but by adopting as an alternative an intrinsic inferiority of light in all the smaller stars of the galaxy. We shall be better able to estimate the probability of this alternative when we shall 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 here taken is in perfect harmony with the general tenor of astronomical facts.

(804.) Hitherto we have spoken of a parallax of 1" as a mere limit below which that of any star yet examined assuredly, or at least very probably falls, and it is not without a certain convenience to regard this amount of parallax as a sort of unit of reference, which, connected in the reader's recollection with a parallactic unit of distance from our system of 20 billions of miles, and with a 34 year's journey of light, may save him the trouble of such calculations, and ourselves the necessity of covering our pages with such enormous numbers, when speaking of stars whose parallax has actually been ascertained with some approach to certainty, either by direct meridian observation or by more refined and delicate methods. These we shall proceed to explain, after first pointing out the theoretical peculiarities which enable us to separate and disentangle its effects from those of the Uranographical corrections, and from other causes of error which being periodical in their nature add greatly to the difficulty of the subject. The effects of precession and proper motion (see art. 852.) which are uniformly progressive from year to year, and that of nutation which runs through its period in nineteen years, it is obvious enough, separate themselves at once by these characters from that of parallax; and, being known with very great precision, and being certainly independent, as regards their causes, of any individual peculiarity in the stars affected by them, whatever small uncertainty may remain respecting the numerical elements which enter into their computation (or in mathematical language their co-efficients), can give rise to no embarrassment. With regard to aberration the case is materially different. This correction affects the place of a star by a fluctuation annual

in its period, and therefore, so far, agreeing with parallax. It is also very similar in the law of its variation at different seasons of the year, parallax having for its apex (see art. 343, 344.) the apparent place of the sun in the ecliptic, and aberration a point in the same great circle 90° behind that place, so that in fact the formula of calculation (the coefficients excepted) are the same for both, substituting only for the sun's longitude in the expression for the one, that longitude diminished by 90° for the other. Moreover, in the absence of absolute certainty respecting the nature of the propagation of light, astronomers have hitherto considered it necessary to assume at least as a possibility that the velocity of light may be to some slight amount dependent on individual peculiarities in the body emitting it.

(805.) If we suppose a line drawn from the star to the earth at all seasons of the year, it is evident that this line will sweep over the surface of an exceedingly acute, oblique cone, having for its axis the line joining the sun and star, and for its base the earth's annual orbit, which, for the present purpose, we may suppose circular. The star will therefore appear to describe each year about its mean place regarded as fixed, and in virtue of parallax alone, a minute ellipse, the section of this cone by the surface of the celestial sphere, perpendicular to the visual ray. But there is also another way in which the same fact may be represented. The apparent orbit of the star about its mean place as a center, will be precisely that which it would appear to describe, if seen from the sun, supposing it really revolved about that place in a circle exactly equal to the earth's annual orbit, in a plane parallel to the ecliptic. This is evident from the equality and parallelism of the lines and directions concerned. Now the effect of aberration (disregarding the slight variation of the earth's velocity in different parts of its orbit) is precisely similar in law, and differs only in amount, and in its bearing

In the actual state of astronomy and photology this necessity can hardly be considered as still existing, and it is desirable, therefore, that the practice of astronomers of introducing an unknown correction for the constant of aberration into their "equations of condition" for the determination of parallax, should be disused, since it actually tends to introduce error into the final result.

reference to a direction 90° different in longitude.

Suppose, in order to fix our ideas, the maximum of parallax to be 1" and that of aberration 20 5", and let A B, a b, be two circles imagined to be described separately, as above, by the star about its mean place S, in virtue of these two causes respectively, ST being a line parallel to that of the line of equinoxes. Then if in virtue of parallax alone, the star would be found at a in the smaller orbit, it would in virtue of aberration alone be found at A, in the larger, the angle a SA being a right angle. Drawing then A C equal and parallel to Sa, and joining SC, it will in virtue of both simultaneously be found in C, i. e. in the circumference of a circle whose radius is S C, and at a point in that circle, in advance of A, the aberrational place, by the angle A SC. Now since SA: AC:: 20-5: 1, we find for the angle ASC 2° 47′ 35",

and for the length of the radius SC of the circle representing the compound motion 20"-524. The difference (0"-024) between this and SC, the radius of the aberration circle, is quite imperceptible, and even supposing a quantity so minute to be capable of detection by a prolonged series of observations, it would remain a question whether it were produced by parallax or by a specific difference of aberration from the general average 20"-5 in the star itself. It is therefore to the difference of 2° 48′ between the angular situation of the displaced star in this hypothetical orbit, i. e. in the arguments

(as they are called) of the joint correction (SC) and that of aberration alone (T SA), that we have to look for the resolution of the problem of parallax. The reader may easily figure to himself the delicacy of an inquiry which turns wholly (even when stripped of all its other difficulties) on the precise determination of a quantity of this nature, and of such very moderate magnitude.

(806.) But these other difficulties themselves are of no trifling order. All astronomical instruments are affected by differences of temperature. Not only do the materials of which they are composed expand and contract, but the masonry and solid piers on which they are erected, nay even the very soil on which these are founded, participate in the general change from summer warmth to winter cold. Hence arise slow oscillatory movements of exceedingly minute amount, which levels and plumblines afford but very inadequate means of detecting, and which being also annual in their period (after rejecting whatever is merely casual and momentary) mix themselves intimately with the matter of our inquiry. Refraction too, besides its casual variations from night to night, which a long series of observations would eliminate, depends for its theoretical expression on the constitution of the strata of our atmosphere, and the law of the distribution of heat and moisture at different elevations, which cannot be unaffected by difference of season. No wonder then that mere meridional observations should, almost up to the present time, have proved insufficient, except in one very remarkable instance, to afford unquestionable evidence, and satisfactory quantitative measurement of the parallax of any fixed star.

(807.) The instance referred to is that of a Centauri, one of the brightest and for many other reasons, one of the most remarkable of the southern stars. From a series of observations of this star, made at the Royal Observatory of the Cape of Good Hope in the years 1832 and 1833, by Professor Henderson, with the mural circle of that establishment, a parallax to the amount of an entire second was concluded on his reduction of the observations in question after his return to England. Subsequent observations by Mr. Maclear,

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partly with the same, and partly with a new and far more efficiently constructed instrument of the same description made in the years 1839 and 1840, have fully confirmed the reality of the parallax indicated by Professor Henderson's ob servations, though with a slight diminution in its concluded amount, which comes out equal to 0"-9128 or about 10ths of a second; bright stars in its immediate neighbourhood being unaffected by a similar periodical displacement, and thus affording satisfactory proof that the displacement indicated in the case of the star in question is not merely a result of annual variations of temperature. As it is impossible at present to answer for so minute a quantity as that by which this result differs from an exact second, we may consider the distance of this star as approximately expressed by the parallactic unit of distance referred to in art. 804.

(808.) A short time previous to the publication* of this important result, the detection of a sensible and measurable amount of parallax in the star N° 61 Cygni of Flamsteed's catalogue of stars was announced by the celebrated astronomer of Königsberg, the late M. Bessel.+ This is a

small and inconspicuous star, hardly exceeding the sixth magnitude, but which had been pointed out for especial observation by the remarkable circumstance of its being affected by a proper motion (see art. 852.), i. e. a regular and continually progressive annual displacement among the surrounding stars to the extent of more than 5" per annum, a quantity so very much exceeding the average of similar minute annual displacements which many other stars exhibit, as to lead to a suspicion of its being actually nearer to our system. It is not a little remarkable that a similar presumption of proximity exists also in the case of a Centauri, whose unusually large proper motion of nearly 4" per annum is stated by Professor Henderson to have been the motive which induced him to subject his observations of that star to that severe discussion which led to the detection of its parallax. M.

• Prof. Henderson's paper was read before the Astronomical Society of London, Jan. 3. 1839. It bears date Dec. 24. 1838.

† Astronomische Nachrichten, Nos. 365, 366. Dec. 13. 1838.