Gore John Ellard
Astronomical Curiosities: Facts and Fallacies
Sculptor. – This constellation lies south of Aquarius and Cetus, and north of Phœnix. Some of its stars are referred to by Al-Sufi under Eridanus as lying within the large triangle formed by β Ceti, Fomalhaut, and α Phœnicis. The brightest star is α, about 12° south of β Ceti (4·39 magnitude Harvard). About 7° south-east of α is the red and variable star R Sculptoris; variable from 6·2 to 8·8 magnitude, with a period of about 376 days. Gould describes it as “intense scarlet.” It has a spectrum of the fourth type.
Phœnix. – This constellation lies south of Sculptor. Some of its stars are referred to by Al-Sufi, under Eridanus, as forming a boat-shaped figure. These are evidently α, κ, μ, β, ν, and γ. α is at the south-eastern angle of Al-Sufi’s triangle referred to above (under “Sculptor”). (See Proctor’s Atlas, No. 3.)
Fornax, the Furnace, lies south of Cetus, west of Eridanus, and east of Sculptor and Phœnix. It was formed by Lacaille, and is supposed to represent a chemical furnace with an alembic and receiver! Its brightest star, α Fornacis, is identical with 12 Eridani.
Cælum, the Sculptor’s Tools, is a small constellation east of Columba, and west of Eridanus. It was formed by Lacaille. The brightest stars are α and γ, which are about 4½ magnitude. α has a faint companion; and γ is a wide double star to the naked eye.
Antlia, the Air Pump, lies south of Hydra, east and north of Argo, and west of Centaurus. It was formed by Lacaille. It contains no star brighter than 4th magnitude. The brightest, α, has been variously rated from 4 to 5, and Stanley Williams thinks its variability “highly probable.”
Norma, the Rule, lies south of Scorpio. It contains no star brighter than the 4th magnitude.
Telescopium. – This modern constellation lies south of Corona Australis, and north of Pavo. Its stars α, δ, and ζ, which lie near the northern boundary of the constellation, are referred to by Al-Sufi in his description of Ara.
Microscopium. – This small constellation is south of Capricornus, and west of Piscis Australis. Its stars seem to be referred to by Al-Sufi as having been seen by Ptolemy, but he does not specify their exact positions. It contains no star brighter than 4½ magnitude.
South of Al-Sufi’s horizon are a number of constellations surrounding the south pole, which, of course, he could not see. Most of these have been formed since his time, and these will now be considered; beginning with that immediately surrounding the South Pole (Octans), and then following the others as nearly as possible in order of Right Ascension.
Octans. – This is the constellation surrounding the South Pole of the heavens. There is no bright star near the Pole, the nearest visible to the naked eye being σ Octantis, which is within one degree of the pole. It was estimated 5·8 at Cordoba. The brightest star in the constellation is ν Octantis (α, Proctor), which lies about 12 degrees from the pole in the direction of Indus and Microscopium. The Harvard measure is 3·74 magnitude.
Hydrus, the Water-Snake, is north of Octans in the direction of Achernar (α Eridani). The brightest star is β, which lies close to θ Octantis. The Harvard measure is 2·90. Gould says its colour is “clear yellow.” It has a large proper motion of 2″·28 per annum. Sir David Gill found a parallax of 0″·134, and this combined with the proper motion gives a velocity of 50 miles a second at right angles to the line of sight. γ Hydri is a comparatively bright star of about the 3rd magnitude, about 15½ degrees from the South Pole. It is reddish, with a spectrum of the third type.
Horologium, the Clock, is north of Hydra, and south of Eridanus. Three of its stars, α, δ, and ψ, at the extreme northern end of the constellation, seem to be referred to by Al-Sufi in his description of Eridanus, but he does not give their exact positions. Most of the stars forming this constellation were below Al-Sufi’s horizon.
Reticulum, the Net, is a small constellation to the east of Hydrus and Horologium. The brightest star of the constellation is α (3·36 Harvard, 3·3 Cordoba, and “coloured”).
Dorado, the Sword Fish, lies east of Reticulum and west of Pictor. It contains only two stars brighter than the 4th magnitude. These are α (3·47 Harvard) and β (3·81 Harvard, but suspected of variation). About 3° east of α Reticuli is the variable star R Doradus. It varies from 4·8 to 6·8, and its period is about 345 days. Gould calls it “excessively red.” It may be followed through all its fluctuations of light with an opera-glass.
Mensa, or Mons Mensa, the Table Mountain, lies between Dorado and the South Pole, and represents the Table Mountain of the Cape of Good Hope. It contains no star brighter than the 5th magnitude.
Pictor, the Painter’s Easel, lies north of Doradus, and south of Columba. It contains no very bright stars, the brightest being α (3·30 Harvard).
Volans, the Flying Fish, is north of Mensa, and south and west of Argo. Its brighter stars, with the exception of α and β, form an irregular six-sided figure. Its brightest star is β (3·65) according to the Harvard measures. The Cordoba estimates, however, range from 3·6 to 4·4, and Gould says its colour is “bright yellow.” Williams rated it 3·8.
Chamælion. – This small constellation lies south of Volans, and north of Mensa and Octans. None of its stars are brighter than the 4th magnitude, its brightest being α (4·08 Harvard) and γ (4·10).
Argo. – This large constellation extends much further south than Al-Sufi could follow it. The most southern star he mentions is ε Carinæ, but south of this are several bright stars. β Carinæ is 1·80 according to the Harvard measures; υ Carinæ, 3·08; θ, 3·03; ω, 3·56; and others. A little north-west of ι is the long-period variable R Carinæ (9h 29m·7, S. 62° 21′, 1900). It varies from 4·5 at maximum to 10 at minimum, and the period is about 309·7 days. A little east of R Carinæ is another remarkable variable star, l Carinæ (R.A. 9h 42m·5, S. 62° 3′). It varies from 3·6 to 5·0 magnitude, with a period of 35½ days from maximum to maximum. All the light changes can be observed with an opera-glass, or even with the naked eye. It was discovered at Cordoba. The spectrum is of the solar type (G).
Musca, the Bee, is a small constellation south of the Southern Cross and Centaurus. Its brightest stars are α (2·84 Harvard) and β (3·26). These two stars form a fine pair south of α Crucis. Closely south-east of α is the short-period variable R Muscæ. It varies from 6·5 to 7·6 magnitude, and its period is about 19 hours. All its changes of light may be observed with a good opera-glass.
Apus, the Bird of Paradise, lies south-east of Musca, and north of Octans. Its brightest star is α, about the 4th magnitude. Williams calls it “deep yellow.” About 3° north-west of α, in the direction of the Southern Cross, is θ Apodis, which was found to be variable at Cordoba from 5½ to 6½. The spectrum is of the third type, which includes so many variable stars.
Triangulum Australis, the Southern Triangle, is a small constellation north of Apus, and south of Norma. A fine triangle, nearly isosceles, is formed by its three bright stars, α, β, γ, the brightest α being at the vertex. These three stars form with α Centauri an elongated cross. The stars β and γ are about 3rd magnitude. β is reddish. ε (4·11, Harvard) is also reddish, and is nearly midway between β and γ, and near the centre of the cross above referred to. α is a fine star (1·88 Harvard) and is one of the brightest stars in the sky – No. 33 in a list of 1500 highest stars given by Pickering. About 1° 40′ west of ε is the short-period variable R Trianguli Australis (R.A. 15h 10m·8, S. 66° 8′) discovered at Cordoba in 1871. It varies from 6·7 to 7·4, and the period is about 3d 7h·2. Although not visible to ordinary eyesight it is given here, as it is an interesting object and all its light changes may be well seen with an opera-glass. A little south-east of β is another short-period variable, S Trianguli Australis (R.A. 15h 52m·2, S. 63° 30′), which varies from 6·4 to 7·4, with a period of 6·3 days; and all its fluctuations of light may also be observed with a good opera-glass.
Circinus, the Compass, is a very small constellation lying between Triangulum and Centaurus. Its brightest star, α, is about 3½ magnitude, about 4° south of α Centauri.
Pavo, the Peacock, lies north of Octans and Apus, and south of Telescopium. Its brightest star is α, which is a fine bright star (2·12 Harvard). κ is a short-period variable. It varies from 3·8 to 5·2, and the period is about 9 days. This is an interesting object, as all the fluctations of light can be observed by the naked eye or an opera-glass. ε Pavonis was measured 4·10 at Harvard, but the Cordoba estimates vary from 3·6 to 4·2. Gould says “it is of a remarkably blue colour.”
Indus. – This constellation lies north of Octans, and south of Sagittarius, Microscopium, and Grus. One of its stars, α, is probably referred to by Al-Sufi in his description of Sagittarius; it lies nearly midway between β Sagittarii and α Gruis, and is the brightest star of the constellation. The star ε Indi (4·74 Harvard) has a remarkably large proper motion of 4″·68 per annum. Its parallax is about 0″·28, and the proper motion indicates a velocity of about 49 miles a second at right angles to the line of sight.
Toucan. – This constellation lies north of Octans, and south of Phœnix and Grus, east of Indus, and west of Hydrus. Its brightest star is α, of about the 3rd magnitude.
There are seven “celestial rivers” alluded to by the ancient astronomers: —
1. The Fish River, which flows from the urn of Aquarius.
2. The “River of the Bird,” or the Milky Way in Cygnus.
3. The River of the Birds – 2, including Aquila.
4. The River of Orion – Eridanus.
5. The River of the god Marduk – perhaps the Milky Way in Perseus.
6. The River of Serpents (Serpens, or Hydra).
7. The River of Gan-gal (The High Cloud) – probably the Milky Way as a whole.
There are four serpents represented among the constellations. These are Hydra, Hydrus, Serpens, and Draco.
According to the late Mr. Proctor the date of the building of the Great Pyramid was about 3400 B.C.450 At this time the Spring Equinox was in Taurus, and this is referred to by Virgil. But this was not so in Virgil’s time, when – on account of the precession of the equinoxes – the equinoctial point had already entered Pisces, in which constellation it still remains. At the date 3400 B.C. the celestial equator ran along the whole length of the constellation Hydra, nearly through Procyon, and a little north of the bright red star Antares.
The star Fomalhaut (α Piscis Australis) is interesting as being the most southern 1st magnitude star visible in England, its meridian altitude at Greenwich being little more than eight degrees.451
With reference to the Greek letters given to the brighter stars by Bayer (in his Atlas published in 1603), and now generally used by astronomers, Mr. Lynn has shown that although “Bayer did uniformly designate the brightest stars in each constellation by the letter α,”452 it is a mistake to suppose – as has often been stated in popular books on astronomy – that he added the other Greek letters in order of brightness. That this is an error clearly appears from Bayer’s own “Explicatio” to his Atlas, and was long since pointed out by Argelander (1832), and by Dr. Gould in his Uranometria Argentina. Gould says, “For the stars of each order, the sequence of the letters in no manner represents that of their brightness, but depended upon the positions of the stars in the figure, beginning usually at the head, and following its course until all the stars of that order of magnitude were exhausted.” Mr. Lynn says, “Perhaps one of the most remarkable instances in which the lettering is seen at a glance not to follow the order of the letters is that of the three brightest stars in Aquila [Al-Sufi’s ‘three famous stars’], γ being evidently brighter than β. But there is no occasion to conjecture from this that any change of relative brightness has taken place. Bayer reckoned both of these two of the third magnitude, and appears to have arranged β before γ, according to his usual custom, simply because β is in the neck of the supposed eagle, and γ at the root of one of the wings.”453 Another good example is found in the stars of the “Plough,” in which the stars are evidently arranged in the order of the figure and not in the order of relative brightness. In fact, Bayer is no guide at all with reference to star magnitudes. How different Al-Sufi was in this respect!
The stars Aldebaran, Regulus, Antares, and Fomalhaut were called royal stars by the ancients. The reason of this was that they lie roughly about 90° apart, that is 6 hours of Right Ascension. So, if through the north and south poles of the heavens and each of these stars we draw great circles of the sphere, these circles will divide the sphere into four nearly equal parts, and the ancients supposed that each of these stars ruled over a quarter of the sphere, an idea probably connected with astrology. As the position of Aldebaran is R.A. 4h 30m, Declination North 16° 19′, and that of Antares is R.A. 16h 15m, Declination South 25° 2′, these two stars lie at nearly opposite points of the celestial sphere. From this it follows that our sun seen from Aldebaran would lie not very far from Antares, and seen from Antares it would appear not far from Aldebaran.
The following may be considered as representative stars of different magnitudes. For those of first magnitude and fainter I have only given those for which all the best observers in ancient and modern times agree, and which have been confirmed by modern photometric measures. The Harvard measures are given: —
CHAPTER XX
The Visible Universe
Some researches on the distribution of stars in the sky have recently been made at the Harvard Observatory (U.S.A.). The principal results are: – (1) The number of stars on any “given area of the Milky Way is about twice as great as in an equal area of any other region.” (2) This ratio does not increase for faint stars down to the 12th magnitude. (3) “The Milky Way covers about one-third of the sky and contains about half of the stars.” (4) There are about 10,000 stars of magnitude 6·6 or brighter, 100,000 down to magnitude 8·7, one million to magnitude 11, and two millions to magnitude 11·9. It is estimated that there are about 18 millions of stars down to the 15th magnitude visible in a telescope of 15 inches aperture.454
According to Prof. Kapteyn’s researches on stellar distribution, he finds that going out from the earth into space, the “star density” – that is, the number of stars per unit volume of space – is fairly constant until we reach a distance of about 200 “light years.” From this point the density gradually diminishes out to a distance of 2500 “light years,” at which distance it is reduced to about one-fifth of the density in the sun’s vicinity.455
In a letter to the late Mr. Proctor (Knowledge, November, 1885, p. 21), Sir John Herschel suggested that our Galaxy (or stellar system) “contained within itself miniatures of itself.” This beautiful idea is probably true. In his account of the greater “Magellanic cloud,” Sir John Herschel describes one of the numerous objects it contains as follows: —
“Very bright, very large; oval; very gradually pretty, much brighter in the middle; a beautiful nebula; it has very much the resemblance to the Nubecula Major itself as seen with the naked eye, but it is far brighter and more impressive in its general aspect as if it were doubled in intensity. Note – July 29, 1837. I well remember this observation, it was the result of repeated comparisons between the object seen in the telescope and the actual nubecula as seen high in the sky on the meridian, and no vague estimate carelessly set down. And who can say whether in this object, magnified and analysed by telescopes infinitely superior to what we now possess, there may not exist all the complexity of detail that the nubecula itself presents to our examination?”456
The late Lord Kelvin, in a remarkable address delivered before the Physical Science Section of the British Association at its meeting at Glasgow in 1901, considered the probable quantity of matter contained in our Visible Universe. He takes a sphere of radius represented by the distance of a star having a parallax of one-thousandth of a second (or about 3000 years’ journey for light), and he supposes that uniformly distributed within this sphere there exists a mass of matter equal to 1000 million times the sun’s mass. With these data he finds that a body placed originally at the surface of the sphere would in 5 million years acquire by gravitational force a velocity of about 12½ miles a second, and after 25 million of years a velocity of about 67 miles a second. As these velocities are of the same order as the observed velocities among the stars, Lord Kelvin concludes that there is probably as much matter in our universe as would be represented by a thousand million suns. If we assumed a mass of ten thousand suns the velocities would be much too high. The most probable estimate of the total number of the visible stars is about 100 millions; so that if Lord Kelvin’s calculations are correct we seem bound to assume that space contains a number of dark bodies. The nebulæ, however, probably contain vast masses of matter, and this may perhaps account – partially, at least – for the large amount of matter estimated by Lord Kelvin. (See Chapter on “Nebulæ.”)
In some notes on photographs of the Milky Way, Prof. Barnard says with reference to the great nebula near ρ Ophiuchi, “The peculiarity of this region has suggested to me the idea that the apparently small stars forming the ground work of the Milky Way here, are really very small bodies compared with our own sun”; and again, referring to the region near β Cygni, “One is specially struck with the apparent extreme smallness of the general mass of the stars in this region.” Again, with reference to χ Cygni, he says, “The stars here also are remarkably uniform in size.”457
Eastman’s results for parallax seem to show that “the fainter rather than the brighter stars are nearest to our system.” But this apparent paradox is considered by Mr. Monck to be very misleading;458 and the present writer holds the same opinion.
Prof. Kapteyn finds “that stars whose proper motions exceed 0″·05 are not more numerous in the Milky Way than in other parts of the sky; or, in other words, if only the stars having proper motions of 0″·05 or upwards were mapped, there would be no aggregation of stars showing the existence of the Milky Way.”459
With reference to the number of stars visible on photographs, the late Dr. Isaac Roberts says —
“So far as I am able at present to judge, under the atmospheric conditions prevalent in this country, the limit of the photographic method of delineation will be reached at stellar, or nebular, light of the feebleness of about 18th-magnitude stars. The reason for this inference is that the general illumination of the atmosphere by starlight concentrated upon a film by the instrument will mask the light of objects that are fainter than about 18th-magnitude stars.”460
With reference to blank spaces in the sky, the late Mr. Norman Pogson remarked —
“Near S Ophiuchi we find one of the most remarkable vacuities in this hemisphere – an elliptic space of about 65′ in length in the direction of R.A., and 40′ in width, in which there exists no star larger than the 13th magnitude … it is impossible to turn a large telescope in that direction and, if I may so express it, view such black darkness, without a feeling that we are here searching into the remote regions of space, far beyond the limits of our own sidereal system.”461
Prof. Barnard describes some regions in the constellation Taurus containing “dark lanes” in a groundwork of faint nebulosity. He gives two beautiful photographs of the regions referred to, and says that the dark holes and lanes are apparently darker than the sky in the immediate vicinity. He says, “A very singular feature in this connection is that the stars also are absent in general from the lanes.” A close examination of these photographs has given the present writer the impression that the dark lanes and spots are in the nebulosity, and that the nebulosity is mixed up with the stars. This would account for the fact that the stars are in general absent from the dark lanes. For if there is an intimate relation between the stars and the nebulosity, it would follow that where there is no nebulosity in this particular region there would be no stars. Prof. Barnard adds that the nebulosity is easily visible in a 12-inch telescope.462
With reference to the life of the universe, Prof. F. R. Moulton well says —
“The lifetime of a man seems fairly long, and the epoch when Troy was besieged, or when the Pharaohs piled up the pyramids in the valley of the Nile, or when our ancestors separated on the high plateaux of Asia, seems extremely remote, but these intervals are only moments compared to the immense periods required for geological evolutions and the enormously greater ones consumed in the developement of worlds from widely extended nebulous masses. We recognize the existence of only those forces whose immediate consequences are appreciable, and it may be that those whose effects are yet unseen are really of the highest importance. A little creature whose life extended over only two or three hours of a summer’s day might be led, if he were sufficiently endowed with intelligence, to infer that passing clouds were the chief influence at work in changing the climate instead of perceiving that the sun’s slow motion across the sky would bring on the night and its southward motion the winter.”463
In a review of my book Astronomical Essays in The Observatory, September, 1907, the following words occur. They seem to form a good and sufficient answer to people who ask, What is there beyond our visible universe? “If the stellar universe is contained in a sphere of say 1000 stellar units radius, what is there beyond? To this the astronomer will reply that theories and hypotheses are put forward for the purpose of explaining observed facts; when there are no facts to be explained, no theory is required. As there are no observed facts as to what exists beyond the farthest stars, the mind of the astronomer is a complete blank on the subject. Popular imagination can fill up the blank as it pleases.” With these remarks I fully concur.
In his address to the British Association, Prof. G. H. Darwin (now Sir George Darwin) said —
“Man is but a microscopic being relatively to astronomical space, and he lives on a puny planet circling round a star of inferior rank. Does it not, then, seem futile to imagine that he can discover the origin and tendency of the Universe as to expect a housefly to instruct us as to the theory of the motions of the planets? And yet, so long as he shall last, he will pursue his search, and will no doubt discover many wonderful things which are still hidden. We may indeed be amazed at all that man has been able to find out, but the immeasurable magnitude of the undiscovered will throughout all time remain to humble his pride. Our children’s children will still be gazing and marvelling at the starry heavens, but the riddle will never be read.”
The ancient philosopher Lucretius said —
“Globed from the atoms falling slow or swift
I see the suns, I see the systems lift
Their forms; and even the system and the suns
Shall go back slowly to the eternal drift.”464
But it has been well said that the structure of the universe “has a fascination of its own for most readers quite apart from any real progress which may be made towards its solution.”465
The Milky Way itself, Mr. Stratonoff considers to be an agglomeration of immense condensations, or stellar clouds, which are scattered round the region of the galactic equator. These clouds, or masses of stars, sometimes leave spaces between them, and sometimes they overlap, and in this way he accounts for the great rifts, like the Coal Sack, which allow us to see through this great circle of light. He finds other condensations of stars; the nearest is one of which our sun is a member, chiefly composed of stars of the higher magnitudes which “thin out rapidly as the Milky Way is approached.” There are other condensations: one in stars of magnitudes 6·5 to 8·5; and a third, farther off, in stars of magnitudes 7·6 to 8. These may be called opera-glass, or field-glass stars.
Stratonoff finds that stars with spectra of the first type (class A, B, C, and D of Harvard) which include the Sirian and Orion stars, are principally situated near the Milky Way, while those of type II. (which includes the solar stars) “are principally condensed in a region coinciding roughly with the terrestrial pole, and only show a slight increase, as compared with other stars, as the galaxy is approached.”466
Prof. Kapteyn thinks that “undoubtedly one of the greatest difficulties, if not the greatest of all, in the way of obtaining an understanding of the real distribution of the stars in space, lies in our uncertainty about the amount of loss suffered by the light of the stars on its way to the observer.”467 He says, “There can be little doubt in my opinion, about the existence of absorption in space, and I think that even a good guess as to the order of its amount can be made. For, first we know that space contains an enormous mass of meteoric matter. This matter must necessarily intercept some part of the star-light.”
This absorption, however, seems to be comparatively small. Kapteyn finds a value of 0·016 (about 1⁄60th) of a magnitude for a star at a distance corresponding to a parallax of one-tenth of a second (about 33 “light years”). This is a quantity almost imperceptible in the most delicate photometer. But for very great distances – such as 3000 “light years” – the absorption would evidently become very considerable, and would account satisfactorily for the gradual “thinning out” of the fainter stars. If this were fully proved, we should have to consider the fainter stars of the Milky Way to be in all probability fairly large suns, the light of which is reduced by absorption.
That some of the ancients knew that the Milky Way is composed of stars is shown by the following lines translated from Ovid: —
“A way there is in heaven’s extended plain
Which when the skies are clear is seen below
And mortals, by the name of Milky, know;
The groundwork is of stars, through which the road
Lies open to great Jupiter’s abode.”468
From an examination of the distribution of the faint stars composing the Milky Way, and those shown in Argelander’s charts of stars down to the 9½ magnitude, Easton finds that there is “a real connection between the distribution of 9th and 10th magnitude stars, and that of the faint stars of the Milky Way, and that consequently the faint or very faint stars of the galactic zone are at a distance which does not greatly exceed that of the 9th and 10th magnitude stars.”469 A similar conclusion was, I think, arrived at by Proctor many years ago. Now let us consider the meaning of this result. Taking stars of the 15th magnitude, if their faintness were merely due to greater distance, their actual brightness – if of the same size – would imply that they are at 10 times the distance of stars of the 10th magnitude. But if at the same distance from us, a 10th magnitude star would be 100 times brighter than a 15th magnitude star, and if of the same density and “intrinsic brightness” (or luminosity of surface) the 10th magnitude would have 10 times the diameter of the fainter star, and hence its volume would be 1000 times greater (103), and this great difference is not perhaps improbable.
The constitution of the Milky Way is not the same in all its parts. The bright spot between β and γ Cygni is due to relatively bright stars. Others equally dense but fainter regions in Auriga and Monoceros are only evident in stars of the 8th and 9th magnitude, and the light of the well-known luminous spot in “Sobieski’s Shield,” closely south of λ Aquilæ, is due to stars below magnitude 9½.
The correspondence in distribution between the stars of Argelander’s charts and the fainter stars of the Milky Way shows, as Easton points out, that Herschel’s hypothesis of a uniform distribution of stars of approximately equal size is quite untenable.
It has been suggested that the Milky Way may perhaps form a ring of stars with the sun placed nearly, but not exactly, in the centre of the ring. But were it really a ring of uniform width with the sun eccentrically placed within it, we should expect to find the Milky Way wider at its nearest part, and gradually narrowing towards the opposite point. Now, Herschel’s “gages” and Celoria’s counts show that the Galaxy is wider in Aquila than in Monoceros. This is confirmed by Easton, who says, “for the faint stars taken as a whole, the Milky Way is widest in its brightest part” (the italics are Easton’s). From this we should conclude that the Milky Way is nearer to us in the direction of Aquila than in that of Monoceros. Sir John Herschel suggested that the southern parts of the galactic zone are nearer to us on account of their greater brightness in those regions.470 But greater width is a safer test of distance than relative brightness. For it may be easily shown than the intrinsic brightness of an area containing a large number of stars would be the same for all distances (neglecting the supposed absorption of light in space). For suppose any given area crowded with stars to be removed to a greater distance. The light of each star would be diminished inversely as the square of the distance. But the given area would also be diminished directly as the square of the distance, so we should have a diminished amount of light on an equally diminished area, and hence the intrinsic brightness, or luminosity of the area per unit of surface, would remain unaltered. The increased brightness of the Milky Way in Aquila is accounted for by the fact that Herschel’s “gages” show an increased number of stars, and hence the brightness in Aquila and Sagittarius does not necessarily imply that the Milky Way is nearer to us in those parts, but that it is richer in small stars than in other regions.