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ASTRON OMISCHE NACHRICHTEN Band 236. Nr. 5647.
~ ~~ ~~ ~~
Zur Ephemeridenrechnung nach Cowell. Von G. Stra.de. Die Berechnung einer genauen (6- oder ystellig aus-
gefuhrten) geozentrischen Ephemeride erfolgte bis vor kurzem fast ausschlieDlich in der Weise, daO man von den KejZer- schen Elementen ausgehend fur jedes einzelne Datum die mittlere Anomalie M, den Radiusvektor r, die wahre Anomalie a, damit die heliozentrischen rechtwinkligen aquatorialen Koordinaten z', y', a' berechnete und diese in geozentrische Pohrkoordinaten a, d verwandelte. Seitdem brauchbare Rechenmaschinen zur Verfugung stehen, ist dem bisherigen Verfahren die Anwendung von Methoden der Extrapolation der ungestorten Koordinaten bei groOerer Ausdehnung der Ephemeride unbedingt vorzuziehen. Bei diesen Methoden werden nur einige wenige heliozentrische Orte nach den bekannten Formelnl)
M = Mo + p (i - iJ
x' = a P,' COSR + a cosy Qz' s inE - a e PA' E = M +eo s inE
(1)
y'=aP, 'cosE+acosy Qy' sinB-aePy' a '=aP, 'cosE+a cosy Q,' sinE-aeP, '
direkt gerechnet, alle weiteren aber unter Verwendung der Differentialgleichungen der ungestorten Bewegung extra- poliert. Die Umwandlung der heliozentrischen in geozen- trische Koordinaten erfolgt dann in der ublichen Weise nach
d c o s d cosa=z '+x '@ d cos d sin a = y' + Y'a Asin6 = a ' + Z ' a .
Neben der vonN. Komendantow 7 gegebenen Methode, die von den Numerowschen Spezialkoordinaten Gebrauch macht, ist wegen seiner grol3en Einfachheit vor allem das Verfahren von CoweN zu empfehlen. Bei seiner praktischen Anwendung l a t sich eine wesentliche Erleichterung der Rechnung durch Tabulierung einer GroOe &ka I/." erzielen. Bevor hier diese Tabelle gegeben 'wird, sei das CoweZZsche Verfahren kurz erlautert.
Setzt man in den Bewegungsgleichungen der unge- storten Bewegung die Masse des bewegten Gestims gleich null und fuhrt als Einheit der Zeit # das Interval1 w ein, so lauten- sie
d2s' S'
di2 9 W' -= - weka- = P(d, i ) (s' = x', y', 8') (3)
wo jd=zIa +y'8+da ist. Angenommen, es seien fur die Argu- mente a - w und a die Funktionswerte f(a-w) = s ' - ~ und f(a) =s,,' der Koordinaten s ' - ~ = X I + , Y ' - ~ , 8'- und sgl = x i ,
yd, 2gl nach (I) berechnet. Es handelt sich darum, den Funktionswert f ( u + w) zu bilden. Da nach dem Differen- zenschema in der GauJ-finckeschen Bezeichnungsweise
ist und f ( u - w) und f ( u ) und damit auch f ' ( u - bw) als ge- geben angenommen werden, so rcduziert sich das Problem der Extrapolation im Prinzip auf die Bestimmung der 2. Diffe- renz f " (a ) . Diese kann nach der CoweZZschen Fundamental- formel
f ( a + w)=f(.) +f'(. - 4.l) +J"(.)=zf(.) -f(. - w)+fI'(a) (4)
f" (4 = F ( 4 + Y (4 ( 5 )
ermittelt werden, worin
und y(a) = ; z F y u ) - &F'V(a) + &$@I(u)T - (7)
ist. Das Intervall w wahlt man so klein, daI3 die GroOe y(u) verschwindet. Dann ist die gesuchte 2. Differenz f " (u) der GroDe nach identisch mit der Newtonschen Beschleunigung. Diese IaBt sich nach G1. (6) berechnen. Setzt man den Wert von f I 1 ( a ) =F(a) in. G1. (4) ein, so lautet die Gleichung zur Bestimmung von f ( u + w)
f ( u + w) =f(a) +f '(u - *w) + F(a) . (8) Die Ermittelung der weiteren 2. Differenzen und Funktions- werte geschieht ganz analog nach
rn3 = xn'2 + y1'2 + 2*12
f " ( u + nw) = P ( u + nw) = - W W 4 rn (9)
f(a+[n+~]w)=f(a+nw)+f'(a+[n-)]w) +fl'(a+nw).
Lastig ist hierin die Berechnung des Ausdrucks wa,&.
Sie wird durch Benutzung der nachfolgenden Tabelle er- leichtert.
Die Tabelle gibt mit dem Argument ra fiir die gebrauch- lichsten Intervalle w = 2, 4, 8 Tage den Ausdruck 1o7wSka//13. Die 8. Dezimale ist mitgegeben, da man sie als Reserve- dezimale bei dem ExtrapolationsprozeD mit Riicksicht auf den schadigenden EinfluB der Abrundungsfehler mitnehmen muI3, wenn man die Ephemeride in 7-stelliger Genauigkeit erhalten will. Aus dem gleichen Grunde legt man den Anfang der Extrapolation zweckmaI3ig nicht an den Anfang, sondem in die Mitte der Ephemeride.
Die Tabelle ist fur alle Planeten mit Ausnahme von 433 Eros und 944 Hidalgo anwendbar.
rn3
l) J.B.A.A. 32.231~234 und G. Strucke, Bahnbestimmung der Planeten und Kometen, S. 204. ') J.O. 10.8. 7
99 5647 I00
1.50
51 52
53 54 55 56 5 7 58 59
I .60 61 62 63 64 65
67
69
1.70
7' 7Q 73 74 75 76 77 78 79
1.80 8 I, 82 83 84 85
87
89
66
68
86
88
1.90 9' 92 93 94 95 96 97 98 9s
2.0c
w=2d
6443'0 - 63.9 6379" 62.9
6254'4 b0.8 61.8 6316.2
6193.6 6133.8 59.8
58.9
57.0
- 55.2
6016.9
5903.7 5959'9 5bm2
5794" s3,6
5584.7 5534.3 49.7
5435.7 4g.I 5387.6
-47.5 534'" 46.8 S293'3 46.1 5247.2 5 2 0 1.8 45.4
44.8
434 5112.9
42.3
4942.5 -41.2
4901.3 4860.8 40'5 40.0 4820.8
39.5
4666.1 4628.7 37'4
4555.4
36.9
-35.9
459'" 36.4
34.1
4280.8
4216.4 32.4
-31.6 4184.8
-221.1
- 189.9 21360.4 187.1
181.7
I 76.6
20988.9 20807.2 20628.1
20105.9 169.2 '99S6'7 166.g 19769.9
- 164.6
- 143.7 18078.1 141.8 17936.3 140.0 17796.3 13g,I
1752 I .8 136.4
17387.2 132.9 17254.3 13r.2
16993.6 12g*o
17658.2
134.6
17123.1 129.5
16865.6 - 126.3
16739.3
w=8d
103087.5 - 1022.3 1005.6
973.2
ro2065.2 r01059.6 rooo70.5 989.1
99097.3 957m5 98139.8 942.1
95358.0 g9gm2
97197.7 96270.6 iz:::
- 884.1 94459.8
- 7594
- 658.1
- 574.7
- 505.4 66957.3
2.00
01
0 2
03 04 05 06 0 7 08 09
2.10
I1 I 2
I3 I4 I 5 16 1 7 I8 I9
2 . 2 0
21 2 2
23 24 2 5 26 2 7 28 29
2.30
3' 32 33 34 35 36 37 38 39
2.40 41 42 43 44 45
47
45
2 . 9
46
48
w=2d
10' W ' P : r' W = A d
-111.8
- 9 9 4
- 89.0 13573.5 gg.I r3485.4 g7.1
13226.9 85.3 13142.6 84.3
13059.' g2.5
'339"3 8bDI 13312.2
83.5 12976.6
12814.0
81.7 12894.9
- 80.0 12734.0 12654.8 79'2
78.3 12576.5 77.5 12499" 76.8 12422.2 12346.2 12271.0
12196.5 12122 .8
'2049.9
76.0 75.2
73.7 72.9
- 72.2
11977.7
CII =tid
- 447-2 62232.0 61790.1 441.9
436.6 61353.5 60922.0 431'5 426.6
60073.8 416.7
59245.2
58435.5
60495'4 421.6
58838.0 407.2 402.5
- 398.0 58037.5 57644.0 393.5 5'1255.0 389.0 56870.3 384.7 56489.9 380.4 56113.7 376.2 55741.7 372-0 55373-8 367.9 55009.9 363.9 54649.9 360.0
- 356.0 54293.9 352.2
52570.4 333.g 52236.6
330.3 51906.3 326.8 5'579.5 51256.1 323m4
- 320.0
5°936'1 316.7 50619.4
49995.8
49084.0
48199.6
50306.0 313'4 310.2
49688.8 307'0 303.9
48786.2 297'8 294.8 48491.4 291.g
..
- 288.9 47910.7
I 0 1 5647
7 2
2.50
51 52 53 54 55 56 57 58 59
2.60 61 62 63 64 65
67
69
2.70
7 1 7 2
73 74 75 76 77 78 79
2.80
81 82
66
68
83 84 85 86 87 88 89
2.90 91 92 93 94 95 96 97 98 99
3.00
107 w'K : r' w=2d
'994-4-17.9
17.5
17.2
17.0
16.7 16.5
- 16.4
16.2 16.0 '5.9
2958.8
2924.0 2906.8
2872.9 2856.2
2941.3 17.3
2889'8 16.9
2 839.7
2823.3 2807.1
2791.1
2728.3 2713.0
2682.9
2668.0 2653.2 2638.6 2624.1
15.3 15.1
- '4.9
14.8 14.6 14-5
14.2
'3.9
2609.7 14.4
2595.5 14.1 2581.4
2539.9 - 13.6
2526.3 2512.8 '3.5
13.3 2499.5 2486.2
13.1 2473.' 13.0 2460.1 12.9 2447'2 12.8
2421.8 12.6
- 12.4
2434'4 12.6
2409.2
23844 12.2 2372.2 2360.1 2348.1
12 .1
12 .0
11.9
2312.5 2300.9 2289.4
2277.9
11.6 11.5
-11.5
W = A U
"977.7 -71.6 11906.1
11765.2 11695.8 11627.1
70.8
69.4 68.7 68.0
"559" 67.4 "49"7 66.8 11424m9 6beI 11358.8
- 65.5
- 59.6 10671.8 10612.8 59'0
58.5 10554.3 57.9
10325.7 55.9
10159.6 54.9
I 0382. I
10269.8 56.4
55.3 10214.5
- 54.4
53.9 5 3 4
10105.2
10051.3 9997.9 53.0
9687.1 50.2
9636.9 - 49.8
-45.8 9111.7
- 261.9
- 238.3
- 2 1 7 . 5
- 199.2
- 183.0 36447.0
- r'
3.00 0 1 0 2
03 04 05 06 0 7 08 09
3.10 I1 I 2
I3 I4 I 5 16 17 18 '9
3.20 2 1
2 2
23 24 2 5 26
.27 28 29
3.30 31 32 33 34 35 36 37 38 39
3.40 41 42 43 44 45 46 47 48 49
3.50
w =2d
2277.9- 11.3 11.3 2266.6
2244.2 2233.1 10.9
10.9 2211.3 10.8 2200 .5 10.8 2189.7 10.6 2179.1
- 10.5 2168.6 10.4 2158.2 10.4 2147.8 10.3
2127.3 2117.2
2107.2
2097.2
2 0 7 7 . 5
2067.7
2255.3 I I . I
11.1
2222 .2
2137.5 10.2
10. I
10.0
10.0
2087.3 9.9
2058.1 9.6 2048.5 9.6
2029.6 9.4 2020.2 94
9.8 - 9.8
9.5 2039.0
9.3 9.2 9.1 9.1
- 9.0
2010.9 2001.7 1992.6 1983.5
1974.5 9.0 'g65'5 8.9 1956.6
8.7 '947.9 8.8 '939" 8.7 '93O.4 8.6 1921.8 8.5
1904.8 1896.4
'9I3.3 8.5
8 4
- 8.4
8.3 1888.0 "79.7 8.2 1871*5 gm2 Ig63.3 8.1 1855.2
1839.1
8.1 184?" 8.0
1831.2 1.9 1823.3 7.9 1815.4 7.9
- 7 . 7 1807.7
W = A d
9111.7 9066.4 - 45'3
45.0 9021.4 44.7
8888.6 43'9
8801.9 43" 42.9
8716.5
8976.7 44.2
8845.1 43.5
8759.0 42.5
8932.5
- 42. I 8674'4 41.8 8632.6 41.5
8550.0 40.8 8509.2 40.5
8428.5
8591.1 41.1
8468.7 40.2
8388.7 39.8
8349-2 39.3 39.5
8309.9 - 38.9
8271.0 8232.4
8156.0 8118.3 37'7 8080.8 37m5
37.1 8006.8 $:: 7933.9
38.6 38.4 "94" 38.0
8043.7
7970e2 36.3
- 36.0
- 33.5
-31.1 7230.7
w=tid
-~ - 168.5
3'591.6 143.0
3'165.7 '39.9
31448.6 31306.6
31025.8 30887.0
3061 2.5
30342.0
142.0 140.9
138.8 137.8
135.8
3074gm2 136.7
30476'7 134.7.
- 133.8
- 124.3 28922.9
7 '
* 0 3 5647 -
* -
3.50 51
5 2
53 54 55 56 57 58 59
3.60 61 62 63 64 65
67
69
3-70 7 1 72
33 74 75 76 77 78 79
3.80 81 82 83 84 85 86 87 88 89
66
68
3.90 91 92 93 94 95 96 97 98 99
4.00
16' wPka : 9
- 29.0
- 2 7 . 0
-25.3 6391.6
25.2 6366.4 zs.o
6341.4 24.g
6291.9 24.7 6267.4 24.5 6243.1 24.3
6194.9 23.g
6316.6
24.2 24.0 6218.9
6171.1 -23-7
6147'4 23.6 6123.8
6077.1 6054.0 6031.0 6008.2
6100.3 23.5 23.2 23.1 23.0 22.8
22.7
5940.5 - 22.3
5918.2
- 115.9 27726.1 27611.0 115.1
114.3 27496.7 I13.5 27383.2 I12.8 27270.4 I I z . o
27158.4 I I I . 2
27047.2 IIo.5 26936.7 Io9.7 26827.0 26718.0 109.0
- 108.2 26609.8 26502.3 107.5
26079.3 Io4.0 25975.3 Io3.3
106.9
105.4
26395'4 106.1 26289.3 26183'9 Io4.6
25872.0
25667.5
102.6
- 101.2
- 94.9
24401.4 93.1
24032.6 91.3
24215.8 91.9
90.7
24 1'2 3.9
2394r.9
23762.1 23851'7 g9.6
- 89.1 23673.0
P
4.00 01
0 2
03 04 05 06 0 7 08 09
4.10 I1
I2
I3 I4 I 5 16 1 7 I8 I9
4.20 2 1
2 2
23 24 25 26 27 28 29
4.30 31 32 33 34 35 36 37 38 39
4.40 41 42 43 44 45 46 47 48 49
4.50
1479'6-5,6 1474.0 5.5
1463.1 5.4
1457.6 5.4
1446.9 5m3
1436.3 5.3
1468.5
5-5
5.3
5.3
1452.2
1441.6
1431.0 - 5.2
1425.8 1420.6 5'2
5 . 2
1410.3 5.1 1405.2 5.1 1400. I 5.'
1390.0
1380.1 4'9 - 5.0
4.8
4.8
1415.4 5.1
1395.0 5.0
1385.0 5.0
'375.' 4.9
1355.7 4m8 1350.9 4.7
1341.5 4.7
1370.2
1360.5
1346.2 4.7
1336.8 4.7 1332.1
-4.6 1327.5 1322.8 4'7
4.5 1318.2 4.6
1304.6 4.5
1295.7 4.4
'3'3.7 4.6 1309.1
4.5 1300.1 4.4
1291.3 4.4 1286.9
- 4.4 1282.5 1278.1 4'4
4.3 1269.5 1265.2 4'3
4.2 1256.7 4.2 1252 .5
4.2
-4.1
1273.8 4.3
1260.9 4.3
1248.3 4.2 I 244. I
1240.0
5918.2 - 2 2 . 1 5896.1
22.0 5874.1 21.8 5852.3 zI.7
5809.0 5787.5 zI.3 5766.2 21.2
5745.0 21.0
5830.6 21.6 21.5
5724.0 - 21.0
5703.0 zo,8 5682.2
5641.0 5620.6 5600.3 5580.1 5560.0 5540.1 5520.3
20.6
20.4 20.3
5661'6 zo.6
20.2
20.1
'9.9 19.8
- 19.7 5500.6 5481.0
5442.2
19.6 19.5
'9-3
5461.5 19.3
5422.9 19.1 5403.8 19.0 5384.8 18.9 5365.9 18.8 5347.1 Ig.7 5328.4
- 18.6 5309.8 18.4 5291.4 18.4 5273.0 18.3 5254.7 18.1
5200.6 17.9
5236.6 5218.5
17.8 17.8 17.6
5182.8 5165.0 5147.4
- 17.6
17.4 17.3
5129.8 5112.4
5060.7
5026.7 5009.8
17.1
16.9 16.8
5O4Sa6 16.9
4993" 16.6 4976.4
4959.8 - 16.6
w=Sd
- 83.7 22812 .2 83.2
82.7
81.7 81.2
80.8 80.2
2 2 7 2 9 . 0
22646.3 gzm2 22564.1 22482.4 2 2401.2
22240.2 22320.4
2 2 160.4 79.8 22081.1 79.3
21846.1 77.9
21691.7 77.0
- 78.8 2 2002.3
78.3
7 7 4
76.5
21924.0
2 I 768.7
21388.3 74.7
- 74.3 21313.6
21239.3 73.g 21165.5 21092.0 73.5
73.1
20802.4
20660.1 20589.6
71.3 71.0 70.5
20731.1
- 2
4.50 51 52 53 54 55 56 57 58 59
4.60 61 62 63 64 65
67
69
4.70 71
72
73 74 75 76 77 78 79
4.80 81 82
66
68
83 84 85
87
89
86
88
4-90 91 92 93 94 95 96 97 98 99
5.00
'05 5647
107wa#:II
W = 2 d
1240.0 1235.8-~"
4.1 4.0 4.1 1223.6
1219.6 4.0
4.1 I2IX.5
1207.6 3'9 3.9
-4.0
1231.7 1227.7
1215.6 4.0
1203.7
"99.7 3.9
1184.3 3.8 I 180.4 3.9
1169.1 3.8 1165.4 3.7
1154.3 3,7
1195.8 1191.9 3.9 1188.1 3*8
1176.6 3'8 3.7 1172.9
-3.7 1161.7 1158.0 3'7
3.7
3.6 1150.6
3.5
1139.9 1136.2 3'7
1147.0 "43.5 3.6
1132.6 3.6 1129.1 3.5
1118.5 3.5
1104.8 3.4
-3.6
3.5
3.4 1115.1
1111.6 3m5 1108.2 3'4
3.4 1101.4 3-4 1098.0 3.4 1094.6
- 3.3 1091.3 1088.0 3'3
3 4 1084.6
1125.5
1122 .0
1081.3 3.3 1078.0 3.3
1068.3 3.2
1061.9 3.2
3.2 1074.8 3.3 1071.5
1065.1 3'2
- 3.2 1058.7
W=dd
-15.7
- 14.9 4646.6 14,8 4631.8 4617.1 4602.5
'4.7 14.6 14.6
4587-9 14.5 4573m4 14.4 ,
4559.0 14.3 4544.7 14.2 4530.5 14.1 4516.4
- 14.2
- '3.4
- 12.8 4234.7
- 62.8
- 59.5 18586.4
59.1 18468.4 58.9
58.5 18351.6
57.9 18236.1 18178.8 57.3
18527.3
Ig293*7 57.6
18121.8 57.0 18065.1 56.7
-51.0
16939.0
9
5.00
0 1
0 2
03 04 05 06 0 7 08 09
5.10 I1 1 2
I3 I4 I 5 16 17 18 I9
5.20 2 1
2 2
23 24 25 26 27 28 29
5-30 3' 32 33 34 35 36 37 38 39
5 -40 41 42 43 44 45 46 47 48 49
5.50
I 06
10' w ~ P : w = 4 a
- 12.1
41 10.8
4086.7
12.1 4098.7 12.0
11.9
4051.1
4027.6
4004.3
11.8
11.7 4039.3 I I . 7
4"5.9 II.6
- 11.5
3992-8 I I .5
3981.3 11*5
3969.8 II.3 3958.5 II.3 3947.2 II.3 3935-9 11.2
3924.7 I I . 2
39'3.5 I I . I
3902.4 I I . I
3891.3 - 11.0
- 10.5 3773.0 Io.4
3752.2 Io.4 3741.8 Io.3 3731.5 Io.3
3700.9 Io.2 3690.7 Io.I
3762.6 I 0.4
3721.2 10.2
10.1 3711.0
3680.6 - 10.0
3670.6
w=sa
-48.5
-46.2
-44.1
-42.0 15092.2 41.8
15008.7 4r.4
14926.0 41 .o 14885.0 40.8
15050.4 41.7
14967.3 41.3
14844.2 40.7
'4762.9 40.3 14803'5 qo.6
14722.6
14682.4 -40.2
107 5647
5.50 51 52
53 54 55 56 57 58 59
5.60 61 62 63 64 65
67
69
5.70 7 1 72
73 74 75 76 77 78 79
5.80 81 82
66
68
83 84 85
87
89
86
88
5.90 91 92 93 94 95 96 97 98 99
6.00
107 waP : r'
9'7.7 -2.5 9'5.2 2.5 912.7 2 m 5
905.3 2.5
910.2 2.5 907.7 2.4
902.8 2 4 900.4
898.0 24 2 4
- 2.4
890.8 '" 2 -4 888.4
886.0 2 4 2.3
883.7 881.4 2'3
2 4 879.0 876.6 2'4
2.3 872.1
869.8
865.2
895.6
893.2
874.3 2 .2
867.5 2.3
862.9 2.2
860.7 2.2
854.0 2 .2
851.8 2.2
847.4 2.2
845.2 2.2
843.0 2*1
840.9 2.2
838.7 2 . 1 836.6
2.2
834.4 2 .1
832.3 2.2 830-J
2.1
825.9 2.1 823.8 2.1
819.7 2.1
815.5 2.0
813.5 2.0 811.5
2.1 809.4 2.0
- 2.3
2 -3
2.3
858.5 856.2 '"
2.2
849.6 - 2.2
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W =ad
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60.2 Om3
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249.8- 1.2
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4.1
9'8.5 - 3.9
9'4.6 G. Stracke.
The rotation period 01' the Sun derived from the H and K calcium lines of the prominences. By K Hase and E. PerepeDin.
Some attempts were made within the last years to determine the rotation period of the Sun from the prominences ; Evershed') applied the spectroscopic method, and PerepeZkzn8) observed the apparition of very quiet prominences on the East and West limb'of the Sun. The last method, although more exact, presents great difficulties in the identification of the objects observed.
Attempts to determine the rotation period of the Sun from the filaments by EvcrsLed3) and d'dsambouja 4, lead to results in close agreement with the spots.
In 1927 Bversieda) renewed his study with the spectro- graph of the Pitch Hill Observatory, his results seemed to indicate the existence of polar retardation and an increase of speed with increasing height over the Sun's chromosphere.
From this standpoint it became interesting to study the speed of the solar rotation as given by prominences of lo? level. . Such a work was carried through by the authors during
July 1928 with a three prism spectrograph attached to the 30" refractor of the Pulkovo Observatory; the dispersion of the spectrograms was about 5 4 A . in the region of N and K. Unhappily the cloudy weather of this summer did not allow to collect a wide material; the total amount of all spectrograms designed for the rotation effect was about 70, from this ma- terial 42 spectrograms with sharp and well defined lines,
whose displacements were not too great, were chosen; 17 spec- trograms relate to the western, 25 to the eastern limb.
The 42 spectrograms were measured with a Repsold engine; the constants of Harfmann were derived for each plate separately from measurement of the lines 3927.924, 3969.262, 4107.494 1.A. of the iron arc, recorded on each plate. To increase the accuracy of measurement of the chosen lines of the prominences K, N and H,, to their wave-lengths computed from H a r t m a d s formula some corrections received from measurement of neighbouring lines in the arc spectrum were added, these are: 3930.302, 3966.068, 3977.745, 4095.976
The obtained values for the displacement of the pro- minence lines were corrected for the rotation of the 'Earth, and its orbital revolution so as to convert synodic periods to sidereal ones.
With these values equations of condition were written, which run:
I. A.
where a is the equatorial speed of the Sun, R its radius and i the height of the prominence, B and 'p the heliographic latitudes of the centrum of the Sun's disc and the prominence respectively, c the so called spectrograph constant, and v the
8
