ASTRON OMISCHE NACHRICHTEN. Band 236. Nr. 5661. 21.

~

The Motions and Status of the Spiral Nebulae and Globular Clusters. Von C. D. Perrine. Investigations of the motions and evolutionary proces-

ses in our stellar system led recently to a more thorough exa- mination of the radial velocities of the spiral nebulae.

This examination has disclosed well marked depen- dences of their radial velocities upon galactic latitude and also upon size and apparent ellipticity or inclination to the line of sight. These relationships appear to have a definite bearing on the origin and status of these objects and upon the evo- lutionary changes in our stellar system.

The velocities available are chiefly due to SZ@hcr with a few from Lick and Mt.Wilson as contained, with the ex- ception of 4, in Vdte 's Second Catalogue of Radial Velocities. The list comprises 49 spiral nebulae and IS globular clusters. Of these I rejected three spiral nebulae for reasons which it is necessary to consider at some length.

Two'of these rejections, NGC 221 and 5195, appear to be connected with their large near-by neighbours, NGC 224 and 5194. NGC 224 is the great Andromeda Nebula and 5194 is the large spiral M 51 in Canes Venatici. Photographs show 5195 to be directly connected to the large one and the radial velocities confirm it. 221 is not joined apparently but its similar radial velocity, large negative, suggests that it may be a dependent of 224.

NGC 404 showed such a disregard of the dependences upon size and ellipticity that an explanation was sought. It was one of the smallest and yet it had a negat ive velocity classing it with the very large ones in that region. The close relationships in the two cases mentioned previously suggested a larger object near the position of 404 of which it might be a dependent. No such large one was found in the catalogue but there was found a nest of small ones over an area of several square degrees. No other velocities in the region are available so that it is not possible to say definitely that they are related and constitute a single entity. The circumstances, however, are suggestive.

Had 404 been included, the numerical changes caused by it would have accentuated the difference due to ellipticity and decreased the change due to size, but in neither case would the changes have been of importance. The physical conditions involved seem to justify the treafment of these pairs as single systems at least for the present.

Preliminary examinations were made of the velocities uncorrected for solar motion as a test and because the com- ponents of such motion are comparatively small, only averaging one third of its full value. Even in the limited number of these nebulae, the effects of neglected solar motion could be expected to fairly well neutralize.

Dependence of Velocity upon Galac t ic L a t i - tude. The supposed cosmical origin of the spirals suggested a possible relationship of radial velocities to galactic latitude.

The results of an examination of the uncorrected velocities are given in table I. Tab le I. Dependence of Rad ia l Veloci ty upon

Ga lac t i c La t i tude .

7 +230 - 20 +117 +rg 2 +z15 . -124 + 3 -84

27 +728 +126 -203 +26 7 +460 + 2 5 + 79 +39

11 3.23 1 6.11 I 0.96 I The simple assumption (I) was first made of a depen-

dence upon the sine of the galactic latitude. The residuals show a fair agreement but a systematic deviation.

If the spirals were effectively ejected at right angles to the galaxy the resulting velocities could be expected to be seen by an observer near the center of the system as varying according to the versed sine of the distance from the plane of the galaxy. Assumption 2 shows the agreement with obser- vation, the deviations being systematically the opposite of assumption I.

Assumption 3 is a simple mean of the sines and versed sines. The agreement with observation is satisfactory and as far as the data are competent, they are not out of harmony with the hypothesis that these objects could have been so ejected with a tendency in addition to outward motion in the galactic plane.

Treating the four groups as normals the above assump- tions give the sums of the squares of the residuals in the last line of table I.

The individual velocities in the groups confirm the dependence as real. All of the largest velocities are found in the latitudes of 50' and over. The few negative velocities are all found in the lower latitudes and the largest negative ones in the lowest latitude group of all.

If the large motions of the spirals were really due to relative motion to our Sun, the largest radial velocities should be found in the latitudes containing the apex of solar motion, which is not the case.

This fact together with the high residual velocities which are left after correcting for such a solar motion (K-term) justifies the treatment of these velocities with respect to the Sun and system of naked'eye stars.

Dependence of Rad ia l Velocity upon Size a n d El l ipt ic i ty . During the investigation of the dependence upon galactic latitude, suspicions were aroused that the larger spirals had the lower velocities and that the velocities of the

23

3 3 1 566 I 3 3 2

Major Axis

=F 2'

Small E I Large E Large - Small v

NO. Dim1 E NO. IDiam. E km

6 11911.15 i-834 4 1 1184.17 +1158 +324,

2' to 5

4.55 + I95 + 74 4.00 + 685 +126 11 " 1 11'35)+55d[~&l 13.84 + 66il + 105

6 97 1.37 + 1 2 1

All

2 $ 5

T R T Exsmination

U - 20 -40.54 V -I- 47 +20.36 W +640 +1046 A 241O D + 59' yo 558km K

km

Mean Res. - 15 9

Average Ren. 237 * (..>/I00 388

12 7.4 + 5 3 2 5 7 + 241 42 + 146 37

10 and ove

3 5 7 km km

+658.0 + 319 + 39.8 + 224

+281.2 + 704 287" 304" 266"

+ 59" + 27' + 42" 326km 399km 478km

+549 * - 22 )) + I 0

212 D 240 D

342

l) E corrected to 4.00 by means of adjacents groups. s, Omitting NGC4565. See text.

It was assumed that these spirals are in fact circular and that the longer axis is the diameter. The major axes have been taken as the measures of size and the ellipticity, B , (for the first 4 solutions of table 2) is simply the ratio of the major to the minor axes. This assumption does not satisfac- torily represent inclinations which is probably the underlying cause but has been adopted for preliminary work.

The dimensions of the Andromeda Nebula are from a photograph by Barnard in Vol. XI of the Lick Obs.Pub1. ; the two larger nubeculae are from G5rdoba photographs; 6822 is from a Mt. Wilson photograph; one frdm Mt. Wilson descrip- tion (4000 km) and 4 are estimates from the NGC. descriptions based upon Curtis' measures of the others. The minor axes (and therefore the ellipticities) were estimated in 6 cases,

The homogeneity of the observations, especially in the matter of dimensions, is of considerable importance.

The rapid increase of velocity with decreasing size and increasing velocity with increasing elongation are so large and consistent as to indicate their reality. Neither are they destroyed by the neglect of any legitimate solar motion, as is shown later.

It can safely be assumed that no systematic errors sufficiently large to affect the conclusions, exist in the deter- minations of radial velocity. Here again a satisfactory homo-

333 566 I 3 3 4

fiance, being a decrease of velocity of 20 km and 40 km respectively per minute of diameter. But in solution 3 ?I

increases from the large to small diameters according to a curve in which the velocity does not depend directly upon diameter but upon a function of the diameter. This curve is referred to later in this paper.

v is the change of velocity per unit of change in elon- gation (or inclination in solution 7). w is the velocity at unity on the pole of the galaxy.

The agreement of the values from the different solutions is satisfactory and confirms the reality of the dependences inferred from the preliminary examination which ignored solar motion.

Inspection of the mean residuals shows that the large K term of -+ 549 km has been satisfactorily accounted for on the theory of the dependences upon size, elongation and galac- tic latitude.

The average residual is still large and examination shows the same tendency as among the stars, i. e. for there to be a higher proportion of large (both positive and negative) residuals than probability would call for.

These residuals show little or no relation to size as indicated below

< 2' Mean 0 - C + I54 2'- 5 - 35 5- 9 - 6

I 0 -20 + 22

Very large including nubeculae - 304 The apparent anomalous behavior of several cases has

already been noted. The explanation of those anomalies is comprehended in the general explanations of these depen- dences.

Two cases remain to be noted, NGC 4565 and a small object observed at Mt.Wilson with the highest velocity yet noted1).

NGC 4565 gives an unusually high velocity for one so large. This fact seems to find its explanation in its high galactic latitude, almost exactly at the North galactic pole, and a small content or mass as indicated by its extreme thinness as compared with its large diameter.

The high velocity object, observed at Mt.Wilson was reserved as a test of the values obtained from the remainder of the data, and is referred to later in this paper.

The data were not thought sufficient to distinguish between the different possible functions of either inclination or galactic latitude particularly that depending upon incli- nation where large inclinations to the sight lme are very uncer- tain, But the systematic deviations of the residuals seem to indicate that these functions should be more accurately defined.

The simple ratio of axes in the case of the dependence upon inclination used in solution I and 3 of table 3 has been changed therefore to cosi for the succeeding solution (7). Likewise the sing used in the earlier ones has been changed to versed sine g.

The residuals from solution 7, however, show but comparatively small changes from which it is evident that the cause of the large residuals is to be sought elsewhere.

The functions defining the solar motion cannot be chan- ged .and assuming that the correct functions are now being used for inclination and galactic latitude, only an unknown and unsuspected effect exists, or some modification of the size function is indicated. The fact that changes in both incli- nation and galactic latitude affected but slightly the residuals and the apparent correlation of these residuals with the size function points to some kind of variation in the latter.

As has been mentioned previously, the most of the objects used in these solutions are in a region of sky where even con- siderable changes in the solar motion have but a secondary effect, so that no changes in that constant which would be consistent with experience can be assumed as accounting to any great extent for these residuals. All the evidence, therefore points to some kind of variation in the size function.

It is desirable to discover if possible whether the depen- dence is upon distance. The mere fact that if dependent upon distance, it is apparently upon the second power, is, to say tkie least, suspicious. However, some direct evidence exists. We can clear the observed radial velocities of solar motion and the dependences upon ellipticity and galactic latitude and then, assuming that the residuals are due only to the size or distance relationship, determine which it is.

In the two nubeculae, 6822, and 598 short period variables have been observed. In these four large objects, in the Andro- meda Nebula (224) and eight others, 1068, 3031, 3627, 4449, 4736, 5194, 5236 and 7331, the brightest stars have been obser- ved. These two methods enable fairly good determinations of their relative distances to be made. In the case of the four large objects the two methods furnish a check, and the means have been used. Six others, 2683, 2841, 3034, 3623, 4826 and 5055 have had limits set to the maximum brightnesses of their component stars and were used as a third group, although with small weight.

Because of the large size, structure and brightness, and small distance of the Andromeda Nebula it was grouped with the four having distances by the two methods.

The principal data and resulting diameters when reduced to the distance af the Small Cloud as unity together with the relative distances, are given in table 4.

The magnitudes of the non-variable stars in the Large and Small Clouds are from determinations at C6rdoba. The magnitudes of the bCephei-stars in the same Clouds are from Harvard observations for a mean period of 6d02).

The magnitudes of the non-variables in all other objects (17) are from Mt. Wilson observations by Nu661e3).

The magnitudes of the dCephei-stars in NGC 6822 and 598 are from observations by Nubble4).

The dimensions of the Large and Small Clouds are from photographs secured here, that of the Andromeda Nebula from a pbotograph by Barnardb), of 6822 by HdSZee), and the remainder measures by Curtis').

1) Science, of January 4, 1929, p. 8. 4) ApJ 62.418 (1925) and 63.252 (1926).

a) Harv. Circ. 280, H. A. 60, part IV and MN 87.428 1927). 9 ApJ 64.358 (1926) 6, Lick Obs. Publ. XI. ApJ 62.49 (1925). 4 Lick Obs. Publ. 13.

a3*

335 566 I 3 36

Nubec. Major 10.8 Minor 11.2

N:c6822 I :::: NGC 224 And NGC598M33 15.6

T a b l e 4. Distances , Diameters a n d Res idua l Velocit ies.

15.7 15.9

"' 20.0

+ 150 i- 28

- 562 - 3 9 +

+ 61

* 303' u 3627

4449 9 4736

5194 )) 5236 * 7331

NGC 2683 * 2841 * 3034 * 3623 8 4826 ') 5055

+ 281 +146

-450 73

+I73

19.0 >zo.o >I94 > I 9 4 >20.0

>'9.5 >19.0

Lclative )int.sce - -

0.9 I .o 7.6 6.6 7.' 16.6 26.3 26.3 19.1 15.1 15.1

2 7 . 5

33.' 69 55 55 69 55 44

Obs. )iam

300' -

2 1 0

20

I20

55 215

16 8 3.5 5 6

I 0

9.5 I 0

6 7 8 8 8

330

5 5 0 440 3 50

385

All are from photographs. (0 - C)' in the last column of table 4 has had the size

eEect restored. The distances and unity dimensions for the third group

were obtained for the magnitudes of the non-variables menti- oned in column two which are obviously uncertain and p r e bably too small.

These results are shown graphically in Fig. 2, 3 and 4, for the three groups of table 4 respectively. In each is given first the curve for distance and second for the diameters reduced to unity. The velocities are the (0 -C)' of the last column.

All three groups agree in showing no evidence of a relation of velocity to distance. They are almost equally as definite in showing a dependence upon size. The first and best determined group (Fig. 2) is the most consistent. By no reasonable interpretation can they be considered as depending upon distance to any appreciable extent but four of the five fall on a curve satisfactorily representing the second power of the diameters.

The second group (Fig. 3) shows less consistency but no apparent relation to distance. Four objects fall on a curve similar to that from the first group, but the remaining four are widely divergent. Closer examination of these latter indicates some possibly significant differences in appearance. NGC 7331 and 5236 appear to be faint for their size not out of harmony with smaller masses which could give such positive residuals, and 4449 and 4736 to be of types which show large negative residuals if the dependence is upon mass.

In the third group (Fig. 4) the resulting distances are uncertain by an unknown amount. Nevertheless they show the same general characteristics as the other two groups. No relationship to distance can be traced but five of the six objects

are not inconsistent with the curve found in the other two groups for diameter.

We thus find that these three groups of 19 objects support the hypothesis that the dependence is not upon distance but that it depends in some way upon size.

Var i a t ion of Rad ia l Velocity with Size of t he Globular Clusters. Their unknown status and the possibility of some sort of relationship make it desirable to examine the globular clusters to determine if they show the same depen- dences of radial velocity as were found in the spiral nebulae.

The radial velocities of 18 globular clusters, determined almost exclusively by SZz)her, were used in the following investigation.

The limited dispersion in galactic latitude of the globular clusters and their general absence of ellipticity preclude any attempt to investigate dependences upon those characteristics as was done in the case of the spiral nebulae. Only three clusters have latitudes of over 4 5 O . The mean for all 18 is 31O or 24' if we omit those 3. There is, however, sufficient range in size to justify investigating that dependence.

Only one, NGC 6273, has a noticeable ellipticity. The dimensions used are from photographs - 3 with

the Astrographic Telescope here and the remainder with the Crossley Reflector of the Lick Observatory').

The measures are all by the writer, with the exception of two by H. D. Curfis.

As in the case of the spiral nebulae the solar motion has been ignored. If the distribution and velocities are examined in detail it is found that they fall into three distinct groups, - two with positive velocities and one negative. One group of positive velocities contains two stars near 5h, - 30', the other with seven stars of o and positive velocities about a center at 17h, - 30'. The group of negative velocities, 9 in number, forms a stream along a great circle from the equator at 2 1 ~ to 13h, +zoo. This stream crosses the Milky Way almost at right angles.

The results of a classification according to size are given in table 5-

T a b l e 5 . Dependence of Rad ia l Velocity upon Size, Glob'ular Clusters .

Diameter I No. I Obs. Y

The cluster NGC 6934 was omitted for the present as the velocity of -350 km was marked uncertain and was highly discordant. The cluster itself also appears to be ab- normal and to lack the symmetry of the typical globular cluster.

These results show a consistent decrease of velocity with increasing apparent size as in the spiral nebulae. As far as the material is competent the range of velocity and the velocities themselves appear to be the same in the clusters as in the spirals when the lower galactic latitudes of the clusters are considered.

l) Lick Bull. 155.

337 566 I 3 38

This dependence of velocity upon size and the general similarities of size and velocities appear to constitute a definite bond between the spirals and the globular clusters, one of the very few between these two very different classes of bodies.

The foregoing investigatians lead to the following con- clusions :

A. The radial velocities of the spiral and globular (structureless) nebulae vary with apparent size, the smaller ones having the higher velocities.

B. The variation is not linear but increases rapidly among the smaller ones, being satisfactorily represented by the inverse square of the diameter.

C . The relationship is to size (or mass) and not to distance.

D. The radial velocities of the elongated nebulae are larger than for those more nearly round of the same diameters.

E. The radial velocities of the spiral nebulae are larger near the galactic poles than near the plane.

F. The radial velocities of the globular clusters also depend upon size apparently in the same way as do the nebulae.

G. The solar motion derived from the spirals agrees well in direction with that from the (fainter) stars.

H. These relationships indicate very definitely, if they do not establish, that the spiral nebulae and globular clusters are dependents of the galactic system.

These relationships suggest a brief consideration of the origin of these objects before discussing in detail the dependences themselves l).

The status of both spiral nebulae and globular clusters has been anomalous, the former being considered by many to be separate universes and by others distant members of the galactic system. The appearance of these nebulae has justified the assumptions of a composition all the way from cosmical matter to fully formed stars.

If the observed displacements of the lines in the spectra of these objects are due to motion, as seems to be established by the fact that some yield displacements to the violet and that upon the assumption of motion, these bodies yield a solar motion agreeing well with that from the fainter and more rapidly moving stars - the above dependences of velocity upon size and galactic latitude ally these objects with the galaxy as dependents.

If they are dependents, the galactic system must be of greater size and mass than has hitherto been supposed, for these objects are systems of appreciable size themselves. And there is a large number of them.

Assuming that the unrepresented one quarter of the sky does not differ from the rest in which the objects with known velocity have been observed, there is an almost over- whelming preponderance of positive or outward velocities. It is this fact which seems to establish beyond reasonable doubt that these objects large as they undoubtedly are, can only be secondary systems subject to some kind of central control, and not completely autonomous.

If these nebulae are dependents then they must somehow lave had an origin which was either in the parent galactic system or closely related to it.

Another very definite fact furnishes a crucial test and eaves no doubt that at least the Magellanic Clouds, the larger spirals and the globular clusters are within the confines If the galactic system. It is that jus t a s fa in t s ta rs a re -ound scat tered over the sky in regions outside the iebulae as in those objects themselves. This is making tllowance for the extreme effect of the spectral-luminosity relationship.

In other words stars of the same spectral type and magni- tude as those in the nebulae and clusters are found scattered 3ver extensive regions of sky'which are outside the limits of those objects.

Obviously, therefore, these nebulae and clusters can not be farther away than those whieh belong to the general system.

The conditions imposed upon any tenable hypothesis 5s to the origin of these bodies, the spiral nebulae and globular clusters, have had to meet at the outset the high and prepon- derant velocities of recession. This was such an obstacle as to prohibit until recent years any serious attempt.

The observational proof, however, of the pressure of light opened the way to a satisfactory explanation of these large velocities of recession, Hypotheses based upon that physical fact were proposed independently by Professor Lindemann and myself in 1923~).

The developments of atomic physics and especially the discoveries of the highly penetrating cosmic rays by MiZZzkarS and his associates have given color and impetus to an exten- sion of those' hypotheses to include radiation itself as a factor if not the principal one.

The above facts appear to be sufficiently well established to justify an attempt to form a working hypothesis of the origin and evolutionary processes of the spiral nebulae and globular clusters, It will be formulated in outline only and with the full realization that it is tentative and subject to revision with the acquisition of more data.

Hypothesis. No attempt is made to account for the very beginnings of our system. The earliest epoch assumed is that at which the material or bodies of the galactic system were in a state to radiate more or less as at present. If we are justified in believing that the nebulae and clusters of today were ))ejected(( from the galactic system it may become possible with the accumulation ef. data and knowledge, to determine from their velocities the time at which they left the central parts of the system. There are, however, many factors involved.

Our present knowledge leads to the conclusion that during their present and earlier history at least, the, spiral (cosmical) nebulae and the globular clusters have not been feeders of the galactic system but on the contrary the galactic system has furnished the mgtterial or energy from which these bodies have been built up.

l) A more extensive consideration of their status and place in the evolutionary processes is being made in another investigation. P) Lindemann, The Observatory, May 1923. Perrinc, The Observatory, September 1923.

339 566 I 340

That wnergyw or ,matter(( or both have been sent out from the parent galaxy and gathered together in outer regions into more or less globular masses of different sizes.

That in some manner, perhaps around larger and more dense nuclei, have condensed the stellar bodies and wonden- sationsu which compose many of them. That those (generally globular) nebulae which show no structure are still in a cosmic state or with the process of star formation only begun or in early states.

The spectral condition of these objects presents some difficulty which may or may not be crucial. The behavior of the giant red stars, however, is some indication that perhaps the spectral condition of these nebulae is not impossible on the hypothesis suggested.

Where the primitive globular masses pursue a solitary course unaffected seriously by the gravitation of other masses, condensation into stars takes place normally and in a shorter space of time and we have the globular clusters.

Where, however, near approaches of such masses occur, tidal effects such as C h a d d i n and Moulfon assumed in their Planetesimal Hypothesis occur and one or both bodies are spread out into thin discs showing streams and spiral struc- tures. Some such result seems to me so obvious that it con- stitutes the strongest evidence we have of the correctness of the principle laid down in that hypothesis.

Consideration of the facts leads me to the conviction that the Planetesimal Hypothesis should be extended to include the spiral nebulae.

Such a process accounts for the fact that the globular clusters are apparently fully condensed into stars ; they have proceeded without the disruptions which have dissipated anew much of the matter as we see it in the spirals.

Our present knowledge of the motions is too limited to justify close analysis. This is especially true of the velocities of approach.

I n t e r p r e t a t i on o f t he s e Re la t ion s h ip s. In attemp- ting to interpret these results three considerations are to be kept in mind:

I. Such relationships as well as other evidence proclaim these nebular objects to be dependents of our galactic system. No other conclusion seems possible.

2. We appear not to be dealing (only, at least) with gravitation as that force is understood at present. Gravitation is an attraction whereas these nebulae appear to be driven away by some force behaving as repulsion.

3. The displacements of the lines in the spectra of these nebulae toward the red cannot be explained on the theory of a gravitational effect upon the light rays producing them. The increase of such displacements with diminishing size (and probably mass) is just the opposite ofwhat is to be expected upon such a gravitational effect.

While not unmindful of the possibility of other explana- tions I shall consider these relationships from the point of view of motion.

The displacements of spectral lines giving rise to these velocities are similar in all other respects to smaller velocities from stars of similar types ; some of these nebulae (and globular clusters) give displacements of the same order of size as the

stars; there is a wide range of velocity and there are several negative velocities.

The general agreement of the solar motion derived from these nebulae with that from the stars and the dependences upon the physical properties, such as size, inclination to line of sight and galactic latitude also strongly support the theory of motion. It is difficult to see how these dserent and very definite relationships and properties can be explained upon any other hypothesis, according to the physical ideas held at present.

Dependence upon Galac t ic La t i tude . The depen- dence upon galactic latitude is in harmony with the theory of ejection and seems to call for no further comment at present.

Solution No. 7 indicates a change from zero at the plane of the galaxy to + 704 km at the poles. From the nature of the case this is probably too small.

Dependence upon El l ipt ic i ty . The same solution indicates that nebulae turned edgewise toward us have velo- cities + 224 km greater on the average than those whose planes are normal to the line of sight. There is a suspicion that the dependence upon inclination is also a function of size-mass and in consequence that these two factors may be connected in some way,

The spectra appear to be normal.

This condition is presumed to be one of the results and to indicate the mode of their formation from the near approach of two globular objects, probably amorphous nebulae, composed of cosmical matter. The subject of their origin will be dealt with in a separate paper on general evolution.

341 5661 342

+ 665 + 591

. + 421) Large

+ I95 3

Dependence upon Size o r Mass. The most sugges- tive of these three dependences is that upon size for it at once raises the question whether it is not in reality a dependence upon mass. We have already seen that it appears not to be a relation to distance.

In making the preliminary and first solutions the significance of the large changes in both groups of ellipticities among the smaller sizes was not fully realized. They were noted but supposed to be merely accidental. Upon examining the results of those solutions more carefully and plotting those values (Fig. I) it was obvious that the dependence was not linear but that the exponent of the coefficient departed widely from unity. With little to guide the choice of a function and whether distance was an appreciable factor, solution No. 3 was made with coefficients derived from a curve based upon table 2.

A study of these results and the trial curve showed that the square root of the observed diameters satisfied the depen- dence sufficiently for these preliminary solutions. Solution No. 7 was then made using the square roots of the diameters .as the coefficient f in the equations of condition. The more logical coefficients for g and h were also used in the last solution.

The residuals do not show any decided improvement over solution 3 due chiefly, it appears either to the fact that there are systematic differences which would require two solutions for solar motion instead of one, or to deviations of the true function of size.

We have here another analogy perhaps to the behavior of the stars used for solar motion whichalso showsthenecessity for different solutions. These are undoubtedly in all these cases evidences of Kapteyn's two streams whose underlying cause is, doubtless, none other than some of the internal motions of a spiral or elliptical nature and may extend to the nebulae.

However this may be, the dependence of velocity upon size in the spirals and the general form of the function are established by the fact that both with and without consideration of solar motion the results agree as well as could be expected from the data, even to the numerical values of the coefficients. The values are so large as to leave no doubt of the reality Qf these dependences.

The form of the function in the case of the dependence upon size is of especial importance. An examination of the solutions and data shows that it is certainly not a linear func- tion of the diameter and the present data indicate a close approach to the square root. Further data are awaited with especial interest in this connection.

Before the last solution (No. 7) was made, the Mt. Wilson .determination of the highest velocity yet observed of this class of object (2500 miles or 4000 km) came to my notice. It was not included because the identity of the object was not known to me, but also because it was desired to use it as a test of the coefficient derived from the other data, The notice I saw1) merely gave the facts that it was the faintest (and presumably the smallest) yet observed, a d near to one of the poles of the galaxy.

l) Science, January 4, 1929, p. 8.

2.05 1363 5 2.72 1608 8

6.401 ;%] 4 7.07 3 -

A glance at these facts shows a general confirmation if the square-root function.

With the discovery that the function was not linear =me the corollary that the product of velocity and square root were sensibly a constant, or

Y. Vd=constant =k. (2)

If we take the data of table 2 and derive such a constant we obtain the results given in table 6. Table 6. Derivat ion of t he Cons tan t Kin Equat ion (2).

Ellipticity I 0bS.y If(m1 Constant 1 No.

1 Mean 1 1141 1 2 2

+I158 I 1-34 I I554 I 4

1720 1 21 1 Mean I I47431 20

1) Omitting NGC 4565, If the Iarge group is corrected for ellipticity to the small

group, and 4565 omitted the mean value of the constant comes out I I 5 I.

These results are sufficiently consistent to justify the tentative assumption of the validity of equation (2) within the limits of the data used. Upon such an assumption it is possible to test the agreement of the velocity of 4000 km as well as the smallest object which was used in the solution, NGC 4884.

If we take the velocity of + 1500 km observed for the latter, from equation (2) we obtain a diameter of 50". The measured diameter from a half tone reproduction of the original negative by Curtis, gave 30" which is in satisfactory agreement when it is remembered that in such cases the reproduction seldom is as extensive as the original, and also that the dependence if upon mass, might be satisfied by a volume ranging between the square and cube root of the dimension.

In the same way we find a diameter of 30" for the one with 4000 km velocity. Its observed diameter is unknown to me, it merely being stated (loc. cit.) that ))it is very faint and probably one of the most distant objects within range of present telescopesa.

These two cases of very small objects and the small or negative velocities of the Magellanic Clouds, NGC 224 and 598, large objects, are direct evidence of the extremities of the curve in Fig. I, and that the square root function repre- sents closely the average relationship of velocity to size.

Until more observations become available in the southern sky, the solar motion cannot be sufficiently well determined to justify a more accurate evaluation of these coefficients or of any deviations from the assumed functions.

This is interpreted to mean small.

For example it is suspected at least that the very large objects, have in general nega t ive velocities. That result is obtained from solution No. 7 as well as No. 3. But the number of relationships involved is such, that the comparatively few observed objects, (with high velocities and considerable uncer- tainties in the resulting velocities) are insufficient to disen- tangle these and other involved questions.

Fig..?

For the present, therefore, discussion is limited to a few broad considerations of the dependence upon size, assu- ming the square-root function

The fact that this function is closely the square root is of itself evidence that the dependence is upon mass. For the volumes of such thin discs as the larger spirals appear to be would be nearly as the squares of their diameters, and as they

+ZOO

c ; 3 s

4m.

Jw L w *

s 'if ; Zod 6 100

0

f 400 + 300 * PO0 im 0 -100 -200 -Joe

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az3* 44:' JOJI - - - - - - - - - - _ _ _ _ _ _ _ - - - - - - - - - . . - - _ _ _ - _ _ _ _ - - - - - - - _ _ _ _ _ _

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- - - - - - - _ _ _ . _ _ _ - - --- ._.___ - - - - _ _ _ d

- - -..=;-- - - _ _ - - - - - _ _ *

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- - 2.-- -.- a - - -

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are essentially of the same spectral types their constitution as to mass and volume could be expected to be similar. A dependence merely on volume does not seem tenable.

The deviations which have been noted (0 - C) appear to be adequately explained as due to departures of mass from the square root function of size.

From the similarity in the spectra of these nebulae it seems highly probable that with some knowledge of the distances, the total light will enable an approximate estimate to be made of their relative masses. A program of this nature is under way here as well as the determination of the radial velocities of southern objects.

545

If the relation is to mass, as it appears to be, equation ( 2 ) would take the form

mv=R (3) where m is mass, v is velocity and K a constant and assumes special interest on account of the possibility that it may extend beyond the limits of the data used.

Obviously the limit at one end of the curve would be zero velocity of an infinite mass and at the other infinite velocity for zero mass. If such a relation holds good over the entire range it would be a fairly strong argument for the equi- valence and transmutability of matter and motion. As it is the range covered by observation is sufficient to justify serious consideration of such a possibility and a careful examination of the evidence of any limitation.

566 1

Notwithstanding the uncertainties and limited data the square root function seems to be definitely indicated.

Figures 2, 3 and 4 show no relation to distance. As these are the larger objects, however, it seems probable that whatever dependence of size upon distance there may be, is obscured and will require more extensive data to disclose. That there is some dependence upon distance seems certain and is indicated by departures of Some objects from the square root function. There Seems little doubt, however, that the chief dependence is upon size.

As the largest objects give negative velocit,ies it would appear that perhaps that end of the curve was practically attained?. The rapid rise of the other end is indicated by several objects from +1300 to +18oo km velocity and

3 46

K9. 4

especially by the one With + 4000 km velocity. While a long way from infinity, nevertheless these velocities are not necessa- rily inconsistent with such an extrapolation. For the mass of such nebulae as give these high velocities must be large on any assumption and the gap from 4000 k m to infinity is of the Same order as that from the mass of such objects to zero.

It is not suggested that equation (3) is true to the limits. Attention is merely called to the consequences of such a condition, to some reasons favorable and that there is no known prohibition.

From orthodox physics we have

momentum = m v (4) m being mass and e~ velocity. Interpreting equation (3) in the light of the above we conclude that t he momenta of

these nebulae a r e cons tan t . This condition is probably significant of their ongin but for the present is not pursued further.

After a careful consideration of the evidence it appears to me sufficient to justify as a working hypothesis, the assump- tion that t h e nebu la r dependence i s upon mass and to favor the thesis that equat ion (3) is no t l imited.

One of the most striking facts about these nebulae appears to be the enormous energy resulting from their high velocities and great masses, energies which compare favorably with subatomic forces and suggest a possible relationship.

Interest attaches to an examination of these results in connection with the recognized relations of mass and velocity.

1) Should these negative velocities of large objects be' confirmed, as seems probable, it will become necessary to consider the question of the graviFtion of the parent system.

24

347 5661 348

Before going further however, it is desirable to note

As accepted and used the general equation for kinetic the equations for energy.

energy is ) m v a = E

where m is mass, v is velocity and E energy in ergs. The Kaufmann-Lorcnt~-E~n~~e~n-equation is

m8=& (6) in which m is mass, c the velocity of light and E the energy in ergs.

Except for the fraction 8 in the first member this equation is identical with equation ( 5 ) for the special value of PI =velocity of light.

One naturally asks why this difference in equations which appear to cover essentially the same ground. The answer appears to be that equation (5) was derived from ordinary dynamics of every-day experience in which the velocity is no t constant, but affected by gravitation or other variable factor yielding accelerated motion. Hence the factor ).

It is not quite clear to me why the case of constant velocity was not included in treatments of this subject of energy for it is one which has an astronomical significance even if not in terrestrial problems. But I have so far failed to find in the usual sources any definite reference even to this point.

It seems obvious, however, from the usual treatment in connection with gravitation that in such case equation ( 5 ) would take the general form

m v ' = E . (7) If that conclusion is correct then the K.-L.-E.-equation

(6) is merely the special case of the velocity of light. The use made of this equation (6) leads to the conclusion

(I have not access to the literature at present) that c is used as a constant about which rn and R revolve, in other words that the velocity of light is considered as the maximum possible.

The behavior of the nebulae as indicated by equation (3) renders doubtful such a limitation without the most positive proof.

The K.-L.-.??.-equation is derived from observations of the behavior of electrons and from theoretical considerations depending upon generally accepted ideas of the constitution and behavior of matter. It conforms to the orthodox attitude towards motion, that there must be something to move, and to the mathematics of the case. Therefore it has finite limits; in the mat'ter of velocity the limit is the square of the

Observatorio Nacional a rdoba , 1929 April 17.

velocity of light, which is assumed as the constant. Neither the mass m nor the energy E are apparently considered as approching closely the limits in either direction.

Equation (3) on the other hand is derived from obser- vations of spiral nebulae, at the other extreme of mass, bodies many times the mass of the stars. It is purely empirical, but based on well established physical phenomena, (the displace- ment of lines in stellar spectra) which do not seem uncertain of interpretatjon.

The range of these velocities is very large, from practical zero to very much the highest in our experience in the whole domain of astronomy. Although these high velocities fall far, far short of infinity or even the velocity of light, they cover a sufficient range to arouse speculation as to whether they may not be extrapolated to the very limits in view of the ever increasing tendency to greater subdivision in successive atomic investigations. And they give a curve which appears to establish the form of the function upon which all depends.

If we can divest our minds of the idea that motion mus t be accompanied by nmattercc simply because in our (limited) experience our senses are only conscious of the more sluggish manifestations which are all accompanied by nmaterialc bodies, and conceive of motion as existing alone, a new field is at once opened.

If we can expand our horizon in that way equation (3) may be considered as an extension of the K.-L.-E.-equation and (7) to the limits. This will not be easy for many for the simple reason that we can (now) easily conceive of something smaller and yet smaller, but can not conceive of the last final step to infinity or zero which is required to pass over to the limits in making such a fundamental equation universal.

Personally I have been able to pass over that step and conceive of motion alone and it has led to some astounding possibilities in the way of explaining gravitation and the ether. But I do not enter into those matters here, for the simple reason that it is first essential to confirm and to extend our knowledge of the dependences in question and the form and nature of the size function.

Both equations (3) and (7) coverrather wide ranges of observed phenomena and make it desirable to study them in detail and rather closely based as they are upon the behavior of such extremes as atomic forces and nebular velocities, very small in one case and very large in the other. But here also more data are necessary. It is scarcely necessary to point out the many questions which have presented themselves in connection with these dependences. They must be left to other times and places even for their enumeration.

C. D. Perrzne.

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