ASTRONOMY. 
lar to EC, C the.place of the eye, and let ab be parallel 
to C E, then it will be that diameter of the circle anbm of 
aberration which is feen mod: obliquely, and confequently 
that diameter which is projected into the minor axis 
of the ellipfe ; let ran be perpendicular to ab, and it will 
be feen directly, being perpendicular to a line drawn from 
it to the eye, and therefore will be the major axis; draw 
C a, C bd, and ad in the projection of ab ; and as ad 
may be confidered as a ftraight line, we have mn, or ab, 
the major axis to ad the minor as rad. is to fin. abd, or 
E Cd the (tar’s latitude. As the angle bad is the comple¬ 
ment of abd, or of the (tar’s latitude, the circle is pro¬ 
jected upon a plane making an angle with it equal to the 
complement of the (tar’s latitude. 
As the minor axis da coincides with a fecondary to the 
ecliptic, it mud be perpendicular to it, and the major axis 
vin is parallel to it, its pofition not being altered by pro¬ 
jection. Hence in the pole of the ecliptic, the fine of the 
dar’s latitude being radius, the ellipfe becomes a circle ; 
and in the plane of the ecliptic, the fine of the dar’s lati¬ 
tude being —o, the minor axis vanifltes, and the ellipfe 
becomes a draight line, or rather a very {mail part of a 
circular arc. 
To find the Aberration in Latitude and Longitude. Let 
A B C D, in the annexed figure, be the Earth’s orbit, fup- 
pofed to be a circle with the Sun in the centre at x, and 
conceive P to be a line drawn from x perpendicular to 
A B CD, and to reprefent the pole of the ecliptic ; let S 
be the true place of the (lar, and conceive apeq to be 
tiie circle of aberration parallel to the ecliptic, and abed 
the,ellipfe into which it is projected; let y'T be an arc 
of the ecliptic, and draw the fecondary PSG to it, and 
it will coincide with the minor axis bd into which the di¬ 
ameter pq is projected; draw GCxA, and it is parallel 
topq, and BxD perpendicular to it mud be parallel to the 
major axis at ; then, when the Earth is at A, the dar is 
in conjunction, and in oppofition when the Earth is at C. 
Now at the.place of the liar in the circle of aberration is 
always ninety degrees^before the Earth in its orbit, when 
Vol, II. No. Si. 
the Earth is at A, B, C, D, the apparent places of the dar 
in the circle'will be at a, p, c, q, or in the ellipfe at a , b, 
c, d j and, to find the place of the dar in the circle when 
the Earth is at any point E, take the angle p S s=zE x B, 
and r will be the correfponding place of the dar in the 
circle ; and to find the projected place in the ellipfe, draw" 
sv perpendicular to Sc, and vt perpendicular to Sc in the 
plane of the ellipfe, and t will be the apparent place of 
the dar in the ellipfe ;■ join st, and it will be perpendicular 
to vt, becaufe the projection of the circle into the elliple 
is in lines perpendicular to the ellipfe ; draw the fecon¬ 
dary PvtK, which will, as to fenfe, coincide withwf, 
unlefs the (lar be very near to the pole of the ecliptic i 
therefore the rules here given will be fufnciently accurate, 
except-in that cafe. Now as cvS is parallel to the eclip¬ 
tic, S and v mud have the (ante latitude, hence vt is the 
aberration in latitude ; and, as G is the true and K the 
apparent place of the dar in the ecliptic, GK is the aber¬ 
ration in longitude. To find thefe quantities, put ?n and 
n for the fine and cofine of the angle rSc, or C.vE the 
Earth’s didance from fyzygies, radius being unity ; and as 
the angle svt— the complement of the dar’s latitude, the 
angle »r<=the dar’s latitude, for the fine and cofine of 
which put v and w, and put.r=S« or Sr; then in the 
right angled triangle S sv, As -i is to m fo is r to sv—rm ; 
hence in the triangle vt s, As i is to v fo is rm to tv—rvm 
the aberration in latitude. Alfo in the triangle S sv, As 
i is to n fo is r to vS—rn, hence, As to is to i fo is rn to 
rn 
G K =— the aberration in longitude. When the Earth 
to 
is in fyzygies, m— o, therefore there is no aberration in la¬ 
titude : and, as n is then greated, there is the greated 
aberration in longitude ; if the Earth beat A, or the dar 
in conjunction, the apparent place of the dar is at a, and 
reduced to the ecliptic at H, therefore GH is the aber¬ 
ration, which diminilhes the longitude of the dar, the or¬ 
der of the figns being Y' G T; bur, when the Earth is at C, 
or the dar in oppofition, the apparent place c reduced to the 
ecliptic is at F, and the aberration GF increafes the lon¬ 
gitude ; hence the longitude is the greated when the dar 
is in oppofition, and lead when in conjunction. When the 
Earth is in quadratures at D or B, then n=o, and m is 
greated, therefore there is no aberration in longitude, but 
the greated in latitude ; when the Earth is at D, the ap¬ 
parent place of the dar is at d, and the latitude is there in- 
creafed ; but, when the Earth is at B, the apparent place 
of the dar is at b, and the latitude is diminidied ; hence 
the latitude is lead in quadratures before oppofition, and 
greated in quadratures after. From the mean of a great 
number of obfervations, Dr. Bradley determined the va¬ 
lue of r to be twenty feconds. 
Ex. i. What is the greated aberration in latitude and 
longitude of y Urfie ntinoris, whofe latitude is 75 0 ifi > 
Here m—i, v— -9669 the fine of 75 0 13'; hence 20" x '966(7 
— 1 9’34" the greated aberration in latitude. For the great¬ 
ed aberration in longitude, n—i, w—-a 551; hence ——— 
• 255 * 
=78-4" the greated aberration in longitude. 
Ex. 2. What is the aberration in latitude and longitude 
of the lame dar, when the Earth is thirty degrees from 
fyzygies? Here ot = '. 5 ; hence 19• 34."-!--5=9-67" the aber¬ 
ration in latitude. If the Earth be thirty degrees beyond 
conjunction or before oppofition, the latitude is diminidied ; 
but, if it be thirty degrees after oppofition or before con¬ 
junction, the latitude is increafed. Alfo n— -866 ; hence 
78'4 "x '8662=267'89" the aberration in longitude. If the 
Earth be thirty degrees from conjunction, the longitude is 
diminidied ; but, if it be thirty degrees from oppofition, 
it is increafed. 
Ex. 3. For the Sun, m=o and n—i, wr=zi • hence it has 
no aberration in latitude, and the aberration in longitude 
— r— 20" conftantly. This quantity twenty feconds of 
aberration of the Sun anfwers to its mean motion in S' 7" 
30'", which is therefore the time the light is moving from 
5 U the 
