Es darf aber nicht unerwahnt bleiben, dafl im Tor- liegenden Falle die Auflosung der Normalgleichungen mit groflen Unsicherheiten verbunden war und dafl diese Un- sicherheiten insbesondere in der Umlaufszeit sehr stark zum Ausdruck kommen. Zur Veranschaulichung dessen ging ich von der Annahme aus, dafl alle jene Systeme noch Anspruch

Synopsis of elements of orbits of some double stars.

also weniger als das Doppelte der kleinsten Fehlerquadrat- summe, ubrig lassen. Obwohl diese obere (;reme fiir die noch wahrscheinlichen Fehlerquadratsummen zienilich niedrig bemessen ist, so schwankt bei dieser Annahme die Umlaufs- zeit trotzdem zwischen 14 Jahre und 00, ein recht deutlicher Beleg dafur, wie nenig es angeht, aus eineni so kurzen

Name

H 1-39 q Cassiopeiae 2 228 40 oy Eridani Sirius Castor 5 Cancri 2 3121 w Leonis 9 Ursae maj. y Centauri y Virginis 42 Coniae 2 5 Canum ven. (Y Centauri F Bootis 44 i Rootis q Coronae bor. pz Bootis y Coronae bor. F Scorpii ci Coronae bor. 5 Herculis B 416 2 2113 p4 Herculis T Ophiuchi 7 0 p Ophiuchi 99 Herculis 5 Sagittarii 02' 387 85 Pegasi

RA .

oh 0"

0 42 2 6 4 10

6 40 7 2 7 8 5 9 I I

9 2 2

9 44 1 2 35 1 2 36 13 4 73 32 I4 3' 14 46 1 5 0 1 5 18 1 5 2 0

' 5 38 '5 58 16 10

16 37 1 7 1 1

1 1 24 '7 42 1 7 51 '7 59 I 8 2

18 5 5 19 44 23 56

Decl.

+ 5 7 O 46' + 5 7 1 1

+46 5 5 - 7 47 -16 33 +32 9 + ' I 8 I

+29 5 + 9 35 +54 38 -48 18 . - 0 47 + I 8 I 0

-60 2 0 +36 54

+ I 9 36 +48 7 +30 43 +37 46 +26 4 1 - 1 1 3 +34 10

+31 49 -34 5' - - o 58 + 2 7 48 - 8 I 1

+ 2 33 +30 33 -30 3 +35 0 +26 2 7

bb

37O 25'

99 13 90 41

341 3 45 49 33 56 - 2 2 9

144 1 7 186 30

3 2 1 40 26

7 7 33 2 5 18

1 7 1 37 58 44 24 5

' 7 5 4 113 5 7

9 38 I 7 7 48 54 4

'35 44 '53 30 62 1 2

76 1 2

28 28

129 33 106 2 0

I 1 I 2

1 2 2 2 2

78 48

Y

46O 5'

'25 58 136 40

73 26

98 73

3' 37 66 o

116 23 I80 0

66 1 2

14 31

1 5 0 8 90 0

123 29 79 3

I47 6 83 4 59 I I

134 2 0

98 50 3 0 54 29 3

132 I I

130 16 99 4 66 23 66 4

1 2 0 5 2

5 2 58 1 1 0 36 114 '5

5 2 5 0

The positions are given for 1880. The elements are referred to the equinox 1900, except in a few cases where precession need not be allowed .for. The angles may be obtained from the formula: tan (4 - bb) = cos y tan (v + A).

The anomalies are reckoned negative before and positive after the periastron passage. Some other orbits are being re- calculated. Direct and retrograde motion is equally frequent as was to be expected. The distribution of binary stars was investigated about 30 years ago (cornp. A. N. 3791). The distribution of the poles is discussed in A. N. 4291. The law connecting periods and excentricities was given in A. N.

1

98'41'

4 5 2 24 '3

150 6 2 7 7 34 176 2 7 148 23 1 2 2 6 342 9 285 2 260 2 2

98 41 I43 2 1

5' 38 '3 8 2 5 2

219 2 1

338 5 106 2 5

3 0 276 2

1 1 2 3 5 68 34

3 1 1 0 176 I

1 7 45 I94 10 1 2 0 6 354 56 284 42 267 54

88 55

c

0.4664 0 . 5 2 2 0

0.3090 0.1 502

0.4409 0.3391 0.2659 0.5601 0.4379 0.2958 0.8874 0.4965 0.9005 0 . 5 0 5 7 0.506 I

0.445 I 0.2783 0.60 I 0

0.3908 0.7837

0.587 I

0.8480 0.4566 0.6 184 0.1361 0.1995 0.5338 0.4989 0.8 1 I I

0.1919 0.6000 0.387 2

P

' 0 5 Y 5 5 507.60 123.10 I 60.2 I

49.49 346.82

60.08

I 16.74 99.70

2 I 1.93 182.30 25.34

78.81 I 79.60 204.74 41-51

275.73 81.49 45-12

679.20 34.53 45.90 46.20 44.20

223.82

3 5.38

5 53.60

8 7.49 64.52

25.36

2 1.62 90.00

T

1836.07 1890.03 1905.19 1783.28 1894.28 1969.82 1870.65 187 9.34 1840.82 1882.46 1851.63 I 836.42 1885.54 1859.15 1875.63

1793.48

1864.59

1901.84

1892.28

1921.22 1860.15 1828.7 I

1863.89 1891.56 1867.88 1879.53 1814.79 1896.04 1884.00 1899.86 1838.00 1908.38

a

1144

0.899 3.883 7.5'3 5.7 56 0.856 0.620 0.844 0.32 1,924 3.7 43 0.674 2.038

17.540 .5.0 I 5 3.578 0.89 I

I .48 2

0.6 I 5 0.680 9.018 1.3 5 5 1-93 1.060 1.370 1.307 4.543 1.282 0.576 0.660 0.84 I

1 2 . 2 I

- A. N.

4145 4296 3525 4400 3981 3970 4144 4169 4144 3912 4063 4235 4276 4383 4189 4322 4346 3370 344 I

4296 4169 405 I

3448 3908 4169 4170 4063 4115 3912 3970 3525 4 1 10

2168 and A. N. 3519, and the hypothetical parallaxes are discussed in A. N. 427 I and 429 I . As pointed out many years ago: orbits are uncertain when the period exceeds 300 years. The average epoch of periastron-passage is 1868. None differs IOO years from this epoch except perhaps Castor. This makes it clear why so many double stars appear to be fixed (A. N. 3519). The average value of the excentricity is 0.484. The probable difference of an actual excentricity from the mean is &o.13, but there are a couple of cases (easily understood) where the excentricity is larger than was to be expected from these figures.

Sutton, Surrey, 1910 Jan. 8. I f : Doberck.