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tance, on the supposition of an equality among the real lights of the stars, would facilitate the expression of speculative ideas on the constitution of the sidereal heavens. On the other hand, it would at first sight appear to make too small a difference between the lights in the lower magnitudes. For example, on this principle of nomenclature, the light of a star of the seventh magnitude would be thirty-six 49ths of that of one of the sixth, and of the tenth 81 hundredths of the ninth, while between the first and the second the proportion would be that of four to one. So far, however, from this being really objectionable, it falls in well with the general tenor of the optical facts already alluded to, inasmuch as the eye (in the absence of disturbing causes) does actually discriminate with greater precision between the relative intensities of feeble lights than of bright ones, so that the fraction 36 for instance, expresses quite as great a step downwards (physiologically speaking) from the sixth magnitude, as į does from the first. As the choice, therefore, so far as we can see, lies between these two scales, in drawing the lines of demarcation between what may be termed the photometrical magnitudes of the stars, we have no hesitation in adopting, and recommending others to adopt, the latter system in preference to the former.
(781.). The conventional magnitudes actually in use among astronomers, so far as their usage is consistent with itself, conforms moreover very much more nearly to this than to the geometrical progression. It has been shown* by direct photometric measurement of the light of a considerable number of stars from the first to the fourth magnitude, that if M be the number expressing the magnitude of a star on the above system, and m the number expressing the magnitude of the same star in the loose and irregular language at present conventionally or rather provisionally adopted, so far as it can be collected from the conflicting authorities of different observers, the difference between these numbers, or M—m, is the same in all the higher parts of the scale, and is less than half armag
See " Results of Observations made at the Cape of Good Hope, &c. &c." p. 371. By the Author.
nitude (om. 414). The standard star assumed as the unit of magnitude in the measurements referred to, is the bright southern star a Centauri, a star somewhat superior to Arcturus in lustre. If we take the distance of this star for unity, it follows that when removed to the distances 1.414, 2:414, 3.414, &c. its apparent lustre would equal those of average stars of the 1st, 2d, 3d, &c. magnitudes, as ordinarily reckoned, respectively.
(782.) The difference of lustre between stars of two consecutive magnitudes is so considerable as to allow of many intermediate gradations being perfectly well distinguished. Hardly any two stars of the first or of the second magnitude would be judged by an eye practised in such comparisons to be exactly equal in brightness. Hence, the necessity, if any. thing like accuracy be aimed at, of subdividing the magnitudes and admitting fractions into our nomenclature of brightness. When this necessity first began to be felt, a simple bisection of the interval was recognized, and the intermediate degree of brightness was thus designated, viz. 1.2 m, 2.3 m, and so on. At present it is not unfrequent to find the interval trisected thus : lm, 1.2 m, 2.1 m, 2 m, &c. where the expression 1.2 m denotes a magnitude intermediate between the first and second, but nearer 1 than 2; while 2.1 m designates a magnitude also intermediate, but nearer 2 than 1. This may suffice for common parlance, but as this department of astronomy progresses towards exactness, a decimal subdivision will of necessity supersede these rude forms of expression, and the magnitude will be expressed by an integer number followed by a decimal fraction; as for instance, 2.51 which expresses the magnitude of y Geminorum on the vulgar or conventional scale of magnitudes, by which we at once perceive that its place is almost exactly half way between the 2d and 3d average magnitudes, and that its light is to that of an average first magnitude star in that scale (of which a Orionis in its usual or normal state * may be taken as a typical specimen) as 12: (2:51), and to that of a
* In the interval from 1836 to 1839 this star underwent considerable and remarkable fluctuations of brightness.
Centauri as 12: (2.924)?, making its place in the photometric scale (so defined) 2.924. Lists of stars northern and southern, comprehending those of the vulgar first, second, and third magnitudes, with their magnitudes decimally expressed in both systems, will be found at the end of this work. The light of a star of the sixth magnitude may be roughly stated as about the hundredth part of one of the first. Sirius would make between three and four hundred stars of that magnitude.
(783.) The exact photometrical determination of the comparative intensities of light of the stars is attended with many and great difficulties, arising partly from their differences of colour ; partly from the circumstance that no invariable standard of artificial light has yet been discovered; partly from the physiological cause above alluded to, by which the eye is incapacitated from judging correctly of the proportion of two lights, and can only decide (and that with not very great precision) as to their equality or inequality; and partly from other physiological causes. The least objectionable method hitherto proposed would appear to be the following. A natural standard of comparison is in the first instance selected, brighter than any of the stars, so as to allow of being equalized with any of them by a reduction of its light optically effected, and at the same time either invariable, or at least only so variable that its changes can be exactly calculated and reduced to numerical estimation. Such a standard is offered by the planet Jupiter, which, being much brighter than any star, subject to no phases, and variable in light only by the variation of its distance from the sun, and which moreover comes in succession above the horizon at a convenient altitude, simultaneously with all the fixed stars, and, in the absence of the moon, twilight, and other disturbing causes (which fatally affect all observations of this nature), combines all the requisite conditions. Let us suppose, now, that Jupiter being at A and the star to be compared with it at B, a glass prism C, is so placed that the light of the planet deflected by total internal reflexion at its base, shall emerge parallel to B E the direction of the star's visual ray. After reflexion, let it be received on a lens D, in whose focus F, it will form a small bright star-like image capable of being viewed by an eye placed at E, so far out of the axis of the cone of diverging rays as to admit of seeing at the same time, and
with the same eye, and so comparing, this image with the star seen directly. By bringing the eye nearer to or further from the focus F, the apparent brightness of the focal point will be varied in the inverse ratio of the square of the distance E F, and therefore may be equalized, as well as the eye can judge of such equalities, with the star. If this be done for two stars several times alternately, and a mean of the results taken, by measuring EF, their relative brightness will be obtained: that of Jupiter, the temporary standard of comparison, being altogether eliminated from the result.
(784.) A moderate number of well selected stars being thus photometrically determined by repeated and careful measurements, so as to afford an ascertained and graduated scale of brightness among the stars themselves, the intermediate steps or grades of magnitude may be filled up, by inserting between them, according to the judgment of the eye, other stars, forming an ascending or descending sequence, each member of such a sequence being brighter than that below, and less bright than that above it; and thus at length, a scale of numerical magnitudes will become established, complete in all its members, from Sirius, the brightest of the stars, down to the least visible magnitude.* It were much to be wished that this branch of astronomy, which at present can hardly be said to be advanced beyond its infancy, were perseveringly and systematically cultivated. It is by no means a subject of mere barren curiosity, as will abundantly appear when we come to speak of the phænomena of variable stars, and being moreover, one in which amateurs of the science may easily chalk out for themselves a useful and available path, may naturally be expected to receive large and interesting accessions at their hands.
* For the method of combining and treating such sequences, where accumulated in considerable numbers, so as to eliminate from their results the influence of er roneous judgment, atmospheric circumstances, &c., which often give rise tu contradictory arrangements in the order of stars differing but little in magnitude,
(785.) If the comparison of the apparent magnitudes of the stars with their numbers leads to no immediately obvious 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 a considerable approach to impartiality over the sphere: a marked preference however being obseryable, especially in the southern hemisphere, to a zone or belt, following the direction of a great circle passing through ɛ Orionis and a Crucis. But if we take in the whole amount visible to the naked eye, we shall perceive a great 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 branches which it sends off from it; so that in fact its whole light is composed of nothing but stars of every magnitude, from such as are visible to the naked eye down to the smallest point of light perceptible with the best telescopes.
(786.) 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 (art. 302.). For it is certain that, to an eye so
as well as for an account of a series of photometric comparisons (in which however, not Jupiter, but the moon was used as an intermediate standard), see the work above cited, note on p. 353. (Results of Observations, &c.)