ASTRO 
the points of the compares will denote the magnitude of 
the angle. This is fufficiently clear; but there is another 
circumftance which readers are not fufficiently aware of, 
and which therefore requires to be well attended to : it is, 
that the angle will be neither enlarged nor diminiffied by 
any change in the length of the legs, provided their po- 
iition remains unaltered ; becaufe it is the inclination of 
the legs, and not their length, which conftitutes the angle. 
So that, if a pair of compaffies, with very long legs, were 
opened to the fame angle as another fmaller pair, the inter¬ 
vals between their refpeftive points would be very diffe¬ 
rent, but the number of degrees on the circles, fuppofed 
to be applied to each, would be equal, becaufe the degrees 
themfelves on a fmaller circle would be exactly propor¬ 
tioned to the fhortnefs of the legs.- This property renders 
the admeafurement of angles very eafy, becaufe the dia¬ 
meter of the meafuring circle may be varied at plealure, 
as convenience requires. 
Magnitude, however, abftraftedly confidered, is capable 
of being increafed to infinity, and isalfo divifible without 
end ; and hence we find in nature, that the limits ot the 
created and leaft dimenfions of things, are actually placed 
at an immenfe diftance from each other. We can perceive 
no bounds of the vaff expanfe in which natural caufes 
operate, and fix no limit, or termination, to the univerfe. 
The objects we commonly call great vaniffi, when we con¬ 
template the vaff body of the Earth; yet the terraqueous 
clobe itfelf is loft in the folar fyftem; the Sun itfelf dwin¬ 
dles into a ftar; Saturn’s vaft orbit, and all the orbits of 
the comets, crowd into a point, when view'ed from number- 
lefs places between the Earth and the neareft fixed ftars. 
Other funs kindle to illuminate other fyftems, where our 
Sun’s rays are unperceived ; but thefe alfo are fwallowed 
up in the vaft expanfe. When we have rifen fo high, as 
to leave all definite meafures far behind us, we ftill find 
ourfelves no nearer to a term, or limit. Thefe views of 
nature, however, ferve to reprefent to us, in a moft fenfi- 
ble manner, that mighty power which prevails throughout, 
afting with a force and efficacy that fuffers no diminution 
from the greateft diftances of fpace, or intervals of time ; 
and prove that all things are ordered by infinite wifdom, 
and perfect goodnefs: ideas which ffiould excite and ani¬ 
mate us to correfpond with the general harmony of nature. 
To calculate the Right Ascension, Declina¬ 
tion, Latitude, and Longitude, of the Heaven¬ 
ly Bodies. 
As the Earth revolves uniformly about its axis, the ap¬ 
parent motion of all the heavenly bodies, ariling from this 
motion of the Earth, mull be uniform ; and, as this motion 
is parallel to the equator, the interval of the times, in 
which any two ftars pafs over any meridian, muft be in 
proportion to the arc of the equator intercepted between 
the two fecondaries palling through them, becaufe this 
arc of the equator contains the fame number of degrees as 
the arc of any frnall circle parallel to it and comprehended 
between the fame fecondaries; and therefore, if one in- 
creafe uniformly, the other muft. Hence the right afcen- 
fion of ftars palling the meridian at different times will dif¬ 
fer in proportion to the difference of the times of their 
ailing ; and, as the clock is fuppofed to go uniformly, we 
ave the following rule : As the interval of the times of 
the paffage of any fixed ftar over the meridian : the inter¬ 
val of the paffage of any tw’o ftars :: 360 degrees : their 
apfarent difference of right afcenfions; which, corrected 
for their aberration in right afcenfion, gives their true dif¬ 
ference of right afcenfions. By the fame method we may 
find the difference of right afcenfions of the Sun or Moon, 
when they pafs the meridian, and a ftar, and therefore, if 
that of the ftar be known, that of the Sun or Moon will; 
which will be rendered more exact if we compare them 
with feveral ftars, and take the mean j remembering to apply 
the liar’s aberration in right afcenfion to the apparent, in 
order to get the true difference. When we thus determine 
the Sun’s 3 right afcenfion from that of a ftar, the Sun’s a- 
N O M Y. 43* 
berration, which in longitude is always 20", is not here 
confidered, becaufe the Sun’s place in the aftronomical 
tables is put down as affedledby aberration; and the ufe 
of obferving the Sun’s right afcenfion is to compare it 
with the tables in order to find their error. 
Now, in order to determine the right afcenfion of a fix¬ 
ed ftar, Mr. Flamflead propofed a method, by comparing 
the right afcenfion of the ftar with that of the Sun when 
near the equinoxes, and having the fame declination; and, 
as this method has not been explained by any writers, we 
fhall give a very full explanation thereof, together with an 
example. Let A G C K E be the equator, A B C W E 
the ecliptic, S the place of a ftar, and S® a fecondary to 
the equator, and let the Sun be at P, very near to A, 
when it is on the meridian; and take CT=PA, and draw 
PL, T CLj perpendicular to AGC, and Q^L parallel to 
A C; then the Sun’s declination is the fame at T as at P. 
Obferve the meridian altitude of the Sun when at P, and 
alfo the time of the paffage of its centre over the meridian; 
obferve alfo at what time the ftar paffes over the meridian, 
and then find the apparent difference Lis of their right af¬ 
cenfions. When the Sun approaches near to T, obferve 
its meridian altitude for feveral days, fo that on one of 
them at t it may be greater, and on the next day at e it 
may be lefs, than the meridian altitude at P, fo that in the 
intermediate time it may have paffed through T; and, 
drawing tb, es, perpendicular to AGCE, obferve on 
thefe two days the differences bn, sm, of the Sun’s right 
afcenfion and that of the ftar; draw alfo sv parallel to Cfe. 
Hence, to find Q^, we may confider the variation both of 
the right afcenfion and declination to be uniform for a 
frnall time, and confequently to be proportional to each 
other; hence vb (the change of the meridian altitudes 
in one day) : sb (the difference of the meridian altitudes 
at t and T, or the difference of declinations) :: sb (the dif¬ 
ference of sm, bm, found by obfervation) : Q _b, which 
added to bm, or fubtraCfed from it, according to the fitua- 
tion of ot, gives Q,ot, to which add Lm, or take their dif¬ 
ference, according to circumftances, and we get QJ-, 
which fubtradfed from AGC, or 180 0 , half the remain¬ 
der will be A L, the Sun’s right afcenfion at the firrt ob¬ 
fervation, to which add L ot, and we get the ftar’s right 
afcenfion at the fame time. Inftead of finding b Q^_, we 
might have found s Q.^ by taking T Q —es for the fecond 
term, and from thence we ffiould have gotten Qm. Thus 
we ffiould get the right afcenfion of a ftar, upon fuppofi- 
tion that the pofition of the equator had remained the 
fame, and the apparent place of the ftar had not varied, 
in the interval of the obfervations. But the interfeClion 
of the equator with the ecliptic having a retrograde mo¬ 
tion, called the preccjfion of the equinoxes; alfo the inclina¬ 
tion of the equator to the ecliptic being fubject to a varia¬ 
tion, called the nutation; together with the aberration of 
the ftar; its apparent place is continually changing. But, 
if the mean right afcenfion o.f any ftar be taken for the be¬ 
ginning of the year, and thefe corrections for the precef- 
fion of the equinoxes, nutation, and aberration, be applied 
to it, according to their ligns, for any day, therefult gives 
the apparent right afcenfion of the ftar for that day. 
Let therefore A B C E be the ecliptic, AGCE the po¬ 
fition of the equator at the firft obfervation when the Sun 
was at P, and aged the pofition of the equator at the time 
of the obfervation at the other equinox, and take T C — 
3 PA* 
