# Popular Science Monthly/Volume 82/March 1913/What Becomes of the Light of the Stars?

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* WHAT BECOMES OF THE LIGHT OF THE STARS?
By FRANK W. VERY
WESTWOOD OBSERVATORY
ONE of the most astounding things in nature is the enormous energy which the sun is continually dispensing as radiation to surrounding space. The earth, as viewed from the sun, is a mere point in space, and receives no more than 1/2,200,000,000 of the radiant energy which the sun is outpouring so lavishly. Yet out of this small fraction of the total radiation, practically all the terrestrial activities of wind and wave, tropical hurricanes and avalanches of ice on alpine slopes and the no less potent but milder forces which clothe the earth with verdure, originate.
If we include all the planets in the solar system, and assess the outgoing solar rays at the maximum tariff imposed by the obstructions in their path, it still remains true that only 1/100,000,000 of their power is directly utilized in maintaining the thermal equilibrium and life of the attendant orbs, dependent from day to day for these gifts upon the dispenser of all of this bounty.
The solar outpouring for even a single day is inconceivably great, yet the same flux of energy has been going on ceaselessly and with very little change in its absolute intensity for at least a hundred million years, as the records of geologic time attest. If only one part of solar radiant energy in one hundred million is directly utilized, what becomes of the other ninety-nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine? Remember, also, that our sun is but one among hundreds of millions of stars made known to us by our photographic telescopes, all outpouring similar torrents of energy, and the question comes home to us accentuated with many millionfold intensity.
Professor Comstock has shown that the theoretical and observed distributions of luminosity among the brighter stars may be reconciled, if we suppose either that the intrinsically brightest stars have a "distinct tendency to cluster about the sun," or else that "there is a sensible absorption of light in its transmission through space, of such average amount that a star having a parallax of a tenth of a second appears one magnitude fainter than it would appear in the absence of absorption." Other modes of attacking the problem must be invoked in order to decide between these alternatives.
​The much more searching analysis of Professor J. C. Kapteyn favors an actual absorption of light from the more distant stars, but a very much smaller one than that demanded by Comstock's result. Kapteyn's method, however, when applied to bodies more remote than the nearer stars, gives about the same amount of absorption for the easily resolvable clusters, N.G.C. 7078 and 7089, and for the irresolvable and very much more distant Andromeda nebula, which indicates that his absorbent medium is a local adjunct to these stellar masses, and that it is perhaps a meteoritic envelope of somewhat greater volume than the stellar agglomeration, but not a universal medium filling all space. The circumferential absorption or scattering depletion of light by a limited envelope can not be taken as an indication of nebular distance, but will vary with the constitution of the enshrouding meteoritic swarm.
To make apparent any general absorption of radiation by the interstellar medium, it becomes necessary to investigate the properties of space far beyond the limits of the Galaxy and its outlying shells of sparsely distributed stars, and, crossing the immense voids of surrounding ether, to inquire whether they contain other galaxies of dimensions comparable with our own, and whether these afford any evidence of a gradual absorption of luminous energy by the intervening medium.
The first scientific enunciation of the doctrine that there are such external galaxies was given in 1734 by Emanuel Swedenborg in his Principiorum Rerum Naturalium, and Herschel's nebular discoveries lent some support to the doctrine; but it was not until after 1864 that further evidence really bearing on the question came. Then, spectroscopic examination at the hands of Huggins and his successors divided the nebulæ into two great classes of the gaseous nebulæ with spectra of a few bright lines, and the white nebulæ with continuous spectra. This furnished the first real criterion for a fundamental distinction.
The gaseous nebulæ are so closely associated with the Milky Way that they obviously belong to our galactic system; and Ranyard's recognition of wide, dark lanes or spots, often branching or dendritic in form, blotting out extensive regions on Barnard's photographs of the Milky Way, showed that not all of the gaseous bodies in its neighborhood are luminous, but that some are to be compared to a dark smoke or mist, obscuring the glories of the brightness which lies back of the widely extended and absorbent cosmic cloud. Among the ​conspicuosly vacant spaces in the Milky Way may be noted those running east from Rho Ophiuchi, others east of Theta Ophiuchi, and mingled star clouds and vacancies in Sagittarius near 181/2 hours right ascension and 11° south declination.
Since there exist these enormously extended masses of gaseous or misty material, capable, whether themselves luminous or dark, of exerting a strong absorption upon the light of any bodies beyond them, and intimately associated with the Milky Way; and since, further, it is inevitable that the broad disk of the galactic accumulation must have gathered into its vicinity great swarms of meteoritic material, acting after the manner of a general, widely distributed mist, forming an envelope analogous to an atmosphere having its greatest depth in the direction of the galactic plane; it follows that this extensive quasi-galactic atmosphere and its associated, but locally limited, gaseous bodies must especially absorb the light from those distant galaxies which lie in or near the plane of the Milky Way. This, it seems to me, is the probable explanation of the extraordinary increase in the numbers of the white nebulæ near the poles of the Galaxy, namely, that the galactic quasi-atmosphere being thinnest along a diameter at right angles to the plane of the swarm, the light of external galaxies is best able to penetrate through the obstructions if coming from this direction.
Kapteyn's recognition of absorption by an interstellar medium also supports the above explanation, since he finds that the absorption diminishes in extra-galactic latitudes. Professor Comstock, it is true, reaches a different result, finding that stars of the 10.5 magnitude have larger proper motions as their galactic latitude increases, whence he concludes that "at right angles to the Galaxy the limits of the stellar system fall within the range of vision," which may be correct, but his explanation that this is so because "the transmission of light through and that this medium offers little obstruction in the direction of the galactic plane does not necessarily follow. The simple explanation that the Galaxy is a discoidal aggregation of stars with limits less remote than is sometimes assumed, permits the supposition that the 10.5-magnitude stars in the galactic plane comprise many relatively bright stars at a double distance and having a mean annual proper motion of 0″.01, whereas the extra-galactic stars are the extra-galactic spaces is impeded by some absorbing medium," ​soon cut off by the external galactic limits and have a mean distance one half as great, represented by a double proper motion of 0″.02. This hypothesis fits the observations and reconciles the conflicting results of the two investigators.
Among the many spiral or discoidal nebulæ there are some which have the plane of the disk presented edgewise, and which are foreshortened into long and narrow shapes, sometimes with a central globular condensation. Several of these elongated objects are centrally divided by a dark band. I take it that these dark bands represent the quasi-atmospheric element in question. One of the best examples is the nebula Herschel II 240 Pegasi, which is a fusiform object (as seen in projection) with a strong central condensation, and fading gradually towards the extremities. The bright mass is almost exactly bisected by a longitudinal black band, sharply defined, and about one fourth of the width of the bright part near the ends. It appears to be an equatorial belt of absorbent material, outside of, or an extension of, the margin of a luminous lenticular mass. Other examples are: HV 19 Andromedæ, HV 8 Leonis, HV 41 Canum Venaticorum, HV 24 Comæ Berenices and HI 43 Virginis. It is very probable that our own Galaxy is a similar disk-like aggregation of stars, involving spiral starstreams, and surrounded or interpenetrated by an absorbing medium which is most extensive in the plane of the disk.
In considering the absorption of light in space beyond the farthest reaches of the Galaxy, the investigation is best limited to luminous bodies of the galactic order which are neither themselves involved within the coils of our own starry system, nor situated in an extension of its plane, that is, we must exclude those objects whose galactic latitude is small. The latter, by the hypothesis, will consist of only a few near and relatively brilliant objects whose light has sufficient intensity to penetrate the galactic absorbent medium; but lest the distinction should be considered too fine, or too hypothetical, it may be waived in the present test.
I find only one nebula among those pictured by Mr. Isaac Roberts which is in a conspicuously vacant region. Of this nebula, H IV 74 Cephei = G.C. 4634 = N.G.C. 7023, Roberts says: "The nebula appears in a region almost devoid of stars." It is situated near the border of a branch of the Milky Way. Sir William Herschel has recorded his impression that nebulæ are apt to be found in regions which are poor in stars. This may be so, but an impartial examination of the photographs seems to indicate that the supposed connection between nebulæ and stellar vacuities is mainly a myth. It will require more extensive material than we now have to decide the point. Where such connection does undoubtedly exist, two different causes may be assigned for it: (1) a gaseous nebula between the Milky Way and ourselves may have a wide border of non-luminous absorbent material ​which blots out the light of the more distant stars; and (2) the misty matter associated with the more condensed star-groups may obscure the light of external galaxies which therefore are better seen through the thinner places in our own stellar mass. Either of these causes would account for the stellar voids which Sir William Herschel describes as even a warning of the proximity of nebulæ; but it will be seen that there is no foundation for the inference which Mr. Herbert Spencer has built upon the supposed fact, namely, that none of the nebulæ can be external galaxies, because "thousands of nebulæ. . . agree in their visible positions with the thin places in our own Galaxy," and that they are necessarily most intimately linked with its structure. The connection, if established, will in no wise invalidate the wider generalization that external galaxies must appear to be most numerous in those regions where the mists or gaseous masses attendant on our Galaxy thin out and permit the light from the outside to penetrate the starry walls.
Mr. Roberts bears this testimony to the fact that the larger part of the nebulæ are situated beyond the confines of the Galaxy: There are "to be seen," he says, "stars apparently in a complete state of development, scattered over the surfaces of the most prominent of the nebulæ, but it will be observed that they do not conform with the trends of the spirals nor with the curves of the nebulous stars [or stellar condensations?] involved in them. This fact I apprehend to be strong evidence that they are independent of the nebulæ—that they are not in any way involved in the nebulosity, but are seen by us either in front, or else in space beyond the nebulæ. If they were beyond them, their light would have to penetrate through the nebulosity, and we should therefore expect it to be duller in character and the margins of the stars to be surrounded by more or less dense nebulous rings; but these effects are not traceable in the photo-images, and we are consequently led to adopt the alternative inference that they are between us and the nebulas. If they were involved in the nebulosity, they would conform with the trends of the convolutions and appear like nebulous stars."
The dark lanes in the Milky Way are sometimes called "rifts," a term which implies that the stars are distributed in a relatively thin sheet which can be rent asunder. Moreover, the word is not used in a merely metaphorical or descriptive sense, but in its full significance, as in the following quotation from "Worlds in the Making" by Svante Arrhenius (p. 173): "The presumption that these rifts represent the tracks of large celestial bodies which have cut their way through widely expanded nebular masses has been entertained for a long time." And ​the same author explains the dark ring around the nebula near Rho Ophiuchi on the supposition that "the smaller and more slowly moving immigrants. . . are stopped by the particles of the nebulæ," and are detained by the gathering crowd. But even if it could be demonstrated that the stars are arranged in thin sheets, and that celestial bodies exist of sufficient size and momentum to plow their way through great aggregations of stars, demolishing everything in their track, it would still be exceedingly improbable that only one layer of stars should exist in a given direction, or that several rifts should coincide. On the other hand, the presence of widely extended masses of dark absorbent matter in the shape of branching streams, sheets or rings, situated between us and the depths of star-strewn space, is not unlikely.
The gaseous nebulæ which form a part of the galactic structure are often very extensive, and are of a great variety of shapes, being frequently strangely irregular; but the more numerous white nebulas are formed more nearly after a common pattern, although still with infinite variation as to details. In general, what is common to nearly all of the white nebulæ is a tendency to form a two-branched spiral, the branches issuing from opposite sides of a central condensation, and coiling either within the boundaries of a plane circular disk, or forming a helix around a cylindrical directrix. The former figure is the more characteristic, and is well exhibited in the Great Nebula in Andromeda.
Another very remarkable and at present unique type is the transient nebulosity which appeared around Nova Persei, issuing from the star as a center, and expanding into the commencement of a vortical ring. It was an electric phenomenon, an exhibition of canal rays, or positive ions, on a grand scale. Facts from the history of these two bodies will be found useful in preparing one of the necessary means for our quest.
It is obvious that we require for this investigation of external galaxies some scale of distances, and equally obvious that at present such a scale can be only approximate. Indeed, it is probably this uncertainty as to the scale on which the universe is constructed which deters astronomers from attempting to discriminate between different galactic orders. I propose to see if this uncertainty can be, in part, removed.
I propose to take the distance of the Andromeda nebula as our celestial "yardstick," which may be called one andromede, and assuming that when we consider a large number of nebulæ, the average size does not vary with the distance, and that consequently the average distances may be taken inversely proportional to the angular diameters of the objects, I shall classify the nebulæ according to apparent size and brightness. It is essential that the subdivision shall not be too minute. ​There is in nature a tendency to wide variation, coupled with a coordinate tendency to uniformity in averages, when the number of classes is limited. Thus the land mammals range in size from elephants, say 15 feet long, to mice and shrews of a few inches. If we divide the earth into a good many faunal regions, the average sizes of the mammals in the different provinces may vary considerably; but if we divide the earth into only two halves, the averages will be almost identical.
For the present research, I take Sir John Herschel's "General Catalogue of Nebulæ and Clusters of Stars," which, coming from a single hand, and that the hand of a master, may be considered fairly homogeneous; and excluding the clusters which are known to be associated with the Milky Way, and are therefore comparatively near, I divide the remaining objects into two classes: (1) large nebulæ, or those having a diameter greater than 2′; and (2) small nebulæ, or those which are less than 2′ across; and I shall assume that the small nebulae are on the average farther away than the large nebulæ in the ratio, x:1, leaving the value of the ratio to be determined by considerations to be drawn from the result, and which will appear in the sequel.
A point-source of light diminishes in brightness as the square of its distance increases; but light from a large number of points so close together that they can not be discriminated must be treated as a luminous surface; and since the angular area of a surface also diminishes proportionally to the inverse square of the distance, the intrinsic brightness, or the brightness of the unit of angular area, does not change with the varying distances of the nebulæ. We must therefore inquire: Is the intrinsic brightness of a small, and therefore presumably distant, white nebula equal to, or less than that of a large one? If the average brightness of the unit of angular area is less for the smaller white nebulæ the presumption is that the light of the smaller and more distant objects has been absorbed in passing through space. To apply this test, I further subdivide each class into three groups—(vf) very faint, (f) faint and (b) bright, or, if desired, the last two may be combined into a single group.
Dividing the nebulæ in Herschel's catalogue into groups of four hundred each, and taking the ratios of the small to the large nebulæ in each of the thirteen groups, I find that without exception the faint and small nebulæ are more numerous than the bright and small in a relatively very much larger ratio than occurs in the corresponding divisions of the large nebulæ. With only three exceptions the same relation is obtained by comparing the very faint and the faint nebulæ. Treating the groups separately, and taking the mean of the ratios, I find
Small divided by large: vf, 8.38; f, 6.83; b, 1.48.
The sums for the entire catalogue are
${\begin{aligned}{\text{Small:}}&&vf=&1765,&f&=897,&b&=241.\\{\text{Large:}}&&vf=&\;\;235,&f&=172,&b&=204.\end{aligned}}$
The division into separate groups with the result that the same general law is given by every one of the groups is of course the more severe test; but taking the ratios for the sums as answering our present purpose, we have for the ratio of
${\frac {\text{Small nebulæ}}{\text{Large nebulæ}}}\colon \quad vf,7.51;\quad f,5.22;\quad b,1.18;$
or approximately vf:f:b = 6:4:1; that is, the very faint nebulæ are in excess over the bright ones among the small nebulæ in the ratio 6:1, but are of nearly equal frequency among the large nebulæ. In other words, the large nebulæ are intrinsically much brighter than the small ones.
I next performed the same operation with the 744 objects in a "Catalogue of New Nebulæ Discovered on the Negatives" taken with the Crossley reflector at the Lick Observatory, dividing them into two groups: (1) very small, or not over one half minute in diameter, and (2) those which are above this size and which may be called "large." These groups were divided into two classes: (a) very faint, including those which are described as "very faint" and "very very faint," and (b) pretty bright, or those given in the catalogue as "faint" to "bright." The result of this examination is that three fourths of the large nebulæ are pretty bright, and one fourth very faint; while the very small nebulæ have just the opposite distribution of brightness, three fourths of them being very faint, and only one fourth pretty bright.
In comparing the two catalogues, it must be recognized that the photographic method is far more delicate. Most of the objects in the photographic catalogue could not be detected by visual examination. The photograph also includes faint margins and therefore increases the apparent size of such nebulæ as are visually perceptible. Consequently, Herschel's small nebulæ are about equivalent to the "large" nebulas of the photographic catalogue, and we should expect that the photograph would include a much wider range of brightness—all of which is confirmed by a discussion of the observations.
Let us suppose that the average distances of the several classes of nebulæ are given in andromedes, and denoted by the letter a, and that the coefficient of transmission of light through space is $t^{a}$; also that the mean distances are inversely proportional to certain assumed apparent diameters which are fairly typical. Each class of nebulæ includes objects having a considerable range of actual diameter, that is, the variation of distance is not as great as that of the apparent diameter. Instead of taking a mean value of 1′/4 to represent the diameter of that class which includes nebulæ less than 1′/2 in diameter, I take ​the upper limit of 1′/2 as representing the class of very small nebulæ. For the intermediate class which includes those objects called "small" by Herschel and "large" in the Lick catalogue, and which may be designated as medium, I take a diameter five times as great, or 21′/2; and for Herschel's "large" nebulæ, I take a diameter of 5′. The reason for these selections shall now be given.
I take for the diameter of the Andromeda nebula, 110′. This subtends the longer axis of the oval figure of the more condensed spiral arms. The fainter extensions are omitted because these are seldom included in the more distant nebulæ. Taking a suitable value for the coefficient of transmission, the curves giving the relation between brightness and distance become congruous for the two catalogues, if we take x, the unknown ratio of distance for large and small nebulæ, equal to 2 for Herschel's catalogue, and x = 5 for the Lick catalogue. This gives the following sequence:
| Nebular Class | Diameter | Diameter | Distance | Distance | Distance | Transmission | Transmission | Transmission |
| Andromeda | 110′.0, | a$_1$ | = | 1.0 | andromede, | t | = | 0.996 |
| Large nebulæ | 5′.0, | a$_2$ | = | 62.5 | andromede, | t$^a$ | = | 0.778 |
| Medium nebulæ | 2′.5, | a$_3$ | = | 125.0 | andromede, | t$^a$ | ${\ce {=}}$ | 0.606 |
| Very small nebulæ | 0′.5, | a$_4$ | = | 625.0 | andromede, | t$^a$ | = | 0.082 |
The statement which was made for the ratio of brightness among the groups in the Lick catalogue (vf and f + b for large and small nebulæ) can be repeated in identical language for Herschel's catalogue by merely substituting the fraction 2/3 instead of 3/4; that is to say, Herschel's nebulæ are not only nearer than the Lick nebulæ, but are more nearly at a common distance; and the fraction expressing the ratio of brightness for the two groups of near and distant objects among the Herschelian nebulæ approaches nearer to the value of equality which it would have if all of the nebulæ were at the same distance, for then there would be equal absorption, and large and small objects should be equally grouped about a mean value.
| Ratio of brightness for large and for small nebulæ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | If equidistant, | 1 : 1 |
| Ratio of brightness for large and for small nebulæ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Herschel, | 2 : 1 |
| Ratio of brightness for large and for small nebulæ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Lick Obs'y | 3 : 1 |
The absorption exerted by the medium between us and the nebula? is in the main a non-selective one. If it were not so, but resembled the ordinary selective absorption of the planetary atmospheres, the most distant nebulæ should be deep red instead of white. Some selective absorption may, however, be exercised by the misty quasi-atmospheric envelopes which we have reason to believe are associated with some or ​all of the galaxies; but these effects will be local and independent of the distance separating us from the galaxy in question.
If the intergalactic absorption is non-selective, and therefore not to be attributed to diffraction from particles comparable in size with the wave-lengths of light, nor to selective scattering produced by gaseous molecules, to what shall we refer it? We believe, on what seems to be good scientific evidence, that meteoric stones and meteoritic dust particles are strewn through the celestial spaces. Can they produce the depletion of the nebular light?
In part, no doubt, the light is absorbed by meteoritic material; but there is a fatal objection to the supposition that all, or even a large part, of the absorption can be produced in this way. If there were enough meteoritic dust to reduce the light from the most distant nebulæ to a small fraction, only this fraction could escape absorption. The rest of the radiant energy from the stars would be absorbed and reradiated from particle to particle, but without being able to escape, and the entire mass of meteoritic material accumulated in the untold depths of space must eventually glow. Long before this, the skies would become a scorching envelope. The universe would be a prison house. There would be no escape from its brazen walls.
Is there any other solution of the problem? I think that there is; but first let us get an approximate conception of the dimensions of this universe of galaxies. By combining the rate at which the nebulosity around Nova Persei expanded, with established principles from known physical laws, and noting further that the nova, like all of its kin, was a galactic object—a member of the condensed swarm of stars which constitutes our Milky Way—also that it was on the more distant branch of that mighty ring, I have deduced a first approximation to the dimensions of the more condensed portion of our Galaxy.
Next, I have passed from the Milky Way to the Great Nebula in Andromeda by asking how much farther the nebula must be in order that a new star which appeared almost at its very center in August, 1885, should have been comparable in brightness with a nova of moderate size in our own Galaxy. The answer is that approximately 1 andromede = 1600 light-years, or 15,000,000,000,000,000 kilometers. An entirely independent computation, on somewhat different lines, by Mr. J. Ellard Gore, leads to a result of the same order. Mr. Gore is not quite as explicit as I have been; but the general agreement between our results makes me feel confident that we are not far from the truth.
No other of the white nebulæ compares with the Andromeda nebula ​in size, and their average distance apart may perhaps be ten times as great. We will suppose that each galaxy is at the center of an otherwise unoccupied cube 10 andromedes on an edge. The radius of a sphere containing 450,000 such cubes is 760,000 light-years. Now Perrine estimates that there are at least 500,000 nebulæ in the heavens within reach by the Crossley reflector, and probably nine tenths of these are white nebulæ or galaxies. It is therefore safe to say that the light of the stars can travel for one million years before becoming so much reduced by intergalactic absorption as to be beyond the grasp of this powerful instrument.
The view which I now wish to present is that it is the ether itself which absorbs the radiation from the stars.
Considered merely as to its volume, the ether is so overwhelmingly immense that all other bodies shrink into nothingness in comparison. The radius of the sun is
$r_{\bigodot }=7\times (10)^{5}\ kilometers.$
Half the distance to the nearest star is
$r_{*}=2\times (10)^{13}\ kilometers.$
An ethereal sphere which may be called the sun's own, being bounded by the similar spheres of neighboring stars, may be drawn with the latter radius. The radius of the sun bears to that of its interstellar sphere the ratio
$r_{\bigodot }:(r_{*}=1:30,000,000,$
and the volume of the associated ether exceeds that occupied by the solar substance in the ratio
$(r)^{3}:(r_{\bigodot })^{3}=2.7\times (10)^{22}:1$.
Since there are vacant spaces between neighboring galaxies, something must be allowed for these. Let us suppose that the ethereal volume is four hundred times greater than that just given, or that its volume ratio is
$Ether\ volume\ :\ Matter\ volume=(10)^{24}:1.$
This allows a considerable extension of thinly scattered stars around each galaxy, and places the galaxies at relatively smaller distances from each other than the stars, if distances are expressed in terms of diameters, an arrangement which is indicated by the evidence already presented.
The next step in the argument demands an estimate of the total light from all of the stars. Call this L. Newcomb gave us such a photometric measurement, and found
$L=600\ stars\ of\ zero\ magnitude.$
${\begin{aligned}&&L'=3.3\times (10)^{10}{\text{stars of zero magnitude.}}\\{\text{Hence}}&&L'={\frac {3.3\times (10)^{10}\times L}{600}}=5.5\times (10)^{7}\times L.\end{aligned}}$
The average illumination in intergalactic space is very likely less than one one-hundred-millionth of that of sunlight; but a majority of the stars have less absorbent atmospheres than our sun, and as sunlight at the earth's distance must be increased in the ratio 1: 46,000 to give the light emitted by the surface of the solar sphere, the average radiant energy at stellar surfaces may be assumed as $(10)^{12}$ times the average radiant energy in the star-lit ether.
If $V$ and $L$ are the volume and average illumination of the ether, $V'=$ the total volume of stellar material, and $L'=$ the total light from the combined surfaces of all of the stars, an instantaneous image of the relation between the two bodies—ether and matter—that is to say, a representation of the relation if there were an instantaneous emission of light with an infinite velocity, would give
$VL:V'L'=(10)^{12}\times 1:1\times (10)^{12},$
or equality. But if the element of time enters, and also the actual velocity of light, the illumination at a given point in the ether will increase with the time. Let the year be the unit of time. After one billion years, supposing that the stellar radiation can have endured as long as this, instead of unity for the ratio $VL/V'L'$ as in the preceding equation, we shall have
$VL=V'L'\times (10)^{12}.$
Considering the limiting surface of the ether to be, not an imaginary circumscribing sphere, but the sum of the combined stellar surfaces across which the sum total of stellar radiant energy is being constantly transferred from matter to ether, the case stands about like this:
| Volume | Radiation (Superficial) | Total Radiant Energy (Volumetric) |
| Stars = 1 | Stars = (10)$^{12}$ | Stars = (10)$^{12}$ |
| Ether = (10)$^{12}$ | Ether = (10)$^{12}$ | Ether = (10)$^{24}$ |
The large amount of the total radiant energy of the free ether, compared with that of the stars may seem surprising, but it results from the fact that the average illumination of the ether is due to the accumulation of radiant energy from depths of space which are greater as the ether is more transparent. Unless the radiant energy were absorbed, it could not do otherwise than accumulate. The accumulation represents the combined radiation of an immense number of stars whose average distance is to be measured in millions of light-years—how many millions depends upon the time that the stellar radiation remains in the ether before it is all absorbed.
According to what precedes, the average ethereal energy can hardly be less than the radiant energy from the stars within a range of a million light-years, and may amount to many times this figure; and as ​the absorption is a gradual one, the actual duration of luminous propagation may have to be reckoned in thousands of millions of years. Now the radiant energy of the ether represents its temporary mass. If we knew the relation between mass energy and radiant energy, we could give the ratio between the permanent energy of mass of the stars and the luminous energy of the ether. For example, if the mass energy of a star is on the average $(10)^{12}$ times its radiant energy, then the total energy of the universe is always equally divided between ether and matter, because the same radiation comes forth from unit volume of matter, and is distributed to $(10)^{12}$ units of ether. Or, if mass energy bears a larger ratio to radiant energy than this, energy may remain longer in its material than in its ethereal form, only a small fraction of the total energy residing in the ether.
To conjoin stellar centers and ethereal expanses, an intermediate order of existence is needed: An order which faces both ways, having relations with the ether and with the stars. Viewed from the side of ether, we begin to dimly apprehend an electric substance, not yet matter, although possessing many of its properties, seeming to be both a substance and a force, mobile, energetic, viscid enough to be localized and to take on intricate forms, a world-plasm, waiting to be incorporated.
Meteorites circulating around a galactic center remain for enormous periods in the neighborhood of their apogalacteum, and moving with extreme slowness, they have time to gather to themselves the scattered atoms of space, even though the attracting masses may average only a few grams. A meteoritic mass of 1 gram which, if quiescent, will attract to itself the particles within a radius of 1 meter in about 2 months, may be expected to leave a clean-swept track of considerable width through that part of its revolution which occurs in intergalactic space. Possibly the meteoritic chondri have thus grown by accretion in the depths of space, even if, as some suppose, their nuclei may have originated by condensation from masses of heated mineral vapor. Such a slow growth is not incompatible with various vicissitudes, and an eventual consolidation of many such masses into compound chondritic complexes, after the manner of the formation of large hail stones.
Particles which are thrown off from luminous stars, or from fine cosmic material near the stars, being driven away by the pressure of light, are not necessarily of dimensions much larger than molecular, and although the swiftness and small mass of such light-repelled particles must prevent them from acquiring additions by attracting the atoms near which they pass, some increase of size is to be anticipated by chance collisions with atoms, the particles being slowed down and reabsorbed by massive attracting bodies. But these are the last steps of an intergalactic process. We must go farther back to reach its inception.
If we attribute the absorption of light in space to the ether itself, ​the radiant energy absorbed performs work upon the ether, presumably the generation of minute ethereal vortex-rings—the elementary particles from which electrons are derived, or possibly the positive and negative electrons themselves out of which the atoms are formed. From associations of electrons to atoms, from atoms to molecules, from molecules to the first tiny beginnings of a cosmical crystalline sublimate, there is a continual progression and increase of size. Finally, this widely dispersed material must be gathered from the immense voids of space into the germs of future worlds, and for this task the meteorites appear to be the appointed instruments.
A process which goes on forever in one direction is inconceivable. For every swing of the pendulum there must be a counter swing. If atoms have been built up by the action of light, they can be torn apart, and the energy of their formation will be once more set free. We may assume that a certain proportion of the atoms disintegrate, a very minute proportion ordinarily in planetary bodies, but a much larger one under solar conditions. The following facts suggest a relation: (1) The known radioactive elements disintegrate with the production of helium, and the evolution of enormous thermal energy. (2) The stars which are, at least externally, the hottest, since they have effective temperatures which have been rated in a few cases as high as 40,000° C, are surrounded by extensive atmospheres of helium. These relations favor the hypothesis that the helium stars contain an exceptional amount of peculiarly unstable elements, and owe their high temperature to the heat set free in the gradual elimination and destruction of these substances. The energy of formation of the atoms is being slowly dissipated as radiation from the stars, but is eventually reabsorbed by the ether, and is thus restored to the material phase of its existence by the formation of new atoms.
A plausible inference may be formed from the behavior of radium. In 1,000 years, 4 grams of radium will have been nearly one third transformed into other forms of matter of less intrinsic energy, the radium being reduced to about 2.8 grams. During this interval of. time, the four grams of radium will have emitted, according to Rutherford's measurement of the annual production of heat from radium,
${\frac {(4.0+2.8)}{2}}\times 876,000\times 1000=3.0\times (10)^{9}$
gram-calories of heat. This is, of course, only a first approximation. The progression is not strictly linear. Since the gram of substance transformed has not, in this case, been annihilated as matter, but has simply been transmuted into other forms of matter, the $3\times (10)^{9}$ gram-calories of thermal energy do not represent the total mass-energy of the gram of matter, but only that portion of the mass-energy which has been lost in this partial transformation. If we suppose that the total original energy is 1,000 times as much as that which has been lost ​in 1,000 years by radio-active transformation, or enough to last at the same rate for 1,000,000 years, the thermal energy corresponding to the mass-energy of one gram is $3\times (10)^{12},$ which is very nearly the same as the $5\times (10)^{12}$ water-units, computed by De Volson Wood for the specific heat of the ether. We seem, at any rate, to be approaching limiting values which are perhaps connected with the transition from ether to matter, or the reverse. If a volume of rotating ether, having a specific heat of $5\times (10)^{12},$ can be condensed, or in any other way transformed into a volume of matter with specific heat unity, since specific heat is capacity for absorbing thermal energy, the tremendous shrinkage of this capacity during the formation of matter out of ether represents the absorption of so much energy, and the almost complete saturation of the original capacity. It follows that if the process is reversed, the thermal energy of atomic formation must be set free.
Since radium decays far more rapidly than most elements, the one million years suggested in the preceding illustration must be greatly extended in order to represent the average duration of matter. Similarly, the one million light-years deduced for the distance of the fainter nebulæ on the Lick Observatory plates is not a limiting distance beyond which light can not penetrate, but it is a distance at which light is reduced to perhaps eight per cent, of its original intensity, or a quantity of that order. It is evident from the phenomena connected with the decay of the radio-active elements, that different elements have different durations. The rarer elements are either those which require a very long time and a long process of successive ethereal modifications in their development, or else they are elements which are relatively unstable, and which decay more rapidly than the others.
Rutherford gives the radius of an electron as $1.4\times (10)^{-13}$ cm., on the supposition that the electron is a sphere, in which case its surface will be $2.5\times (10)^{-25}$ sq. cm., and its volume $1.1\times (10)^{-38}$ cub. cm. The mass of an electron being, according to Sir J. J. Thomson, 1/1700 times that of a hydrogen atom, and the latter weighing $1.1X(10)^{-24}$ gram, the density of an electron works out
$D=\left({\frac {1.1\times 10^{-24}}{1.7\times 10^{3}}}\right)\div \left(1.1\times 10^{-38}\right)=5.9\times 10^{-10}\ (water=1)$
This value is so extraordinary that obviously we are not dealing with any ordinary problem in material density. The only phenomenon which has any resemblance to it is the increment of mass which the electron acquires at velocities approaching that of light in Kaufmann's experiment. Add to this the fact that the velocity of light is a constant, and the conclusion apparently follows that if the velocity of wave-motion in the ether can be diminished to even the smallest extent below that of light, the medium ceases to be ether, and the motion ceases to be ethereal wave-motion, but is left behind as the beginning ​of a materialized etheric energy. The enormous density found for the electron is an average density and must be still more exceeded if the mass-giving energy is not distributed uniformly within the volume. By all electric analogies it is natural to assume a superficial concentration of energy in the electron itself. The large apparent density of the electron is perhaps explicable on the assumption that the mass-giving substance is condensed in a very thin surface-layer where it revolves with a velocity smaller than that of light by only a very minute amount. The substance of such a shell should have an almost infinite density. The average density of the enclosed volume should still be very great. If, for example, the electron is a vortex-ring of ether of the same surface as the sphere, an almost infinitesimally thin shell of ether revolving ever so little slower than the velocity of light, is no longer free ether, but becomes matter of almost infinite density, the velocity-gradient falling off very rapidly in the interior of the vortex, and the internal density being negligible. Such a body should possess surface potential, polarity, strong elastic resistance, and other properties demanded of the electron.
If it be admitted that a definite volume of ether can receive a permanent limit, it seems necessary that some surface of discontinuity, as well as a stress, akin to fluid viscosity, exerted between the volume and its surface, should be set up. Calling $E$ the ethereal viscosity, $A$ the surface of discontinuity, and $V$ a velocity, such as the mean velocity in the volume, or the limiting velocity at the surface, to be determined by the nature of the viscous mechanism which is at present unknown, the viscous stress $(F)$, so far as it depends on dynamic considerations, is equal to a momentum transferred through a definite volume of fluid to a limiting surface at a given speed, and may be represented as in fluid viscosity by the equation
$F=EAV,$
but with this distinction: The ether has no mass except as it acquires mass by receiving a rotary motion. The dimensional equation for viscosity,
becomes
$E=M/LT,$
$E=L^{3}\times {\frac {L^{2}}{T^{2}}}\times {\frac {1}{LT}}={\frac {L^{4}}{T^{3}}},$
since the etheral mass is proportional to the energy (which varies as the square of the velocity) impressed upon a volume proportional to $r^{3},$ where $r$ is the mean radius of the gyrating volume. In the case of a ring rotating in its own plane, or of a surface rotating around an axis which is a closed curve, $r$ may be the radius of the ring or of the surface. Substituting the value of $E$ in the expression for $F$, we have
$F={\frac {L^{4}}{T^{3}}}\times L^{2}\times {\frac {L}{T}}=L^{3}\times {\frac {L^{4}}{T^{4}}},$
$F\ \alpha \ r^{3}\times \ v^{4}$.
The ethereal viscosity being excessively small, either very high velocities, or very long durations are required to produce appreciable ether drift. As Lagrange has demonstrated, there can be no surface of discontinuity in a perfect fluid, because such a surface implies a continuous generation of rotation in portions of a fluid of constant density. Conversely, if any discontinuity can be imposed upon the ether, it must be a viscous fluid. Any structures formed from a viscous fluid must eventually decay. The duration of the material phase may be enormous, but its ultimate transition is inevitable. The point I wish to make is that there is evidence of an absorption of light by the ether, and that there is also evidence of atomic disintegration. The two processes interlock into necessary and concomitant parts of a consistent whole. What I have tried to demonstrate is the existence of a phenomenon and its approximate law, without attempting a refinement which would be unwarranted at the present stage of the investigation.
Conclusion
In brief, we may conclude that space contains myriads of galaxies which would make the midnight sky one blaze of light, were it not for the absorption of light by the ether of space. This absorption can not be a selective scattering by gaseous molecules, because this would deplete the radiation of short wave-length unduly, and would redden the light of the more distant nebulæ, whereas no such change of color with distance is found. Neither can the absorption be due to the general absorption of radiation of every wave-length by coarser meteoritic dust, since the meteoritic material would in time become heated to incandescence, as Arrhenius has noted, and in this case also the entire heavens must glow. There remains, then, the supposition that the ether itself absorbs the radiation from the stars, and that in this fixation of energy, matter originates.
There is, I apprehend, a close analogy between the sequences of cosmogony and of geogeny. Upon the earth there are wide expanses of oceanic depths which have apparently remained such from the beginning of denudation. That remarkable property of saline solutions whereby suspended solid particles are quickly precipitated, causes the marginal deposition of those sediments brought to the sea by the rivers. The oceanic depths are the counterparts of the intergalactic spaces. In both, change progresses very slowly.
But around the borders of the continents, sediments accumulate in geosynclines which are self perpetuating. The increasing weight of the deposit deepens the depression, until after the accumulation has ​reached a depth of 10 to 15 kilometers a reaction sets in. The deeply buried beds of water-bearing detrital formations soften, very likely under the influence of heat generated by the concentrated radioactive minerals, as Professor Joly supposes. Long eras of crumpling, elevation and mountain-formation follow, to be in turn succeeded by other ages of denudation. "The energy which determines the place of yielding and upheaval, and ordains that the mountains shall stand around the continental border," passes through a rhythmic interchange or cycle. The cosmogonical process which I have described embodies an analogous cycle, embracing the formation of matter from the ether, and most abundantly in the vicinity of stellar aggregates, by the fixation of the radiant energy, outpouring from the disintegrating stellar substance. Then follow, in turn, the concentration of the material on the borders of the earlier galaxies and the birth of new heavens. In proof of this association of old and new along a border region, the similar distribution of the fourth-type and helium stars, which probably represent the extremes of a thermal series, may be cited.
The conception of a universal ether is to many so vague that the distinction between ether and a purely spiritual atmosphere seems slight; yet the difference is fundamental. The mind of man is not conditioned by space. Thought can not be measured by the yardstick. Ether, on the contrary, occupies space. The dimensions of its waves have been made the fundamental standards of our units of length. Nevertheless, we still grope and guess as to the real structure and nature of the ether. Some of its properties seem to verge on the metaphysical. Back of it, we have glimpses of a source of energy which is inexhaustible, as if it were most intimately linked with the Infinite Source of all existence. Matter which used to be looked upon as dead, and as incapable of exhibiting energy except as this was thrust upon it from without by physical forces, begins to look almost alive. "It moves," said Galileo, of the solid earth; and to-day the delighted physicist, armed with the spectroscope and spinthariscope, Crookes's tube and the electrometer, finds, in the Zeeman effect or the radium emanation, evidence that the atom is an orderly maze of bewildering motion. Its inertia is a gyroscopic inertia. Absolute rest would be nonentity. Everywhere the universe speaks of never-ending life and motion. Creation is not the bringing forth of an infinite number of dead structureless particles, sent out as a set of miserable little waifs at some indefinitely remote epoch and left to clash without guidance, without purpose. Creation is perpetual. The interiors of matter are seen to be more and more wonderful, more and more intensely active, as we approach the sacred portals where divine influx from the Soul of the Universe quickens into the energy which is matter.
* ↑ George C. Comstock, "The Luminosity of the Brighter Lucid Stars," Publications of the Astronomical and Astrophysical Society of America, Vol. 1, p. 307.
* ↑ Contributions from the Mount Wilson Solar Observatory, No. 42.
* ↑ "Emanuel Swedenborg-Opera quædam aut inedita aut obsoleta de rebus naturalibus nunc edita sub auspieiis Regiæ Academiæ Scientiarum Suecicæ. Holmiæ, 1908." II Cosmologica-Pars tertia, Paragraphus prima, N. 8 et 11, pp. 271–272.
* ↑ See A. Cowper Ranyard's completion of Proctor's "Old and New Astronomy," where the subject is discussed at some length, pp. 739–746.
* ↑ The central regions of a galactic accumulation of stars may be expected to be relatively free from meteoritic material, for here we have a space swept clean by the stellar attraction which gathers in the material and places it where it can be readily absorbed. In the more distant intergalactic spaces, the meteoritic material is widely dispersed, but upon the borders of the galaxies there are accumulations of finely divided matter, not yet incorporated in the stars.
* ↑ Contributions from the Mount Wilson Solar Observatory, No. 42, pp. 23–24.
* ↑ Publications of the Astronomical and Astrophysical Society of America Vol. 1, p. 282; see also Astronomical Journal, No. 558.
* ↑ Of the larger spiral nebulæ, Professor G. W. Ritchey says (Astrophys. J., Vol. 32, p. 32, July, 1910): "All of these contain great numbers of soft star-like condensations which I shall call nebulous stars." It appears not improbable that these represent irresolvable stellar groups.
* ↑ "Photographs of Stars, Star Clusters and Nebulæ," Vol. 2, pp. 23–24.
* ↑ The class of white nebulæ exhibits various stages of development, and includes objects of mixed type. See E. A. Fath, "The Spectra of Spiral Nebulæ and Globular Star Clusters," Astrophysical Journal, Vol. 33, p. 58, January, 1911.
* ↑ For the details of this investigation reference may be made to my paper, "Are the White Nebulæ Galaxies?" Astronomische Nachrichten, No. 4536, Bd. 189, 441–454, November, 1911.
* ↑ In Knowledge for September, 1912, I conclude that Lord Kelvin's estimate of the diameter of the Galaxy, which was five times as great as mine, is probably the better of the two, whence it follows that 1 andromede = 8,000 lightyears. But we are concerned at present with rough estimates of an order of magnitude only, and may waive all minute details.
* ↑ Philosophical Magazine for November, 1885, pp. 402–403.
* ↑ As suggested in my paper, "A Cosmic Cycle," Am. Jour. Sci., Ser. 4, Vol. 13, p. 189, March, 1902.
* ↑ J. Joly, "Radioactivity and Geology. An Account of the Influence of Radioactive Energy on Terrestrial History."