ay. 
DEGREE. 
has been evinced in the ufe of them, and the fcrupulous accu- 
racy with which the obfervations have beencomputed. But 
notwithftanding the fanguine hopes that were entertained 0 
removing every "doubt on this queftion, have been ae dif- 
appointed, yet the iio we have obtained by thefe 
operations 1s by no means inconfidera The remaining 
uncertainty is now reftri ts, an 
w 
Two caufes are fuggefted as mott 
likely to produce the difcordance: either a 
larity in the actual figure of the earth, or an extremely va- 
viable denfity of the materials that lie beneath its pone 
Both thefe caufes are probably concerned, but what prec 
abe is to = attributed to each, future binadoa: nas 
an determin 
This 5 fabjee will be again refumed under figure of the 
ARTH, to which the reader is referred for an account of the 
other methods that have been employed in the folution of 
this problem. 
The great improvements that have been made in the con- 
ftrudion of inftruments defigned for einen - eo nature, 
have been the means of-creatin ng almo 
“o derive ail eae — ie bie ation ‘of fuch 
extreme precifion, it was requifite to devife new for ~~ 
new modes of ca cies the Ganges and many new co 
re€tions that were cither imperfe&ly applied, or totally ne- 
glected by former obfervers. For thefe valuable additions 
e 
found difperfed in the tranfaCtions and oe rs of differe 
learned on and in the couse of the furveys ee 
enumerated, 
Profe for Playfair has given acomplete inveRigation oo 
formule requifite for calculating the different par 
ridian line, and other circ'es on a {pheroid. (See Edin, Phil. 
Tranf. vol. v.) Inthe Englifh furvey, a method rl 
new, of calculating agers triangles, is given by 
Dalby, and the account of th ole work begu pes 
ral Roy, and continued by éslone nel Mudge, is in itfelf a moft 
complete treatife on ee {cience of t trigonometria furveying. 
The French method of obfervation neceffarily required cor- 
reCtio er more eae nature than ours. And ‘Delambre, 
with the account he has publifhed of his own obfervations, 
has given a great number of practical rules, which, though 
derived from the moft profound analyfis, he has reduced to 
{uch a convenient form, that they may be employed by per- 
em 
n 
both oe gio to the improvement of this 
icien 
We lave hitherto entered but little into the mathematical 
uninterrupted a form as po we are defirous that 
ould be om'tted aa relates “either to the theor 
of aftronomy, or the {ciences connected with it, 
_ we propofe to fubjoin, by way of appendix to this article, 
fhort treatife on that part of geodetical trigonometry, cas is 
ca PaRAy 
On -" Method ae eles and fend the Angles. 
The angles may be obferved either with a theodolite, or, 
what is nearly the fame, a portable aftronomical circle, or 
with the repeating circle o 
A circular inflrument, a two microfcopes to its azimuth 
circle, will giv o meafures of the angle required without 
changing the sot of die whole inftrument ; 
each microfcope, but with three verniers we obtain fix’ 
meatfures of the fame angle. Three verniers are therefore 
better than two microfcopes. 
If this inftrument be placed in the centre of the ftation, no 
correGtions will be required, except fuch as relate to the 
eaasdes excefs, or reduction to the chord, according to the 
mode of computation adopted, as will be explained hereafter 
but if th t of the centre of the fta- 
ating circle 
repeating 
soree on will be ee a fome decd ng on the mecha- 
nical conftruction of the inftrument, and others on its pofition 
the nature and method of application of thefe we {hall en- 
eavour to explain 
Und er Crncun t and DecuiinaTion, a full account has ale 
ready an given of the mechanical conitruétion of this inftru- 
ment, of the requifite oe ns, and mode o 
aftronomical purpofes. It no 
method of employing it for goede obferva 
The method of obferving an ae eee two objects 
with the repeating circle is as fo 
Firft, bring the plane of the cirele into the plane of the 
angle to be obferved ; if this is rightly performed, the inter- 
fection of the wires of the micromete er nas the moveable tele- 
a fhould pafs over each obje& i revolution round its 
ntre. To effe& this readily. regis a ‘little dexterity and 
Sees: Theplaneof the inftru when vertical, fhould fir 
objects, ea 
inclined with the hand till the two objects feem to the eye 
equally diftant from the plane of the circle. The inftrument is 
then tobe eae roundits vertical axis, till oneobjectis brought 
into the front, or upper telefcope fixed at zero, The back or 
dee elec: fhou 
the joint aGtion of the f 
as above, to ~ left, and the lower to the right hand o te 
on 
directed to t oer hand objeé. 
When each goal is cone bifected at the fame time, one 
obfervation is a and the verniers will fhew the double 
of the meafured angle. ‘This is to be repeated tiil a fuffi- 
cient degree of certainty is obtained. 
We fhall give an srglee of an angle aii by an 18 
inch circle, bale ucted 
y Mr. Troughton 
No. of Obf. © gt given by Inft. Angle deduced. 
2 127° 7’ 45" 63° 33! 52"5 
4 254 15 24 33 54 
6 2I 23 00 63 33 50 
8 148 30 30 63 33 48.7 
IO 275 38 I0 63 33 49.3 
12 42 45 50 63 33 49-1 
14. 169 §3 20 63 33 48.6 
16 297 00 50 63 33 48.5 
. 20 19t 16 17 63 33 49 
Corredion 
