【摘要】 <正> 坎贝耳于1911年,古伦堡于1915年,计算了各光谱型恒星的视线速度绝对值的平均值(?),发现了中型(F,G)和晚型(K,M)星的运动速度比早型(B,A)星大.卡普坦也曾经得出同样的结果。坎贝耳和古伦堡的结果列于表1内,他们的 V_r是作过太阳运动改正的.n 是所用的星数,V_r 以公里/秒为单位.在表1内也列出威尔逊和雷蒙于1930年对4233个恒星进行空间速度计算的结果.更多还原

【Abstract】 Forty years ago,Campbell as well as Gyllenberg found that mean absolute radial velocities（mean radial speeds）（?） of stars get larger as the spectral type gets later.Their results are listed in Table 1;n is the number of stars used（Campbell’ s results-2nd & 3rd columns,Gyllenberg’ s results—4th & 5th columns）.In the same table are listed Wilson and Raymond’ s results of analysis of the space velocities of 4233 stars（main sequence-6th,giants-7th,supergiants-8th column）. The number of stars with known radial velocities has now exceeded （?）5000.It seems worth while to take up this problem again and to relate it to problems in stellar evolution.Every star contained in R.E.Wilson’ s General Catalogue of Stellar Radial Velocities is given a card.All the available data concerning this star are written down on the card,including galactic coordinates l and b,which are found with the help of Ohlsson’ s table All the stars whose values of V_r have quality e,as well as all spectroscopic binaries,are ex-cluded from this analysis.Preliminary results of analysis are given in Table 2,a stands for dispersion.So far the radial velocities have not yetbeen corrected for solar motion and galactic rotation.The results for emission stars of various types will be given in a separate paper. Variable stars of known types are also excluded from this analysis. If correction for solar motion and galactic rotation were made for every individual star,it would take very much time and labor（the number of stars involved in this analysis exceeded 12000）.So a statistical method is devised to make this correction en bloc for stars of each spectral type. If there is sufficient number of stars of a certain type in a not too big volume of space,then for these stars we can apply a mean correction for solar motion and galactic rotation △V_r,as given by formula（1）,in which a,δ,（l,b）r are the spherical coordinates of the midpoint of this volume, A and D are the coordinates of the solar apex.Let q=|△V_r|.It is not difficult to show that the correction F that should be applied to the mean absolute radial velocity of these stars is given by（9）,whether △V_r is positive or negative.（?）（V_r²）represents the frequency distribution of V_r.A formula equivalent to（9）is given in Smart’ s Stellar Dynamics,P.47,but here we use a different method of derivation.It is natural（and proved by fact）to take （?）（V_r²）to be the Gaussian function[formula（16）].Then F is given by（17）. We divide the whole sky into 56 regions,using as dividing lines the big circles l=32.°5,77.°5,122.°5,167.°5,212.°5,257.°5,302.°5,347.°5,and the parallels of galactic lattitudes b=±10°,±30°±70°.Each of these 56 regions is again divided into 4 distance intervals:0-200,200-400, 4o0-600,600-800 parsecs.For the midpoints of these 224 volumes of space, we take the points determined by r=100,300,500,700 parsecs;l=325°, 10°,55°,100°,145°.190°,235°,280°;b=0°,±20°,±45°,±70°.The fact that these volumes are different in size does not matter much,as we shall use only the weighted means of F. Among the various types ef stars we consider,only the main sequence stars and giants of G,K,M types are sufficiently large in number for ap- plying the statistical correction.It is now well-known that the velocity and apex of solar motion are different for different types of stars.Moreover, it was discovered recently that the main sequence consists of two parts, having different kinematical characteristics and mass-luminosity relations, and occupying different places on m-C diagram.So instead of using the standard apex,we use the apices obtained by Parenago for the first part （mean of B,A,F）and the second part（mean of G,K,M）of the main sequence,and for giants of G,K,M types,as given in Table 3.△V_r are calculated for these three groups separately. In order to calculate F,we must know h,which is related to σ by the formula h=1/σ^1/22.The values of a for the 9 types with bigger numbers of stars are already listed in Table 2.In obtaining these values,we omitted the stars with |V_r|>105 km/sec.The values of σ are for the whole sky, and are in general somewhat bigger than that for a small region of the sky. We have obtained the values of a for 8 separate volumes of space in which there are from 60 to 100 stars of a certain type.On the average,these values are 20% smaller than the values for the whole sky,but they are less reliable.The spectral types A,F,G,K,M in the Catalogue of Stellar Radial Velocities rarer to stars whose luminosity class has not yet been determined. From our final results it can be seen that a large portion of them are giants or subgiants.The values of a given in Table 2 are for A+dA,…M+ dM.Had we used only dF,dG,dK,dM,the values of a obtained would be bigger.After these considerations,we still use the valtms of σ given in Table 2 to calculate F.Values of F are given in Table 4. Distance is calculated from the apparent magnitude m and the mean absolute magnitude M of that spectral sub-type to which the star belongs, taking into account interstellar absorption.Parenago’ s absorption formula [（18）]is nsed,a₀ is taken to be 2.8 visual magnitude.For statiscat purpose it is sufficient to use the mean value of a₀.All the G,K,M stars used are within 200 parsecs,99.4% of the F stars and 94.3% of the A stars are also within 200 parsecs.All the giants are within 800 parsecs,but 13.7% of B stars are beyond 800 parsecs.For B0-B5 stars with m≤5.5,K effect is also considered,taking K=+4.3 km/sec.The use of cards facilitates the work a great deal. In Table 5 is illustrated the calculation of （?） for K stars.If we discard the stars with |V_r|>105 km/sec,we shall get in most cases smaller values of （?）,which we designate by （?）,and list in the 3rd column of Table 6. In the 5th and 6th columns of Table 6 are given the values of （?） and （?） after correction,i.e.after subtracting F.Comparing them with Table 2,we see that they agree in general trend:late type stars have larger velocities than early type stars,giants have smaller velocities than dwarfs. Many astronomers often attribute the relation of velocity and spectral type to the equipartition of energy.But there are facts which are in contradiction with this view.From this work it is seen that M dwarfs have smaller velocities than K and G dwarfs,O stars have larger velocities than main sequence stars of B,A,F types.It is also known that early type subdwarfs have larger velocietes than dwarfs of later types.It is more probable that the velocity of motion does not depend on mass alone,but also on the mode of formation and the evolution of the star considered.The meaning of the division of the main sequence into two parts is not clear yet;the accumulation of kinematical data will certainly contribnte to the final solution of this problem. （?）is a measure of the mean value of space velocities and its dispersion. Since the distribution of space velocities,is in most cases not spherical but ellipsoidal,the calculation of （?） cannot take the place of more detailed calculations of the kinematical characteristics of a stellar group.But it is much easier to obtain （?）,from it can be derived a preliminary knowledge of the kinematical properties of the group.When radial velocity data grow to a much bigger quantity than at present,the statistical method of correc- tion for solar motion and galactic rotation will become an indispensable tool for the analysis of data.更多还原