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with certain other orbital similarities, led to the conclusion that we had now positively passed the threshold, and gained an insight of the true elements. As I had the pleasure of seeing Mr. Hind soon after he wrote, we talked over the case, and considered that it constituted a fact which some of the stellar inquirers would like to be acquainted with; and, as these sheets are only destined to a limited circulation, we agreed upon the eligibility of his communicating it to the Royal Astronomical Society, at their meeting on the following evening, April 11th. ,
This is the statement, as copied from the Minutes, and inserted in vol. xi. No. 5, of the Society's Monthly Notices :
On the Elements of the Binary Star y Virginis, resulting from a Discussion of the Measures taken
by Capt. W. H. SMYTH, R.N. between the years 1831 and 1850. By J. R. HIND, Esq. Foreign Secretary.
It is well known to the members of the Royal Astronomical Society, that amongst the stars observed for the Bedford Cycle by Captain Smyth, the interesting binary system y Virginis occupied a prominent place. During the period included by the Bedford measures, a very critical and important part of the orbit was passed over, and great pains were bestowed upon the observations to render them as accurate as the nature of the object would permit In 1831 the component stars were separated about 1"}, the smaller one being situate in the north following quadrant about 120 above the parallel of declination. From this position it was watched by Captain Smyth during its passage through the same quadrant, the central distance diminishing each year until in the early part of the year 1836 the star was pronounced single under the best atmospheric conditions. Before the close of the spring the Bedford telescope again afforded indications of duplicity, and two nights' observations showed that the companion had just completed a fourth part of its orbit, its position being now 12° north preceding the principal star. In 1837 a further change of no less than 83° in the same direction had taken place, the comes lying in the angle 265° at a distance of rather more than half a second of arc from the primary. In 1847 Captain Smyth found it still on the preceding side, but at a central distance of 2":6, and his observations early in the year 1848 showed that it had just passed the vertical point, the measures yeilding an angle of 1799.5; and at the date of the last observations in 1850, the angle had further diminished to 1770-1.
It thus appears that the whole series of measures taken with the Bedford telescope include a change in the position of the companion-star of 260°, or nearly three-fourths of a revolution, extending, as before remarked, over a very important part of the orbit. The question, therefore, naturally suggests itself, whether an investigation of the elements from this series of measures to the exclusion of all others, might not be one of some value, as showing, by comparison with elements founded upon the whole of the measures of other astronomers, including the valuable alignments of Bradley and Pound in 1718 and 1720, what kind of dependence we may place upon elements for other binary systems computed under similar circumstances, where, during the interval between the earliest and latest observations, a portion only of the ellipse has been described, which is to be traced chiefly from the measures of one observer.
In the present instance the investigation promised to lead to results of especial interest; the measures of , Virginis, published in the Bedford Cycle, were taken by one of the most experienced observers of the present day in this particular department of astronomy, were made throughout with the same instrument, and under the most favourable conditions as regards the state of the atmosphere, the powers employed, &c. With data derived under these promising circumstances, an orbit fairly approximating to the true one (or to that which we have strongest reason to rely upon) might be expected as the result of their discussion ; but I confess I had no idea that this series of measures (leaving untouched, as it does, the more distant part of the apparent ellipse when observations are made with comparative facility and proportionally greater accuracy,) would produce a set of elements bearing such close resemblance to those of Sir John Herschel, which, having been calculated upon the whole course of observations, on a method possessing peculiar recommendations, we may fairly presume to be the most exact system at present in the hands of astronomers. For the sake of immediate comparison the two orbits are subjoined together :
In comparing these orbits, it must be borne in mind that in the present case an alteration in the position of the node of 10 has but very little influence upon the computed angles of position ;
' and for this reason the node and the angle between the lines of nodes and apsides cannot be exactly ascertained. The agreement between the other elements is I think, very remarkable; and as regards the period, the observations of Capt. Smyth furnish us with the time of revolution of the companion-sun round the other, differing less than twelve years from that which, under existing circumstances, may be regarded as the true one
After having heard this interesting communication read, on returning homewards in company with my friend Mr. J. C. Adams, of Neptunian celebrity, we entered into a discussion of the several orbits of , Virginis; and I was not scrupulous in pressing him into the question, since, feeling fully persuaded that sidereal physics must one day become of the highest paramount interest to transcendental investigators, I am well aware of the advantages of combination. After a few preliminaries, I found him “nothing loath " in the matter, and he undertook to attack the problem after a method of his own. The result I had the pleasure to receive, under date of the 29th of last June; and I hope the details, with a full account of them, will be given at the next meeting of the Royal Astronomical Society. Meantime the following extract from his letter shall form the satisfactory conclusion of this lengthy “ Story:"-
I have great pleasure in sending you the results which I have obtained respecting the orbit of y Virginis, and I feel the more indebted to you for having called my attention to the subject, inasmuch as the problem of determining the orbits of double stars is one with which I had previously only a theoretical acquaintance. The orbit given by Sir John Herschel in the Results of his Cape Observations, was taken as the basis of the calculations, and equations of condition for the correction of the elements were formed by comparing certain selected angles of position deduced from observation with the values calculated by means of Sir John Herschel's elements.
The positions employed are those given by Bradley's observation in 1718, Sir William Herschel's observations in 1781 and 1803, a normal position for 1825 deduced from the observations of 1822, 1825, and 1828, one for 1833 from the observations of 1832, 1833, and 1834, another for 1839 from the observations of 1838, 1839, and 1840, and, lastly, a normal position for 1848 from the observations of 1846, 1847, 1848, 1849, and 1850. The number of these positions being greater by one than that absolutely necessary for the determination of the elements, I at first omitted the equation of condition for 1718, and solved the remaining ones in such a manner as to shew the effect which would be produced in each of the elements by a small given change in any one of the observed angles of position. The result proved that the elements would be greatly affected by small errors in the observed positions for 1781 and 1803, and I therefore called in the observation of 1718 to the rescue, and solved the equations anew, supposing the positions for 1825, 1833, 1839, and 1848 to be correct, and distributing the errors among the other three, according to the rules supplied by the method of least squares, giving double weight to the observations of 1781 and 1803.
The following are the resulting elements :-
Inclination of the orbit to the plane of projection
or ex-centricity Perihelion passage Period
The following table shews the differences between the observed positions and those calculated from the above elements:
A better agreement could scarcely be desired. The observations made about the time of perihelion
passage are liable to great errors in consequence of the excessive closeness of the stars, and therefore I did not take them into account in forming the equations of condition.
Sir John Ilerschel was obliged to admit large differences between these observations and the results of his theory, and these differences are considerably increased by using my elements. I am inclined to think that these observations cannot be satisfied without materially increasing the errors on both sides of the perihelion passage.
My elements agree very well with the latest observations which have come to my knowledge, as is shewn by the following comparison :
A detailed account of this gaseous wanderer will be found in the first volume of my Cycle of Celestial Objects; but, as a plate of its appearance on the 22nd of September, 1818, when caught up by my son, Professor C. Piazzi Smyth, with the Hartwell telescope, has been prepared for this volume, a few discursive remarks may be added. When found, the comet was so faint as to