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gellanic clouds, serve to give us the highest give a first approximation to the orbits and idea of the indomitable patience of Sir J. periods of this highly interesting class of Herschel as an observer. There are two bodies. The accurate Lacaille visited the sections attached to this chapter-one on the Cape before such observations were attended Law of Distribution of Nebula and Clus-to; and Mr. Dunlop's Paramatta Catalogue lers of Stars over the Surface of the Heavens, of 253 Double Stars (Mem. Astr. Society, the other on the Classification of Nebulæ, vol. iii.) appears to be little more worthy of which presents some interesting general re confidence than this Catalogue of Nebulæ. marks :
Even the few years which elapsed between
the period of Mr. Dunlop's first observations “The distribution of nebulæ is not, like that of and those of Sir J. Herschel would have sufthe Milky-way, in a zone or band encircling the ficed to give a first approximation to the orheavens; or, if such a zone can be traced out, bits of the faster moving of these twin-suns. it is with so many interruptions, and so faintly But Dunlop, through negligence, indolence, marked out through by far the greater part of its circumference, that its existence as such can be
or something worse, has failed to be the elder hardly more than suspected. One-third of the
Herschel of Antarctic Astronomy. The diswhole nebulous contents of the heavens are inclu crepancies are so great and frequent, that ded in a broad, irregular patch, occupying about we can have scarcely any confidence in those one-eighth of the whole surface of the sphere, whose agreement with the recent observachiefly (indeed almost entirely) situated in the tions is sufficient to allow us to suppose that northern hemisphere, and occupying the constel
they might possibly be correct. It must have lations Leo, Leo Minor, the body, tail, and hind legs of Ursa Major, the nose of the Camelopard, down such a judgment as this : “
been disheartening to Sir J. Herschel to put and the point of the tail of Draco, Canes Venatici, Coma, the preceding leg of Bootes, and the many mistakes appear to have been commithead, wings, and shoulders of Virgo. This, for ted in the catalogue alluded to (Dunlop's), distinction, I shall call the nebulous region of either in the places, descriptions, or measures Virgo.”—p. 134.
of the objects set down in it.” p. 167. Again,
“It is useless reasoning on such hypothetiThe chapter concludes with a detailed de- cal data,” (Dunlop's Angles of Position), p. scription of the two Magellanic clouds, or ne- 288. bulous regions, in which (with his accustom Sir John has two catalogues of double ed perseverance) Sir J. Herschel has deter stars. The first contains 2102 such objects, mined the positions of a vast number of in observed and placed by the 20-feet reflector, dividual stars, which he has made subser- with the angles of position, and a rough guess vient to the construction of a general chart
of their distances. The second contains acof the greater cloud in Plate X. of his work. curate measures of the distances of the more
The second chapter is devoted to the interesting objects, and also of their angles subject of Double Stars. The great inte of position by means of the 7-feet achromarest of these observations is altogether pio tic. There are appended some very interestspective. Sir John has now done for the ing“ special remarks on the measures of parSouthern Hemisphere what his father com ticular double stars in the foregoiuy catamenced in the Northern more than half a logues." With the two exceptions already century before; that is to say, he determined referred to, no double star not visible in Euthe existence and marked the relative posi rope can be said to have its orbital motion tion of many pairs of stars, which might even roughly ascertained by these observaafterwards prove to be not merely optically tions. But there will be a great harvest to double, or seen by the effect of perspective be reaped some 20 or 30 years hence, when nearly in the same direction, but physically the objects in the Herschel Catalogue sha double, that is, really in each other's neigh- be re-examined by some equally conscienborhood (relatively speaking); and in the tious observer. circumstances of a planet and satellite, one There is one discussion introduced here circulating under the law of gravitation round too interesting to be passed over-it is as to the other, or, to speak more correctly, both the orbit of Virginis, a double star on the circulating round their common centre of confines of the two hemispheres, and theregravity. With only one or two exceptions fore observable in either. This discussion (such as a Crucis and a Centauri), Sir J. (p. 291 et seq.) is a continuation of one by Herschel found no previous observations of Sir J. Herschel in 1832, printed in the 5th old date upon double stars not visible in vol. of the Memoirs of the Astronomical SoEurope, which, combined with his own, might ciety, as an example of a new method of dis
covering the form and position of the orbits | a few years after the latter date the variaof double stars from observation. In that tion both of position and distance became topaper he deduced, by peculiar methods, the tally irreconcilable with the old ellipse, and elements of the orbit from 19 observations, a new orbit was first computed by the Gerpartly of position and partly of distance, since man astronomer Mädler,* which has its ma1780; he included also two older observa- jor axis almost at right angles with the fortions by Bradley and Mayer, in 1718 and mer one, and an area 11 times smaller. 1756, and the whole appeared to be quite Sir J. Herschel, with his usual candor, sufficiently satisfied by supposing the one does not attempt to gloss over the error into star to revolve round the other in 513 years, which he had fallen. The error was quite in an orbit having a major semi-axis (as seen natural, and the remark he makes is most from the earth) subtending 11'83. He also just, namely, that “this is not the first by made (in 1832) this prediction: “ The latter many instances in the history of scientific end of the year 1833 or beginning of the progress, where, of two possible courses, year 1834 will witness one of the most strik- each at the moment equally plausible, the ing phenomena which sidereal astronomy wrong has been chosen.”! Sir John's final has yet afforded, viz., the perihelion passage result is an orbit described in 182 years, of one star round another, with the immense with a major semi-axis of only 31158. But angular velocity of between 600 and 70° per other astronomers are of opinion that a peannum, that is to say, of a degree in five riod of about 143 years is the true one. days.”'* This occurrence actually took place Mädler and Henderson were of this opinion, during Sir John's residence at the Cape, which shows that some uncertainty still exthough not exactly at the predicted time, but ists—an uncertainty inherent in the probrather towards the middle of 1836, for some lem, since both hypotheses satisfy the obtime before and after which the appulse of servations fairly, as may be seen by compar, the two stars was so close, that even in the ing Sir J. Herschel's Table of Calculated 20-feet reflector, under the sky of the Cape, and Observed Places with Professor Henderand by the eye of Herschel, they could not son’s in Captain Smyth's Cycle of Celestial be divided.
Objects, vol. i. p. 486. A good deal deThe elements of 1832 did not, however, pends on the choice of observations to be satlong satisfy the requirements of this quickly isfied; those by different astronomers, and moving star.
Next year Sir John modified particularly by the elder Struve, appearing to them, increasing the period to 629 years and have peculiar and constant sources of error. the major semi-axis to 12'':09. The com But there is a circumstance purely geomeparison of the new elements with the obser- trical which creates great ambiguity. The vations from 1718 to 1833 agreed, as he inclination of the plane of the real elliptic stated, “so well throughout the whole series orbit (for, throughout, the conformity of the as to leave nothing to desire."| What a les- elliptic motion to the law of gravity is asson this to physical philosophers in drawing sumed) to the radius of vision or to the ideal conclusions! So far from leaving nothing concave surface of the celestial sphere, is abto desire, these elements, with the exception solutely unknown à priori. But though an of the eccentricity, had little or no resem- ellipse seen obliquely always appears as an blance to the true elements of the apparent ellipse, the position of the focus (the princiorbit ; and the revolving star, instead of de pal or central star) may be totally distorted scribing only about one-fifth of its ellipse in by the effect of perspective; and as the law 115 years during which it had been observed, of the equable description of areas will also had in reality completed two-thirds of its hold in the distorted ellipse, we are wholly period, perhaps more. To understand how this could possibly happen, we must refer to * Astronomische Nachrichten, No. 363, for 1838, the interesting diagram, p. 293 of the work and No. 452. for 1842. before us, which shows the true ellipse nes
+ Fontenelle, we think, adds that the least protled so snugly into one end of the former hy- bable is commonly the true one.
similar, but less justifiable, mistake occurs in Propothetical orbit intersecting it in four points, fessor Playfair's estimate of the shortest time rethat they nearly coincide for a large portion quired by a heavy body to describe the slide of of the smaller orbit, and precisely that por- Alpnach, supposing it a cycloid, which he makes tion described between 1718 and 1833 ; but about a fourth part too small
. But it is just to recollect contrary instances, when they do occur, show
ing that fate is not always adverse to the bold in* Mem. Astr. Society, v 194.
quirer. Of this several circumstances in the recent Ibid., vi. p. 152.
discovery of Neptune offer striking instances.
A curious and
destitute of a perception of incongruity, which in the present case for 1781, 1803, 1822,) it would immediately flow from attempting to seems to us to leave far too much in the satisfy observations by an apparent ellipse hands of the interpolator. And, indeed, whose focus should coincide with the posi- this may be gathered from the fact that Sir tion of the greater star.
interpolations of the older obSir John Herschel's method of determin- servations, in his paper of 1832 and in the ing sidereal orbits (described in the 5th vol. present work, lead to considerable differences of the Astronomical Memoirs) will undoubt- in estimating the angular velocities, and, edly be mainly judged of by the fact whether consequently, the radii vectores ; differences his orbit or that of Mädler and Henderson which we believe will be found pretty much shall be found to be correct, which future equivalent to the chances of error in the diobservations must soon determine. Its rect measurement of the latter. It is indeed principle is twofold: first, to take mean re- plain from the present work that Sir John sults deduced by graphical interpolation, in- has had trouble with his micrometers, and stead of single results of observation, for the that they are instruments still in point of basis of calculation ; secondly, to reject all accuracy very far below the requirements of measures of distance between the stars for astronomy; but the very Table which he the determination of the elements, saving gives, comparing the computed and observed only the axis of the ellipse, and to effect distances (p. 299) satisfies us that the obserthis by the use of angles of position merely. vations cannot be so very bad; the extreme The first principle, we can hardly doubt, will difference of those micrometrically measured) be ultimately assented to. Upon the second amounting to only a quarter of a second, and we are more doubtful, offering however our the average to less than half that quantity. scruples with the deference due to so great It is fair to add, however, that some of these an authority. It may be very true that an numbers are the mean of several distinct regles of position are far more accurately ob- sults.* tained relatively to the speed with which The third chapter, which contains two they vary; but this is not enough. The sections, appears to us to be the most novel, relation of the corresponding distances (or curious, and ingenious, perhaps even the radii vectores) must be in some way or other most practically important of the whole. It ascertained ; and Sir J. Herschel deduces is upon AsTROMETRY, or the measurement of them from the well-known principle that by the relative brilliancy of different stars. the equality of areas the radii vary inversely Every one knows that the stars visible to the as the square roots of the angular velocily. naked eye are divided into six classes or But to obtain the ungular velocity, we incur magnitudes, the first being the brightest and chances of error far greater than that of de- least numerous. It is also well known that termining angles of position merely. Sir J. such a subdivision has hitherto been wholly Herschel determines them by drawing tan- arbitrary, not even a standard star having gents to an interpolating curve. We have been fixed upon as the representative of had some experience of such interpolation, each class; and that it has also been most and we can affirm that when the points of inaccurate, since many stars marked of the observation are at all distant or irregular, third and even of the fourth magnitude are the drawing of tangents is a process attended found to be brighter than those of the secwith the utmost hazard of error—in very ond, and this in far too great a number of many cases exceeding, we should think, the instances to allow us to suppose that such probable error arising from micrometric er- inversions of order are always or generally rors of distance. * It is in fact determining due to actual changes in the apparent lustre a quantity of a lower order of magnitude of the objects themselves. than that obtained from observation, whereas the errors in the direct distance are at least * In the Comptes-Rendus of the French Academy of the same order as those of observation. (29th of November, 1847) we find an interesting reWhen the observations of position are multi- search, by M. Otto Struve, of the orbit of the satelplied and close, some allowance may be lite of Neptune, an inquiry of exactly the same kind
as that in the case of double stars; with this differmade for the goodness of the method; but ence, however, that the orbit is described in the when the observations are 20 years apart (as short space of less than six days. The greatest er:
ror of distance (compared with the hypothetical * Captain Smyth mentions that Sir J. Herschel orbit) is about 1' or of the distance measured. has abandoned the method of tangents, and em The greatest error of position is 51°. The method ploys first and even second differences. (Cycle, vol. pursued for finding the orbit is not mentioned, but ii. p. 280, note.)
was probably Encke's or Mädler's
That Sir John Herschel should have suc and regular system (to be explained presently) ceeded (and we are persuaded all competent are employed to obtain in one unbroken series a judges will admit that he has done so) in graduating scale of steps, from the brightest down classifying a great number of the more im
to the faintest stars visible to the eye. Numeriportant stars in both hemispheres in the the scale in this case is entirely arbitrary, and no
cal values are then subsequently assigned, and as exact order of their brightness at the time photometric relations but those of more and less his catalogue was made, and this (in the first bright are used, these numbers may be so assigned instance) without the aid of any other instru as to conform on a general average to any usage ment than his unassisted eye; that he should
or nomenclature which may be fixed upon or tahave been able to put a determinate value Waiving all discussion of the greater or less pro;
ken as the general average of astronomers. upon the vague definition of “ magnitude," priety of the magnitudes assigned by this or that and that conformable to the average value observer, I have thought it best on the whole to which practical astronomers have chosen to adopt as my standard of astrometrical nomenclagive it; that he should have been able not ture the catalogue of the Astronomical Society of only to assign the order of the intermediate 2881 stars, published in 1827, being well aware stars, but to give numerical fractional values that the magnitudes there assigned are those of to the intensity of their light, and by the co
different epochs and different observers (but all of incidence of independent results show that considerable errors exist. The mode in which I
eminence,) and that in individual cases many and these numbers may be depended on in most have eliminated these errors and secured a true cases to within one-twentieth of the interval coincidence between the results of my observaseparating two “magnitudes," is a result not tions and the magnitudes of the catalogue in only of the highest importance to astronomy question taken as a whole, will be explained in by converting what is vague into what is due course, and will I believe be found to be quite definite, and by declaring to all generations free froin objection."--p. 305. the gradation of the brightness of stars in our day, but it is a splendid example of an We have then a tabular view of the reinduction in science; an admirable lesson to sults of individual nights' observation, in the student of natural philosophy, of that in which a larger or smaller number of stars tellectual alchemy (known, alas! to how are arranged simply in the order in which few) by which precious truth may be ex- they appear more or less bright; these are tracted from a seemingly hopeless mass of the Observed Sequences. One of these lists rubbish, like an ounce of silver from a ton of is then taken and compared with the other lead. We must attempt to give some ac
lists in the following way; any two or more count of these ingenious processes.
stars common to two lists ought to be found The first section is on “ Astrometry, or in the same gradation of brightness. If the the Numerical Expression of the apparent stars be temporarily denoted by the letters Magnitude of the Stars, by the method of Se- A, B, C, D, &c., in the true order of their quences." We shall introduce it in Sir J. brightness, this order ought never to be inHerschel's own words:
verted in the sequences, but if it is so
(through unfavorable circumstances or er“ Without dissuading from the introduction of
rors of observation) it will be restored by the new, and the improvement of old instrument contrivances (or astrometers) for this
of all the comparisons of the given purpose
average I am disposed to rely mainly for the formation of stars. In the case when a star C, for ina real scale of magnitudes on comparisons made stance, has been noted an equal number of by the unassisted judgment of the naked eye. times briyhter, and less bright, than D, then The method which I have followed for this pur- they will be provisionally assumed to be pose, and which, to distinguish it from others
equal. which have been or may hereafter be proposed, I shall term the method of Sequences, is in some
By compendious methods which we cansort an extension and carrying out of Sir Wil
not stop to describe, the average result of liam Herschel's method of naked eye comparisons, all the direct comparisons of stars by two described in his papers above-mentioned, so modi and two in a continued chain from the fied and generalized as to afford a handle for brightest to the least bright, is presented in educing from it a numerical scale of values of the one table called a Normal Sequence. This magnitudes of the stars compared, which it was includes about 140 stars, from the brightest not capable of doing in its original form and as
of the first down to the fifth full magnitude practised by him. In this method, stars visible at one time, and favorably, or rather not unfavorably with all the certainty which belongs to direct
(p. 334,) every individual of which is known, situated for comparison, are arranged in by the mere judgment of the naked eye, and these ocular comparison, to be less bright than its sequences treated according to a certain peculiar | predecessor on the scale, but more bright
than its immediate successor. But this list | sequence* to which they belong a star is very far from including all the stars in the brighter and one less bright, which have original sequences, for many or most stars had numerical values assigned to them by will not happen to have been directly com the process last described. The mean of pared with the particular star which ought these values is to be regarded provisionally immediately to precede or to follow them in as that of the interpolated star. a perfectly graduated list.
Take, for example, ß Ceti; this star, in let A, B, C, D, &c., now represent the un the corrected sequence No. 21, is found bebroken chain or normal sequence. By this tween 8 Argus (2-55+) and Orionis (2.68,) we understand that on one or more occasions being the only star in that sequence interC has been compared in the heavens with B, mediate between them. The arithmetical and seen to be less bright, and has also mean between these values is 2.61. Again, been compared with D, and been found in the corrected sequence No. 28, I find inbrighter than it. But we may suppose an- terposed between a Arietis (2:48) and B other star c,
which has been directly com- Hydræ (3:23) three stars, ß Ceti, a Phepared with B, and found less bright, but not nicis, and a Ceti, from which, supposing having been compared with D, but only these arithmetical means equidistant from with E or F, and found brighter than them, each other and the two extremes, we find its place will be uncertain, because we the value 2.67. And again, in the corrected should not know whether to place it before sequence No. 30, I find B Ceti singly interor after D or E; and the compared stars posed between B [a ?) Arietis (2:48) and x may be even more distant on the scale. Orionis, (2.68,) which affords a third value Sir J. Herschel extricates himself from the of 2.58 for the numerical expression of its difficulty with admirable address in the fol- magnitude on this scale. The mean of these lowing way.
three determinations, 2.62, may be regarded Having written the names of the stars in as the magnitude (on this scale) within very the unbroken or normal sequence, he adds to moderate probable limits of error.”—p. 336. each its “magnitude,” taken from Mr. Baily's What has now been stated explains so catalogue of 2881 stars before mentioned. fully the scope of the method employed by These are confessedly but rude, often inac- Sir. J. Herschel, that we spare our readers curate indications. We find, for instance, the detail of a final interpolation and adstars marked as of the third and fifth magni- ditional rounding off of individual errors by tudes occurring (in the true scale of bright- a geographical process which completes the ness) intermediate between two of the second. discussion ; its success may be best judged This looks hopeless enough. Sir John, how- of by its results. The following are the ever, first “equalizes” these magnitudes by final estimates of “ magnitude" of stars seascribing to each star the mean of its own lected almost at random from amongst those and of the two preceding and two following pretty frequently observed: the numbers in magnitudes in his list; and then projecting question are derived from independent obthese equalized magnitudes on paper, he served sequences on different nights. pares down the remaining ruggedness of the
y Virginis. transitions from the one to the other by
3.05 drawing a smooth curve amongst the points
3:08 representing the “ equalized” tabular magni
2.95 tudes of each. One awkwardness occurs in
3:11 the notation; there are stars brighter than
3:45 the average of the first magnitude, such as
3:00 Sirius, Canopus, and a Centauri. These are
2.93 denoted by fractions less than unity, and as
3:17 such fractions tend to no definite standard,
2.97 they remain, as Sir. J. Herschel observes, at present wholly arbitrary, having no pre Mean 2.82
Mean 3.08 tension to photometrical accuracy; thus Sirius has its magnitude denoted by 0'1. * Corrected sequences are formed from the obThe next step, which is to include stars
served sequences, when by mutual comparison they
have been freed from conflicting errors. The normal not directly compared with their nearest
sequence is constructed from the corrected sequences. rivals in splendor, is very easily conceived,
+ The magnitude of 0 Argûs in the normal sefor we can generally find in the orvrected