Scheiner says “the previous suspicion that the spiral nebulæ are star clusters is now raised to a certainty,” and that the spectrum of the Andromeda nebula is very similar to that of the sun. He says there is “a surprising agreement of the two, even in respect to the relative intensity of the separate spectral regions.”[362]
In the dynamical theory of spiral nebulæ, Dr. E. J. Wilczynski thinks that the age of a spiral nebula may be indicated by the number of its coils; those having the largest number of coils being the oldest, from the point of view of evolution.[363] This seems to be very probable.
In the spectrum of the gaseous nebulæ, the F line of hydrogen (Hβ) is visible, but not the C line (Hα). The invisibility of the C line is explained by Scheiner as due to a physiological cause, “the eye being less sensitive to that part of the spectrum in which the line appears than to the part containing the F line.”[364]
An apparent paradox is found in the case of the gaseous nebulæ. The undefined outlines of these objects render any attempt at measuring their parallax very difficult, if not impossible. Their distance from the earth is therefore unknown, and perhaps likely to remain so for many years to come. It is possible that they may not be farther from us than some of the stars visible in their vicinity. On the other hand, they may lie far beyond them in space. But whatever their distance from the earth may be, it may be easily shown that their attraction on the sun is directly proportioned to their distance—that is, the greater their distance, the greater the attraction! This is evidently a paradox, and rather a startling one too. But it is nevertheless mathematically true, and can be easily proved. For, their distance being unknown, they may be of any dimensions. They might be comparatively small bodies relatively near the earth, or they may be immense masses at a vast distance from us. The latter is, of course, the more probable. In either case the apparent size would be the same. Take the case of any round gaseous nebula. Assuming it to be of a globular form, its real diameter will depend on its distance from the earth—the greater the distance, the greater the diameter. Now, as the volumes of spheres vary as the cubes of their diameters, it follows that the volume of the nebula will vary as the cube of its distance from the earth. As the mass of an attracting body depends on its volume and density, its real mass will depend on the cube of its distance, the density (although unknown) being a fixed quantity. If at a certain distance its mass is m, at double the distance (the apparent diameter being the same) it would have a mass of eight times m (8 being the cube of 2), and at treble the distance its mass would be 27 m, and so on, its apparent size being known, but not its real size. This is obvious. Now, the attractive power of a body varies directly as its mass—the greater the mass, the greater the attraction. Again, the attraction varies inversely as the square of the distance, according to the well-known law of Newton. Hence if d be the unknown distance of the nebula, we have its attractive power varying as d3 divided by d2, or directly as the distance d. We have then the curious paradox that for a nebula whose distance from the earth is unknown, its attractive power on the sun (or earth) will vary directly as the distance—the greater the distance the greater the attraction, and, of course, conversely, the smaller the distance the less the attractive power. This result seems at first sight absurd and incredible, but a little consideration will show that it is quite correct. Consider a small wisp of cloud in our atmosphere. Its mass is almost infinitesimal and its attractive power on the earth practically nil. But a gaseous nebula having the same apparent size would have an enormous volume, and, although probably formed of very tenuous gas, its mass would be very great, and its attractive power considerable. The large apparent size of the Orion nebula shows that its volume is probably enormous, and as its attraction on the sun is not appreciable, its density must be excessively small, less than the density of the air remaining in the receiver of the best air-pump after the air has been exhausted. How such a tenuous gas can shine as it does forms another paradox. Its light is possibly due to some phosphorescent or electrical action.
The apparent size of “the great nebula in Andromeda” shows that it must be an object of vast dimensions. The nearest star to the earth, Alpha Centauri, although probably equal to our sun in volume, certainly does not exceed one-hundredth of a second in diameter as seen from the earth. But in the case of the Andromeda nebula we have an object of considerable apparent size, not measured by seconds of arc, but showing an area about three times greater than that of the full moon. The nebula certainly lies in the region of the stars—much farther off than Alpha Centauri—and its great apparent size shows that it must be of stupendous dimensions. A moment’s consideration will show that whatever its distance may be, the farther it is from the earth the larger it must be in actual size. The sun is vastly larger than the moon, but its apparent size is about the same owing to its greater distance. Sir William Herschel thought the Andromeda nebula to be “undoubtedly the nearest of all the great nebulæ,” and he estimated its distance at 2000 times the distance of Sirius. This would not, however, indicate a relatively near object, as it would imply a “light journey” of over 17,000 years! (The distance of Sirius is about 88 “light years.”)
It has been generally supposed that this great nebula lies at a vast distance from the earth, possibly far beyond most of the stars seen in the same region of the sky; but perhaps not quite so far as Herschel’s estimate would imply. Recently, however, Prof. Bohlin of Stockholm has found from three series of measures made in recent years a parallax of 0″·17.[365]
This indicates a distance of 1,213,330 times the sun’s distance from the earth, and a “light journey” of about 19 years. This would make the distance of the nebula more than twice the distance of Sirius, about four times the distance of α Centauri, but less than that of Capella.
Prof. Bohlin’s result is rather unexpected, and will require confirmation before it can be accepted. But it will be interesting to inquire what this parallax implies as to the real dimensions and probable mass of this vast nebula. The extreme length of the nebula may be taken to represent its diameter considered as circular. For, although a circle seen obliquely is always foreshortened into an ellipse, still the longer axis of the ellipse will always represent the real diameter of the circle. This may be seen by holding a penny at various angles to the eye. Now, Dr. Roberts found that the apparent length of the Andromeda nebula is 2⅓ degrees, or 8400 seconds of arc. The diameter in seconds divided by the parallax will give the real diameter of the nebula in terms of the sun’s distance from the earth taken as unity. Now, 8400 divided by 0″·17 gives nearly 50,000, that is, the real diameter of the Andromeda nebula would be—on Bohlin’s parallax—nearly 50,000 times the sun’s distance from the earth. As light takes about 500 seconds to come from the sun to the earth, the above figures imply that light would take about 290 days, or over 9 months to cross the diameter of this vast nebula.
Elementary geometrical considerations will show that if the Andromeda nebula lies at a greater distance from the earth than that indicated by Bohlin’s parallax, its real diameter, and therefore its volume and mass, will be greater. If, therefore, we assume the parallax found by Bohlin, we shall probably find a minimum value for the size and mass of this marvellous object.
Among Dr. Roberts’ photographs of spiral nebulæ (and the Andromeda nebula is undoubtedly a spiral) there are some which are apparently seen nearly edgeways, and show that these nebulæ are very thin in proportion to their diameter. From a consideration of these photographs we may, I think, assume a thickness of about one-hundredth of the diameter. This would give a thickness for the Andromeda nebulæ of about 500 times the sun’s distance from the earth. This great thickness will give some idea of the vast proportions of the object we are dealing with. The size of the whole solar system—large as it is—is small in comparison. The diameter and thickness found above can easily be converted into miles, and from these dimensions the actual volume of the nebula can be compared with that of the sun. It is merely a question of simple mensuration, and no problem of “high mathematics” is involved. Making the necessary calculations, I find that the volume of the Andromeda nebula would be about 2·32 trillion times (2·32 × 1018) the sun’s volume! Now, assuming that the nebulous matter fills only one-half of the apparent volume of the nebula (allowing for spaces between the spiral branches), we have the volume = 1·16 × 1018. If the nebula had the same density as the sun, this would be its mass in terms of the sun’s mass taken as unity, a mass probably exceeding the combined mass of all the stars visible in the largest telescopes! But this assumption is, of course, inadmissible, as the sun is evidently quite opaque, whereas the nebula is, partially at least, more or less transparent. Let us suppose that the nebula has a mean density equal to that of atmospheric air. As water is about 773 times heavier than air, and the sun’s density is 1·4 (water = 1) we have the mass of the nebula equal to 1·16 × 1018 divided by 773 × 1·4, or about 1015 times the sun’s mass, which is still much greater than the probable combined mass of all the visible stars. As it seems unreasonable to suppose that the mass of an individual member of our sidereal system should exceed the combined mass of the remainder of the system, we seem compelled to further reduce the density of the Andromeda nebula. Let us assume a mean density of, say, a millionth of hydrogen gas (a sufficiently low estimate) which is about 14·44 times lighter than air, and we obtain a mass of about 8 × 107 or 80 million times the mass of the sun, which is still an enormous mass.