘The eee of 
the products, as obtained above, may, by means of this 
table, be multiplied by fec. H, fec. 4, as required by the 
formula, If greater precifion be ‘required, the whole calcula- 
tion may be repeated with the corrected angle, initead of 
the obferved angle 
Table V. is for calculating the fpherical excefs. 
ake ufe of this table, it is neceffary to have a plan of 
the triangles with a fcale. The arguments are one fide of 
the triangle as a bate, § aod ade height. 
Ce 
Obferved Angle. Zenith Diftance. peace el 
32° 20' 15".7 A = 89° 41 54.6 A = 18283 
B= 88 49 15.6 D == 24425 
7 178 31 10.2. 
H+h= 3: 28 498 
H-s4= 52 39 
- Tab. I. "Tab. IL 
Se eee nen 
Argument H+4 -H ae P+ Q P =O 
Faétors + 1.669 --+o0.587 —oO112 — 0.003 
Tab. IV 5-09 —7-106 + 5.99 — 7.106 
15021 3522 — 0.67 +0.2 ~ 
15021 0587 + 0.02 — 
8345 4109 
— 0,65 = redu&ion 
to the chords. 
+ 9.99731 —41.71222 
Obferved an i - 
Reduétion to horizon - 
32° 20° 15%.7 
31.7 
Horizontal angle = 32 
gie 1d 44.0 
Reduétion to the- diode - . 0.65 
| omen nace 
32 19, 43-45 
When the depreffions are f{mall, we may, inftead of the 
tables, ute this for cae | 
Angle of the chords - 
~yy\? 
#= { (90° £*) tong. gC — (: —) cot 3c} 
fin. 1”. : 
Example by the Formula. 
d= 89° 41! 54"6 
v=: 88 49 15.6 
o+0 = 1478 31 10.2 3 —¥ = 0° 42 39" 
SLY 7 —. 52 39 
9O°——-—- = 0 44 24.9 =0 26 19.5 
= 2664".9 =p = 2579".5= 9 
Sin. 1” = 4.68557 68557 
Log. p? 6.85136 Log. g 6.39704 
Tang. 3C 9. kia Cot.$C 0.53764 
+ 0.99921 = 9" .98 — 1.62025 = 41.72 
— 41.71 
31.73 = Reduction required. 
32° 20 15.7 70 
Reduced angle=32 19 43.97 the fame as above. 
- Reduétion of the obferved Angle to the Centre of the Station. 
Ic frequently pe Lager in trigonometrical furveys, that the 
obfervation cannot be taken in the centre of the flation; in 
this cafe, a correction becomes neceflary. 
(Plate VIL. fig. 59-) Let C be the centre of the ftation, 
the place of the oe 
Then ACB=A 
Sin. A= fin. OAC Of - AO Cz 
r fin.(O + BOC) 
D 
hence C=O tiet0-49 os) ) _ rfany 
D fin. 1” G fin. 1” 
This formula is general, and fuffers no exception 
€ 3 the angle required at the centre; O, the obferved 
