86
THE HONGKONG GOVERNMENT GAZETTE, 29TH JANUARY, 1887.
When a and d resp. a1 and d1 represent the geocentric right ascensions, and declinations of Jupiter at two epochs, A and D the coordinates of his north-pole referred to the terrestrial equator, p and pl the observed position angles and i the angle between the Jovian axis, and the plane on which it is projected, perpendicular to the line of vision, we have the well-known equations:
sin D-sin d cos i + cos d sin i cos p........
cos i sin d sin D + cos d cos D cos (a¬A)............
cos D sin (a-A) cosec p
sin i
-
Eliminating i from (1) by aid of (2) and (3) we obtain :
tan D-tan d sin (N −a+A) cosec N.........
where: tan N-sin d tan P,
and cos N is of the same sign as cos p.
Equating the two equations of the form (4) we obtain :
where: From (5) we obtain :
M sin (N-a+A)=sin (N1-a1+A),
tan d cot d' sin N1 cosec N-M.
tan A:
+M sin (Na)-sin (N1-a1) M cos (N -a)+cos (N1— a1)
...(1)
.(2)
.(3)
.(4)
(5).
...(6)
The value of A is obtained by aid of (6) and D is then obtained from either of the two equations of the form (4).
From the mean of the figures in the sixth and the seventh columns it follows, that the equatorial and polar diameters at the mean distance (5.20273) of Jupiter are 38′′.207 and 35".942 respectively and that the equatorial semi-diameter at the mean distance of the Earth from the Sun is 99.39. The polar is 0.9407 times the equatorial diameter and the ellipticity, or about a seventeenth. Its diameter is about 11 times that of the Earth, and as its mass is 309.8 times as large it follows that its density is of the mean density of the Earth. It appears therefore that the apparent mean density of Jupiter does not considerably exceed that of water, but of course this includes the no doubt extensive gaseous envelope so that the matter nearer the centre may be much denser.
4.3
MICROMETRIC MEASURES OF SATURN.
Ring-Diam.
Planet.
Obs. Cale.
Epoch.
Pos.
m.
n. M.P.
1879, Jan. 3, +4°.37 +0°.17
4 200
Ext. Cass.
39".12
Int.
17".48
Equ. Pol.
16".00
Pos.
Ext.
Int.
+0°.04 +0".54
4,
4 .25
.20
4 600
-0.07
12
"
14,
4 .89
.14
4 200
37..26
17.53
16 .81
27
23
+0.63 -0.65
15,
4 .14
.24 4
37 .75
17.08
16 .66
29
1880, Oct. 21,
0.11
*00 2
J3
46,39
39'.35
30".87
19 .31
19.12
23,
1 .32
.23 4
46 .91
30.78
19 .93
18 .88
"
"S
93
28,
1..20
.20 4
46.72
30.80
19 .53
18.90
22
وو
Nov. 3, 1.37
.15 4
46 .22
39 .37
30.78
19:58
18.85
29
Dec. 1, +1 10
.20
1
44.59
37.90
30.44
19.11 18.33
-0.11 -0.12
-1.39 +1..33 +0".90 -0.20 +1.88 +0.83 -0.35 +1.76 +0.89 -0°.24 +1.38 +0.98 -0.70 +1.02 +1.46
1882, Oct. 27,
وو
46.66
39 .87
20.30
+0.91
"
Dec. 5,
300
46.92
40.64
19 .40
+1.25
"
""
7,
200
47 .26
40 .41
19.65
+1.66
1883, Jan. 8,-2.50
.25
4
45.56
"
:
18 .17
-1.03 +1.81
1885, Dec. 23,
**
6.42 27, 7.97 28, 8.50
.28 4 340 0.50 3
"
+0.28
-1.30
1.27 6 600
-1.83
1886, Apr. 5,-7 .31
0.70 7 110
-0.79
The first column exhibits the epoch. The second, third, fourth and fifth columns are arranged as in the previous table. The sixth to the tenth columns inclusive exhibit the external diameter, the diameter of Cassini's division, the internal diameter of the Ring and the equatorial and polar diameters of the planet. The three last columns exhibit the differences between the observed values and those given in the Nautical Almanac for the position of the semi-minor axis and the external and internal diameters of the Ring.
24.95.
From the measures the following proportions between the different diameters and the external diameter of the Ring were obtained: Ext. 1.0000, Cass. 0.85434, Int. 0.66573, Equ. 0.42733, and the proportion between the polar and the equatorial diameter of the planet 0.95992 and the ellipticity The dimensions at the mean distance (9.5388) of Saturn are: External diameter of Ring 40′′.28, Cassini's division 34".42, Internal diameter 26′′.82, Equatorial diameter of the planet 17′′22 and Polar 16′′.53. The equatorial semi-diameter at the mean distance of the earth from the Sun is 82′′.11. Its diameter is about 94 times that of the Earth and as its mass is 102.7 times as large it follows that its density is, or about, of the mean density of the Earth.
Hongkong Observatory, 8th January, 1887.
W. DOBERCK, Government Astronomer.