1234567891011121314NamePositionDistanceMotionMagnitudeSpectrum(αδ)SquarelbπrμWmMSpm′sir.sir./st.m′1Barnards star(175204)GC12358°+12°0″.5150.4010″.29-199m.7+11m.7Mb11.52C. Z. 5h.243(050744)GE7218-350.3190.658.75+519.2+10.1K210.63Groom. 1830(114738)GA1135+750.1022.027.06-206.5+5.0G57.64Lac. 9352(225936)GE10333-660.2920.716.90+27.5+8.2K8.95C. G. A. 32416(235937)GF2308-750.2300.896.11+58.2+8.5G9.1661 Cygni(210238)GD250- 70.3110.665.27-135.6+6.5K57.27Lal. 21185(105736)GB5153+660.4030.514.77-187.6+9.1Mb8.98ε Indi(215557)GE9304-470.2840.734.70-84.7+5.4K56.39Lal. 21258(110044)GB4135+640.2031.024.47+148.5+8.5Ma10.310O2Eridani(041007)GE5168-360.1741.194.11-94.7+4.3G55.811Proxima Centauri(142262)GD10281- 20.7800.263.85..11.0+13.9..13.512Oe. A. 14320(150415)GB9314+350.0355.903.75+619.0+5.1G09.913μ Cassiopeiæ(010154)GD493- 80.1121.843.73-215.7+4.4G36.814α Centauri(143260)GD10284- 20.7590.273.68-50.3+3.2G1.215Lac. 8760(211139)GE10332-440.2480.833.53+36.6+7.0G7.516Lac. 1060(031543)GE7216-550.1621.273.05+185.6+5.1G56.717Oe. A. 11677(111466)GB8103+500.1981.043.03..9.2+9.1Ma11.018Van Maanens star(004304)GD892-580.2460.843.01..12.3+12.7F012.9sir.sir./st.m′Mean.........41°0″.2980.875″.0017.87m.3+7m.6G88.7
That the great proper motion does not depend alone on the proximity of these stars is seen from column 10, giving the radial velocities. For some of the stars (4) the radial velocity is for the present unknown, but the others have, with few exceptions, a rather great velocity amounting in the mean to 18 sir./st. (= 85 km./sec.), if no regard is taken to the sign, a value nearly five times as great as the absolute velocity of the sun. As this is only the component along the line of sight, the absolute velocity is still greater, approximately equal to the component velocity multiplied by √2. We conclude that the great proper motions depend partly on the proximity, partly on the great linear velocities of the stars. That both these attributes here really cooperate may be seen from the absolute magnitudes (M).
The apparent and the absolute magnitudes are for these stars nearly equal, the means for both been approximately 7m. This is a consequence of the fact that the mean distance of these stars is equal to one siriometer, at which distancemandM, indeed, do coincide. We find that these stars have a small luminosity and may be considered asdwarfstars. According to the general law of statistical mechanics already mentioned small bodies upon an average have a great absolute velocity, as we have, indeed, already found from the observed radial velocities of these stars.
As to the spectral type, the stars with great proper motions are all yellow or red stars. The mean spectral index is +2.8, corresponding to the type G8. If the stars of different types are put together we get the table
TypeNumberMean value of MG85.3K47.5M49.6
We conclude that, at least for these stars, the mean value of the absolute magnitude increases with the spectral index. This conclusion, however, is not generally valid.
Stars with the greatest radial velocities.There are some kinds of nebulae for which very large values of the radial velocities have been found. With these we shall not for the present deal, but shall confine ourselves to the stars. The greatest radial velocity hitherto found ispossessed by the star (040822) of the eighth magnitude in the constellation Perseus, which retires from us with a velocity of 72 sir./st. or 341 km./sec. The nearest velocity is that of the star (010361) which approaches us with approximately the same velocity. The following table contains all stars with a radial velocity greater than 20 sir./st. (= 94.8 km./sec.). It is based on the catalogue ofVoutementioned above.
Regarding their distribution in the sky we find 11 in the galactic equator squares and 7 outside. A large radial velocity seems therefore to be a galactic phenomenon and to be correlated to a great distance from us. Of the 18 stars in consideration there is only one at a distance smaller than one siriometer and 2 at a distance smaller than 4 siriometers. Among the nearer ones we find the star (050744), identical with C. P. D. 5h.243, which was the “second” star with great proper motion. These stars have simultaneously the greatest proper motion and very great linear velocity. Generally we find from column 9 that these stars with large radial velocity possess also a large proper motion. The mean value of the proper motions amounts to 1″.34, a very high value.
In the table we find no star with great apparent luminosity. The brightest is the 10thstar in the table which has the magnitude 5.1. The mean apparent magnitude is 7.7. As to the absolute magnitude (M) we see that most of these speedy stars, as well as the stars with great proper motions intable 3, have a rather greatpositivemagnitude and thus are absolutely faint stars, though they perhaps may not be directly considered as dwarf stars. Their mean absolute magnitude is +3.0.
Regarding the spectrum we find that these stars generally belong to the yellow or red types (G, K, M), but there are 6 F-stars and, curiously enough, two A-stars. After the designation of their type (A2 and A3) is the letterp(= peculiar), indicating that the spectrum in some respect differs from the usual appearance of the spectrum of this type. In the present case the peculiarity consists in the fact that a line of the wave-length 448.1, which emanates from magnesium and which we may find onplate IIIin the spectrum of Sirius, does not occur in the spectrum of these stars, though the spectrum has otherwise the same appearance as in the case of the Sirius stars. There is reason to suppose that the absence of this line indicates a low power of radiation (low temperature) in these stars (compareAdams).
1234567891011121314NamePositionDistanceMotionMagnitudeSpectrum(αδ)SquarelbπrμWmMSpm′sir.sir./st.m′1A. G. Berlin 1366(040822)GD5141°-20°0″.00730.80″.54+728m.9+1m.4F09.42Lal. 1966(010361)GD493- 20.01612.90.64-697.9+ 2.3F38.53A. Oe. 14320(150415)GB9314+350.0355.93.75+619.0+ 5.1G09.94C. Z. 5h.243(050744)GE7218-350.3190.68.75+519.2+10.1K210.65Lal. 15290(074730)GC6158+260.0239.01.96-518.2+ 3.4G09.1653 Cassiop.(015563)GC498+ 2....0.01-445.6..B85.57A. G. Berlin 1866(055719)GD6159- 20.0219.80.76-409.0+ 4.0F09.98W Lyræ(181136)GC231+21......-39var...Mdvar.9Boss 1511(055926)GD7200-200.01217.00.10+395.2- 1.0G56.410ω Pavonis(184960)GD11304-24....0.14+385.1..K6.511A. Oe. 20452(201721)GE10351-310.01513.51.18-388.1+ 2.4G8p9.412Lal. 28607(153710)GB10325+340.0336.21.18-367.3+ 3.3A2p7.413A. G. Leiden 5734(161132)GB121+450.00289.20.04-358.3- 1.5K49.914Lal. 37120(192932)GC233+ 60.0504.10.52-346.6+ 3.5G27.615Lal. 27274(145421)GB9308+340.01316.20.79+348.3+ 2.2F48.916Lal. 5761(030225)GD5126-280.0395.10.86-328.0+ 4.4A3p8.117W. B. 17h.517(172906)GC12358+200.01414.10.63-318.6+ 2.8F19.118Lal. 23995(124717)GB8271+460.01217.00.88+308.2+ 2.0F38.8sir.sir./st.m′Mean.........23°.90″.04116.71″.3416.77m.7+3m.0F98.5
The nearest stars.The star α in Centaurus was long considered as the nearest of all stars. It has a parallax of 0″.75, corresponding to a distance of 0.27 siriometers (= 4.26 light years). This distance is obtained from the annual parallax with great accuracy, and the result is moreover confirmed in another way (from the study of the orbit of the companion of α Centauri). In the year 1916Innesdiscovered at the observatory of Johannesburg in the Transvaal a star of the 10thmagnitude, which seems to follow α Centauri in its path in the heavens, and which, in any case, lies at the same distance from the earth, or somewhat nearer. It is not possible at present to decide with accuracy whetherProxima Centauri—as the star is called byInnes—or α Centauri is our nearest neighbour. Then comesBarnard's star (175204), whose large proper motion we have already mentioned. As No. 5 we find Sirius, as No. 8 Procyon, as No. 21 Altair. The others are of the third magnitude or fainter. No. 10—61 Cygni—is especially interesting, being the first star for which the astronomers, after long and painful endeavours in vain, have succeeded in determining the distance with the help of the annual parallax (Bessel1841).
From column 4 we find that the distribution of these stars on the sky is tolerably uniform, as might have been predicted. All these stars have a large proper motion, this being in the mean 3″.42 per year. This was a priori to be expected from their great proximity. The radial velocity is, numerically, greater than could have been supposed. This fact is probably associated with the generally small mass of these stars.
Their apparent magnitude is upon an average 6.3. The brightest of the near stars is Sirius (m= -1.6), the faintest Proxima Centauri (m= 11). Through the systematic researches of the astronomers we may be sure that no bright stars exist at a distance smaller than one siriometer, for which the distance is not already known and well determined. The following table contains without doubt—we may call them briefly allnearstars—all stars within one siriometer from us with an apparent magnitude brighter than 6m(the table has 8 such stars), and probably also all near stars brighter than 7m(10 stars), or even all brighter than the eighth magnitude (the table has 13 such stars and two near the limit). Regarding the stars of the eighth magnitude or fainter no systematic investigations of the annual parallax have been made and among these stars we may get from time to time a new star belonging to the siriometer sphere in the neighbourhood of the sun. To determine the total number of stars within this sphere is one of the fundamental problems in stellar statistics, and to this question I shall return immediately.
1234567891011121314NamePositionDistanceMotionMagnitudeSpectrum(αδ)SquarelbπrμWmMSpm′sir.sir./st.m′1Proxima Centauri(142262)GD10281°- 2°0″.7800.263″.85..11m.0+13m.9..13.52α Centauri(143260)GD10284- 20.7590.273.68- 50.33+ 3.2G1.253Barnards p. m. star(175204)GC12358+120.5150.4010.29-199.7+11.7Mb11.54Lal. 21185(105736)GB5153+660.4030.514.77-187.6+ 9.1Mb8.95Sirius(064016)GD7195- 80.3760.551.32- 2-1.58- 0.3A-1.586..(111357)GC6158+ 30.3370.602.72........12.57τ Ceti(013916)GF1144-740.3340.621.92- 33.6+ 4.6K04.68Procyon(073405)GC7182+140.3240.641.24- 10.48+ 1.5F50.909C. Z. 5h.243(050744)GE7218-350.3190.658.75+519.2+10.1K210.61061 Cygni(210238)GD250- 70.3110.665.27-135.6+ 6.5K57.211Lal. 26481(142515)GB9124-400.3110.660.47..7.8+ 8.7G58.912ε Eridani(032809)GE5153-420.2950.700.97+ 33.8+ 4.6K04.813Lac. 9352(225936)GE10333-660.2920.716.90+ 27.5+ 8.2K8.914Pos. Med. 2164(184159)GC256+240.2920.712.28..8.9+ 9.6K10.315ε Indi(215557)GE9304-470.2840.734.70- 84.7+ 5.4K56.316Groom. 34(001243)GD384-200.2810.732.89+ 18.1+ 8.8Ma9.517Oe. A. 17415(173768)GC865+320.2680.771.30..9.1+ 9.7K10.518Krüger 60(222457)GC37200.2560.810.94..9.2+ 9.6K510.819Lac. 8760(211139)GE10332-440.2480.883.53+ 36.6+ 7.0G7.520van Maanens p. m. star(004304)GE392-580.2460.843.01..12.3+12.7F012.921Altair(194508)GD115-100.2380.870.66- 70.9+ 1.2A51.1222C. G. A. 32416(235937)GF2308-750.2300.896.11+ 58.2+ 8.5G9.123Bradley 1584(112932)GC6252+280.2160.951.06- 56.1+ 6.2G6.9sir.sir./st.m′Mean......30°.80″.3440.673″.429.16m.3+7m.3G67.5
The mean absolute magnitude of the near stars is distributed in the following way:—