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C O N T E N T S . (A ) C lassification of stellar and nebular spectra;(B ) Stellar temperatures, masses, and densities; (C ) Stellar diam-eters. (Data pertaining to the solar spectra will be found withother spectroscopic data; consult index.)A. CLASSIFICATION OF STELLAR AND NEBULAR

SPECTRA

The system1 is that developed at Harvard C ollege O bservatory,as used by Miss C annon in the Henry Draper C atalogue. E xceptwhere the exact nature of the spectral changes is not fully under-stood, decimal sub-classes, representing progressive steps towardthe succeeding class, are used. In denoting objects by theircatalogue numbers, the following abbreviations are used: B. D. =Bonn Durchmusterung; C. D. M. = C ordoba D urchmusterung;I. C. = Dreyer's Index Catalogue of nebulae and clusters; N. G. C.= New General C atalogue by Dreyer. The number, or numbers,following the abbreviation is the catalogue designation of theobject.Class P includes practically all the gaseous nebulae. Its uniquecharacteristic is the appearance of lines from an unknow n origin(nebulium). In addition there are ma ny lines of H, He, C, He+,C+, and N -K All lines are bright and usually sharp. (Theorder of the Harvard ( 2 ) subdivisions should proba bly be reversedto indicate decreasing intensity of radiation.)

Class Typical object] Spectral criteriaPa I . C . 418 X5007 and X4959 faint, X3869 not seenPb O rion nebula X5007 and X4959 strongerPc I . C . 4997 X4363 conspicuousP d N . G . C . 6826 X5007 and X4959 strongPe N . G . C . 7662 X4686 presentPf I N . G. C . 40 X4686 strongWright (ll) has divided these spectra into three classes: ClassI, having X4686 present, C lass II, with X4686 absent but X3869present, and Class III with both X4686 and X3869 absent.Class O is distinguished by the presence of the Pickering seriesof ionized helium, upon a strong continuous spectrum with maxi-mu m intensity far in the violet. The elements present are H,He, He+, C+, N+, Mg+, O+, CHI, Nili, Siili, OHI, SiIV.Broad emission bands occu r in the earlier subdivisions. Fewabsorption lines are found in sub-classes O a , O b , O c , which makeup the group known as Wolf-Rayet stars. (The Harvard sub-classes O d , O e, and O e5 which have absorption lines and in somecases narrow emission lines as well, are included in the subclassesO 5 to O 9 as suggested by H. H. Plaskett (7), the basis of classifi-cation being the absorption lines.)1 Adopted by International Astronomical Union. It defines a temperaturescale which is linear within the present errors of measurement.

C lass T ypical object | Spectral criteriaO a B. D. +35 4013 Band X4648 stronger than XO b B. D. +35 4001 X4686 stronger than X4648O c C . D . M . -41 10972 Bands narrower. X4686X463805 B. D. +4 1302 Pickering series very stronglines weak, X4634 and X(N III) present06 B. D. +44 3639 N eutral helium appears07 9 Sagittae X4471 (He), 1.4 X X4541. (SiIV), 0.8 X X4097 (N I II )08 X O rionis X4481 (Mg+) appears09 10 Lacertae H stronger, He weak. X2.7 X X4541. X4089, 1X4097Class B is characterized by the presence of helium, whicits max imum intensity in B2. T he principal elements areof class O , with the addition, in the later sub-classes, of linthe ionized atom of several of the metals, such as Sr, Ba,Fe. T he H and K lines of calcium are found in increasing strein this class. The hydrogen lines increase throu gh the sub-cla

reaching a strong maximum at Ao of the following class.C lass I T ypical object | Spectral criteriaBO T O rionis Pickering series wea k, X4649 (X4116 (SiIV), and X4089 (SiIV) mmum intensityBl Canis MaJoris He more prominent than O and S iB2 T O rionis X4116 not seen. X4089 and X4649B3 7 7 Aurig ae S trongest lines are heliumB5 q Taur i X4128 and X 4131 (S iII) strongerX4121 (He). X4481, 0.7 X X447B8 O rionis X4481 equal to X4471B9 X Aquilae H strong. He weak. Several prnent enhanced metallic linesClasses A 1 F 1 G, K and M, which contain the largest numof the stars, show a gradual increase in the nu m ber and inteof the lines of neutral metallic elements of the lower atomic weiand a decrease in the intensity of lines due to ionized elemC ompounds produce bands in the later classes. Thespectrum is Go, and is intermediate between that of the wan d the red stars.

C lass I T ypical objec t | S pectral criteriaAo a Lyrae H maximum strength. Very few lines except X4481 (Mg+)A5 p Sagittarii K (Ca+) stronger than HS . Xwell marked. X4481 weakerFo ( T Bootis K 3.0 X Hd and equal to H + H

S E LE CT E D P H Y S ICAL PROPERTIES OF STARS AND NEBULAEALFRED H. JOY

LITERA TU RE(For a key to the periodicals see end of volume)

C 1 ) Barrell, 336, 28: 745; 17. (2) Blomstrand, in Dana's Mineralogy, p.741. (3) Boltwood, 12, 23: 77; 07. (4) C . W. D avis, U. S. Bureau ofMines, O. (5) Dunstan and Blake, 5, 76A: 253; 05. ( ) Ellsworth, 12,9:127; 25. (7) Ge ige rand Ruth er ford, S, 20: 691; 10. (8) Hess and Hender-son, 143, 200: 235; 25. (9) Hess and Wells, 143, 189: 225; 20. ( 1 O )Hidden and Mackintosh, 12, 38: 481; 89.(U) Hillebrand, 12, 42: 390; 91. 156, No. 78; 91. (") Hillebrand andRansome, 12, 10: 120; 00. O3) Holmes, 5, 85A: 248; 11. O4) Holmes

and Lawson, 3, 28: 823; 14. (ig) Kovarik and McKeehan, 337, N25. (16) Lacroix, Mineralogie, V: 93. (17) Lane, Trans. Lake SuMining Inst., Aug., 1925. (i) Larsen and Brown, 328, 2: 75; 17.Lawson, 75, 126: 721; 17. ( 2 < > ) Russell, Introduction to the ChemiRadioactive Substances, Murray, London, 1922.(21 ) Rutherford, Radioactive Substances and Their Radiations, PuSons, New York, 1913. (22) Soddy and H ym an, 4, 105: 1402; 14.Strutt, 5A, 76: 88; 05. 80: 572; 08. 81: 272; 08. 82; 166; 09. 8298; 09. 84: 377; 10. ( 2 4 ) Walker, Univ. Toronto Studies, N23. (25 ) Wells, Bibliography on the relation of radioactivity to geoproblems. National Research Council, 1924.

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Class I Typical object | Spectral criteriaF5 c t Canis Minoris Fraunhofer band G first seen. Numer-ous solar linesGo a Aurigae Solar type. H not conspicuous. Gband well defined, H5 = X4226.G5 r j Piscium HT fainter than X4325Ko a Bootis G band conspicuous, X4226 strong.Hydrogen weakerK5 a Tauri X4226 very wide. X4254 and X4274

(Cr) strong. Titanium bands veryfaintM o Andrmedae Titanium bands well markedM5 a Herculis Titanium bands very stong. Metalliclines fewerCla s s R and N stars show the carbon bands in increasingstrength. The more advanced stars of class N have very littlelight in the violet or blue portions of the spectrum. They are thereddest stars known. Typical stars: Class R, B. D. -10 5057;Class N, 19 Piscium.Clas s S spectra resemble those of class K5 except for the presenceof bands of zirconium, and other peculiarities in the region nearX4650. The line X4554 of Ba + is conspicuous.Cla s s Q stars are the novae. Near maximum of outburst theirspectra are characterized by numerous wide emission bands ofhydrogen and helium, and by absorption lines of ionized elements,especially titanium and iron. As the star decreases in light, bothabsorption and emission lines of N and O become more prominent.In the later stages, bright nebular bands appear; these are ulti-mately superseded by the bright bands of the Wolf-Rayet spectrum.

B. STELLAR TEMPERATURES, MASSES, AND DENSITIESGiant stars are characterized by large mass, low density, andgreat total luminosity. Dwarf stars have smaller mass, higherdensity, and less total luminosity. Both are found in all classes,

but the greatest contrasts between the two are found in the coolerstars of classes K and M. The continuous spectrum of dwarfs hasits maximum shifted towards the violet, as compared with that ofgiants of the same spectral class, indicating that their absolutetemperature is about 15% higher than that of the giants. Evenwith small dispersion, pronounced differences between giantsand dwarfs may be noticed in the distribution of intensity in theirline spectra. These differences probably arise from differences inthe density gradients; they show a correlation with the absolutemagnitude and mass of the stars. The low densities of giantsfavor the enhancement of those lines (absorption) which areproduced under conditions of high excitation, such as the sparklines of the metals; the high density of dwarfs favor those pro-duced by low excitation, such as the resonance lines of neutralatoms. The lines X4077, X4215 (ionized Sr) are much strengthenedin giants, and weakened in dwarfs; the reverse is true of X4226(Ca), X4454 (Ca), X4607 (Sr).

STELLAB TEMPEBATUBES, MASSES AN D DENSITIESUnits: Temperature, 100O 0C abs.; Mass, Mass of Sun; Deg/cm3.E ffective temperature Mean Mean den(giants*) mass ( ) ( )

Class .gfi co fi

H .M- e, t- .3 JJ .$^ P n O o Q f ^ O Q O Oa 23 23O5 30 50 (6)Bo 20 13 18 19 10B3 16 9 0B8 16 7.3 0.Ao 14 11 8 12 10 7.06.0 0.16 A 5 9 5. 64. 0 0.071 Fo 7.5 9 7.5 4.32.5 0.025 F5 6 7.2 6 3.21.5 0.0078 Go 5.8 6.5 6 7 6 2.61.0 0.0025 G5 4.5 2.80.760.00087Ko 3.7 4 4.5 3.00.680.00018K5 3 3.5 3.5 3.9 2.60.620.000026M o 3 3 5 3 2.00.590.0000096M5 2.5 2.95 4N 2J3

* Temperatures of dwarfs are 10 % to 20 % higher than giants of sam(indirect methods).t Abbot C 1). By radiometer. Potsdam observations. Wilsing et al. (10). Coblentz (3). By thermocouple.I J Saha (8). Calculated from initial appearance of certain spectral linespressure of 0.1 atmosphere. (See note U " . )if Fowler an d Milne (4). Calculated from maximum intensity of cspectral lines under pressure of 1.31 X 10 ~4 atmospheres, assuming 1corresponds to maximum of Balmer lines of H. These temperaturesthose of Saha, are for the reversing layer; true effective temperature iswhat higher. STELLAR DIAMETERSUnit: Linear Diameter, IO 6 km.

c ix -r , n DiameterStar Class Parallax ~ - Angular * LinTauri K5 0.055" 0.022" 6aOrionis M2 0.019 0.044 34a Bootis Ko 0.088 0.022 3aScorpii Ml 0.017 0.040 35* Measured by means of interferometer (5).

LITERATURE(For a key to the periodicals see end ofvolume)

O) Abbot, 81, 60: 105; 24. (2) Cannon, Harvard College Obs. Annals19; 16. (3) Coblentz, SlA, 17: 725; 22. (* ) Fowler and Milne, MNotices, R. A. S., 83: 403; 23. (5) Michelson and Pease, 21, 53: 24Pease, Pubi. Ast. Soc. Pacific, 33: 171, 204; 21. 34: 346; 22. ( )Plaskett, PuU. Domin. Astrop. Obs., 2: 298; 24. (7) H. H. Plaskett,1: 366; 22. (8) Saha, o, 99: 151; 21. (9) Scares, 21, 55: 202; 22.(10) Wilsing, Scheiner and Miinch, Pubi. As t rop . Obs. Po t s dam, 24: 2(U) Wright, Pubi. Lick Obs. , 13: 262; 18.

DISTRIBUTION OF STARSFREDERICK H. SEARES

Restriction.No account is here taken ofglobular starclusters norof stars included in spiral nebulae, many of which contain objectswhose essentially stellar character can no longer be doubted.Apparent Distribution and Number.Statistically considered,the stars are distributed over the face of the sky with a high degreeof regularity, their numbers gradually increasing as the Milky

Way is approached from either side. The Milky Way dewhat is very nearly a plane of symmetry, and for a first appmation, systematic difference between the two hemisphprogressive changes in galactic longitude, and all Jocal irrlarities can be ignored. The resulting mean distribution, as fby Scares and van Rhijn, is shown in Table 1.

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TABLE 1.LO GARITHMS OF NUMBERS (Nm) OF STARS, OF MAGNITUDES LESS T H A N m, PE R SQUARE DEGREE IN DIFFERENT GALALATITUDES (!)Units: Last column; m = visual magnitude; average JV m = 1, if w =8. Other columns; m = international photographic matude (2);Nm= 1, if m = 8, Lat, = O. Galactic pole: R. A. 12M1>20S, Dec. +27 21' (1875) (Gould).Log1 0 Nm at latitude | Logio (average Nm) between latitu

V Y I 0 90 40 O n0 5 10 15 20 25 30 35 40 50 60 70 80 90 0 0 0 0 g()U04.0 2.19 2.17 2.12 2.05 3.99 3.93 3.87 3.82 3.78 3.74 3.71 3.69 3.67 3.66 2.12 OS 3V73|704 24.5 2.42 2.40 2.35 2.28 2.22 2.16 2.10 2.05 2.01 3.97 3.94 3.92 3.90 3.88 2.35 2.11 3.96 2.17 25.0 2.65 2.63 2.58 2.51 2.45 2.39 2.33 2.28 2.24 2.20 2.17 2.15 2.13 2.12 2.58 2.34 2.19 2.40 25.5 2.88 2.86 2.80 2.74 2.68 2.62 2.56 2.51 2.47 2.43 2.40 2.38 2.36 2.34 2.80 2.57 2.41 2.63 26.0 .ll .08 .03 2.97 2.90 2.84 2.79 2.74 2.70 2.65 2.62 2.60 2.58 2.57 1.03 2.80 2.64 2.85 6.5 .33 .31 .26 1.19 ,1.13 1.07 1. .Ol 2.97 2.92 2.88 2.85 2.83 2.80 2.79 1.26 1.03 2.86 1.08 7.0 .56'.53 T.48 .42 .35 .29 .24 T.19 .15 .10 .07 .05 .02 .01 .48 .25 .09 .30 7.5 .78 .76 .70 .64 1.57 1.52 1.46 1.41 1.37 1.32 1.29 1.27 1.24 1.23 1.70 1.47 1.31 1.52 8.0 0.00 .98 1.92 1.86 1.79 1.74 1.68 1.64 1.59 1.54 1.51 "l .48 1.46 1.44 1.92 1.69 1.53 1.74 08.5 0.23 0.20 0.14 0.08 0.01 .95 .90 .85 .81 .76 .73 .69 .67 .65 0.14 .91 .74 .96 09.0 0.45 0.42 0.36 0.29 0.22 0.17 0.12 0.07 0.03 1.98 1.94 1.90 1.88 1.86 0.36 0.13 1.96 0.18 09.5 0.67 0.64 0.57 0.50 0.44 0.38 0.33 0.28 0.24 0.19 0.15 0.11 0.08 0.06 0.58 0.34 0.16 0.39 010.0 0.89 0.85 0.79 0.72 0.65 0.59 0.54 0.50 0.45 0.40 0.35 0.30 0.28 0.26 0.79 0.55 0.37 0.60 010.5 1.10 1.07 1.00 0.93 0.86 0.80 0.75 0.70 0.66 0.60 0.55 0.50 0.47 0.45 1.00 0.76 0.57 0.81

11.0 1.3fe 1.28 1.21 1.14 1.06 1.01 0.96 0.91 0.86 0.80 0.74 0.69 0.65 0.64 1.22 0.96 0.76 1.02 111.5 1.53 1.49 1.42 1.34 1.27 1.21 1.16 1.11 1.06 0.99 0.92 0.87 0.84 0.82 1.43 1.17 0.95 1.22 112.0 1.74 1.70 1.63 1.54 1.47 1.41 1.36 1.30 1.25 1.18 1.11 1.05 1.01 1.00 1.63 1.36 1.14 1.42 112.5 1.96 1.91 1.83 1.75 1.67 1.61 1.55 1.49 1.44 1.36 1.28 1.23 1.18 1.17 1.84 1.56 1.32 1.62 113.0 2.16 2.12 2.04 1.95 1.87 1.80 1.74 1.68 1.62 1.54 1.46 1.39 1.35 1.33 2.04 1.75 1.50 1.82 213.5 2.37 2.32 2.24 2.14 2.06 1.99 1.92 1.86 1.80 1.71 1.62 1.56 1.51 1.49 2.24 1.93 1.67 2.01 214.0 2.57 2.52 2.43 2.34 2.24 2.17 2.10 2.03 1.97 1.88 1.78 1.72 1.67 1.65 2.44 2.11 1.83 2.20 214.5 2.77 2.72 2.63 2.52 2.43 2.34 2.27 2.20 2.14 2.04 1.94 1.87 1.82 1.80 2.63 2.29 1.99 2.38 215.0 2.96 2.91 2.82 2.71 2.60 2.51 2.44 2.36 2.30 2.19 2.09 2.01 1.96 1.94 2.82 2.45 2.14 2.56 215.5 3.15 3.10 3.01 2.89 2.77 2.68 2.60 2.52 2.45 2.34 2.24 2.15 2.10 2.08 3.01 2.62 2.29 2.73 316.0 3.33 3.28.3.19 3.07 2.94 2.84 2.75 2.67 2.60 2.48 2.37 2.29 2.23 2.21 3.19 2.77 2.43 2.90 316.5 3.51 3.46 3.37 3.24 3.10 2.99 2.90 2.81 2.74 2.61 2.50 2.42 2.36 2.34 3.37 2.92 2.56 3.07 317.0 3.68 3.64 3.54 3.41 3.26 3.14 3.04 2.95 2.87 2.74 2.63 2.54 2.48 2.46 3.54 3.07 2.69 3.23 317.5 3.85 3.81 3.71 3.57 3.41 3.28 3.17 3.08 3.00 2.86 2.75 2.66 2.60 2.57 3.70 3.20 2.81 3.39 318.0 4.01 3.97 3.87 3.73 3.56 3.42 3.30 3.20 3.12 2.98 2.86 2.77 2.71 2.68 3.86 3.34 2.93 3.54 318.5 4.16 4.12 4.03 3.88 3.70 3.55 3.42 3.32 3.23 3.08 2.97 2.88 2.82 2.79 4.02 3.46 3.04 3.68 419.0 4.32 4.28 4.18 4.02 3.84 3.67 3.54 3.43 3.34 3.19 3.08 2.98 2.92 2.89 4.17 3.59 3.14 3.82 419.5 4.46 4.42 4.32 4.16 3.97 3.79 3.65 3.53 3.44 3.29 3.17 3.07 3.01 2.98 4.31 3.70 3.24 3.96 420.0 4.60 4.56 4.46 4.29 4.09 3.90 3.75 3.63 3.53 3.38 3.26 3.16 3.10 3.07 4.45 3.81 3.33 4.09 420.5 4.74 4.69 4.59 4.42 4.21 4.01 3.85 3.72 3.62 3.46 3.34 3.25 3.18 3.15 4.58 3.91 3.42 4.2121.0 4.87 4.82 4.72 4.54 4.33 4.11 3.94 3.81 3.70 3.54 3.42 3.33 3.26 3.22 4.71 4.01 3.50 4.33

Distribution of Intrinsic Brightness.The range in intrinsic at present, the frequencies are but imperfectly known. brightness among stars is enormousat least twenty magnitudes, assuming that the mean parallaxes of stars of apparent magncorresponding to an intensity ratio of 100 000 000 to 1. A m and proper motion /* can be represented by a linear functioknowledge of the frequencies of different luminosities among.the m and log /* supposed to be valid for all magnitudes and prstars in a given volume of space is essential (unless questionable motions, Kapteyn and van Rhijn derived for the distributioassumptions are to be introduced) for the calculation of the space the absolute magnitudes a Gaussian error curve whose ordindistribution of the stars. It is, however, difficult to obtain, and, are given in the second column of Table 2. Scares (4) has sh

To apparent magnitude (see p. 39) m 13.5 the results dependon data covering a large portion of the sky. From m = 13.5 to18.5 they are derived from counts of stars on photographs of the139 Selected Areas of Kapteyn between the North Pole anddeclination 15. For still higher values of ra, the values oflog Nm are extrapolated, but the uncertainty consequent to theextrapolation itself is probably small. Excepting in low galacticlatitudes, there is little or no systematic uncertainty arising fromthe particular choice of fields used for the counts. To m = 16the magnitude scale is the mean of several closely accordantdeterminations made at different observatories, and is probablyaccurate within a few hundredths of a magnitude. Below thislimit the scale depends wholly upon observations made at theMount Wilson Observatory. Although this part of the scale hasnot been confirmed by independent measures made elsewhere, it

has been established by methods successfully used for the brigstars.The indicated total, to the twenty-first photographic magniof all stars in the sky is 890 000000, and to the twentieth vmagnitude, 1 000000 000. Barring losses of light by absorpscattering etc., the increase in log Nm for a uniform distributiostars throughout space would be 0.6 per unit of magnitude. observed increase nowhere attains this value; the stars thinwith increasing distance from the sun, and at great distancesthin out more rapidly than near the sun; these changes arepronounced in the direction of the poles of the Milky Waythe law of decreasing space density indicated by the stars accesto observation holds for those beyond present telescopic rethe total number of luminous stars in the galactic system be of the order of 3 X IO 10 .

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that their adopted mean parallax formula does not represent thedistances of the stars of large motion and faint apparent magnitude,all of which are of low luminosity. A revision of the parallaxformula, still only provisionally determined, and a recalculationof the luminosity function from about 500 stars of large propermotion leads to the frequencies in the third column of Table 2.TABLE 2. APPROX IMATE LUMINOSITY FUNCTION

0(Af) = number of stars, absolute magnitude M 1 per cubic parsecin the neighborhood of the sun. Unit of distance for M is 10parsecs. 1 parsec = 3.26 light years = 30.8 X 1012km.10 + Logio < f > ( M )

M Kapteyn a ... Diff." /* \ Seares (4)v. Rmjn (3 ) ^-4.64 2.61-3.64 3.42-2.64 4.17-1.64 4.85-0.64 5.46 5.58 0.12+0.36 6.00 6.16 0.161.36 6.47 6.66 0.192.36 6.88 7.05 0.173.36 7.21 7.34 0.13

4.36 7.47 7.58 0.115.36 7.67 7.74 0.076.36 7.80 7.84 0.047.36 7.85 7.87 0.028.36 7.84 7.86 0.029.36 7.76 7.88 0.1210.36 7.61 7.92 0.3111.36 7.39 8.06 0.6712.36 7.10 8.11 1.0113.36 6.75 8.11 1.3614.36 6.3 8.13 1.8For the stars of low luminosity, the departure of Seares' curvefrom the error curve, shown by the differences in the fourthcolumn, is important and must be accepted as real, althoughquantitatively the results are still very uncertain. The possibilityof a maximum within the range of absolute magnitude consideredis not excluded, but any such maximum must be well below theKapteyn-van Rhijn limit, M = 7.7. Since the frequencies ofstars of very low luminosity are still unknown, it is impossibleat present to express the luminosity function as a true frequencyfunction.Space Distribution of Stars.The space distribution is defined bya density function, preferably in a form expressing the totalnumber of stars per unit volume at different distances from thesun. At present, however, we must be content with so expressingthe number of stars which are brighter than some limit of absolutemagnitude.Analytically, the problem is to determine the density function,

A(p), from th e integral equation-/o"*W )pwhere the left hand member can be found from the data in Table1; co is a constant, p = distance from sun. Since < j > ( M ) , for M >8,is still very uncertain, the general solution cannot be found atpresent. Values of the density for the neighborhood of the sun(Table 3) can, however, be calculated incidentally in deriving thedata in Table 2. Results in the second column of Table 3 (M =7.86) are in good agreement with similar results by Kapteyn aridvan Rhijn; the other tabular values indicate what is to be expectedfor lower limiting values of M. The uncertainty of the luminosityfunction for M >8scarcely justifies the effort required to completethe table.

TABLE 3. AVEBAGE N UMBER O F STARS, BRIGHTER THAN ABSOMAGNITUDE M 1 PE R CUBIC PARSE C AT DISTANCE p F R O M S UUnit of p is 1parsec; of distance for M 1 10parsecs. 1pars3.26 light years = 30.8 X IO 12 km.

7 \j 7.86 8.86 9.8610.8611.8612.8613.86Log i o p - ^O UT 0.0280.0350.0420.0500.0600.0730.08701.1 .026 .033 .040 .048 .058 .069 .01.3 .024 .030 .035 .0411.5 .023 .028 .0331.7 .0221.9 .0202.1 .0172. 3 .014 !2.5 .0112.7 .0082.9 .004

(Values based upon 0(Af) fo r stars near the sun, and on the assumptiothe relative frequencies of M are the same at all distances.)Average densities for the whole sky give a very imperfect piof the real distribution in space, as the latter varies greatly galactic latitude. Broadly speaking, the surfaces of equal s

density are concentric, and approximately similar, ellipsoirevolution, similarly situated, with axes in the ratio of aboto 1. See Table 4.TABLE 4. RADII O F EQUIDENSITY ELLIPSOIDS(6)

A(p) = number of stars per cubic parsec at distance p from(Values require revision for recent star counts (Table 1) anerror in luminosity function (cf. Table 2)).Unit of radius = 1 parsec. I parsec = 3.26 light yea30.8 X IO 12 km. Latitude is galactic.Latitude

A(P) 90 I 01.00 O O0.63 118 6020.40 198 10100.25 296 15100.16 413 21060.100 553 28200.063 717 36560.040 9 02 4600

Size of the Galactic System.At present we have no ceindication as to the distance of the most remote stars belonginthe galactic system; but if ordinary blue stars of absolute matude zero occur among the faintest objects listed in Table 1diameter of the system cannot be less than a million light ySuch objects are not to be expected in high galactic latituwhere the stars of very faint apparent magnitude are alcertainly all dwarfs; but their occurrence in the Milky Way no means excluded. We have, indeed, strong, though notclusive, evidence of the existence in the Milky Way of stars ofabsolute magnitude among those of the sixteenth apparent matude. The corresponding diameter of the system is a hunthousand light years. This value may be accepted with sassurance as a lower limit for the size of the system in the pof the Milky Way, exclusive of such objects as globularclusters and spiral nebulae, whose relation to the general stsystem about us is not yet clearly defined.Position of the Sun.The symmetrical distribution ofadopted in Table 1 tacitly assumes the sun to be at the centthe system. This is not actually the case, as is shown by sysatic deviations from the adopted mean distribution. Shapley

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The term nebula is applied to objects of such diversity of form,size, distance, and physical characteristics that any study of theirdistribution presupposes a consideration of the question ofclassification. The following general classification by Hubbleprovides for two mutually exclusive divisions, characterized byposition in the sky as well as by physical peculiarities, and fivesub-classes representing physical differences.A GENERAL CLASSIFICATION OF NEBULAE

I. Galactic nebulae, characterized by (1) tendency to concen-trate about the Milky Way, (2) conspicuous association withindividual stars from which they probably derive theirluminosity, (3) early-type spectra, either emission or absorp-tion, depending upon the spectral type of the associated stars,and (4) smooth and cloudy or wispy texture. They include(a) Planetaries, distinguished by symmetrical distribution ofnebulosity about central stars, sharply defined edges,and emission spectra.(& ) Diffuse nebulae, clouds in low galactic latitudes, usuallyassociated with early-type stars. This type ranges fromluminous to dark and from semi-transparent to opaque.Subdivided into predominantly luminous, predomi-nantly obscure, and conspicuously mixed.u.Non-galactic nebulae, characterized by (1) tendency to avoidthe Milky Way, (2) no conspicuous association with stars,(3) late-type absorption spectra, and (4) usually a rotationalsymmetry about dominating non-stellar nuclei. Theyinclude(a) Elliptical nebulae, amorphous objects whose forms can berepresented as successive stages of an original globularmass flattening underthe influence of increasing rotation.(6) Spirals of two kinds, logarithmic and barred, which, onceformed, appear to develop along parallel lines, the armsunwinding and the granulation of the material becomingmore and more conspicuous.(c) Irregular nebulae, including a few non-galactic objects hav-ing no dominating nuclei and, significantly, showing norotational symmetry.Physically, the planetaries and diffuse nebulae, Ia and Ib, aredistinct and apparently without genetic relationship, except that

the planetaries, which, in some cases at least, seem to be latestages in the development of novae, may represent the catas-trophic consequences of the penetration of a star within a nebulouscloud of the diffuse sub-class. The spirals lib, on the other hand,are apparently an evolutionary development from ellipticalnebulae, Ua, although it does not follow that all elliptical nebulaewill necessarily become spirals. The few irregular nebulae, Uc,present features that might be expected in the case of spirals inthe absence of or through the neutralization of dominating dynam-ical characteristics.The distribution of the various classes of nebulae is not ingeneral easily shown in tabular form. The following summaryfor each of the important sub-classes includes, however, referencesto diagrams which exhibit the main features of the distribution.

Ia. Planetary Nebulae.In the whole sky only about 1these objects are known, many of which are so small as trecognizable only from their gaseous emission spectra. smallest objects are closely associated with the Milky Way,show a marked concentration in the Aquila-Sagittarius reWith increasing size the mean galactic latitude increases, anlargest known objects, to the extent of a dozen or so, aretered over the sky with some approach to uniformity ( 3 6 This suggests that the linear distances of planetaries fromgalactic plane are relatively small and that their angular deters are correlated with their distances from the sun. small nebulae thus appear in low galactic latitudes because distances from the sun are many times their distances fromgalactic plane.The actual distances of planetary nebulae are still very utain. Van Maanen (15 ) has measured the parallaxes of a20 of these objects and finds distances ranging from 50 to ahundred parsecs; but, as he points out, these values are in flict with the fact that the radial velocities average aboukm/sec, while the proper motions are apparently small, oorder of the parallaxes themselves.Ib. Diffuse Nebulae.The distant star clouds of the MWay define the galactic circle. A secondary galaxy, incsome 12 to the galactic circle proper, is outlined by the bhelium stars of the much-flattened local cluster immediatelyrounding the sun, most of whose members are within 500 pa(14). The diffuse nebulae outside the Magellanic Clouds, hundreds in all,1 are closely associated with the primarysecondary galactic circles (7). Since the mean galactic latof those following the primary galaxy is only about 2, and the space within the two circles is not well filled, the infeis that these nebulae are directly connected either with the MWay star clouds or with the local cluster, and that few are tfound in the intervening regions. We thus have a group of dnebulae whose members are within a few hundred parsecs osun; the others, forming a widely scattered group associatedthe Milky Way, are at distances probably to be counted insands of parsecs (10). Both groups include both luminousdark nebulae; the luminous members of the two groups prsomewhat different physical characteristics, most marketheir spectra, which may be either emission, or predomincontinuous or absorption in type. The continuous and absorspectra occur mostly among the nearer objects connected witlocal cluster. The luminous diffuse nebulae are conspicuoassociated with stars of high temperature from which they dtheir luminosity, either by excitation or reflection.II. Non-galactic Nebulae.The members of this class, sisting chiefly of the related sub-classes, elliptical nebulaeand spirals (lib), are far more numerous than the galactic nebOn the whole, the elliptical nebulae out number the spirals mtimes; but if only bright objects are considered, the spirals armore numerous. The distribution in galactic latitude is show1 Less than 200 luminous ones known; no complete list published (vMost complete list of dark nebulae (182small objects) is given by Barnar

DISTRIBUTION OF NEBULAEFREDERICK H. SEARES

value for the distance of the sun from the galactic plane is about60 parsecs, to the north, which is certainly of the right order ofmagnitude. The sun's distance from the center is much lesscertain, and different estimates range from a few hundred tomany thousand parsecs, according to the underlying assumptionsand the method of attack. The question is much complicatedby the fact that the sun lies within a local cluster whose membersform a considerable fraction of the stars of the brighter apparent

magnitudes, and a final answer must await the detailed discuof the distribution of faint stars in galactic longitude.

LITERATURE(For a key to the periodicals see end of volume)

C 1 ) Scares and van Rhijn, 197, 11 : 358; 25; a more detailed account appe!Bl, 62: 320;25. (2) Trans. Internat. As tronomica l Union, 1:69; 2Q . (Sard magnitudes of stars.) (3) Kapteyn and van Rhijn, 21, 52: 23; 20Scares, 21, 59: 310; 24. (5) Shapley, 2I1 49: 333, 19. (6) Kaptey55: 302; 22.

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Table 1, which gives to limiting magnitude 18.6 on the inter-national photographic scale the average number per square degreeat various latitudes in each hemisphere. The data are compiledfrom Fath 's list ( 4), based on Mount Wilson photographs (exposuretime 1 hour with 60-inch reflector) of the 139 Selected Areasbetween the N orth Pole and declination 15. That part of thenorthern galactic hemisphere within which nebulae are frequentis wholly covered. About one-half the southe rn hemisphe re isincluded, but not the south pole itself. Fath's counts have beencorrected fo r losses caused by poor definition in the corners of thenegatives (13).T A B L E 1 . N O N - G A L A C T I C N E B U L A E : N U M B E R P E B S Q U A R E

DEGREE(4)Average number; international photographic magnitude ^18.6;

c f . Table 2 .HemisphereGalactic latitude ;J N j fe_ _ _

15 0.8 0.425 2.5 5.435 13.2 8.245 10.3 5.855 12.2 7.065 22 .2 11.974 3183 (68)

Fath's list includes all classes of nebulae, but the galactic nebulaeare relatively so infrequent that it is practically one of non-galacticnebulae alone. T hese objects begin to appear at about 20latitude and increase rapidly in the interval 20 to 35. From 40 to 70 the numbers increase slowly. The concentration near thenorth galactic pole is very pronoun ced. Below latitude 70 thei numbers in the southern hemisphere average about three-fourthsthose of the northern. T he assumption of a similar ratio for theregions 70 to 90 leads to integrated totals of 170 000 and 128 000for the northern and southern hemispheres, a round total of 30 0 00 0for the w hole sky (lim iting phot. mag. for stars 18.6).T he sum mary in T able 2 emphasizes the d ependence of thedistribution on galactic latitude. T he uncertainty in the averagenumber per square degree in the region 70-90 is considerable,and since the number of nebulae in this region is large (29% or50 000 in the northern hemisphere), the total given for the wholesk y is in doubt by many thousand. C urtis (2) has estimated thetotal (to an undetermined limiting m agnitude) to be over 700 000.T he difference in the estimates may arise from a difference inmagnitude limits or from th e fact that the fields counted byC urtis are not certainly representative of the sky as a whole.

T A B L E 2.DISTRIBUTION O F N O N - G A L A C T I C NEBULAELat. = interval in galactic latitude. Sky = % area ofNeb . = % number of nebulae. N = northern, S = souhemisphere.~-

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TABLE 1. SO LAR APEX AND THE SUN'S VELOCITY(Referred to apparently bright stars. Unit: velocity, km/sec)

T ) V 1 0'R. A. 1900 *~ Method of Lit.1900 Cl ty stars18h 03m +34.3 Proper Motions P. G. C.* 5413 (2)18 11 +31.6 Proper Motions m )18 40 +32 29 Space VeL of nearby stars I 83 (7)* Preliminary General C atalogue by L. Boss, Washington, 1910.t Stars brighter than the 6th magnitude (apparent).Although the agreement between the different determinationsis fairly good, a detailed study shows that the sun's motion cannot be regarded as a constant vector. The A stars and giant starsin general give a small velocity for the sun; and dwarf stars, amuch higher velocity.

AVERAGE PECULIAR MOTIONS OF THE STARSAfter the effect of the sun's motion has been removed, theresidual or "peculiar" velocities show certain regularities. Theaverage peculiar velocities are different fo r stars of differentspectral types, and vary also with the intrinsic brightness of thestars.

TABLE 2. AVERAGE RES IDUAL RADIAL VELOC ITIES (6 ) O F STARSO F DIFFEREN T SPEC TRAL CLASSES (Sp) AND ABSO LUTEMAGNITUDES (M )Unit of O = 1 km/sec

S p M * I 6 I Lit. [ I S p I M * I B I Lit.05 to 09 -3 20.7 (") K +1 18.4 O)B -1 6.5 (3) K +6 27.0 O)A +1 11.0 O1) M +1 21.6 (1)F +2 15.8 (i) M +9 29.6 (U)G +1 18.0 O) Met O 40.1 (")G I +5 26.3 I ( i ) I Pt - 28.6 | Q *)

* The apparent magnitude as observed from a distance of 10 parsecs.t C ontains M stars with bright hydrogen-lines; all are variable stars of longperiod. Bright-line nebulae.PREFERENTIAL MOTION

The peculiar velocities of the stars are not distributed at ran-dom. In general the stars show a tendency to move parallel tothe galactic plane. To describe the distribution of the peculiarvelocities, a distribution-function is adopted, which gives therelative numbers of stars moving in different directions and withdifferent velocities. The simplest distribution-function is thespherical distribution-law,

where x, y, and z are the velocity-components referred to the"centroid" of the group. N is the number of stars in the group,an d o - is the dispersion or the square-root of the mean of thesquares of the velocity-components. The number of stars ofvelocity-components between x % dx y y %dyj z % dz is thengiven by ~ F ( x y z ) dxdydz. In a spherical distribution, the fre-quency of a velocity is independent of its direction and onlydependent upon its size. Spherical velocity-distributions occurfor several classes of stars, but in general the distribution in

velocity-space is either flattened (B stars) or elongatedF, and dwarf stars). Two functions have been used to desthe elongated distribution. Kapteyn and Eddington used a sum of two spherical functions and have regardedstars as belonging to two intermingled systems, "two sthypothesis." Schwarzschild has introduced the ellipsoidal dbution defined by the distribution-function

with three principal dispersions a, 6, and c, which definethree axes of the "velocity-ellipsoid." The velocity-compoX 7 y, an d z are here projected on the principal axes ofellipsoid. The major axis of the velocity-ellipsoid correspto the line joining the two centers in the two stream theory.direction of this fundamental axis, which is common in thetheories, is about R. A. 6h 6m, Dec. + 9, (true vertex).dwarf stars give a somewhat higher declination for the true veIn the analysis of proper motions, the two stream theory two vertices, which correspond to the directions of motion otwo streams relative to the sun. The coordinates of these veare R. A. 6h 14m, Dec. -13 (first stream) and R. A. 19hDec. 6 0 (second stream).Analyzing stellar motions on the basis of the two stream thwe find a number of stars which cannot be regarded as belongieither of the two streams. The B stars and stars of spclass M, for instance, have a group-motion intermediate betthe two streams. For this reason Halm has introduced astream (Ostream). But these streams taken together cafairly well represented by an ellipsoidal distribution ussmaller number of parameters.Charlier (4) has introduced a generalization of the ellipstheory which makes it possible to take into account deviafrom a strictly ellipsoidal distribution, but it is only whendeviations are small that this generalization is practicable.

M O V I N G CLUSTERS OR GROUPSSeveral stars move nearly parallel to one another, theknown example being 5 of the 7 bright stars in the constellUrsa Major. Another moving group or cluster is the Hyadthe constellation Taurus (Taurus Group). The proper moof the stars belonging to such a group converge towards a pothe sky, the "convergent point," whose position in the skythe direction of motion of the group relative to the sun. Thevergent point for 17 stars belonging to the Ursa Major GroR. A. 20h 30m, Dec. -40; for the Taurus Group (39stars)6h 7m, Dec. + 7. A number of other moving groups are kn

THE G E N E R A L DISTRIBUTION OF COSMIC VELOCIWhen the sun's motion is referred to different clases of obit has been found that this motion is not a constant vecto

varies greatly, from about 12 km/sec for the A stars anCepheids of long period up to 300 km/sec for the fast moobjects, the globular clusters and the spiral nebulae. A gerelationship between group-motion and dispersion exists, waccording to Strmberg (11), holds for all classesof objects, bua small deviation for the B star system. This variation in gmotion produces an asymmetry in the velocity distributiosuch a way that all fast moving objects move, relative to thetowards the same hemisphere. This asymmetry defines analong which the group-motion increases with increasing intvelocity-dispersion. The direction of this axis is R. A. 8hDec. 57, and the motion of objects with small velocitpersion relative to those of high velocity-dispersion is aboukm/sec in the opposite direction. The group-motion of ob

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C H R O N O L O G I C A L E RASGregorian Calendar

Era Year Begins, 1925 A, D.Byzantine*! 7434 September 14Diocletian^ 1642 September 11^ M T oooT /September 14Grecian* 2237 \ ~\, ,A( October 14Hegira 1344J July 21Japanese 2585f January 1Jewish 5686J September 18Julian calendar 1925 January 14Julian period 6638 January 14Mohammedan 13441 July 21NabonassarH 2674 May 12RomeH 267811 January 14Seleucidaelf 2237 (See Grecian)

* In present-day usage of Syrians, begins in September or October dependingupon the sect. In ancient usage of Damascus and Arabia Petraea, began withvernal equinox.t The 14th year of period Taisho. Begins at sunset. Julian day number of January 1, 1925 (Gregorian) is 2 424 152.

I l Since foundation of Rome, according to Varr.T f Based upon Julian calendar. TIMEInterval Days*

Year:Tropical! 365.2422Sidereal 365.2564Anomalistic 365.2596Month :Synodicalf 29.530 59Tropical 27.321 58Sidereal 27.321 66Day:Sidereal 0.997 2696

* Mean solar days. f Ordinary.

EQUA TION OF T IME *(A = mean apparent)Unit of A is minute. Time is Greenwich mean noon

Date A Date A Date AI 1 + 3 . 4 VI l -3.8 1X18 -5

6 5.8 16 -3.8 23 - 11 7.8 21 -3.7 28 - 16 9.7 26 -3.3 X 3 -21 11.3 31 -2.6 8 -26 12.6 VI 5 -1.8 13 -31 13.6 10 -1.0 18 -II 5 14.1 15 0.0 23 -10 14.4 20 +1.1 28 -15 14.3 25 2.2 XI 2 -20 14.0 30 3.2 7 -25 13.3 VII 5 4.2 12 -III 2 12.4 10 5.0 17 -7 11.4 15 5.6 22 -12 10.0 20 6.1 27 -17 8.7 25 6.3 XII 2 -22 7.2 30 6.3 7 - 27 5.7 VIII 4 6.0 12 - IV 1 4.2 9 5.4 17 - 6 2.7 14 4.7 22 - 11 1.2 19 3.7 27 + 16 + 0.0 24 2.5 31 + 21 - 1.2 29 +1.126 - 2.2 IX 3 -0.4V l - 2.9 8 -2.16 - 3.4 13 -3.8* A is the amount by which mean time exceeds apparent time whennoon at Greenwich;it is the excess of the right ascension of the actual sunthat of the mean sun at that instant. It varies continuously with the

and does not exactly repeat its values in successive years ; those given areag e values for Greenwich mean noon of an ordinary year, an d will seldomfrom the actual values for that time by as much as 0.2 min., except in Jaand December, when the difference may amount to 0.3 min. In leap yeadates in the table after February must be reduced by one day.

TIME

with high velocity-dispersion is approximately the same as thatof the globular clusters and spiral nebulae.The general distribution of cosmic velocities can be approxi-mately represented by a product of two symmetrical distributionsSi and 82. The first of these is a sum of concentric and co-axialellipsoidal distributions, the velocity of the sun relative to thecenter of the distribution Si being 14.8 km/sec in the directionR. A. 17h 43m, Dec. +22. The sun's motion relative to thesecond distribution, S 2, is 300 km/sec in the direction R. A. 20h28m, Dec. +56. The first distribution can be regarded as thevelocity-distribution in our local system of stars, the second as a

velocity-restriction in a universal world-frame of enormous disions. Other interpretations, however, may be possible.LITERATURE

(For a key to the periodicals see end of volume)(M Adams, Strmberg and Joy, 81, 54: 9; 21. (2) Boss, 326, 26: 11(3) Campbell, Lick Obs. Bull. No. 196; 11. (4) Charlier, Lund O

torium, Meddelanden, II: No. 13; 15. (5) Charlier and Wicksell,H: No. 12: 45; 15. (6) Gyllenberg, Ibid., II: No. 13; 15. (7) LAnnals Harvard College Obs.85: N o. 5; 23 . (8) Raymond, 326,SO: 19(9) Strmberg, 21, 47: 7; 18.(10) Strmberg, 21, 56: 265; 22. ( 1M Strmberg, 21, 61: 363; 25.

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SOLAR SYSTEMORBITAL DATA; SOLAR SYSTEM (1925)Units: Distance, IO 6 km; period, tropical year

Mean longitude SiderePlanet Distance* Eccentricity Inclinationf TTTT 1 ^ M ,. oiaereaNodeJ I Perihelion period$ Mercury 5 7 ^ 9 0 . 2 0 5 6 7 O ' 12.0" 47 2 6 ' 3 2 . 1 " 7 6 17 ' 18.9" 0.240C Venus 108.1 0.0068 3 23 3 8. 0 76 016.7 1303056.8 0.6150 Earth 149.5 0.01674 10139 2.3 1.000c? Mars 227.8 0.0933 1 51 0.6 485845.0 3344042.2 1.880U Jupiter 778 0.0484 1 1826.4 994126.3 13 65 1 . 4 11.862

Saturn 1426 0.0558 2 2 9 2 8 . 7 1 1 3 O 5 . 7 913442.0 29.458O Uranus 2869 0.0471 O 46 22.1 73 36 57.7 169 26 56.8 84.015ty Neptune 4496 0.00855 | 1 46 36.7 | 130 57 13.3 43 58 27.9 164.788* Mean distance.t Angle between plane of orbit and plane of ecliptic. Ascending node.

CHARACTERISTICS O F MEMBERS O F SOLAR SYSTEMUnits: Linear diameter, 1000 km; density, g/cm3; time, mean solar^ Diameter Massf X 10 Dengit Sidereal NuLinear | Angular* Mass sun rotation satelMercury 4.84 10.90" 0.1670 sT Venus 12.19 I / O . 80 2.451 5.1 OEarth 12.76 3.036J 5.52 23 hr 56.07 min lMars 6.78 17.88 0.3233 3.9 24 37.4 OJupiter 142.7 46.86 954.8 1.4 9.8hr 7Saturn 120.8 19.52 285.6 0.7 10.2 hr 9Uranus... 49.7 3.76 43.7 1.3+ 4Neptune 53.0 2.52 50.8 1.3 1Sun H 1391 3159.26 1001341 1. 4 25.3 daMoon I 3.48 31 5 . 1 6 U 0.037** 3.3 | 27.32 da

* At distance = difference mean distance sun to object and mean distance sun to Earth; nearly at distance of nearest approach to Earth,t Includes satellite (or planetary) system, if any.J Mass of Earth alone = 2.999 X 10~ mass of sun. Equatorial diameter. Polar diameter: Earth = 12.71; Jupiter = 133.2, 43.74"; Saturn = 108.1, 17.46". Diameter of sphere of volume = Ea12.74.Il At mean distance of Earth, gravitational acceleration due to Sun is k2 = 2.9592 X 10~* (mean distance) per day 2 = 0.5926 cm per sec2. Fo rspectrum etc., see index.T f A t mean distance from Earth. Apparent diameter varies, with distance, from 29.5' to 33.5'.** Moon alone. Mass Moon = 0.01227 mass Earth.

SOLAR DATAInclination of equator to ecliptic, about.... 7Longitude of ascending node of equator.... 7 4 . 5 Period of rotation, about 28 da*Sun spot period, about 11 yr

TERRESTRIAL AN D LUNAR DAT AJGeneral precession (retro-grade) 50.2564" + 0.000222"(* - 1900) per yrObliquity of theecliptic 23 27' 8.26" - 0.4684"(* - 1900)

* From observations of sun spots near latitude 45; spots near equator rotatein about 24 da; those near lat. 80, in 30 da.t For geodetic and geophysical data, see p. 393.

Constant of notation 9.21"Constant of aberration 20.47" [Paris conference valSolar parallax 8.80"From parallax measurements 8.From velocity of light 8.From mass of Earth 8.From motion of Moon 8.Equatorial horizontal parallax of Moon* 57' 2.70" (BrMean distance Earth to Moon 384 403 kmInclination of Moon's equator to ecliptic 1 32.1"Inclination of Moon's orbit to ecliptic, about 5Eccentricity of Moon's orbit (average) 0.055Revolution of Moon's nodes (retrograde) 18.6 yr

* Mean of greatest and least values; actual values vary from 53' to 61

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TABLE 1. CO MPOS ITION OF DRY AIR AT SEA-LEVEL (4> 5)v volume of the gas in volume V of dry air

Gas N 2 C ^ A C O 2 H 2* Ne He K r X ( TIQWF 78032099 94 3 1 0.1230.04 0.0050.0006* Values found by analysis vary ; the o ne here given is that accepted by Hann

and the Recueil de Constantes Physiques.TABLE 2 .C OMPOSITION OF ATMOSPHERE AT VARIOUS LEVELSComputed from data of Table 1 on the assumptions: (I ) atsurface, H2O vapor supplies 1.2% of the total number of gasmolecules, (2) absolute humidity decreases rapidly to a negligibleamount at about 10 km, (3) temperature = U0C at sea-level,decreases normally (60C per km) to 550C at 11 km, remainsconstant above 11 km, (4) relative proportions of the gases, watervapor excepted, remains constant up to 11 km, (5) above 11 km,distribution is in accordance with their molecular weights (3).The amount of H2 is in doubt (see note Table 1), especially above11 km; it may become oxidized to H2O before reaching the upperatmosphere.v = volume of the gas contained in volume V of atmosphere.Unit of height = 1 km = 0.621 mi.; of pressure = 1 mm of Hg~~ lOQv/V TotalHeight pres-N 2 I O 2 H 2O I A C Q 2 H2 I H e sure140 0.01 99.15 0.84 0.0040130 0.04 99.00 0.96 0.0046120 0.19 98.74 1.07 0.0052110 0.67 0.02 0.02 98.10 1.19 0.0059100 2.95 0.11 0.05 95.58 131 0.006790 9.78 0.49 0.10 88.28 1.35 0.0081

1000/7 ToHeight prN 2 Q 2 I H2Q A C O 2 H, He su80 32.18 1.85 0.17 64.70 1.10 0.7 0 61.83 4.72 0.20 0.03 32.61 0.61 0.6 0 81.22 7.69 0.15 0.03 10.68 0.23 0.50 86.7810.17 0.10 0.12 2.76 0.07 040 86.4212.61 0.06 0.22 0.67 0.02 1.830 84.2615.18 0.03 0.35 0.01 0.16 0.01 8.620 81.2418.10 0.02 0.59 0.01 0.04 40.15 79.5219.66 0.01 0.77 0.02 0.02 8911 78.0220.99 0.01 0.94 0.03 0.01 168.5 77.8920.95 0.18 0.94 0.03 0.01 405.O 77.0820.75 1.20 0.93 0.03 0.01 760TABLE 3 . M AS S E S OF THE ATMOSPHERE AND ITS CO NS TITU

Based upon Table 1, the assumptions of Table 2, and the asstion that the average atmospheric pressure at the surface oearth = 73.7 cm and at base of stratosphere = 14.5 cm ( *Area of earth is taken as 51 X IO 17 cm 2.Total mass M = m X 10* kg; 1000 kg = 1.102 tons (of 200Gas All I N 2 I O 2 I A JH2O C O 2 | H2 | Ne | Kr | Hem 511 387 116 624 133 217 129 471 64 63 n 16 16 16 14 14 13 12 11 11 11

LITERATURE(For a key to the periodicalssee end of volume)

C 1 ) Hann, Lehrbuch de r Meteorologie (3rd ed.) . (2) Humphreys, MWeather Review, 49 : 341; 21 . (3) Humphreys, Physics of the Air, p. 6(4) Ramsay, 6 , 80 : 599; 08. (5) Variousauthorities.M I S C E L L A N E O U S GEODETIC DATA

W. D. LAMBERTWith certain exceptions which are especially noted, those of thefollowing data which depend upon the dimensions of the earthhave been calculated strictly in accordance with the INTER-N A T I O N A L ELLIPSOID O F R E F E R E N C E , adopted by the Sectionof Geodesy of the International Geodetic and GeophysicalUnion, meeting at Madrid, October 6 and 7, 1924. This ellipsoidis based upon the results obtained by J. F. Hayford (Supplemen-tary Investigation in 1909 of the Figure of the Earth and Isostasy,Washington, 1910), but is not absolutely identical with Hayford'sellipsoid. (For some of the other spheroids that are used forgeographical purposes, see Special Publication #100, U. S. Coastand Geodetic Survey. Recent attempts have been made to showthat the actual figure of the earth can be represented more closely

by an ellipsoid of three unequal axes, than by one of revolution,systematic departures from the latter being of the order of 100 to200 meters in elevation and depression.)If the positions of the two ends of a line are determined geodetic-ally for any assumed spheroid of reference, the uncertainty in thelength of the line as measured along the earth depends almostentirely upon the errors in the survey; for geodetic surveys of thehighest class, the uncertainty is a little less than one in 100 000and for an ordinary fair survey it is about four times as great.The proportional error in the straight-line distance is greater,mainly because the geoid does not coincide with the ellipsoid;these additional errors are not serious for a short line, but for twopoints almost diametrically opposite may amount to 100 or 200meters.

If the end points are determined astronomically, the prinerror in the computed length is due to the difference in the defleof the plumb-line at the two points; unless the measured lishort, the average uncertainty so introduced is of the order ometers, but may be much more, especially in rugged countryLatitude.The latitude of a place is defined as the angle wsome line of reference makes with the equatorial plane. lines of reference, defining four distinct kinds of latitude, areThree of these lines pass through the place considered; vizThe plumb-line, defining the as tronomical latitude, (2) the noto the spheroid of reference, defining the geographical latiand (3) the line to the center of the earth, defining the geoclatitude. The fourth line of reference passes through the c

of the earth and that point which is upon the circumscsphere (radius = equatorial radius of the spheroid) and asame distance from the axis of rotation as is the point onspheroid representing the place considered; this defines the pmetric, or reduced, latitude.Gravity.1 If the earth's sea-level surface were accurately rsented by the International Ellipsoid of Reference, and iattracting matter projected above this surface, then the variof gravity at sea-level (y 0) would be represented by the equa- Y o = 7.(I + 0.005 288sinV - 0.000 006sin2 2 < f > )= 74o(l - 0.002 637 cos 2 < p + 0.000 006cos2 2?)

1 The resultant acceleration arising from the gravitational attraction anrotation of the earth.

COMPOSITION OF THE ATMOSPHEREW. J. HUMPHREYS

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where < f> is the geographic latitude, and T C ,745 are the values of J0at the equator and at latitude 45, respectively. These equationsdiffer slightly from that used in computing the table on p. 396;the latter corresponds to an ellipticity of 1/297.4.TABLE 1. FORM AN D SIZE OF THE EARTH

Based upon International Ellipsoid of Reference; acceptedconstants, from which the others are computed, are a = 6 378 388meters, ellipticity [ = (a b) /a ] = 1/297. T he indicated uncer-tainties are estimates, by Lambert, based upon a consideration ofsystematic errors as well as of internal discordances.a = semi-major axis = 6 378 388(60)m5 = semi-minor axis = 6 356 911.946 mRadius of sphere of same area = 6 371 227.7 mRadius of sphere of same volume = 6 371 221.3 mLength of equatorial quadrant =1 0 019 148.4 mLength of meridonal quadrant = 10 002 288.3 m/ - ellipticity = ( -~ = 0.003 3670034j = reciprocal of ellipticity = 297.0(0.4)e 2 = (eccentricity)2 = /2 0 - I = 2 ~ '.. =0.006 722 6700Area of the ellipsoid = 510 100 934 km 2Land area = 148 847 000 km SOcean area = 361 254 000 km 2Volume of the ellipsoid = 1 083 319.78 X 106 km Mass of the ellipsoid* (d = 5.527 g/cm*, p. 395) = 5.988 X IO 24 kgPrincipal moments of inertia (A B < C )t:A % = Bl = 0.332 35 #a*C % = 0.33344.Ea2C-A = 0.001 0921 Ea*( )-(SoOa)1 - -32774

* For discussion of variation of density with depth below surface, seeAdamsand Williamson, Smithsonian Annual Report, 1923, p. 241.t E = mass of earth.t Computed values vary but little with any admissible assumption regardingthe constitution of the interior of the earth. Values are based upon computa-tions of De Sitter (64V, 27: 233; 24); ellipticity taken as 1/296.92. Deduced from precession of equinoxes; involves no hypothesis regardingconstitution of interior of earth.TABLE 2 . DIST ANC ES U P O N SURFACE OF THE INTERNATIONALELLIPSOID O F R E F E R E N C E

M = length of meridian from equator to geographic latitude < ? ;Sm length of meridian from latitude ( ) to (< ? + iA + c sin 4 b sin A V cos 2 d cos 6 ^ > ; SP = a cos +c cos 5 < f > ; where the coefficients and their logarithms have thefollowing values:Unit of length = 1 meter; of angle = 1

""" M* I Sm*Value log I Q Value logioa 111 136.537 5.045 856 86 111 136.537 5.045 856 86b 16 107.035 4.207 015 6 32 214.069 4.508 045 6c 16.976 1..229 84 33.952 1..53O 87

^ d 0.022 2.348 0.045 2.649

Sm* for Ay = 1 I Sp*Value logio Value | logio

a 111 136.537 5.045 856 86 111 417.657 5.046 954b 562.213 2.749 901 93.904 1.972 686c 1.185 0.073 7 0.119.074 6d 0.002 3.37

* Owing to uncertainty regarding the actual size of the earth, actual disupon the earth at sea-level may differ from these computed distances by2 in 100 000 near the equator or the poles, by somewhat less in middle latiTABLE 3 . E X C E S S O F GEOGRAPHIC LATITUDE ( b sin 4 ^ ? -j- c sin & < ?= a sin 2 < f > ' + b sin 4 ^ > ' + c sin 6 + c' sin 6 ^ >= a! sin 20 + b' sin 40 -f c' sin 60where the coefficients and their logarithms have the follovalues: Unit of coefficients = 1"I Value I logio || | Value | logio

~~a695.66352.842 3 9 9 2 ^ 3 4 7 . 8 3 2 7 2 . 5 4 1 36 1.1731 0.069 34 6' 0.2933 1.467 2c I 0.0026 I 3.421 c' 0.0003 4.52TABLE 4. MISC ELLANE OUS T ERRESTRIAL DATA

Angular velocity of rotation 72.921 X 10~6 radians/Rotational energy 2.160 X IO 36 ergsRotational energy lost by tidal fric-tion 1.1 X IO 19 ergs/secfWork required to dissipate thematerial of the earth to infinity.. 2.46 X IO 39 ergsMean elevation of land above sea-level 825mMean depth of the oceans 3681 mMean effective viscosity is notknown, but perhaps between IO 20 and IO 25 poisesf* Mean solar second.t Jeffreys, 62, 221A: 239;20; The Earth, Its Origin, History and\ PhConstitution, 205-237,; 24. Heiskanen, 175, ISA: 1; 21.J Schweydar, Verffentl. desPreuss. Geodt . Inst., No. 79; 19; Jeffreys, M

Notices, Roy. Ast. Soc., 75: 648; 15. 76: 84; 16. 77: 449; 17; also Theus Origin, History, and Physical Constitution, 222; 1924.

Rigidity ( M ) . From the yielding of the solid portions (revby observations with horizontal pendulums), and on assumof incompressibility, Schweydar (Zentralbureau Int.ErdNeue Folge No. 38, 1921) deduces /* = 30.8 (1 - 0.90r2/2) Xdynes/cm2, and mean effective rigidity = 17.6 X IO 11 dynes(r = distance from center, a mean radius). T o allowcompressibility, these values must be increased by about(Lambert, preliminary, unpublished computations) ; even thevalue computed for the outer shell of half-radius thickness ismless than that deduced from earthquake data. (See AdamWilliamson, Smithsonian Annual Report, 1923.) The discrepmay arise from Schweydar's assumption of high rigidity incentral portions, which may possibly behave as a fluid. (Knott, 68, 39: 157;19; Sieberg, Geologische, physikalischeangewandte Erdbebenkunde, 364; 23.)

44919_05A

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