grounded on precise photometrical experiments, of the apparent brightness of each star. This would afford a

definite character in natural history, and serve as a term of comparison to ascertain the changes which may take place in them; changes which we know to happen in several, and may therefore fairly presume to be possible in all. Meanwhile, as a first approximation, the following proportions of light, concluded from Sir William Herschel's experimental comparisons of a few selected stars, may be borne in mind:

Light of a star of the average 1st magnitude

2d

3d

4th

5th

6th

= 100 = 25 = 12?

By my own experiments, I have found that the light of Sirius (the brightest of all the fixed stars) is about 324 times that of an average star of the 6th magnitude.t

(585.) If the comparison of the apparent magnitudes of the stars with their numbers leads to no definite conclusion, it is otherwise when we view them in connection with their local distribution over the heavens. If indeed we confine ourselves to the three or four brightest classes, we shall find them distributed with tolerable impartiality over the sphere; but if we take in the whole amount visible to the naked eye, we shall perceive a great and rapid increase of number as we approach the borders of the milky way. And when we come to telescopic magnitudes, we find them crowded beyond imagination, along the extent of that circle, and of the branch which it sends off from it; so (art. 253.) that in fact its whole light is composed of nothing but stars, whose average magnitude may be stated at about the tenth or eleventh.

Phil. Tr. 1817.

+ Trans. Astron. Soc. iii. 183.

(586.) These phænomena agree with the supposition that the stars of our firmament, instead of being scattered in all directions indifferently through space, form a stratum, of which the thickness is small, in comparison with its length and breadth; and in which the earth occupies a place somewhere about the middle of its thickness, and near the point where it subdivides into two principal laminæ, inclined at a small angle to each other. For it is certain that, to an eye so situated, the apparent density of the stars, supposing them pretty equally scattered through the space they occupy, would be least in a direction of the visual ray (as S A), perpendicular to the lamina, and greatest in that of its breadth, as S B, SC, SD; increasing rapidly in passing from one to the other direction, just as we see a slight haze in the atmosphere thickening into a decided fog bank near the horizon, by the rapid increase of the mere length of the visual ray. Accordingly, such is the view of the construction of the starry firmament taken by Sir William Herschel, whose powerful telescopes have effected a complete analysis of this wonderful zone, and demon

B

So

strated the fact of its entirely consisting of stars. crowded are they in some parts of it, that by counting the stars in a single field of his telescope, he was led to conclude that 50000 had passed under his review in d zone two degrees in breadth, during a single hour's observation. The immense distances at which the remoter regions must be situated will sufficiently account for the vast predominance of small magnitudes which are observed in it.

(587.) When we speak of the comparative remoteness of certain regions of the starry heavens beyond others, and of our own situation in them, the question

immediately arises, What is the distance of the nearest fixed star? What is the scale on which our visible firmament is constructed? And what proportion do its dimensions bear to those of our own immediate system? To this, however, astronomy has hitherto proved unable to supply an answer. All we know on this subject is negative. We have attained, by delicate observations and refined combinations of theoretical reasoning to a correct estimate, first, of the dimensions of the earth; then, taking that as a base, to a knowledge of those of its orbit about the sun; and again, by taking our stand, as it were, on the opposite borders of the circumference of this orbit, we have extended our measurements to the extreme verge of our own system, and by the aid of what we know of the excursions of comets, have felt our way, as it were, a step or two beyond the orbit of the remotest known planet. But between that remotest orb and the nearest star there is a gulf fixed, to whose extent no observations yet made have enabled us to assign any distinct approximation, or to name any distance, however immense, which it may not, for any thing we can tell, surpass.

(588.) The diameter of the earth has served us as the base of a triangle, in the trigonometrical survey of our system (art. 226.), by which to calculate the distance of the sun but the extreme minuteness of the sun's parallax (art. 304.) renders the calculation from this "ill-conditioned" triangle (art. 227.) so delicate, that nothing but the fortunate combination of favourable circumstances, afforded by the transits of Venus (art. 409.), could render its results even tolerably worthy of reliance. But the earth's diameter is too small a base for direct triangulation to the verge even of our own system (art.449.), and we are, therefore, obliged to substitute the annual parallax for the diurnal, or, which comes to the same thing, to ground our calculation on the relative velocities of the earth and planets in their orbits (art. 414.), when we would push our triangulation to that extent. It might be naturally enough expected, that by this

enlargement of our base to the vast diameter of the earth's orbit, the next step in our survey (art. 227.) would be made at a great advantage; - that our change of station, from side to side of it, would produce a perceptible and measurable amount of annual parallax in the stars, and that by its means we should come to a knowledge of their distance. But, after exhausting every refinement of observation, astronomers have been unable to come to any positive and coincident conclusion upon this head; and it seems, therefore, demonstrated, that the amount of such parallax, even for the nearest fixed star which has hitherto been examined with the requisite attention, remains still mixed up with, and concealed among, the errors incidental to all astronomical determinations. Now, such is the nicety to which these have been carried, that did the quantity in question amount to a single second (i. e. did the radius of the earth's orbit subtend at the nearest fixed star that minute angle) it could not possibly have escaped detection and universal recognition.

(589.) Radius is to the sine of 1", in round numbers, as 200000 to 1. In this proportion, then, at least, must the distance of the fixed stars from the sun exceed that of the sun from the earth. The latter distance, as we have already seen, exceeds the earth's radius in the proportion of 24000 to 1; and, lastly, to descend to ordinary standards, the earth's radius is 4000 of our miles. The distance of the stars, then, cannot be so small as 4800000000 radii of the earth, or 19200000000000 miles ! How much larger it may be, we know not.

(590.) In such numbers, the imagination is lost. The only mode we have of conceiving such intervals at all is by the time which it would require for light to traverse them. Now light, as we know, travels at the rate of 192000 miles per second. It would, therefore, occupy 100000000 seconds, or upwards of three years, in such a journey, at the very lowest estimate. What, then, are we to allow for the distance of those

innumerable stars of the smaller magnitudes which the telescope discloses to us! If we admit the light of a star of each magnitude to be half that of the magnitude next above it, it will follow that a star of the first magnitude will require to be removed to 362 times its distance to appear no larger than one of the sixteenth. It follows, therefore, that among the countless multitude of such stars, visible in telescopes, there must be many whose light has taken at least a thousand years to reach us; and that when we observe their places, and note their changes, we are, in fact, reading only their history of a thousand years' date, thus wonderfully recorded. We cannot escape this conclusion, but by adopting as an alternative an intrinsic inferiority of light in all the smaller stars of the milky way. We shall be better able to estimate the probability of this alternative, when we have made acquaintance with other sidereal systems, whose existence the telescope discloses to us, and whose analogy will satisfy us that the view of the subject we have taken above is in perfect harmony with the general tenour of astronomical facts.

(591.) Quitting, however, the region of speculation, and confining ourselves within limits which we are sure are less than the truth, let us employ the negative knowledge we have obtained respecting the distances of the stars to form some conformable estimate of their real magnitudes. Of this, telescopes afford us no direct information. The discs which good telescopes show us of the stars are not real, but spurious-a mere optical illusion.* Their light, therefore, must be our only guide. Now Dr. Wollaston, by direct photometrical experiments, open, as it would seem, to no objections †, has ascertained the light of Sirius, as received by us, to be to that of the sun as 1 to 20000000000. The sun,

therefore, in order that it should appear to us no brighter than Sirius, would require to be removed to 141400 times its actual distance. We have seen, however, that the distance of Sirius cannot be so small as 200000 times *See Cab. Cyc. Optics. + Phil. Trans. 1829, p. 24.