ASTRONOMY, 
436 
+ 
0-3 
cof. mean ano. Q 
4 - 
0*2 
cof. (mean ano. (( —- mean ano. Q) 
+ 
9 * I 
cof. (2 dift. Qa ([ -f mean ano. d ) 
Let r—i the femiaxis major, f=~- the femiaxis minor, 
rv=. the line, m the coline of the angle OCE ; then, from 
Conics, the fine of the horizontal polar parallax : fine of 
the hor. parallax at 0 :: f rV-j-pV ; rf; hence the fine 
of the hor. par. at 0 =z -— — -X the fine of the hor. 
■\J rV-j-pV 
polar parallax. If r : p :: 230 : 229, we have the follow¬ 
ing Table for the horizontal parallax for every degree of 
latitude, that at the pole being unity : 
Lat. 
Hor. Par. ] 
Lat. 
Hor. Par. 
Lat. 
Hor. Par. 
0° 
100438 
31° 
100321 
61° 
IOOIO3 
I 
100438 
32 
100314 
62 
100097 ! 
2 ! 
100437 
33 
IOO3O7 
63 
IOOO9I 
3 
100436 
34 
IOO3OO 
64 
100085 
4 
100433 
35 
100293 
65 
100079 
5 
100434 
3 6 
100286 
66 
100073 
6 
100432 
37 
I00279 
67 
100067 
7 
100430 
38 
100272 
68 
100062 
8 
10042S 
39 
100265 
69 
100057 
9 
100426 
4 ° 
100257 
7 ° 
100052 
IO 
IOO424 
4 i 
100250 
71 
100047 
I I 
I00421 
42 
100243 
72 
100042 
1 2 
100418 
43 
100235 
73 
100038 
13 
IOO.4 15 
44 
100227 
74 
100034 
14 
IOO4I2 
45 
100219 
75 
100030 
1.5 
100408 
46 
100211 
76 
100026 
16 
IOP404 
47 
100203 
77 
100023 
17 
IOO4OO 
48 
100195 
78 
100020 
18 
100396 
49 
100187 
79 
100017 
19 
100391 
5 ° 
100180 
80 
IOOOI4 
20 
100386 
5 i 
100173 
81 
100012 
21 
100381 
5 2 
100166 
82 
IOOOIO 
22 
100376 
53 
100159 
83 
100008 
23 
100371 
54 
IOOI52 
84 
100006 
24 
100365 
55 
100145 
85 
IOOOO4 
25 
100359 
56 
100138 
86 
IOOOO3 
26 
100353 
57 
100131 
87 
100002 
27 
100347 
58 
IOOI24 
8g 
IOOOOI 
28 
100341 
59 
100117 
89 
IOOOOO 
29 
100335 
60 
100110 
90 
100000 
3 ° 
100328 
Hence, by multiplying the polar parallax by the num¬ 
ber conefponding to any latitude, it gives the horizontal 
parallax at that latitude. From the theorem, the parallax 
may be very eafily calculated for any other ratio of the 
diameters of the Earth. 
In tire fpheroid, befides the parallax in right afeenfion 
and declination, latitude and longitude, there is alfoa pa¬ 
rallax in azimuth, and alfo a correction of the parallax in 
altitude. For the plane, which is perpendicular to the fur- 
face at O, always palles through O N, and therefore the 
azimuth feen from O or N and from C mult be different, 
except when the body is on the meridian, in which cafe 
the plane alfo paffes through C ; and the altitude feen 
from N mult alfo be different from that feen from C. 
Hence, having compared the parallax between O and N in 
altitude, we fhall want a correction for the difference be¬ 
tween the altitudes and azimuths feen from N and C, in 
the figure prece¬ 
ding the lalt. Let, 
therefore, CN in 
this figure, rep re- 
fent CN in the 
foregoing figure ; 
L the Moon, LCR. 
a plane perpendi¬ 
cular to the hori¬ 
zon, and then will 
N C R be the azimuth feen from C i draw N M perpendi¬ 
cular tpCR, M S perpendicular to CL, and LR per¬ 
pendicular to the horizon ; and let m and n be the fine and 
coline of NCM, r the fine of M C S, a — CN, the 
line of CON in the firlt figure above-mentioned, and 
c the cofine of I, NR, and let d^z the diftance of the 
Moon ; then «fc=RN, wta—MN. Now, the line CO, or 
unity, at the diltance d appears under an angle k when 
fecndireCUy; hence - : h :: : the angle NRC™—~ 
d cd c 
the difference of the azimuths feen from C and N. Alfo, 
as the arc parallel to the horizon between any two fecon- 
daries to it varies as the coline of the altitude, the arc of 
the difference of the azimuths at the altitude of the Moon 
—hma—hx MN. Now, as the plane NML is perpendi¬ 
cular to CLM, and NM is extremely fmall, the altitudes 
feen from N and M will not fenfibly differ ; hence the dif¬ 
ference between the altitudes at N and C is the angle 
CLM—/;xSM— /iXrxCM=j 5 x ! 'X'tX«' If the Moon 
be to th ej'outk of the prime vertical, we mu ft fubtrad this 
correction from the altitude at N to get the altitude at C; 
if it be to the north , we mull add the correction. 
But the molt elegant and (imple method of finding the 
parallax in latitude and longitude on a fpheroid, is the fol¬ 
lowing, given by Mayer. The parallax at any place 0 in 
the fpheroid is the fame as on a fphere whofe radius is CO, 
and latitude OCE, as ftiewn in the figure above-mentioned, 
preceding the two laft; fubtraCt therefore the angle COK 
(found in the following Table) from the latitude OvE on 
the fpheroid, and you get the angle OCE the latitude of 
the point 0 reduced to a fphere. Alfo the horizontal pa¬ 
rallax which is made ufe of muft be adapted to the radius 
OC , by diminifhirig the equatorial horizontal parallax by a 
quantity correfponding to the difference between CE and 
CO. This diminution is alfo found in the fame Table. 
The latitude thus reduced, and the horizontal parallax 
thus found, are to be employed in computing the Moon’s 
parallaxes in longitude, latitude, right afeenfion, and de¬ 
clination, which will now be performed by the rule above 
given, founded on the hypothefis of the Ea'rth being a 
fphere; for, by means of the Table, both the bafe of the 
parallax, and the latitude of the place, are referred to the 
Earth’s centre. 
ARGUMENT. 
Elevation of the Pole, and Equatorial Parallax. 
Elev.of 
Pole. 
Equatorial Parallax. 
Reduct, of 
Elevat. 
of Pole. 
54 ' | 
57 ' I 
6 o' 
Reduction of Parallax. 
o° 
— o - o* 
— o-o" 
— O’O" 
— o' 0" 
6 
0 * 2 
O* 2 
O’ 2 
3 6 
12 
o-6 
0-7 
0-7 
6 4 
18 
1 '4 
i *4 
i ‘5 
8 57 
24 
2‘3 
2’5 
2 ‘6 
ii 6 
30 
3'5 
3'7 
3*9 
12 56 
3 6 
4‘9 
yl 
5‘4 
14 12 
42 
6-3 
6-7 
7 *o 
14 5 1 
48 
7.7 
8-2 
8-6 
14 5 1 
54 
9 '2 
9*7 
IO “ 2 
1412 
60 
10-5 
in 
11 '7 
12 56 
66 
1 1 ‘7 
I 2 8 4 
13-0 
11 6 
72 
12*7 
i 3’4 
I 4 ' 1 
8 57 
78 
i 3'4 
I 4'3 
14-9 
6 4 
84 
13*9 
J 4’6 
15-4 
3 6 
90 
i 4 'i 
14.8 
15-6 
0 0 
Ex. If the latitude on the fpheroid be 63°, and the 
equatorial parallax be 56', what are the reductions ? The 
reduction of the parallax is 11-5", and of the elevation of 
the pole it is 35" ; hence the reduced latitude is~6a° 59' 5", 
and the parallax 55' 48‘s". 
1 To 
