DEGREE. 
Correction for the Eccentricity of the lower Telefcope. 
When ei ia theobfervation of an angle AC B,(P/.VII. 
Jig» 58.) the upper i e is directed to the objec 
to the a in the io the lower telefcope 
was concentric, we fhould dee it towards C B, and the in- 
ercepted arc would give — the limb the seaore re- 
quired. ie on acco 
n to the inftrument 
DCF, and not to oe ACB. 
is equal to the 2 
ACD=ACE—BCD 
Now DGE = ACE — 
—~BCA =ACE~—~BCD+BCA = (90° — A) 
— (goe° ~— B) + BCA go° A—o90 + B+ 
: CD CE 
BCA=BCA+B—A=BCA + 25~—a5; 
for the 4’s A . ba very {mall, we may ufe the 
fines inflead of t he upper telefcope is thus 
turned to the iefe aun o the Z ntity = 
BCA 3 then, to bring it back to B, it 
CD CE 
GB Gat ACB=2z2ACB 
at then, taking half the arc meafured on 
CD CE 
the limb, we find ACB + ——; SCR TCA % (are 
CB” GA 
CA 
muft deferibe ACB + 
CD 
+ CB 
meafured); then ACB = & (arc meafured) + <s - 
cD zt RE erie 
>CB To find AC B, we muft add +—— ———— = 
ee, hs eines OB, fon he cee 
and G, the diftance e A, from the 
obje hich Shy rds the left. In the figure, the 
eccentricity is to the left; if it had been to the right, it 
would have been ne and the correction would have 
had contrary figns. The corre€tion is always 
Peouene reduced to feconds, and divided by the diftance 
the objeGt on the fame fide with the eccentricity, minus 
4 eccentricity, divide the diftance from the other 
fide, relatively to the eccentric telefcope. 
n circles conftruéted in this country by Mr. Troughton, 
the eccentricity of the lower telefcope is one inch and four 
which is to the ee 
& w 
I. 
tenths, and ala = — : this quantity, reduced to 
. I fathom 103 
. 206264.8  R” 
feconds, will be 2002", [= piesa ae re therefore, 
u “ 
ee, he following 
the correction will be —— 
table, which is calculated se ey above-mentioned eccen- 
tricity, 13 of very eafy applica 
With the diftance of the objet, which is on the fame 
with the eccentric telefcope, that is, the diftance of the 
diftance of the on to the ria — fathoms 
gi 
bate 
<" 
om 
on 
Right 22,000 Biome -_ — 0. ets 
Total correction - O51 
If the two diftances are ae the terms deftroy each 
other, and the correction bec 
he annexed table is calelated “for an 19-inch circle of 
Mr. faa sc on. 
onftru 
hens fan right to left ; the obferva- 
places his d 
tions, eon, bee as with - left-hand objea. 
Fathom 
1000 2".00 
2000 1.cO 
3000 0.67 
4000 0.50 
5000 0.40 
6000 0.33 
47000 0.30 
S020 0.25 
gooo 0.22 
10,000 0.20 
I1,0C0 0.18 
12,000 0.16 
13,000 O.1g 
14,090 0.13 
15,000 O43 
16,000 0.12 
17,000 0.12 
18,0c0 O.1T 
19,000 0.10 
20,000 0.10 
21,000 ite) 
22,000 cg 
23,000 Rese) 
24,000 .08 
25,000 0.08 
t is a curious circumftance, firft noticed by Legendre, 
that this correétion for poanasbenle when applied to the 
thes 2€ oo in a triangle, becom 
a, b, e, eee the fides ‘of a triangle, we have 
the aon for the a 
I 
de de 
Cc b 
1 i 
5 e ge 
which together = 0. . 
Redud&tion of the cbferved Angle to the Hortzon. 
The repeating circle does not give direétly the horizontal 
et 
angle between s, but the oblique angle; it is 
enith diftances of the ob- 
fide 
lef hand objeét in our inftruments, enter the table, and take neceflary, therefore, i take the z 
a correétion, to which you will prefix the figa +. With ferved objects, and then calcu ites, the azimuthal angle by 
the refolution of a nee | trian a 
fe diftance of the right-hand objet take a fecond core 
reCtion, which is to have the fign 
to be di- 
000 fathoms, and the right-hand o t 
left, the 
flant 22,000 fathoms, and the eccentricity to the 
2 
Suppofe the rete of the left- hand objec 
The reduction is as follows 
Let A = angle of pofition, or obferved angle. 
Hs= altitude o fignal A 
bh = altitude of Genal B. 
