,,extra-,,galactic ,,nebulae#a ,by ,,edwin ,,hubble ,transcriber's ,note3 ,this etext was produced from3 ,the ,astrophysical ,journal1 ,vol4 ,,lxiv1 pp4 #cba-cfi1 #aibf4 ,the plain text version of this ebook includes mathematical formulae in ,te,x notation4 ,these formulae are enclosed between dollar signs4 ,the ,,html version includes the same formulae rendered in their original form4 ,,abstract ,this contribution gives the results of a statistical investigation of #djj extra-galactic nebulae for which ,holetschek has determined total visual magnitudes4 ,the list is complete for the brighter nebulae in the northern sky and is representative to #ab4e mag4 or fainter4 ,the classification employed is based on the forms of the photographic images4 ,about #c per cent are irregular1 but the remaining nebulae fall into a sequence of type forms characterized by rotational symmetry about dominating nuclei4 ,the sequence is composed of two sections1 the elliptical nebulae and the spirals1 which merge into each other4 ,luminosity relations4--,the distribution of magnitudes appears to be uniform throughout the sequence4 ,for each type or stage in the sequence1 the total magnitudes are related to the logarithms of the maximum diameters by the formula1 m,t ,c - #e log d1 where ,c varies progressively from type to type1 indicating a variation in diameter for a given magnitude or vice versa4 ,by applying corrections to ,c1 the nebulae can be reduced to a standard type and then a single formula expresses the relation for all nebulae from the ,magellanic ,clouds to the faintest that can be classified4 ,when the minor diameter is used1 the value of ,c is approximately constant throughout the entire sequence4 ,the coefficient of log d corresponds with the inverse-square law1 which suggests that the nebulae are all of the same order of absolute luminosity and that apparent magnitudes are measures of distance4 ,this hypothesis is supported by similar results for the nuclear magnitudes and the magnitudes of the brightest stars involved1 and by the small range in luminosities among nebulae whose distances are already known4 ,distances and absolute dimensions4--,the mean absolute visual magnitude1 as derived from the nebulae whose distances are known1 is -#ae4b4 ,the statistical expression for the distance in parsecs is then log ,d #d4jd #j4b m,t1 where m,t is the total apparent magnitude4 ,this leads to mean values for absolute dimensions at various stages in the sequence of types4 ,masses appear to be of the order of #b4fajh 4 ,distribution and density of space4--,to apparent magnitude about #af4g1 corresponding to an exposure of one hour on fast plates with the #fj-;inch reflector1 the numbers of nebulae to various limits of total magnitude vary directly with the volumes of space represented by the limits4 ,this indicates an approximately uniform density of space1 of the order of one nebula per #ajag cubic parsecs or #a4eaj-ca in ,c4,g4,s4 units4 ,the corresponding radius of curvature of the finite universe of general relativity is of the order of #b4gajaj parsecs1 or about #fjj times the distance at which normal nebulae can be detected with the #ajj-;inch reflector4 ,recent studies have emphasized the fundamental nature of the division between galactic and extra-galactic nebulae4 ,the relationship is not generic2 it is rather that of the part to the whole4 ,galactic nebulae are clouds of dust and gas mingled with the stars of a particular stellar system2 extra-galactic nebulae1 at least the most conspicuous of them1 are now recognized as systems complete in themselves1 and often incorporate clouds of galactic nebulosity as component parts of their organization4 ,definite evidence as to distances and dimensions is restricted to six systems1 including the ,magellanic ,clouds4 ,the similar nature of the countless fainter nebulae has been inferred from the general principle of the uniformity of nature4 ,the extra-galactic nebulae form a homogeneous group in which numbers increase rapidly with diminishing apparent size and luminosity4 ,four are visible to the naked eye2#b #da are found on the ,harvard 8,sky ,map02#c #gjj are on the ,franklin-,adams plates2#d #cjj1jjj are estimated to be within the limits of an hour's exposure with the #fj-;inch reflector4#e ,these data indicate a wide range in distance or in absolute dimensions4 ,the present paper1 to which is prefaced a general classification of nebulae1 discusses such observational material as we now possess in an attempt to determine the relative importance of these two factors1 distance and absolute dimensions1 in their bearing on the appearance of extra-galactic nebulae4 ,the classification of these nebulae is based on structure1 the individual members of a class differing only in apparent size and luminosity4 ,it is found that for the nebulae in each class these characteristics are related in a manner which closely approximates the operation of the inverse-square law on comparable objects4 ,the presumption is that dispersion in absolute dimensions is relatively unimportant1 and hence that in a statistical sense the apparent dimensions represent relative distances4 ,the relative distances can be reduced to absolute values with the aid of the nebulae whose distances are already known4 ,,part ,i4 ,,classification ,,of ,,nebulae ,,general ,,classification ,the classification used in the present investigation is essentially the detailed formulation of a preliminary classification published in a previous paper4#f ,it was developed in #aibc1 from a study of photographs of several thousand nebulae1 including practically all the brighter objects and a thoroughly representative collection of the fainter ones4#g ,it is based primarily on the structural forms of photographic images1 although the forms divide themselves naturally into two groups3 those found in or near the ,milky ,way and those in moderate or high galactic latitudes4 ,in so far as possible1 the system is independent of the orientation of the objects in space4 ,with minor changes in the original notation1 the complete classification is as follows1 although only the extra-galactic division is here discussed in detail3 ,,classification ,,of ,,nebulae ,i4 ,galactic nebulae3 ,symbol ,example ,a4 ,planetaries ,p ,n4,g4,c4 #gffb ,b4 ,diffuse ,d #a4 ,predominantly luminous ,,dl ,n4,g4,c4 #ffah #b4 ,predominantly obscure ,,do ,barnard #ib #c4 ,conspicuously mixed ,,dlo ,n4,g4,c4 #gjbc ,,ii4 ,extra-galactic nebulae3 ,a4 ,regular3 _/ ,n4,g4,c4 #ccgi ,e#j #a4 ,elliptical ,en _/ #bba ,e#b 7n #a1 #b1 4441 #g indicates the #dfba ,e#e ellipticity of the image #baag ,e#g without the decimal point7 #b4 ,spirals3 a7 ,normal spirals ,s 7#a7 ,early ,sa ,n4,g4,c4 #deid 7#b7 ,intermediate ,sb #bhda 7#c7 ,late ,sc #edeg b7 ,barred spirals ,,sb 7#a7 ,early ,s,ba ,n4,g4,c4 #bhei 7#b7 ,intermediate ,s,bb #ccea 7#c7 ,late ,s,bc #gdgi ,b4 ,irregular ,irr ,n4,g4,c4 #dddi ,extra-galactic nebulae too faint to be classified are designated by the symbol 8,q40 ,,regular ,,nebulae ,the characteristic feature of extra-galactic nebulae is rotational symmetry about dominating non-stellar nuclei4 ,about #ig per cent of these nebulae are regular in the sense that they show this feature conspicuously4 ,the regular nebulae fall into a progressive sequence ranging from globular masses of unresolved nebulosity to widely open spirals whose arms are swarming with stars4 ,the sequence comprises two sections1 elliptical nebulae and spirals1 which merge into each other4 ,although deliberate effort was made to find a descriptive classification which should be entirely independent of theoretical considerations1 the results are almost identical with the path of development derived by ,jeans#h from purely theoretical investigations4 ,the agreement is very suggestive in view of the wide field covered by the data1 and ,jeans's theory might have been used both to interpret the observations and to guide research4 ,it should be borne in mind1 however1 that the basis of the classification is descriptive and entirely independent of any theory4 ,elliptical nebulae4--,these give images ranging from circular through flattening ellipses to a limiting lenticular figure in which the ratio of the axes is about #a to #c or #d4 ,they show no evidence of resolution1#i and the only claim to structure is that the luminosity fades smoothly from bright nuclei to indefinite edges4 ,diameters are functions of the nuclear brightness and the exposure times4 ,illustration3 ,,plate ,,xii ,elliptical and ,irregular ,nebulae ,e#j ,,ngc #ccgi1 ,e#b ,,ngc #bba 7,m #cb71 ,e#e ,,ngc #dfba 7,m #ei71 ,e#g ,,ngc #caae1 ,,ngc #cjcd 7,m #hb71 ,,ngc #dddi ,the only criterion available for further classification appears to be the degree of elongation4 ,elliptical nebulae have accordingly been designated by the symbol 8,e10 followed by a single figure1 numerically equal to the ellipticity 7a - b7_/a with the decimal point omitted4 ,the complete series is ,e#j1 ,e#a1 4441 ,e#g1 the last representing a definite limiting figure which marks the junction with the spirals4 ,the frequency distribution of ellipticities shows more round or nearly round images than can be accounted for by the random orientation of disk-shaped objects alone4 ,it is presumed1 therefore1 that the images represent nebulae ranging from globular to lenticular1 oriented at random4 ,no simple method has yet been established for differentiating the actual from the projected figure of an individual object1 although refined investigation furnishes a criterion in the relation between nuclear brightness and maximum diameters4 ,for the present1 however1 it must be realized that any list of nebulae having a given apparent ellipticity will include a number of tilted objects having greater actual ellipticities4 ,the statistical average will be too low1 except for ,e#g1 and the error will increase with decreasing ellipticity4 ,normal spirals4--,all regular nebulae with ellipticities greater than about ,e#g are spirals1 and no spirals are known with ellipticities less than this limit4 ,at this point in the sequence1 however1 ellipticity becomes insensitive as a criterion and is replaced by conspicuous structural features which now become available for classification4 ,of these1 practically speaking1 there are three which fix the position of an object in the sequence of forms3 7#a7 relative size of the unresolved nuclear region2 7#b7 extent to which the arms are unwound2 7#c7 degree of resolution in the arms4 ,the form most nearly related to the elliptical nebulae has a large nuclear region similar to ,e#g1 around which are closely coiled arms of unresolved nebulosity4 ,then follow objects in which the arms appear to build up at the expense of the nuclear regions and unwind as they grow2 in the end1 the arms are wide open and the nuclei inconspicuous4 ,early in the series the arms begin to break up into condensations1 the resolution commencing in the outer regions and working inward until in the final stages it reaches the nucleus itself4 ,in the larger spirals where critical observations are possible1 these condensations are found to be actual stars and groups of stars4 ,the structural transition is so smooth and continuous that the selection of division points for further classification is rather arbitrary4 ,the ends of the series are unmistakable1 however1 and1 in a general way1 it is possible to differentiate a middle group4 ,these three groups are designated by the non-committal letters 8a10 8b10 and 8c0 attached to the spiral symbols 8,s10 and1 with reference to their position in the sequence1 are called 8early10 8intermediate10 and 8late0 types4#aj ,a more precise subdivision1 on a decimal scale for example1 is not justified in the present state of our knowledge4 ,in the early types1 the group ,sa1 most of the nebulosity is in the nuclear region and the arms are closely coiled and unresolved4 ,n4,g4,c4 #ccfh and #dbgd are among the latest of this group4 ,the intermediate group1 ,sb1 includes objects having relatively large nuclear regions and thin rather open arms1 as in ,m #ha1 or a smaller nuclear region with closely coiled arms1 as in ,m #id4 ,these two nebulae represent the lateral extension of the sequence in the intermediate section4 ,the extension along the sequence is approximately represented by ,n4,g4,c4 #dhbf1 among the earliest of the ,sb1 and ,n4,g4,c4 #ceef and #gcca1 which are among the latest4 ,the resolution in the arms is seldom conspicuous1 although in ,m #ca1 a typical ,sb1 it is very pronounced in the outer portions4 ,illustration3 ,,plate ,,xiii ,normal and ,barred ,spirals ,sa ,,ngc #deid1 ,s,ba ,,ngc #bhei1 ,sb ,,ngc #bhda1 ,s,bb ,,ngc #ehej1 ,sc ,,ngc #edeg 7,m #aja71 ,s,bc ,,ngc #gdgi ,the characteristics of the late types1 the group ,sc1 are more definite--an inconspicuous nucleus and highly resolved arms4 ,individual stars cannot be seen in the smaller nebulae of this group1 but knots are conspicuous1 which1 in larger objects1 are known to be groups and clusters of stars4 ,the extent to which the arms are opened varies from ,m #cc to ,m #aja1 both typical ,sc nebulae4 ,barred spirals4--,in the normal spiral the arms emerge from two opposite points on the periphery of the nuclear region4 ,there is1 however1 a smaller group1 containing about #bj per cent of all spirals1 in which a bar of nebulosity extends diametrically across the nucleus4 ,in these spirals1 the arms spring abruptly from the ends of this bar4 ,these nebulae also form a sequence1 which parallels that of the normal spirals1 the arms apparently unwind1 the nuclei dwindle1 the condensations form and work inward4 ,h4 ,d4 ,curtis#aa first called attention to these nebulae when he described several in the intermediate stages of the series and called them -type spirals4 ,the bar1 however1 never extends beyond the inner spiral arms1 and the structure1 especially in the early portion of the sequence1 is more accurately represented by the ,greek letter 4 ,from a dynamical point of view1 the distinction has considerable significance4 ,since ,greek letters are inconvenient for cataloguing purposes1 the ,english term1 8barred spiral10 is proposed1 which can be contracted to the symbol 8,,sb40 ,the ,,sb series1 like that of the normal spirals1 is divided into three roughly equal sections1 distinguished by the appended letters 8a10 8b10 and 8c40 ,the criteria on which the division is based are similar in general to those used in the classification of the normal spirals4 ,in the earliest forms1 ,s,ba1 the arms are not differentiated1 and the pattern is that of a circle crossed by a bar1 or1 as has been mentioned1 that of the ,greek letter 4 ,when the bar is oriented nearly in the line of sight1 it appears foreshortened as a bright and definite minor axis of the elongated nebular image4 ,such curious forms as the images of ,n4,g4,c4 #ajbc and #cchd are explained in this manner4 ,the latest group1 ,s,bc1 is represented by the ,s-shaped spirals such as ,n4,g4,c4 #gdgi4 ,,irregular ,,nebulae ,about #c per cent of the extra-galactic nebulae lack both dominating nuclei and rotational symmetry4 ,these form a distinct class which can be termed 8irregular40 ,the ,magellanic ,clouds are the most conspicuous examples1 and1 indeed1 are the nearest of all the extra-galactic nebulae4 ,n4,g4,c4 #fhbb1 a curiously faithful miniature of the ,clouds1 serves to bridge the gap between them and the smaller objects1 such as ,n4,g4,c4 #dbad and #dddi4 ,in these latter1 a few individual stars emerge from an unresolved background1 and occasional isolated spots give the emission spectrum characteristic of diffuse nebulosity in the galactic system1 in the ,clouds1 and in ,n4,g4,c4 #fhbbab ,these features are found in other irregular nebulae as well1 notably in ,n4,g4,c4 #aaef and #dfef1 and are just those to be expected in systems similar to the ,clouds but situated at increasingly greater distances4 ,the system outlined above is primarily for the formal classification of photographic images obtained with large reflectors and portrait lenses4 ,for each instrument1 however1 there is a limiting size and luminosity below which it is impossible to classify with any confidence4 ,except in rare instances1 these small nebulae are extra-galactic1 and their numbers1 brightness1 dimensions1 and distribution are amenable to statistical investigation4 ,for cataloguing purposes1 they require a designating symbol1 and the letter 8,q0 is suggested as convenient and not too widely used with other significations4 ,illustration3 ,,plate ,,xiv ,irregular ,nebula ,n4,g4,c4 #dbad ,direct photograph with #ajj-;inch reflector ,march #ah1 #aibe4 ,scale #a mm #c4c ,slitless spectrogram at primary focus of #ajj-;inch reflector1 ,march #ai1 #aibe ,,part ,,ii4 ,,statistical ,,study ,,of ,,extra-,,galactic ,,nebulae ,,the ,,data ,the most homogeneous list of nebulae for statistical study is that compiled by ,hardcastle#ac containing all nebulae found on the ,franklin-,adams charts4 ,these are uniform exposures of two hours on fast plates made with a ,cooke astrographic lens of #aj-;inch aperture and #de-;inch focal length4 ,the scale is #a mm #c4 ,the entire sky is covered1 but since the plates are centered about #ae apart and the definition decreases very appreciably with distance from the optical axis1 the material is not strictly homogeneous4 ,moreover1 the published list suffers from the usual errors attendant on routine cataloguing2 for instance1 four conspicuous ,messier nebulae1 ,m #fj1 ,m #hg1 ,m #id1 and ,m #aja1 are missing4 ,in general1 however1 the list is thoroughly representative down to about the thirteenth photographic magnitude and very few conspicuous objects are overlooked4 ,it plays the role of a standard with which other catalogues of the brighter nebulae may be compared for completeness1 and numbers in limited areas may be extended to the entire sky4 ,when known galactic nebulae1 clusters1 and the objects in the ,magellanic ,clouds are weeded out1 the remaining #gjj nebulae may be treated as extra-galactic4 ,very few can be classified from the ,franklin-,adams plates2 for this purpose photographs on a much larger scale are required4 ,until further data on the individual objects are available1 ,hardcastle's list can be used only for the study of distribution over the sky4 ,this shows the well-known features--the greater density in the northern galactic hemisphere1 the concentration in ,virgo1 and the restriction of the very large nebulae to the southern galactic hemisphere4 ,fortunately1 numerical data do exist in the form of total visual magnitudes for many of the nebulae in the northern sky4 ,these determinations were made by ,holetschek1#ad who attempted to observe all nebulae within reach of his #f-;inch refractor4 ,he later restricted his program2 but the final list is reasonably complete for the more conspicuous nebulae north of declination -#aj1 and is representative down to visual magnitude about #ab4e4 ,out of #dag extra-galactic nebulae in ,holetschek's list1 #djh are north of -#aj1 as compared with #djj in ,hardcastle's4 ,the two lists agree very well for the brighter objects1 but diverge more and more with decreasing luminosity4 ,at the twelfth magnitude about half of ,holetschek's nebulae are included by ,hardcastle4 ,since the two lists compare favorably in completeness over so large a region of the sky1 ,holetschek's may be chosen as the basis for a statistical study and advantage taken of the valuable numerical data on total luminosities4 ,hopmann#ae has revised the scale of magnitudes by photometric measures of the comparison stars used by ,holetschek4 ,new magnitudes were thus obtained for #he individual nebulae and from these were derived mean correction tables applicable to the entire list4 ,the revised magnitudes are used throughout the following discussion4 ,hopmann's corrections extend to about #ab4j mag41 and have been extrapolated on the assumption that they are constant for the fainter magnitudes4 ,the errors involved are unimportant in view of selective effects which must be present among the observed objects near the limit of visibility4 ,the nebulae were classified and their diameters measured from photographs of about #cjj of them taken with the #fj-;inch and #ajj-;inch reflectors at ,mount ,wilson4 ,most of the others are included in the great collection of nebular photographs at ,mount ,hamilton1 which have been described by ,curtis2#af and1 through the courtesy of the ,director of the ,lick ,observatory1 it has been possible to confirm the classification inferred from the published description by actual inspection of the original negatives4 ,types1 diameters1 and total visual magnitudes are thus available for some #djj of the nebulae in ,holetschek's list4 ,the few unclassified objects are all fainter than #ab4e mag4 ,the data are listed in ,tables ,i-,,iv1 in which the ,n4,g4,c4 numbers1 the total magnitudes1 and the logarithms of the maximum diameters in minutes of arc are given for each type separately4 ,a summary is given in ,table ,v1 in which the relative frequencies and the mean magnitudes of the various types will be found4 ,,relative ,,luminosities ,,of ,,the ,,various ,,types ,the frequency distribution of magnitudes for all types together and for the elliptical nebulae and the spirals separately is shown in ,table ,,vi and ,figure #a4 ,with the exception of the two outstanding spirals1 ,m #ca and ,m #cc1 the apparent luminosities are about uniformly distributed among the different types4 ,the relative numbers of the elliptical nebulae as compared with the spirals decrease somewhat with decreasing luminosity1 but this is very probably an effect of selection4 ,the elliptical nebulae are more compact than the spirals and become more stellar with decreasing luminosity4 ,for this reason some of the fainter nebulae are missed when small-scale instruments are used1 although the same luminosity spread over a larger area would still be easily detected4 ,the effect is very pronounced on photographic plates4 ,it accounts also for the slightly brighter mean magnitude of the elliptical nebulae as compared with the spirals in ,table ,v4 ,,table ,i ,elliptical ,nebulae ,n4,g4,c4 m,t log d ----------------------------- ,e#j 7#ag7 ----------------------------- #djd #aa4a #j4aa #dgd #ab4f - 4#dj #adjg #aj4i 4#ae #ccdh #aa4h - 4#ae #ccgi99 #i4d 4#cj #dbhc #ab4b - 4#eb #ddhf99 #i4g 4#cj #ddid99 #aj4a - 4#ae #deeb99 #i4i 4#bc #dehi #aa4d - 4#cj #dfdh #ab4c 4#eb #ejdd #aa4h 4#cj #ebaf #ac4c 4#gj #ebgc #ab4a 4#eb #eeeg #ab4c 4#dj #ehab #ab4j - 4#dj #ehdf #aj4i #j4j -------------------- ,mean #aa4dj -#j4bjd ------------------------------ ,e#a 7#ac7 ------------------------------ #dfg #ac4j -#j4gj #eif #aa4h 4#bb #adjj #aa4a 4#bb #bhhj #ab4j 4#eb #cbbf #ab4j 4#aj #cifb #aa4h - 4#cj #dbgh99 #aj4h 4#j #dcgd99 #i4i 4#jh #ddgb #h4h 4#cj #ddgh #aa4e - 4#aj #dfcf #aj4i 4#jh #ehac #ab4f - 4#cj #gfbf #ab4c -#j4cj ------------------------------ ,mean #aa4dc -#j4agg ------------------------------ ,e#b 7#ad7 ------------------------------ #bba99 #h4h #j4db #adec #aa4i - 4#aj #bfgb #ab4h - 4#dj #caic #ab4a #j4j #ceii #ab4j -#j4cj #cfjh #aa4f 4#bb #cfdj #aa4a - 4#je #dbfa #aa4a 4#bj #dbia #ab4c - 4#eb #dcgg #aa4i - 4#je #ddjf99 #aj4j 4#cj #ddgf #ab4h - 4#cj #dfdi99 #i4e 4#cj #eabg #ac4c -#j4eb ------------------------------ ,mean #aa4eb -#j4jhh ------------------------------ ,e#c 7#aj7 ------------------------------ #ajeb #aa4h -#j4ae #afjj #ab4g 4#ag #cbbb #ac4c - 4#ae #dcai #ab4h - 4#eb #dcfe #aa4d 4#jd #dchf #ab4c - 4#eb #ecbb99 #i4f 4#ae #eihb #aa4d 4#j #gefb #ab4h - 4#bb #gfai #aa4h - 4#ae ------------------------------ ,mean #aa4ii -#j4acc ------------------------------ ,e#d 7#ac7 ------------------------------ #ehd #aj4i #j4cj #agjj #ab4e - 4#aj #bigd #aa4h 4#ae #cfje #ab4e - 4#eb #cfaj #aa4h 4#ae #chid #ab4h - 4#je #dabe99 #aj4c 4#cj #dcgh #ab4a - 4#ae #dchb99 #aj4j 4#dh #deea #ab4h 4#jd #dgdb #ab4c 4#j #eegf #ab4c - 4#ae #gded #ac4c #j4j ------------------------------ ,mean #aa4ie -#j4jaa ------------------------------ ,e#e 7#f7 ------------------------------ #gbj #aj4i 4#aa #bfic #ab4c - 4#ae #ccgg #aj4i 4#ag #ddgc #aj4c 4#aa #dfba99 #aj4j 4#cj #dffj #aa4d #j4j ------------------------------ ,mean #aj4ig #j4jij ------------------------------ ,e#f 7#g7 ------------------------------ #hba #aa4h #j4j #bgfh #aj4g 4#ah #cfac #aa4h 4#be #dagi #aa4h 4#cd #ddce99 #aj4e 4#aa #dedf99 #aj4c 4#ah #dfig99 #i4f #j4dh ------------------------------ ,mean #aj4ic #j4bbj ------------------------------ ,e#g 7#e7 ------------------------------ #caae99 #i4e #j4fj #daaa #aj4a 4#ed #dbgj #ab4a 4#j #degj #aa4a 4#ch #ecjh #ab4c #j4bh ------------------------------ ,mean #aa4jb #j4cfj ------------------------------ ,peculiar 7#h7 ------------------------------ #ahe #ab4c #j4dh #bje99 #i4c 4#ij #ebd #aa4i 4#da #cfjg #i4i 4#aa #ciih #ab4a 4#bc #ddei #aa4c - 4#bb #edhe #ab4c 4#je #egci #ac4c -#j4dj ------------------------------ ,the various types are homogeneously distributed over the sky1 their spectra are similar1 and the radial velocities are of the same general order4 ,these facts1 together with the equality of the mean magnitudes and the uniform frequency distribution of magnitudes1 are consistent with the hypothesis that the distances and absolute luminosities as well are of the same order for the different types4 ,this is an assumption of considerable importance1 but unfortunately it cannot yet be subjected to positive and definite tests4 ,none of the individual similarities necessarily implies the adopted interpretation1 but the totality of them1 together with the intimate series relations among the types1 which will be discussed later1 suggests it as the most reasonable working hypothesis1 at least until inconsistencies should appear4 ,,table ,,ii ,barred ,spirals ,n4,g4,c4 m,t log d ------------------------------ ,s,ba 7#bf7 ------------------------------ #icf #aa4a #j4dh #ajbc99 #aj4b 4#gh #bgcb #ab4c 4#aa #bgha #ab4c 4#aa #bghg #aa4d 4#cf #bhei #aa4a 4#bh #biej #aa4f 4#ae #cchd99 #aj4g 4#dh #cdab99 #aa4b 4#dj #cdah #ac4a 4#j #cdeh #ab4h - 4#bb #cide #aa4e 4#bj #djbf #aa4a 4#dh #dbjc #aa4a 4#cf #dcdf #ab4j 4#bj #dcga #ab4j 4#ah #ddba #ab4h 4#ag #dddb #aj4i 4#ej #ddgg #aj4i 4#dj #deif #ab4j 4#be #dfdc #aa4a 4#bf #dged #aj4i 4#dh #edgc #ab4j 4#jh #eegd #ac4j - 4#je #efhi #ab4j 4#cj #egja #ab4c #j4ag -------------------- ,mean #aa4ff #j4bfg ------------------------------ ,s,bb 7#af7 ------------------------------ #ajbb #aa4h #j4jd #bfej #ab4h 4#j #ccea99 #aa4d 4#dh #cdjj #ab4e - 4#aj #cdad #aa4e 4#bf #cejd #aa4d 4#cj #cgah #aa4h #j4dh #dajb #ab4j #j4cf #dbde #aa4a 4#ae #dcid #aa4e 4#fj #dedh #aa4a 4#fj #dfii99 #aj4j 4#eg #dgbe99 #i4b 4#gj #ebah #ab4h 4#be #eeff #aa4a 4#bj #ggbc #aa4h #j4ah -------------------- ,mean #aa4dh #j4cag ------------------------------ ,s,bc 7#ae7 ------------------------------ #fac #aj4f #j4fj #ggi #ab4a 4#dh #cbjf #ac4c 4#de #ccdd #aa4d 4#fj #ccdf #ab4c 4#dj #cfbe #ac4c 4#j #cfhf #ab4j 4#cj #cgfi #ab4h 4#dc #ciec #aa4a 4#gd #ciib #aa4e 4#he #dcjc99 #aj4f 4#gh #degi99 #i4g 4#de #echc #ab4f 4#dj #eiba #ab4h 4#gj #gdgi #ab4a #j4dh -------------------- ,mean #aa4hg #j4eji ------------------------------ ,peculiar 7#b7 ------------------------------ #bghb #ab4c #j4bf #dcad #aa4a #j4cd ------------------------------ ,,table ,,iii ,normal ,spirals ,n4,g4,c4 m,t log d ------------------------------ ,sa 7#di7 ------------------------------ #dhh #aa4h #j4dh #fgf #ac4c 4#cj #accb #aj4i 4#dc #bfee #aa4a 4#fj #bfha #aj4g 4#dh #bgge #aj4i 4#cb #bhaa #ab4c 4#bh #bhee #ab4h 4#aa #cafi #ab4c 4#fj #cbde #aa4h 4#cj #ccja #ab4d 4#ae #ccfh99 #aj4j 4#he #ceaf #ab4a 4#bj #cfai #ab4c 4#j #cfbf99 #aa4c 4#bh #cffe #ab4j 4#j #cfhb #ab4a 4#jh #chih #ab4j 4#dc #cida #aj4c 4#cj #djcf #aj4i 4#fj #dach #ab4a 4#bj #dadc #aa4c 4#aa #daej #ab4j 4#aa #dbea #aj4d 4#bf #dbfh #ab4h 4#j #dbgd #aa4a #j4ed #dbha #aa4e #j4ah #ddbi #aa4e 4#dh #ddeb #ab4f 4#ae #debf #aa4a 4#gj #deej #ab4a 4#dc #degj #aa4a 4#ch #deid #i4a 4#he #dffe #aa4h 4#jh #dfhd #ab4b - 4#bb #dfih #aa4i 4#dc #dgaj #aa4h 4#ed #dgfb #aa4e 4#eg #dhff #ab4j 4#ej #dieh #aa4d 4#fj #ecgg #aa4h 4#dh #echi #ab4e 4#be #edbb #ab4a 4#dj #efca #ab4j - 4#je #ehff99 #aa4g 4#dh #gjac #ab4h 4#jh #gdeg #ab4h 4#cj #ggbg #aa4c 4#dc #ghad99 #aa4d #j4dh -------------------- ,mean #aa4fi #j4ccc ------------------------------ ,sb 7#gj7 ------------------------------ #bbd #e4j #b4be #fgb #ab4h #j4ed #ggb #aa4a 4#gj #idi #ac4c 4#j #iee #ab4i 4#dj #ajfh #i4a 4#dj #acji #ab4j 4#ae #bfci #ab4b 4#j #bgae #ab4e 4#dj #bgdh #ab4j 4#cb #bhda99 #i4d 4#gh #bihe #aa4d #j4dh #cjca99 #h4c #a4bj #cahb #ab4i -#j4bb #caij #aa4i 4#dh #cbbg #ab4j 4#dh #cbgg #ab4f 4#j #ccaj #aj4d 4#ah #cchj #ab4a - 4#je #cdhi99 #aa4b #j4dj #ceef #aa4a #j4ij #ceic #aa4i 4#fj #cfbc99 #i4i 4#ij #cfbg99 #i4a #j4ij #cfbh #aa4d #a4jh #cfcb #ac4c -#j4aj #cfge #aa4d 4#dh #cfha #ac4j 4#j #cfhd #ac4j 4#jh #chie #ac4c - 4#je #cijj #ab4a 4#be #cich #ab4a 4#fe #djbj #ab4c 4#ag #djcj #aa4a 4#cj #djea99 #aa4i 4#fj #djhe #ab4e 4#cf #daea #ab4j 4#dj #daib #aj4i 4#ij #dbaf99 #aj4h #j4he #dbdd #ab4c #a4aa #dbeh99 #h4g #a4cj #dbgc #aa4h #j4bj #ddch99 #aj4c 4#ed #dddh #aa4h 4#dh #ddej #aj4f 4#eg #ddea #ab4h - 4#ae #dejj #ab4h #j4ag #defe99 #aa4j #a4ag #dgcf99 #h4d #j4gj #dgej #aa4h 4#bf #dhjj #aa4h 4#jd #dhad #ab4g 4#ef #dhbf #i4j 4#ij #ejee99 #i4f 4#ij #ecgf #ab4h 4#ag #ecgi #ab4i -#j4je #ecid #ac4c #j4ag #efcc #ac4j - 4#aj #egac #ab4c 4#cb #egdj #ab4c 4#dh #egdf #aj4d 4#hg #egej #ab4h 4#ae #eggb #ab4j 4#be #ehjf #ab4c 4#cj #eihe #ab4j 4#fj #fbjg #aa4h 4#cj #ffdc #aa4i 4#dh #gcca99 #aj4d 4#ie #geda #ab4g 4#da #gfjf #ab4j #j4gh -------------------- ,mean #aa4ee #j4dga ------------------------------ ,sc 7#aae7 ------------------------------ #aeg #aa4d #j4dj #bec #i4c #a4cd #bgh #ab4j #j4jh #dgj #ac4a #j4bj #eih #g4j #a4gh #fae #ab4c #j4dc #fbh99 #aj4f 4#ij #ijh #aa4i 4#fj #ajhd #aa4d 4#cd #ajhg #ab4a 4#cf #afcg #ab4f 4#dh #bcci #ac4a #j4bh #bdjc99 #h4g #a4bj #becb #ac4c #j4ag #bfhc #i4i #a4jj #bgab #ab4c #j4bj #bgdb #aa4h 4#dj #bggf #ab4c #j4cd #bijc99 #i4a #a4jd #bifd #aa4f 4#dj #bigf #ab4j 4#ej #cjjc #ac4c 4#gh #cjba #ab4c 4#aa #cjgi #ab4j 4#ij #cadg #aa4d 4#cj #caff #ab4j 4#j #cahd #ab4g 4#gh #caih #ac4j 4#ie #cbed #ab4h 4#fj #cbid #ab4j 4#dh #cchi #ac4a #j4cj #ccie #ab4f #j4aa #ccif #ac4c - 4#aj #cdcj #ab4f 4#di #cdcb #ab4j 4#gi #cdcg #ab4d 4#bh #cdde #ac4a 4#jh #cddh #ab4c 4#bf #cdhf #aa4h 4#eh #cdhh #ab4h 4#be #ceab #ab4c 4#j #ceba99 #aj4a 4#fe #cedi #ac4c 4#dc #ceif #ac4c 4#fj #cfca #aa4h 4#ff #cfdb #ab4j 4#gc #cfee #aa4i 4#jd #cfff #aa4h 4#ed #cfgb #ac4j 4#ed #cfhc #ab4j 4#ae #cghj #ac4j 4#dj #chaj #aa4c 4#fb #chac #ab4c 4#cb #chgg #aa4h 4#fd #chhg #ab4c 4#dj #chic #aa4h 4#fa #cidi #aa4h 4#cd #cihb #ab4a 4#cf #djac #ac4c 4#fj #djda #aa4d 4#cj #djfb #ab4f 4#dh #djhh #aa4e #j4gb #djif #ab4c #j4gh #dajj #ab4c 4#fj #dade #ab4c 4#gj #daeg #ab4c 4#gg #dbab #ab4c 4#cj #dbbj #ab4a #j4dj #dbcf #ab4h #a4jd #dbed #aj4d #j4fe #dcba99 #aj4e 4#gj #ddad #aj4a 4#dh #ddai #aa4h 4#cf #ddfj #ab4a 4#bj #ddij99 #aj4b 4#fj #deja99 #aj4e 4#gj #dejd #ab4a #j4dh #deag #ab4e #a4jj #decf #ab4c #j4he #deei #aj4g 4#ij #defi99 #aj4i 4#fe #dehj #ab4c 4#ae #dfje #i4i #j4dh #dfca99 #i4e #a4jh #dfcb #ac4a #j4ej #dfff #ab4j 4#fj #dgac #ab4c 4#ch #dgha #aa4h 4#dh #dgic #ab4d 4#bj #dhjh #ab4f #j4cd #diie #aa4h #j4cf #ejje99 #aa4a 4#gj #ejab #aa4i 4#dc #ejcc99 #aa4h #j4gh #eaid99 #g4d #a4jh #ebjd #ab4h #j4ei #ebcf #aj4d #a4jj #ebdg #ac4c #j4gj #ebdh #aa4e 4#ej #ebij #ab4e 4#dh #ebig #ab4f 4#fj #ecfd #ac4c 4#fj #ecie #ab4h #j4cj #edeg #i4i #a4cd #edgd #ab4j #j4fj #eehe #ab4c 4#fj #efgf #aa4h 4#dh #efgh #aa4h 4#da #ehcb #ac4a #j4ef #eijg #aa4i #a4jd #faha #ab4e #j4cj #fbag #ab4a 4#be #fejc #i4i 4#gj #gddh #aa4h 4#cj #gfga #ac4c - 4#ae -------------------- ,mean #aa4ge #j4ecg ------------------------------ ,peculiar ,spirals 7,unclassified7 ------------------------------ #igb #ac4c #j4ag #becg #ac4c 4#j #dijj #aa4h #j4bc ------------------------------ ,,relation ,,between ,,luminosities ,,and ,,diameters ,among the nebulae of each separate type are found linear correlations between total magnitudes and logarithms of diameters4 ,these are shown in ,figures #b-e for the beginning1 middle1 and end of the sequence of types and also for the irregular nebulae4 ,in ,figures #b and #c adjacent types have been grouped in order to increase the material1 and in ,figure #e the ,magellanic ,clouds have been added to increase the range4 ,the correlations can be expressed in the form m,t ,c - ,k log d1 7#a7 where ,k is constant from type to type1 but ,c varies progressively throughout the sequence4 ,the value of ,k cannot be accurately determined from the scattered data for any particular type1 but1 within the limits of uncertainty1 it approximates the round number #e4j1 the value which is represented by the lines in ,figures #b-e4 ,when ,k is known1 the value of ,c can be computed from the mean magnitude and the logarithm of the diameter for each type4 ,this amounts to reading from the curves the magnitudes corresponding to a diameter of one minute of arc1 but avoids the uncertainty of establishing the curves where the data are limited4 ,,table ,,iv ,irregular ,nebulae ,n4,g4,c4 m,t log d ------------------------------ #bifh #ab4f #j4jh #cjcd99 #i4j 4#he #cjgg #aa4d 4#dh #cgbi #aa4h 4#ag #dbad99 #aa4c 4#ij #dddi99 #i4e 4#fe #dfah #ab4c #j4dj #dfef #aa4e #a4cj #dgec #aa4d #j4dc #eadd #ab4h - 4#cj #ecfc #aa4a #j4bj ------------------------------ ,mean #aa4cd #j4dfi ------------------------------ ,,notes ,,to ,,tables ,i-,,iv 99 ,magnitude from ,hopmann4 ,n4,g4,c4 #ebd and #ciih are late elliptical nebulae in which the equatorial planes are perpendicular to the line of sight4 ,they might be included with the ,e#f or ,e#g nebulae4 ,absorption very conspicuous4 ,n4,g4,c4 #cfjg1 #ddei1 and #edhe appear to be elliptical nebulae with narrow bands of absorption between the nuclei and the peripheries4 ,the progressive change in the value of ,c throughout the sequence may be expressed as a variation either in the magnitude for a given diameter or in the diameter for a given magnitude4 ,both effects are listed in ,table ,,vii and are illustrated in ,figure #f1 in which magnitudes and diameters thus found are plotted against types4 ,with the exception of the later elliptical nebulae1 for which the data are wholly inadequate for reliable determinations1 the points fall on smooth curves4 ,in the region of the earlier elliptical nebulae1 the curves should be somewhat steeper in order to allow for objects of greater ellipticities which are probably included4 ,,reduction ,,of ,,nebulae ,,to ,a ,,standard ,,type ,the slope1 ,k1 in the formula relating magnitudes with diameters1 appears to be closely similar for the various types1 but accurate determinations are restricted by the limited and scattered nature of the data for each type separately4 ,with a knowledge of the parameter ,c1 however1 it is possible to reduce all the material to a standard type and hence to determine the value of ,k from the totality of the data4 ,the mean of ,e#g1 ,s,ba1 and ,sa was chosen for the purpose1 as representing a hypothetical transition-point between the elliptical nebulae and the spirals1 and was designated by the symbol 8,s#j40 ,the corresponding value of ,c1 in round numbers1 is #ac4j4 ,corrections were applied to the logarithms of the diameters of the nebulae of each observed class1 amounting to ,delta log d #j4b 7#ac4j - ,c7 where ,c is the observed value for a particular class4#ag ,when the values of ,c are read from the smooth curve in ,figure #f1 these corrections are as shown in ,table ,,viii4 ,,table ,v ,frequency ,distribution of ,types ,type ,number ,percentage ,mean ,mag4 ---------------------------------------- ---- ,elliptical ,nebulae ---------------------------------------- ---- ,e#j #ag #ah #aa4dj #a #ac #ad #aa4dc #b #ad #ae #aa4eb #c #aj #aa #aa4ii #d #ac #ad #aa4ie #e #f #f #aj4ig #f #g #h #aj4ic #g #e #e #aa4jb ,pec #h #i #aa4ee ----------------------------------- ,total #ic #bc99 #aa4ec ---------------------------------------- ---- ,normal ,spirals ---------------------------------------- ---- ,sa #di #ba #aa4fi b #gj #bi #aa4ee c #aae #di #aa4ge ,pec #c #a #ab4hj ----------------------------------- ,total #bcg #ei99 #aa4fh ---------------------------------------- ---- ,barred ,spirals ---------------------------------------- ---- ,s,ba #bf #dd #aa4ff b #af #bg #aa4dh c #ae #bf #aa4hg ,pec4 #b #c #aa4gj ----------------------------------- ,total #ei #ae99 #aa4ff ---------------------------------------- ---- ,irregular ,nebulae ---------------------------------------- ---- #aa #c99 #aa4cd ---------------------------------------- ---- ,totals ---------------------------------------- ---- ,all types #djj #ajj #aa4fc ---------------------------------------- ---- 99 ,percentages of #djj1 the total number of nebulae investigated4 ,the percentages of the subtypes refer to the number of nebulae in the particular type4 ,,table ,,vi ,frequency ,distribution of ,magnitudes ,numbers of ,nebulae ,magnitude ,interval ------------------------ ,e ,s ,all ---------------------------------------- ---- #h4a- #h4e #j #b #b #h4f- #i4j #b #d #g #i4a- #i4e #d #f #aa #i4f-aj4j #g #g #ai #aj4a-aj4e #g #ac #bj #aj4f-aa4j #h #ad #cb #aa4a-aa4e #i #bd #di #aa4f-ab4j #ba #eg #hh #ab4a-ab4e #bj #eb #hf #ab4f-ac4j #aj #cc #ea ---------------------------------------- ---- ,the corrected values of log d were then plotted against the observed magnitudes4 ,this amounts to shifting the approximately parallel correlation curves for the separate types along the axis of log d until they coincide4 ,since the mean magnitudes of the various types are nearly constant1 the relative shifts will very nearly equal the differences in the mean observed log d1 and hence the effect of errors in the first approximation to the values of ,k will be negligible4 ,illustration3 ,fig4 #a4--;,frequency distribution of apparent magnitudes among nebulae in ,holetschek's list4 ,illustration3,fig4 #b4--,relation between luminosity and diameter among nebulae at the beginning of the sequence of types--,e#j and ,e#a nebulae4 ,the plot is shown in ,figure #g1 in which the two ,magellanic ,clouds have been included in order to strengthen the bright end of the curve which would otherwise be unduly influenced by the single object1 ,m #ca4 ,the magnitudes #j4e and #a4e1 which were assigned to the ,clouds1 are estimates based upon published descriptions4 ,illustration3 ,fig4 #c4--,relation between luminosity and diameter among nebulae at the middle of the sequence of types--,e#g1 ,sa1 and ,s,ba nebulae4 ,illustration3 ,fig4 #d4--,relation between luminosity and diameter among nebulae at the end of the sequence of types--,sc and ,s,bc nebulae4 ,the correlation of the data is very closely represented by the formula m,t #ac4j - #e log d4 7#b7 ,this falls between the two regression curves derived from least-square solutions and could be obtained exactly by assigning appropriate weights to the two methods of grouping4 ,the nature of the data is such that a closer agreement can scarcely be expected4 ,no correction to the assumed value of the slope appears to be required4 ,the material extends over a range of #ab mag41 and the few cases which have been investigated indicate that the correlation can be extended another #c mag41 to the limit at which nebulae can be classified with certainty on photographs made with the #ajj-;inch reflector4 ,the relation may therefore be considered to hold throughout the entire range of observations4 ,illustration3,fig4 #e4--,relation between luminosity and diameter among the irregular nebulae4 ,the ,magellanic ,clouds are included4 ,n4,g4,c4 #dfef is an exceptional case in that it shows a narrow1 greatly elongated image in which absorption effects are very conspicuous2 hence the maximum diameter is exceptionally large for its apparent luminosity4 ,the residuals without regard to sign average #j4hg mag41 and there appears to be no systematic effect due either to type or luminosity4 ,the scatter1 however1 is much greater for the spirals1 especially in the later types1 than for the elliptical nebulae4 ,the limiting cases are explained by peculiar structural features4 ,the nebulae which fall well above the line usually have bright stellar nuclei1 and those which fall lowest are spirals seen edge-on in which belts of absorption are conspicuous4 ,,table ,,vii ,type m,t log d ,c99 d ---------------------------------------- --- ,e#j #aa4dj -#j4bjd #aj4ch #a4b #a #aa4dc 4#agg #aj4ed #a4c #b #aa4eb 4#jhh #aa4jh #a4f #c #aa4ii 4#acc #aa4cc #a4h #d #aa4ie - 4#jaa #aa4ij #b4d #e #aj4ig 4#jij #aa4db #a4i #f #aj4ic 4#bbj #ab4jc #b4e #g #aa4jb 4#cfj #ab4hb #c4g ,sa #aa4fi 4#ccc #ac4ce #d4g b #aa4ee 4#dga #ac4ij #f4j c #aa4gd 4#edj #ad4dd #g4g ,s,ba #aa4ff 4#bfg #ac4jj #d4j b #aa4dh 4#cag #ac4af #d4c c #aa4hg 4#eji #ad4da #g4f ,irr #aa4cd #j4dfi #ac4fh #e4d ------- --------------------------------- 99 ,c overlinem,t #e overlinelog d4 log d #j4b 7,c -- m,t72 m,t #aj4j4 ,,effects ,,of ,,orientation ,the effect of the orientation is appreciable among the spirals in general4 ,in order to illustrate this feature1 they have been divided into three groups consisting of those whose images are round or nearly round1 elliptical1 and edge-on1 or nearly so4 ,the mean values of m,t #e log d were then computed and compared with the theoretical value1 #ac4j4 ,the residuals are negative when the nebulae are too bright for their diameters and positive when they are too faint4 ,the results are given in ,table ,,ix1 where mean residuals are followed by the numbers of nebulae1 in parentheses1 which are represented by the means4 ,the numbers of the barred spirals are too limited to inspire confidence in the results1 but among the normal spirals there is conclusive evidence that the highly tilted and edge-on nebulae are fainter for a given diameter than those seen in the round4 ,a study of the individual images indicates that the effect is due very largely to dark absorption clouds1 which become more conspicuous when the nebulae are highly tilted4 ,these clouds are generally1 but not universally1 peripheral features4 ,an extensive investigation will be necessary before any residual effect due to absorption by luminous nebulosity can be established with certainty4 ,even should such exist1 it clearly cannot be excessive4 ,illustration3 ,fig4 #f4--,progressive characteristics in the sequence of types4 ,the upper curve represents the progression in total magnitude with type for nebulae having maximum diameters of one minute of arc4 ,the elliptical nebulae and the normal spirals are included as representing the normal sequence1 but the barred spirals and the irregular nebulae are omitted4 ,the figures give the number of objects observed in each type4 ,among the later elliptical nebulae the numbers are so small that means of adjacent types have been plotted4 ,the lower curve represents the progression in diameter along the normal sequence for nebulae of the tenth magnitude4 ,,table ,,viii ,type ,c log d -------------------------- ,e#j #aj4cj #j4ed #a #aj4fe 4#dg #b #aa4jj 4#dj #c #aa4ce 4#cc #d #aa4gj 4#bf #e #ab4je 4#ai #f #ab4dj 4#ab #g #ab4ge #j4je ,sa #ac4ca -#j4jf ,sb #ac4ij 4#ah ,sc #ad4de 4#bi ,s,ba #ac4jj 4#jj ,s,bb #ac4af 4#jc ,s,bc #ad4da 4#bh ,irr #ac4fh -#j4ad ------------------------- ,illustration3 ,fig4 #g4--,relation between luminosity and diameter among extra-galactic nebulae4 ,the nebulae have been reduced to a standard type1 ,s#j1 which1 being the mean of ,e#g1 ,sa1 and ,s,ba1 represents a hypothetical transition point between elliptical nebulae and spirals4 ,the ,magellanic ,clouds have been included in order to strengthen the brighter end of the plot4 ,,significance ,,of ,,the ,,luminosity ,,relation ,the correlations thus far derived are between total luminosities and maximum diameters4 ,in the most general sense1 therefore1 they express laws of mean surface brightness4 ,the value1 ,k #e4j1 in formula 7#a7 indicates that the surface brightness is constant for each separate type4 ,the variations in ,c indicate a progressive diminution in the surface brightness from class to class throughout the entire sequence4 ,the consistency of the results amply justifies the sequence as a basis of classification1 since a progression in physical dimensions is indicated1 which accompanies the progression in structural form4 ,although the correlations do not necessarily establish any generic relation among the observed classes1 they support in a very evident manner the hypothesis that the various stages in the sequence represent different phases of a single fundamental type of astronomical body4 ,moreover1 the quantitative variation in ,c is consistent with this interpretation1 as is apparent from the following considerations4 ,,table ,,ix ,residuals in m,t #e log d as a ,function of ,orientation ,type ,round ,elliptical ,edge-,on ---------------------------------------- --------------- ,sa -#j4jb 7#ac7 -#j4bg 7#ac7 #j4eg 7#bc7 ,sb 4#gg 7#bd7 4#j 7#ce7 #a4ga 7#aa7 ,sc -#j4jh 7#ce7 -#j4ac 7#eg7 #j4ff 7#bb7 ,all ,s -#j4bf 7#gb7 -#j4aa 7#aje7 #j4hc 7#ef7 ,s,ba #j4j 7#aj7 -#j4cj 7#g7 #j4ca 7#h7 ,s,bb - 4#af 7#aj7 4#jg 7#f7 ,s,bc #j4ai 7#i7 -#j4ej 7#d7 #j4cb 7#b7 ,all ,,sb #j4ja 7#bi7 -#j4ba 7#ag7 #j4ca 7#aj7 ,all spirals -#j4bb 7#aja7 -#j4ac 7#abb7 #j4gc 7#ff7 ---------------------------------------- --------------- ,among the elliptical nebulae it is observed that the nuclei are sharp and distinct and that the color distribution is uniform over the images4 ,this indicates that there is no appreciable absorption1 either general or selective1 and hence that the luminosity of the projected image represents the total luminosity of the nebula1 regardless of the orientation4 ,if the observed classes were pure1 that is1 if the apparent ellipticities were the actual ellipticities1 formula 7#a7 could be written ,ce m,t #e log b - #e log 7#a - e71 7#c7 where b is the minor diameter in minutes of arc and e is the ellipticity4 ,the term m,t #e log b is observed to be constant for a given type4 ,if it were constant for all elliptical nebulae1 then the term ,ce #e log 7#a - e7 would be constant also4 ,on this assumption1 ,ce #e log 7#a - e7 ,c#j1 where ,c#j is the value of ,c for the pure class ,e#j4 ,hence ,ce - ,c#j -#e log 7#a - e71 7#d7 a relation which can be tested by the observations4 ,an analysis of the material indicates that this is actually the case1 and hence that among the elliptical nebulae in general1 the minor diameter determines the total luminosity1 at least to a first approximation4#ah ,the observed values of ,c vary with the class1 as is seen in ,table ,,vii and ,figure #f1 but1 excepting that for ,e#g1 they are too large because of the mixture of later types of nebulae among those of a given observed class4 ,it is possible1 however1 to calculate the values of ,ce - ,c#j for the pure classes and then to make approximate corrections for the observed mixtures on the assumption that the nebulae of any given actual ellipticity are oriented at random4 ,in this manner1 mean theoretical values can be compared with the observed values4 ,the comparisons are shown in ,table ,,xii in the form ,c#g - ,ce1 because ,e#g is the only observed class that can be considered as pure4 ,the significance of the table will be discussed later4 ,the following method has been used to determine the relative frequencies with which nebulae of a given actual ellipticity1 oriented at random1 will be observed as having various apparent ellipticities4 ,in ,figure #h1 let the co-ordinate axes ,,ox and ,,oy coincide with the major and minor axes1 a and b1 of a meridian section of an ellipsoid of revolution4 ,let ,,oo be the line of sight to the observer1 making an angle i with ,,ox1 and let ,,or be perpendicular to ,,oo4 ,let ,,pp be a tangent to the ellipse1 parallel to and at a distance from ,,oo4 ,let x#j and y#j be the intercepts of the tangent on the ,x- and ,y-axis1 respectively4 ,the apparent ellipticity is determined by bx1 which1 for various values of the angle i1 ranges from b to a4 ,the problem is to determine the relative areas on the surface of a sphere whose center is ,o1 within which the radius ,,oy must pass in order that the values of b#a1 and hence of the apparent ellipticity1 e#a may fall within certain designated limits4 ,this requires that the angle i be expressed in terms of b#a4 ,illustration3 ,fig4 #h ,from the equation of the tangent1 ,,pp1 y -x tani sqrta#b tan#b;i b#b y#j sqrta#b tan#b;i b#b ,since b#a y#j cos7i7 b#ab a#b sin#b;i b#b cos#b;i4 ,let a #a1 then cos#b;i frac#a - b#aba - b#b1 where b#a #a - e#a12;b i - e4 ,from these equations1 the values of i can be determined for all possible values of e#a4 ,the limits for the observed classes ,e#j to ,e#g were chosen midway between the consecutive tenths1 ,e#j ranging from e #j to e #j4je2 ,e#a1 from e #j4je to e #j4ae2 ,e#g1 from e #j4fe to e #j4ge4 ,the relative frequencies of the various observed classes are then proportional to the differences in sin i corresponding to the two limiting values of e#a4 ,these frequencies must be calculated separately for nebulae of different actual ellipticities4 ,the results are given in ,table ,x1 where the actual ellipticities1 listed in the first column1 are followed across the table by the percentages which1 on the assumption of random orientation1 will be observed as having the various apparent ellipticities4 ,the bottom row will be seen to show the percentages of apparent ellipticities observed in an assembly of nebulae in which the numbers for each actual ellipticity are equal and all are oriented at random4 ,,table ,x ,actual ,apparent --------------------------------------- ,e#j ,e#a ,e#b ,e#c ,e#d ---------------------------------------- ------- ,e#g #j4jee #j4aaa #j4aad #j4aaf #j4aba ,e#f 4#jei 4#abc 4#abf 4#acc 4#adh ,e#e 4#jfg 4#adj 4#adh 4#aff 4#baf ,e#d 4#jgi 4#afi 4#aij 4#bej #j4cab ,e#c 4#ajj 4#bbe 4#bii #j4cgf ,e#b 4#ade 4#cgh #j4dgg ,e#a #j4cjj #j4gjj ,e#j #a4jjj --------------------------------------- ,total #a4hje #a4hdf #a4ced #a4jda #j4gig #j4bbf #j4bca #j4afi #j4acj #j4ajj ---------------------------------------- ------- ,actual ,apparent ---------------------------------------- -- ,e#e ,e#f ,e#g ,total ---------------------------------------- -- ,e#g #j4acb #j4afd #j4ahg #a4jjj ,e#f 4#ahg #j4bbd ,e#e #j4bfc ---------------------------------- ,total #j4ehb #j4chh #j4ahg #h4jjj #j4jgc #j4jdi #j4jbc #a4jjj ---------------------------------------- -- ,from this table and the actual numbers in the observed classes as read from a smoothed curve1 the numbers of each actual ellipticity mingled in the observed classes can be determined4 ,for instance1 the four nebulae observed as ,e#g represent #j4ahg of the total number of actual ,e#g4 ,the others are distributed among the observed classes ,e#j to ,e#f according to the percentages listed in ,table ,x4 ,six nebulae are observed as ,e#f1 but #c4f of these are actually ,e#g4 ,the remaining #b4d actual ,e#f nebulae represent #j4bbd of the total number of that actual ellipticity1 the others1 as before1 being scattered among the observed classes ,e#j to ,e#e4 ,table ,,xi gives the complete analysis and is similar to ,table ,x except that the percentages in the latter are replaced by the actual numbers indicated by the observations4 ,finally1 the mean values of ,c#g - ,ce are calculated from the numbers of nebulae in the various columns of ,table ,,xi together with the values of ,c#g - ,ce for the pure classes as derived from formula 7#d74 ,the results are listed in the fourth column of ,table ,,xii following those for the pure and the observed classes4 ,in determining the observed values1 ,n4,g4,c4 #ebd and #ciih are included as ,e#j and ,e#a1 although in ,table ,i they are listed as peculiar1 because they are obviously much flattened nebulae whose minor axes are close to the line of sight4 ,,table ,,xi ,apparent ,actual ------------------------------------- ,e#j ,e#a ,e#b ,e#c ,e#d ---------------------------------------- --------- ,e#g #a4b #b4d #b4e #b4e #b4f ,e#f 4#f #a4c #a4d #a4e #a4f ,e#e 4#h #a4g #a4h #b4j #b4g ,e#d 4#h #a4g #a4i #b4e #c4a ,e#c #j4i #b4a #b4h #c4e ,e#b #a4a #b4i #c4f ,e#a #a4g #c4i ,e#j #i4i ---------------------------------------- --------- ,total99 #ag4j #af4j #ad4j #ab4j #aj4j ---------------------------------------- --------- ,apparent ,actual ------------------------------- ,e#e ,e#f ,e#g ,total ---------------------------------------- ,e#g #b4i #c4f #d4j #ba4g ,e#f #b4j #b4d #aj4h ,e#e #c4a #ab4a ,e#d #aj4j ,e#c #i4c ,e#b #g4f ,e#a #e4f ,e#j #i4i ---------------------------------------- ,total99 #h4j #f4j #d4j #hg4j ---------------------------------------- 99 ,the totals represent the numbers in the observed classes as read from a smooth curve4 ,the observed values in general fall between those for the pure classes and those corresponding to random orientation4 ,they are of the same order as the latter1 and the discrepancies are perhaps not unaccountably large in view of the nature and the limited extent of the material4 ,there is a systematic difference1 however1 averaging about #j4b mag41 in the sense that the observed values are too large1 and increasing with decreasing ellipticity4 ,one explanation is that the observed classes are purer than is expected on the assumption of random orientation4 ,this view is supported by the relatively small dispersion in ,c1 as may be seen in ,table ,i and ,figure #b1 among the nebulae of a given class1 but it is difficult to account for any such selective effect in the observations4 ,the discrepancies may be largely eliminated by an arbitrary adjustment of the numbers of nebulae with various degrees of actual ellipticity2 for instance1 the values in the last column of ,table ,,xii1 calculated on the assumption of equal numbers1 agree very well with the observed values1 although the resulting numbers having the various apparent ellipticities differ slightly from those observed4 ,the observed values1 however1 can again be accounted for by the inclusion of some flatter nebulae among the classes ,e#f and ,e#g4 ,very early ,sa or ,s,ba nebulae might easily be mistaken for ,e nebulae when oriented edge-on1 although they would be readily recognized when even slightly tilted4 ,if the numerical results fully represented actual statistical laws1 the explanation would be sought in the physical nature of the nebulae4 ,the change from ellipsoidal to lenticular figures1 noticeable in the later-type nebulae1 would affect the results in the proper direction1 as would also a progressive shortening of the polar axis4 ,the discrepancies1 however1 are second-order effects1 and since they may be due to accidental variations from random orientation1 a further discussion must await the accumulation of more data4 ,,table ,,xii ,differential ,values of ,c ,random ,orientation --------------------- ,class ,pure ,classes ,observed ,no4 as ,observed ,equal ,no4 ---------------------------------------- -------------------- ,c#g-;,c#g #j4jj #j4jj #j4jj #j4jj ,c#f #j4fc #j4ce99 #j4be #j4ce ,c#e #a4aj #j4gj99 #j4eh #j4gj ,c#d #a4ea #j4he #a4aa #a4ja ,c#c #a4hd #a4db #j4hg #a4bh ,c#b #b4ac #a4fg #a4cc #a4ee ,c#a #b4ci #b4ja #a4ed #a4hc ,c#j #b4fb #b4ag #b4ae #b4be ---------------------------------------- -------------------- 99 ,read from smooth curve in ,fig4 #f4 ,the small numbers of observed ,e#e and ,e#f nebulae justify this procedure4 ,the other values are the means actually observed4 ,n4,g4,c4 #ebd and #ciih are included as ,e#j and ,e#a1 respectively4 ,meanwhile1 it is evident that1 to a first approximation at least1 the polar diameters alone determine the total luminosities of all elliptical nebulae1 and the entire series can be represented by the various configurations of an originally globular mass expanding equatorially4 ,a single formula represents the relation1 in which the value of ,c is that corresponding to the pure type ,e#j4 ,from ,table ,,xii1 this is found to be #b4fb mag4 less than the value of ,c#g ,the latter is observed to be #ab4ge1 hence m,t #e log b #aj4ac4 7#e7 ,if this relation held for the spirals as well1 the polar diameters could be calculated from the measured magnitudes4 ,unfortunately1 it has not been possible to measure accurately the polar diameters directly1 and hence to test the question1 but they have been computed for the mean magnitudes of the ,sa1 ,sb1 and ,sc nebulae as given in ,table ,,iii1 and the ratios of the axes have been derived by a comparison of these hypothetical values with the means of the measured maximum diameters4 ,the results1 #a to #d4d1 #a to #e4g1 and #a to #g4c1 respectively1 although of the right order1 appear to be somewhat too high4 ,an examination of the photographs indicates values of the order of #a to #e4e1 #a to #h1 and #a to #aj1 but the material is meager and may not be representative4 ,the comparison emphasizes1 however1 the homogeneity and the progressive nature of the entire sequence of nebulae and lends some additional color to the assumption that it represents various aspects of the same fundamental type of system4 ,from the dynamical point of view1 the empirical results are consistent with the general order of events in ,jeans's theory4 ,thus interpreted1 the series is one of expansion1 and the scale of types becomes the time scale in the evolutionary history of nebulae4 ,in two respects this scale is not entirely arbitrary4 ,among the elliptical nebulae the successive types differ by equal increments in the ellipticity or the degree of flattening1 and among the spirals the intermediate stage is midway between the two end-stages in the structural features as well as in the luminosity relations4 ,one other feature of the curves may be discussed from the point of view of ,jeans's theory before returning to the strictly empirical attitude4 ,the close agreement of the diameters for the stages ,e#g and ,sa suggests that the transition from the lenticular nebula to the normal spiral form is not cataclysmic4 ,if the transition were gradual1 however1 we should expect to observe occasional objects in the very process1 but among the thousand or so nebulae whose images have been inspected1 not one clear case of a transition form has been detected4 ,the observations jump suddenly from lenticular nebulae with no trace of structure to spirals in which the arms are fully developed4 ,if the numerical data could be fully trusted1 the ,s,ba forms would fill the gap4 ,among these nebulae1 the transition from the lenticular to the spiral with arms is gradual and complete4 ,it is tempting to suppose that the barred spirals do not form an independent series parallel with that of the normal spirals1 but that all or most spirals begin life with the bar1 although only a few maintain it conspicuously throughout their history4 ,this would also account for the fact that the relative numbers of the ,s,ba nebulae are intermediate to those of the lenticular and of the ,sa4 ,the normal spirals become more numerous as the sequence progresses1 while the numbers of barred spirals1 on the contrary1 actually decrease with advancing type4 ,,relation ,,between ,,nuclear ,,luminosities ,,and ,,diameters ,visual magnitudes have been determined by ,hopmann for the nuclei of #cg of the nebulae included in the present discussion4 ,these data1 together with types and diameters of the nebulae1 are listed in ,table ,,xiii4 ,when the magnitudes are plotted directly against the logarithms of the diameters1 they show little or no correlation4 ,when1 however1 the nebulae are reduced to the standard type 7by applying corrections for differences in diameter along the sequence71 a decided correlation is found whose coefficient is #j4gf4 ,this is shown in ,figure #i4 ,the simple mean of the two regression curves is mn #ad4de - #d4id log d1 7#f7 where the slope differs by about #a per cent from that in formula 7#b74 ,the list contains #af elliptical nebulae1 #ae normal1 and #f barred spirals4 ,the nebulae are fairly representative1 except that few late-type spirals are included4 ,this is an effect of selection due to the fact that nuclei become less and less conspicuous as the sequence progresses4 ,the same result can be derived from a study of the differences1 mn - m,t1 for the individual nebulae4 ,the mean value is #a4ee #j4jh1 and the average residual is #j4fj mag4 ,means for the separate types are to be found in ,table ,,xiv4 ,,table ,,xiii ,diameters and ,nuclear ,magnitudes ,n4,g4,c4 ,type log d mn ,hopmann mn ,reduced ---------------------------------------- ------------------- #bba ,e#b #j4db #i4hd #aa4he #ajbc ,s,ba 4#gh #aa4hf #aa4hf #bhda ,sb #j4gh #ab4jh #aa4ai #cjca ,sb #a4bj #aj4id #aj4je #caae ,e#g #j4fj #aj4hc #aa4ji #ccea ,s,bb 4#dh #ab4ca #ab4ae #ccfh ,sa 4#he #aa4fh #aa4dc #ccgi ,e#j 4#cj #aa4ee #ad4bg #cdab ,s,ba 4#dj #aa4ei #aa4ei #cdhi ,sb 4#dj #aa4ed #aj4fe #cfbf ,sa 4#bh #ab4cg #ab4ab #cfbg ,sb 4#ij #ab4jc #aa4ad #dabe ,e#d 4#cj #aa4gd #ac4jd #dbaf ,sb 4#he #aa4fe #aj4gf #dbgh ,e#a 4#j #ab4jb #ad4ch #dcgd ,e#a 4#jh #aa4dc #ac4gi #dchb ,e#d 4#dh #aa4gg #ac4jg #ddce ,e#f 4#aa #aa4fe #ab4bf #ddch ,sb 4#ed #aa4hc #aj4id #ddhf ,e#j 4#cj #aa4bc #ac4ie #dedf ,e#f 4#ah #aa4ge #ab4cf #deeb ,e#j 4#bc #aa4ei #ad4ca #defi ,sc 4#fe #ab4je #aj4eg #degi ,s,bc 4#de #aa4dh #aj4jg #dfba ,e#e 4#cj #aa4fj #ab4ef #dfcf ,e#a 4#jh #aa4ig #ad4cc #dfdi ,e#b 4#cj #aa4eg #ac4eh #dfig ,e#f 4#dh #aj4ij #aa4ea #dfii ,s,bb 4#eg #aj4gb #aj4ef #dgbe ,s,bb 4#gj #aa4ig #aa4ha #dgcf ,sb 4#gj #aj4cf #i4dg #ejje ,sc 4#gj #ab4jd #aj4ef #ejcc ,sc #j4gh #ab4ch #aj4ij #eaid ,sc #a4jh #aa4ch #i4ij #ecbb ,e#c #j4ae #ab4aj #ac4gf #ehff ,sa 4#dh #aa4gf #aa4ea #gcca ,sb #j4ie #aa4hb #aj4ic ,means #j4eji #aa4fj #aa4ij ---------------------------------------- ------------------- ,the low value for ,sa-,s,ba is due to ,n4,g4,c4 #ehff1 for which the magnitude difference of #j4jf is certainly in error1 and the high value for ,sc and ,s,bc1 to ,m #ea1 for which the difference of #c4ih mag4 is not representative4 ,the latter is accounted for in part by the fact that the m,t refers to the combined magnitude of the main spiral and the outlying mass1 ,n4,g4,c4 #eaie4 ,when these two cases are discarded1 the final mean becomes #a4eb #j4je1 and the average residual1 #j4eb mag41 is consistent with the probable errors of the magnitude determinations4 ,the small numbers of objects within each class are insufficient for reliable conclusions concerning slight variations along the sequence4 ,from the constancy of mn - m,t1 the relation expressed by formula 7#f7 necessarily follows1 the small difference in the constant being accounted for by the different methods of handling the data4 ,illustration3 ,fig4 #i4--,relation between nuclear magnitudes and diameters4 ,the nebulae have been reduced to the standard type by applying corrections to the magnitudes4 ,the parallelism of the two curves representing formulae 7#b7 and 7#f7 indicates that the regular extra-galactic nebulae1 when reduced to the standard type1 are similar objects4 ,the mean surface brightness is constant1 and the luminosity of the nucleus1 as measured by ,hopmann1 is a constant fraction1 about one-fourth1 of the total luminosity of the nebulae4 ,if there is a considerable range in absolute magnitude and hence in actual dimensions1 the smaller nebulae must be faithful miniatures of the larger ones4 ,,absolute ,,magnitudes ,,of ,,extra-,,galactic ,,nebulae ,reliable values of distances1 and hence of absolute magnitudes1 are restricted to a very few of the brightest nebulae4 ,these are derived from a study of individual stars involved in the nebulae1 among which certain types have been identified whose absolute magnitudes in the galactic system are well known4 ,the method assumes that the stars involved in the nebulae are directly comparable with the stars in our own system1 and this is supported by the consistency of the results derived from the several different types which have been identified4 ,,table ,,xiv ,type mn - m,t ,number ---------------------------------------- ---------------------------- ,e#j-;,e#c #a4fd 7#i7 ,e#d-;,e#g #a4dc 7#g7 ,sa-,s,ba #j4ig 7#e7 #a4bg when ,n4,g4,c4 #ehff is omitted ,sb-,s,bb #a4gj 7#aa7 ,sc-,s,bc #a4gf 7#e7 #a4ai when ,n4,g4,c4 #eaid is omitted ---------------------------------------- ------------- ,unweighted mean #a4ej 7#cg7 #a4de 7#ce7 ,weighted mean #a4ee 7#cg7 #a4eb 7#ce7 ---------------------------------------- ---------------------------- ,,table ,,xv ,absolute ,magnitudes of ,nebulae ,system ,m,t ,m,s ---------------------------------------- ------ ,galaxy -#e4e ,m #ca -#ag4a #f4e ,,lmc #ag4j #h4j ,,smc #af4j #e4e ,m #cc #ae4a #f4e ,n4,g4,c4 #fhbb #ac4g #e4h ,m #aja #ac4e -#f4c ,m #cb -#ac4c --------------------------------- -#f4c -#i4j ,m,s - ,m,t --------------------------------- ,means -#ae4a -#ae4c ,adopted -#ae4b ---------------------------------------- ------ ,in ,table ,,xv are listed absolute magnitudes of the entire system and of the brightest stars involved1 for the galaxy and the seven nebulae whose distances are known4 ,the data for the ,magellanic ,clouds are taken from ,shapley's investigations4 ,the absolute magnitudes of the remaining nebulae were derived from ,holetschek's apparent magnitudes and the distances as determined at ,mount ,wilson1 where the stellar magnitudes were also determined4 ,m #cb is generally assumed to be associated with the great spiral ,m #ca1 because the radial velocities are nearly equal and are unique in that they are the only large negative velocities that have been found among the extra-galactic nebulae4 ,m #aja has been added to the list on rather weak evidence4 ,the brightest stars involved are slightly brighter than apparent magnitude #ag4j1 and several variables have been found with magnitudes at maxima fainter than #ai4j4 ,sufficient observations have not yet been accumulated to determine the light-curves of the variables1 but from analogy with the other nebulae they are presumed to be ,cepheids4 ,on this assumption1 both the star counts and the variables lead to a distance of the order of #a4g times the distance of ,m #cc4 ,the inclusion of ,m #aja does not change the mean magnitude of the brightest stars involved1 but reduces the mean magnitude of the nebulae by #j4b4 ,the range in the stars involved is about #b4e mag41 and in the total luminosities of the nebulae1 about #c4h mag4 ,this latter is consistent with the scatter in the diagram exhibiting the relation between total luminosities and diameters4 ,the associated objects1 ,m #ca and #cb1 represent the extreme limits among the known systems1 and the mean of these two is very close to the mean of them all4 ,,luminosity ,,of ,,stars ,,involved ,,in ,,nebulae ,the number of nebulae of known distance is too small to serve as a basis for estimates of the range in absolute magnitude among nebulae in general4 ,further information1 however1 can be derived from a comparison of total apparent magnitudes with apparent magnitudes of the brightest stars involved1 on the reasonable assumption1 supported by such evidence as is available1 that the brightest stars in isolated systems are of about the same intrinsic luminosity4 ,the most convenient procedure is to test the constancy of the differences in apparent magnitude between the brightest stars involved and the nebulae themselves1 over as wide a range as possible in the latter quantities4 ,an examination of the photographs in the ,mount ,wilson collection has revealed no stars in the very faint objects or in the bright elliptical nebulae and early-type spirals4 ,this was to be expected from the conclusions previously derived4 ,observations were therefore confined to intermediate- and late-type spirals and the irregular nebulae to the limiting visual magnitude #aj4e4 ,the ,magellanic ,clouds and ,n4,g4,c4 #fhbb were added to the nebulae in ,holetschek's list4 ,altogether1 data were available for #cb objects1 or about #fj per cent of the total number in the sky to the adopted limit4 ,for this reason it is believed that the results are thoroughly representative4 ,,table ,,xvi ,difference in ,magnitude between ,nebulae and ,their ,brightest ,stars ,n4,g4,c4 ms m,t ms - m,t ---------------------------------------- ---------- ,sb ---------------------------------------- ---------- #bbd #ae4e #e4j #aj4e #ajfh #ag4e #i4a #h4d #bhda #ai4e #i4d #aj4a #cjca #ah4e #h4c #aj4b #ccaj #ai4j #aj4d #h4f #cfbc #bj4j #i4i #aj4a #cfbg #ah4e #i4a #i4d #ddch #ai4j #aj4c #h4g #ddej #ai4e #aj4j #i4e #dgcf #ag4c #h4d #h4i #dhbf #ai4e #i4b #aj4c #ejee #ai4j #i4f #i4d #egdf #ai4e #aj4d #i4a #gcca #ai4j #aj4d #h4f ---------------------------------------- ---------- ,s,bb ---------------------------------------- ---------- #dfii #ai4e #aj4j #i4e ---------------------------------------- ---------- ,sc ---------------------------------------- ---------- #bec #ah4c #i4c #i4j #eih #ae4f #g4j #h4f #bdjc #ag4c #h4g #h4f #bfhc #bj4j #i4i #aj4a #bijc #ai4j #i4a #i4i #dbed #ah4e #aj4d #h4a #dcba #ah4h #aj4e #h4c #ddad #ai4e #aj4a #i4d #ddij #ah4h #aj4b #h4f #eaid #ag4c #g4d #i4i #ebcf #ah4f #aj4d #h4b #edeg #ag4j #i4i #g4a ---------------------------------------- ---------- ,irr4 ---------------------------------------- ---------- ,,lmc #i4e #j4e #i4j ,,smc #ab4j #a4e #aj4e #cjcd #ai4e #i4j #aj4e #dddi #ag4h #i4e #h4c #fhbb #ae4h #h4e #g4c ---------------------------------------- ---------- ,the data are listed in ,table ,,xvi and are shown graphically in ,figure #aj4 ,the luminosities of the brightest stars are given in photographic magnitudes4 ,for the ,magellanic ,clouds1 ,m #cc1 and ,n4,g4,c4 #fhbb1 these were obtained from published star counts4 ,for ,m #ca1 #ea1 #fc1 #ha1 #id1 and ,n4,g4,c4 #bdjc1 they depend upon unpublished counts1 for which the magnitudes were determined by comparisons with ,selected ,areas4 ,for the remaining nebulae1 the magnitudes of stars were estimated with varying degrees of precision1 but are probably less than #j4e mag4 in error4 ,illustration3 ,fig4 #aj4--,relation between total magnitudes of extra-galactic nebulae and magnitudes of the brightest stars involved4 ,differences between total visual magnitudes of nebulae and the photographic magnitudes of the brightest stars are plotted against the total magnitudes4 ,the dots represent cases in which the stars could actually be detected2 the incomplete crosses represent cases in which stars could not be detected1 and hence give lower limits for the magnitude differences4 ,the diagonal line indicates the approximate limits of observation1 fixed by the circumstance that1 in general1 stars fainter than #ai4e probably would not be detected on the nebulous background4 ,the sloping line to the right in ,figure #aj represents the limits of the observations1 for1 from a study of the plates themselves1 it appeared improbable that stars fainter than about #ai4e could be detected with certainty on a nebulous background4 ,points representing nebulae in which individual stars could not be found should lie in this excluded region above the line1 and their scatter is presumably comparable with that of the points actually determined below the line4 ,when allowance is made for this inaccessible region1 the data can be interpreted as showing a moderate dispersion around the mean ordinate ms - m,t #i4j4 7#g7 ,the range in total magnitudes is sufficiently large in comparison with the dispersion to lend considerable confidence to the conclusion4 ,the total range of four1 and the average dispersion of less than #a mag41 are comparable with those in ,table ,,xv and in ,figure #g1 and agree with the former in indicating a constant order of absolute magnitude4 ,the mean absolute magnitude of the brightest stars in the nebulae listed in ,table ,,xv1 combined with the mean difference between nebulae and their brightest stars1 furnishes a mean absolute magnitude of -#ae4c for the nebulae listed in ,table ,,xvi4 ,this differs by only #j4b mag4 from the average of the nebulae in ,table ,,xv1 and the mean of the two1 -#ae4b1 can be used as the absolute magnitude of intermediate- and late-type spirals and irregular nebulae whose apparent magnitudes are brighter than #aj4e4 ,the dispersion is small and can safely be neglected in statistical investigations4 ,this is as far as the positive evidence can be followed4 ,for reasons already given1 however1 it is presumed that the earlier nebulae1 the elliptical and the early-type spirals1 are of the same order of absolute magnitude as the later4 ,the one elliptical nebula whose distance is known1 ,m #cb1 is consistent with this hypothesis4 ,conclusions concerning the intrinsic luminosities of the apparently fainter nebulae are in the nature of extrapolations of the results found for the brighter objects4 ,when the nebulae are reduced to a standard type1 they are found to be constructed on a single model1 with the total luminosities varying directly as the square of the diameters4 ,the most general interpretation of this relation is that the mean surface brightness is constant1 but the small range in absolute magnitudes among the brighter nebulae indicates that1 among these objects at least1 the relation merely expresses the operation of the inverse-square law on comparable objects distributed at different distances4 ,the actual observed range covered by this restricted interpretation is from apparent magnitude #j4e to #aj4e4 ,the homogeneity of the correlation diagrams and the complete absence of evidence to the contrary justify the extrapolation of the restricted interpretation to cover the #b or #c mag4 beyond the limits of actual observation4 ,these considerations lead to the hypothesis that the nebulae treated in the present discussion are all of the same order of absolute magnitude2 in fact1 they lend considerable color to the assumption that extra-galactic nebulae in general are of the same order of absolute magnitude and1 within each class1 of the same order of actual dimensions4 ,some support to this assumption is found in the observed absence of individual stars in the apparently fainter late-type nebulae4 ,if the luminosity of the brightest stars involved is independent of the total luminosity of a nebula1 as is certainly the case among the brighter objects1 then1 when no stars brighter than #ai4e are found1 the nebulae must in general be brighter than absolute magnitude m,t - #be4h where m,t is the total apparent magnitude4 ,on this assumption1 the faintest of the ,holetschek nebulae are brighter than -#ab4e and hence of the same general order as the brighter nebulae4 ,once the assumption of a uniform order of luminosity is accepted as a working hypothesis1 the apparent magnitudes become1 for statistical purposes1 a measure of the distances4 ,for a mean absolute magnitude of -#ae4b1 the distance in parsecs is log ,d #j4b m,t #d4jd4 7#h7 ,,dimensions ,,of ,,extra-,,galactic ,,nebulae ,when the distances are known1 it is possible to derive actual dimensions and hence to calibrate the curve in ,figure #f1 which exhibits the apparent diameters as a function of type1 or stage in the nebular sequence1 for nebulae of a given apparent magnitude4 ,the mean maximum diameters in parsecs corresponding to the different mean types are given in ,table ,,xvii4 ,for the elliptical nebulae1 values are given both for the statistical mean observed diameters and for the diameter as calculated for the pure types4 ,spirals at the last stage in the observed sequence have diameters of the order of #cjjj parsecs4 ,assuming #a3aj as the ratio of the two axes1 the corresponding volume is of the order of #a4daji cubic parsecs1 and the mean luminosity density is of the order of #g4g absolute magnitudes per cubic parsec as compared with #h4ae for the galactic system in the vicinity of the sun4 ,these results agree with those of ,seares who1 from a study of surface brightness1 concluded that the galactic system must be placed at the end of1 if not actually outside1 the series of known spirals when arranged according to density4#ai ,,table ,,xvii ,type ,diameter in ,parsecs ,type ,diameter in ,parsecs ---------------------- ,obs4 ,cal4 ---------------------------------------- ------------------ ,e#j #cfj #cdj ,sa #adej ,e#a #dcj #chj ,sb #aijj ,e#b #ejj #dcj ,sc #bejj ,e#c #eij #dij ,e#d #gjj #egj ,s,ba #abhj ,e#e #haj #fhj ,s,bb #acbj ,e#f #ifj #hej ,s,bc #bbej ,e#g #aacj #aacj ,irr #aejj ---------------------------------------- ------------------ ,,masses ,,of ,,extra-,,galactic ,,nebulae ,spectroscopic rotations are available for the spirals ,m #cabj and ,n4,g4,c4 #deid1ba and from these it is possible to estimate the masses on the assumption of orbital rotation around the nucleus4 ,the distances of the nebulae are involved1 however1 and this is known accurately only for ,m #ca2 for ,n4,g4,c4 #deid it must be estimated from the apparent luminosity4 ,another method of estimating masses is that used by pik#bb in deriving his estimate of the distance of ,m #ca4 ,it is based on the assumption that luminous material in the spirals has about the same coefficient of emission as the material in the galactic system4 pik computed the ratio of luminosity to mass for our own system in terms of the sun as unity1 using ,jeans's value#bc for the relative proportion of luminous to non-luminous material4 ,the relation is ,mass #b4f,l4 7#i7 ,the application of this method of determining orders of masses seems to be justified1 at least in the case of the later-type spirals and irregular nebulae1 by the many analogies with the galactic system itself4 ,moreover1 when applied to ,m #ca1 where the distance is fairly well known1 it leads to a mass of the same order as that derived from the spectrographic rotation3 ,,mass ,,of ,m #ca ,spectrographic rotation #c4eaji pik's method #a4faji ,the distance of ,n4,g4,c4 #deid is unknown1 but the assumption that it is a normal nebula with an absolute magnitude of -#ae4b places it at #gjj1jjj parsecs4 ,the orders of the mass by the two methods are then ,,mass ,,of ,n4,g4,c4 #deid ,spectrographic rotation #b4jaji pik's method #b4fajh ,here again the resulting masses are of the same order4 ,they can be made to agree as well as those for ,m #ca by the not unreasonable assumption that the absolute luminosity of the nebula is #b mag4 or so brighter than normal4 pik's method leads to values that are reasonable and fairly consistent with those obtained by the independent spectrographic method4 ,therefore1 in the absence of other resources1 its use for deriving the mass of the normal nebula appears to be permissible4 ,the result1 #b4f #ajh 1 corresponding to an absolute magnitude of -#ae4b1 is probably of the right order4 ,the two test cases suggest that this value may be slightly low1 but the data are not sufficient to warrant any empirical corrections4 ,,numbers ,,of ,,nebulae ,,to ,,different ,,limiting ,,magnitudes ,the numbers of nebulae to different limiting magnitudes can be used to test the constancy of the density function1 or1 on the hypothesis of uniform luminosities1 to determine the distribution in space4 ,the nebulae brighter than about the tenth magnitude are known individually4 ,those not included in ,holetschek's list are3 the ,magellanic ,clouds1 the two nebulae ,n4,g4,c4 #ee and #ajig1 between #i4j and #i4e mag41 and the seven nebulae ,n4,g4,c4 #acd1 #bhi1 #acfe1 #aecc1 #aeei1 #agib1 and #cgbf1 all between #i4e and #aj4j mag4 ,a fair estimate of the number between #aj4j and #aa4j mag4 can be derived from a comparison of ,holetschek's list with that of ,hardcastle1 an inspection of images on the ,franklin-,adams charts and other photographs1 and a correlation between known total magnitudes and the descriptions of size and brightness in ,dreyer's catalogues4 ,it appears that very few of these objects were missed by ,holetschek in the northern sky--not more than six of ,hardcastle's nebulae4 ,for the southern sky1 beyond the region observed by ,holetschek1 the results are very uncertain1 but probable upper and lower limits were determined as #ej and #bj1 respectively4 ,the brighter nebulae are known to be scarce in those regions4 ,a mean value of #ce leads to a total #bie for the entire sky1 and this is at least of the proper order4 ,the number of nebulae between #aa4j and #ab4j mag4 can be estimated on the assumption that the two lists1 ,holetschek's and ,hardcastle's1 are about equally complete within this range4 ,they are known to be comparable for the brighter nebulae1 and1 moreover1 the total numbers included in the two lists for the same area of the sky1 that north of declination -#aj1 are very nearly equal--#djj as compared with #djh4 ,the percentages of ,holetschek's nebulae included by ,hardcastle were first determined as a function of magnitude4 ,within the half-magnitude interval #aa4j to #aa4e1 for instance1 #fj per cent are in ,hardcastle's list4 ,if the two lists are equally complete and1 taken together1 are exhaustive1 the total number in the interval will be #a4d times the number of ,holetschek's nebulae4 ,the latter is found to be #ej from smoothed frequency curves of the magnitudes listed in ,tables ,i-,,iv4 ,the total number north of -#aj is therefore #gj4 ,this can be corrected to represent the entire sky by applying the factor #a4ge1 which is the ratio of the total number of ,hardcastle's nebulae1 #gjj1 to the number north of -#aj1 #djj4 ,in this manner a reasonable estimate of #abc is obtained for the number of nebulae in the entire sky between #aa4j and #aa4e mag4 ,similarly1 between #aa4e and #ab4j1 where #ej per cent of ,holetschek's nebulae are included in ,hardcastle's list1 the total number for the entire sky is found to be #bcf4 ,the greatest uncertainty in these figures arises from the assumption that the two lists together are complete to the twelfth magnitude4 ,the figures are probably too small1 but no standards are available by which they can be corrected4 ,it is believed1 however1 that the errors are certainly less than #ej per cent and probably not more than #be per cent4 ,this will not be excessive in view of the possible deviations from uniform distribution where so limited a number of objects is considered4 ,beyond #ab4j mag4 the lists quickly lose their aspect of completeness and cannot be used for the present purpose4 ,there are available1 however1 the counts by ,fath#bd of nebulae found on plates of ,selected ,areas made with the #fj-;inch reflector at ,mount ,wilson4 ,the exposures were uniformly #fj minutes on fast plates and cover the ,areas in the northern sky down to and including the -#ae zone4 ,the limiting photographic magnitudes for stars average about #ah4e4 ,the counts have been carefully revised by ,seares#be and are the basis for his estimate of #cjj1jjj nebulae in the entire sky down to this limit4 ,approximate limiting total magnitudes for the nebulae in two of the richest fields1 ,s4,a4 #ef and #hj1 have been determined from extra-focal exposures with the #ajj-;inch reflector4 ,the results are #ag4g in each case1 and this1 corrected by the normal color-index of such objects1 gives a limiting visual magnitude of about #af4g1 which can be used for comparison with the counts of the brighter nebulae4 ,the various data are collected in ,table ,,xviii1 where the observed numbers of extra-galactic nebulae to different limits of visual magnitude are compared with those computed on the assumption of uniform distribution of objects having a constant absolute luminosity4 ,the formula used for the computation is log ,n #j4f m,t textrm,constant1 where the constant is the value of log ,n for m,t #j4 ,the value --#d4de is found to fit the observational data fairly well4 ,the agreement between the observed and computed log ,n over a range of more than #h mag4 is consistent with the double assumption of uniform luminosity and uniform distribution or1 more generally1 indicates that the density function is independent of the distance4 ,the systematic decrease in the residuals ,o - ,c with decreasing luminosity is probably within the observational errors1 but it may also be explained as due to a clustering of nebulae in the vicinity of the galactic system4 ,the cluster in ,virgo alone accounts for an appreciable part4 ,this is a second-order effect in the distribution1 however1 and will be discussed at length in a later paper4 ,,table ,,xviii ,numbers of ,nebulae to ,various ,limits ,,log ,n99 m,t ------------------ ,o - ,c ,,log ,d ,o ,c ---------------------------------------- ----- #h4e #j4he #j4fe #j4bj #e4gd #i4j #a4jh #j4ie 4#ac #e4hd #i4e #a4de #a4be 4#bj #e4id #aj4j #a4gc #a4ee 4#ah #f4jd #aj4e #a4ie #a4he 4#aj #f4ad #aa4j #b4ag #b4ae 4#jb #f4bd #aa4e #b4dc #b4de - 4#jb #f4cd #ab4j #b4gj #b4ge 4#je #f4dd #af4g #e4dh #e4eg -#j4ji #g4ch 7#ah4j7 7#f4ce7 7#g4fd7 ---------------------------------------- ----- 99 ,log ,n #j4f m,t - #d4de4 ,log ,d #j4b m,t #d4jd4 ,distances corresponding to the different limiting magnitudes1 as derived from formula 7#h71 are given in the last column of ,table ,,xviii4 ,the #cjj1jjj nebulae estimated to the limits represented by an hour's exposure on fast plates with the #fj-;inch reflector appear to be the inhabitants of space out to a distance of the order of #b4d #ajg parsecs4 ,the #ajj-;inch reflector1 with long exposures under good conditions1 will probably reach the total visual magnitude #ah4j1 and this1 by a slight extrapolation1 is estimated to represent a distance of the order of #d4dajg parsecs or #a4dajh light-years1 within which it is expected that about two million nebulae should be found4 ,this seems to represent the present boundaries of the observable region #c of space4 ,,density ,,of ,,space ,the data are now available for deriving a value for the order of the density of space4 ,this is accomplished by means of the formulae for the numbers of nebulae to a given limiting magnitude and for the distance in terms of the magnitude4 ,in nebulae per cubic parsec1 the density is beginalign log rho log ,n - log ,v 7#j4f m,t - #d4de7 - logfrac #dc - #c7d4jd #j4b m,t7 -#ag4ai endalign 7#aa7 ,this is a lower limit1 for the absence of nebulae in the plane of the ,milky ,way has been ignored4 ,the current explanation of this phenomenon in terms of obscuration by dark clouds which encircle the ,milky ,way is supported by the extra-galactic nature of the nebulae1 their general similarity to the galactic system1 and the frequency with which peripheral belts of obscuring material are encountered among the spirals4 ,the known clouds of dark nebulosity are interior features of our system1 and they do not form a continuous belt4 ,in the regions where they are least conspicuous1 however1 the extra-galactic nebulae approach nearest to the plane of the ,milky ,way1 many being found within #aj4 ,this is consistent with the hypothesis of a peripheral belt of absorption4 ,the only positive objection which has been urged to this explanation has been to the effect that the nebular density is a direct function of galactic latitude4 ,accumulating evidence#bf has failed to confirm this view and indicates that it is largely due to the influence of the great cluster in ,virgo1 some #ae from the north galactic pole4 ,there is no corresponding concentration in the neighborhood of the south pole4 ,if an outer belt of absorption is assumed1 which1 combined with the known inner clouds1 obscures extra-galactic nebulae to a mean distance of #ae from the galactic plane1 the value derived for the density of space must be increased by nearly #dj per cent4 ,this will not change the order of the value previously determined and is within the uncertainty of the masses as derived by pik's method4 ,the new value is then #iaj-ah nebulae per cubic parsec4 7#ab7 ,the corresponding mean distance between nebulae is of the order of #egj1jjj parsecs1 although in several of the clusters the distances between members appear to be a tenth of this amount or less4 ,the density can be reduced to absolute units by substituting the value for the mean mass of a nebula1 #b4fajh 4 ,then1 since the mass of the sun in grams is #bajcc and #a parsec is #c4aajah cm1 #a4eaj-ca grams per cubic centimeter4 7#ac7 ,this must be considered as a lower limit1 for loose material scattered between the systems is entirely ignored4 ,there are no means of estimating the order of the necessary correction4 ,no positive evidence of absorption by inter-nebular material1 either selective or general1 has been found1 nor should we expect to find it unless the amount of this material is many times that which is concentrated in the systems4 ,,the ,,finite ,,universe ,,of ,,general ,,relativity ,the mean density of space can be used to determine the dimensions of the finite but boundless universe of general relativity4 ,de ,sitter#bg made the calculations some years ago1 but used values for the density1 #aj-bf and greater1 which are of an entirely different order from that indicated by the present investigations4 ,as a consequence1 the various dimensions1 both for spherical and for elliptical space1 were small as compared with the range of existing instruments4 ,for the present purpose1 the simplified equations which ,einstein has derived for a spherically curved space can be used4#bh ,when ,r1 ,v1 ,m1 and represent the radius of curvature1 volume1 mass1 and density1 and k and c are the gravitational constant and the velocity of light1 ,r fraccsqrt#dk cdot frac#asqrtrho1 7#ad7 ,v #bb,r#c1 7#ae7 ,m c#b_/bk ,r4 7#af7 ,substituting the value found for 1 #a4eaj-ca1 the dimensions become ,r #h4eajbh cm #b4gajaj parsecs1 7#ag7 ,v #a4aajhh cm #c4eajcb cubic parsecs1 7#ah7 ,m #a4hajeg grams #iajbb 4 7#ai7 ,the mass corresponds to #c4eajae normal nebulae4 ,the distance to which the #ajj-;inch reflector should detect the normal nebula was found to be of the order of #d4dajge parsecs1 or about #afjj the radius of curvature4 ,unusually bright nebulae1 such as ,m #ca1 could be photographed at several times this distance1 and with reasonable increases in the speed of plates and size of telescopes it may become possible to observe an appreciable fraction of the ,einstein universe4 ,mount ,wilson ,observatory ,september #aibf #a ,contributions from the ,mount ,wilson ,observatory1 ,no4 #cbd4 #b ,these are the two ,magellanic ,clouds1 ,m #ca1 and ,m #cc4 #c ,bailey1 ,harvard ,annals1 #fj1 #aijh4 #d ,hardcastle1 ,monthly ,notices1 #gd1 #fii1 #aiad4 #e ,this estimate by ,seares is based on a revision of ,fath's counts of nebulae in ,selected ,areas 7,mt4 ,wilson ,contr41 ,no4 #big2 ,astrophysical ,journal1 #fb1 #afh1 #aibe74 #f 8,a ,general ,study of ,diffuse ,galactic ,nebulae10 ,mt4 ,wilson ,contr41 ,no4 #bda2 ,astrophysical ,journal1 #ef1 #afb1 #aibb4 #g ,the classification was presented in the form of a memorandum to the ,commission on ,nebulae of the ,international ,astronomical ,union in #aibc4 ,copies of the memorandum were distributed by the chairman to all members of the ,commission4 ,the classification was discussed at the ,cambridge meeting in #aibe1 and has been published in an account of the meeting by ,mrs4 ,roberts in ,l',astronomie1 #dj1 #afi1 #aibf4 ,further consideration of the matter was left to a subcommittee1 with a resolution that the adopted system should be as purely descriptive as possible1 and free from any terms suggesting order of physical development 7,transactions of the ,i4,a4,u41 #b1 #aibe74 ,mrs4 ,roberts' report also indicates the preference of the ,commission for the term 8extra-galactic0 in place of the original1 and then necessarily non-committal1 8non-galactic40 ,meanwhile ,k4 ,lundmark1 who was present at the ,cambridge meeting and has since been appointed a member of the ,commission1 has recently published 7,arkiv fr ,matematik1 ,astronomi och ,fysik1 ,band #ai;,b1 ,no4 #h1 #aibf7 a classification1 which1 except for nomenclature1 is practically identical with that submitted by me4 ,dr4 ,lundmark makes no acknowledgments or references to the discussions of the ,commission other than those for the use of the term 8galactic40 #h ,problems of ,cosmogony and ,stellar ,dynamics1 #aiai4 #i ,n4,g4,c4 #ddhf 7,m #hg7 may be an exception4 ,on the best photographs made with the #ajj-;inch reflector1 numerous exceedingly faint images1 apparently of stars1 are found around the periphery4 ,it was among these that ,belanowsky's nova of #aiai appeared4 ,the observations are described in ,publications of the ,astronomical ,society of the ,pacific1 #ce1 #bfa1 #aibc4 #aj 8,early0 and 8late10 in spite of their temporal connotations1 appear to be the most convenient adjectives available for describing relative positions in the sequence4 ,this sequence of structural forms is an observed phenomenon4 ,as will be shown later in the discussion1 it exhibits a smooth progression in nuclear luminosity1 surface brightness1 degree of flattening1 major diameters1 resolution1 and complexity4 ,an antithetical pair of adjectives denoting relative positions in the sequence is desirable for many reasons1 but none of the progressive characteristics are well adapted for the purpose4 ,terms which apply to series in general are available1 however1 and of these 8early0 and 8late0 are the most suitable4 ,they can be assumed to express a progression from simple to complex forms4 ,an accepted precedent for this usage is found in the series of stellar spectral types4 ,there also the progression is assumed to be from the simple to the complex1 and in view of the great convenience of the terms 8early0 and 8late10 the temporal connotations1 after a full consideration of their possible consequences1 have been deliberately disregarded4 #aa ,publications of the ,lick ,observatory1 #ac1 #ab1 #aiah4 #ab ,h is brighter than ,n#b4 ,patches with similar spectra are often found in the arms of late-type spirals--,n4,g4,c4 #bec1 ,m #cc1 ,m #aja4 ,the typical planetary spectrum1 where ,h is fainter than ,n#b1 is found in the rare cases of apparently stellar nuclei of spirals2 for instance1 in ,n4,g4,c4 #ajfh1 #djea1 and #daea4 ,here also the emission spectra are localized and do not extend over the nebulae4 #ac ,monthly ,notices4 #gd1 #fii1 #aiad4 #ad ,annalen der ,wiener ,sternwarte1 #bj1 #aijg4 #ae ,astronomische ,nachrichten1 #bad1 #dbe1 #aiba4 #af ,publications of the ,lick ,observatory1 #ac1 #aiah4 #ag ,since ,c is constant for all nebulae in a given class1 the linear relation between log d and ,c for the different classes is something more than a mere geometrical relation arising from the observed equality of the mean m,t in the various classes4 #ah ,this is apparent even among the observed classes4 ,referring to formula 7#c71 m,t #e log b will be constant in so far as ,ce #e log 7#a - e7 is constant4 ,the following table indicates that the latter term is approximately constant throughout the sequence of elliptical nebulae4 ,the values of ,ce were read from the smooth curve in ,fig4 #f4 e ,ce #e log 7#a - e7 ,c#j ,res4 ---------------------------------------- ------------ #j #aj4cj #j4j #aj4cj -#j4ad #a #aj4fe - 4#bc #aj4db - 4#jb #b #aa4jj 4#dh #aj4eb 4#aj #c #aa4ce #j4gh #aj4eg 4#ac #d #aa4gj #a4aa #aj4ei 4#ae #e #ab4je #a4ej #aj4ee 4#aa #f #ab4dj #a4ii #aj4da - 4#jc #g #ab4ge -#b4fb #aj4ac -#j4ca ---------------------------------------- ------ ,mean #aj4dd #j4ab ---------------------------------------- ------------ #ai ,mt4 ,wilson ,contr41 ,no4 #aia2 ,astrophysical ,journal1 #eb1 #afb1 #aibj4 #bj ,pease1 ,mt4 ,wilson ,comm41 ,no4 #ea2 ,proceedings of the ,national ,academy of ,sciences1 #d1 #ba1 #aiah4 #ba ,pease1 ,mt4 ,wilson ,comm41 ,no4 #cb3 ibid41 #b1 #eag1 #aiaf4 #bb ,astrophysical ,journal1 #ee1 #djf1 #aibb4 #bc ,monthly ,notices1 #hb1 #acc1 #aibb4 #bd ,astronomical ,journal1 #bh1 #ge1 #aiad4 #be ,mt4 ,wilson ,contr41 ,no4 #big2 ,astrophysical ,journal1 #fb1 #afh1 #aibe4 #bf ,the latest and most reliable results bearing on the distribution of faint 7hence apparently distant7 nebulae are found in ,seares's revision and discussion of the counts made by ,fath on plates of the ,selected ,areas with the #fj-;inch reflector4 ,when the influence of the cluster in ,virgo is eliminated the density appears to be roughly uniform for all latitudes greater than about #be4 #bg ,monthly ,notices1 #gh1 #c1 #aiag4 #bh ,haas1 ,introduction to ,theoretical ,physics1 #b1 #cgc1 #aibe4 ,transcriber's ,notes #a4 ,footnotes have been renumbered and moved to the end of the paper4 #b4 ,tables have been moved to avoid splitting paragraphs4 ,in some cases the tables have been reconfigured or split in order to work better with e-readers4 #c4 ,except as mentioned above every effort has been made to replicate this text as faithfully as possible1 including non-standard punctuation1 inconsistently hyphenated words1 etc4 #d4 ,the original printed text is available from ,hathi,trust at3 https3_/_/hdl4handle4net_/#bjbg_/uc#a4;b #chjefhj 7see pg #cec74 ,the outline 8,,classification ,,of ,,nebulae0 starting on page #c lists ,n4,g4,c4 #baag as a type ,e#g nebula4 ,the version of this paper printed in ,contributions from the ,mount ,wilson ,observatory ,no4 #cbd lists ,n4,g4,c #caae4 ,otherwise the papers are essentially identical4 ,special notation for the plain text version3 #a4 ,text enclosed by underscores 80 is italicised4 #b4 ,text enclosed by macrons 80 has a line draw over it4 #c4 ,text enclosed in braces following an underscore 8 0 is subscript4 #d4 ,text enclosed in braces following a circumflex accent 8 0is superscript4 ,if only a single character1 the braces may be omitted4 #e4 ,text enclosed in heavy angle brackets 8 0 is bold4 #f4 ,text enclosed in dollar signs is in ,te,x notation4