only, on that occasion, is mention made of one star being occulted 10s before the other. On the 21st January, 1794, the occultation was observed by four astronomers; yet no one mentions duplicity. This is passing strange, because Cassini had, in 1720, perceived and recorded the two stars, noting that the western disappeared 30 before the other, behind the Moon's dark limb, but they emerged nearly together. He could not divide them with a telescope of eleven feet, but with one of sixteen they were well severed, and of equal magnitudes. He watched the immersion, which was oblique, with great care, hoping by refraction or discoloration to detect a lunar atmosphere; but though the circumstances were favourable, he perceived no symptom. Yet the observation was held to be of importance, for, by enlisting that able astronomer and Bradley, Sir John Herschel considered that he gained some useful points in the orbital departure; and the results of more than a century, previous to my measures, may be thus shortly stated:

A mere inspection of the conditions below stated, shows the vast acceleration of the revolving star on approaching its periastre, and the retardation of its getting away again. These are the annual rates of retrograde angular progress:

As the rigorous observations and computations of this object must be deemed a sort of experi mentum crucis of the sidereal connected systems, I may be excused for entering into rather fuller details of the detection and establishment of so wonderful an elliptic motion, than I have yet indulged in among the binaries; and it will thereby serve as an example of the method of procedure with those interesting objects.

The various observations were most ably and zealously discussed by Sir John, and treated in a

straight-forward, geometrical mode, so as to be widely available; as will be seen on consulting the Fifth Volume of the Memoirs of the Royal Astronomical Society. The method is equally novel and ingenious. Assuming that the motions of binary stars are governed by the universal law of gravitation, and that they describe conic sections about their common centre of gravity and about each other, he was bent on relieving their discussion from the analytical difficulties attending a rigorous solution of equations, where the data are uncertain, irregular, and embarrassing. Measures of position were to be the sheet-anchor; for distances, with the exception of the major semi-axis, were peremptorily excluded from any share of consideration in the investigation, because of their notorious looseness and insecurity.

"The process," said he, "by which I propose to accomplish this, is one essentially graphical; by which term I understand, not a mere substitution of geometrical construction and measurement for numerical calculation, but one which has for its object to perform that which no system of calculation can possibly do, by bringing in the aid of the eye and hand to guide the judgment, in a case where judgment only, and not calculation, can be of any avail.”

Under the assumption, therefore, that gravitation governs, and one of the components revolves, while the other, though not necessarily in the focus, is at rest, the curve is constructed by means of the angles of position and the corresponding times of observation; and tangents to this curve, at stated intervals, yield the apparent distances at each angle, they being, by the known laws of elliptical motion, equal to the square roots of the apparent angular velocities.

γ

Thus armed, Sir John proceeded with the orbit of 7 Virginis. From the above positions and epochs, with interpolated intermediates, a set of polar co-ordinates was derived, and thence, for the apparent ellipse, the following elliptical elements :

Major semi-axis

Position of major semi-axis
Eccentricity

Maximum of distance

Position at the maximum distance

Minimum of distance

Position at the minimum distance

Date of next arrival at minimum distance

Greatest apparent angular velocity
Least apparent angular velocity

5"-862

67° 20'

0.70332

9"-423
218° 55'

0514

1° 15'
1834:39

- 682.833
-0°.193

The next process was to obtain the elements of the real ellipse, and the whole consequent investigation is so succinctly described in the paper alluded to, that any zealous tyro may tread in the same steps, with a little attention. The results, together with a comparison of the elements and observations up to the period of the computation, and an ephemeris of the system for the years 1832, 1833, 1834, and 1835, were inserted in the Supplement to the Nautical Almanac for 1832. But, finding a discrepancy between the measures then obtained and the places predicted, Herschel, nothing daunted, again took the field, and recalculated the orbit, as described in the Sixth Volume

of the Astronomical Memoirs. In this process, my measures of 1832 and 1833 were included, and the two conclusions stood thus:

In giving the first part of these remarkable elements to the astronomical world, Sir John said:

:

"If they be correct, the latter end of the year 1833, or the beginning of the year 1834, will witness one of the most striking phenomena which sidereal astronomy has yet afforded, viz. the perihelion passage of one star round another, with the immense angular velocity of between 60° and 70° per annum, that is to say, of a degree in five days. As the two stars will then, however, be within little more than half a second of each other, and as they are both large, and nearly equal, none but the very finest telescopes will have any chance of showing this magnificent phenomenon. The prospect, however, of witnessing a visible and measurable change in the state of an object so remote, in a time so short (for, in the mean of a very great number of careful measures with equal stars, a degree can hardly escape observation), may reasonably be expected to call into action the most powerful instrumental means which can be brought to bear on it."

From the extreme delicacy of so novel a case, all the conditions were not yet met, so that this bold prediction was not circumstantially verified, although it was admirably correct in substance. Whilst rushing towards the nearest point of contact, or shortest distance of the revolving star from its primary, and the proximity became extreme, the field was left, as far as I know, to Sir John Herschel at the Cape of Good Hope, Professor Struve at Dorpat, and myself at Bedford. Our measures afforded unquestionable proofs of the wonderful movement under discussion; yet they certainly exhibited greater discrepancies than might have been expected from the excellence of the instruments employed. But the increased angular velocity which so eccentric a star acquired when gaining its periastre, and the closeness of its junction, rendered the operations extremely difficult : added to which, the brightness of two such stars was sufficient to call forth that disadvantage, arising from the inflection of light, which the wire micrometer labours under, and which interferes in the exact contact between the line and the luminous body.

The accelerating velocity of angular change was thus vigilantly watched, until the commencement of the year 1836, when an unexpected phenomemon took place. Instead of the appulse which a careful projection drawn from the above elements had led me to expect, I was astonished, on gazing at its morning apparition in January, to find it a single star! In fact, whether the real discs were over each other or not, my whole powers, patiently worked from 240 to 1200, could only make the object round. I instantly announced this singular event to my astronomical friends, but the notice was received with less energy than such a case demanded; none of the powerful refractors in this country were pointed to it in time; and it is to be regretted that we had not the benefit of the unexcelled Dorpat telescope's evidence at the critical epoch in question. This state of apparent singleness may have existed during the latter part of 1835; for, when I caught it, as may be seen in the observations above, it was very near a change. At length, about the beginning of June, 1836, a letter arrived from Sir John Herschel, addressed to Mr. Baily, wherein he detailed his observations on the single state of this star at the villa of Feldhausen, Cape of Good Hope, in his twenty-foot reflector. Under the date of February 27th, that unwearied astronomer says:

"Virginis, at this time, is to all appearance a single star. I have tormented it under favourable circumstances, with the highest powers I can apply to my telescopes, consistently with seeing a well-defined disc, till my patience has been exhausted; and that lately, on several occasions, whenever the definition of the stars generally, in that quarter of the heavens, would allow of observing with any chance of success, but I have not been able to procure any decisive symptom of its consisting of two individuals.”

The companion now took such a movement as quite to confute a large predictive diagram I had constructed, showing that the orbit was extremely elongated, more like a comet's than a planet's; which gave me a suspicion that we had been looking at the ellipse the wrong way. Hereupon I returned to the Herschelian process to obtain the elements of the apparent and the true ellipse with my new measures, but could neither accommodate the period nor arrive at any satisfactory conclusions. When, therefore, M. Mädler's masterly computations appeared in the Astronomische Nachrichten, my views were greatly countenanced; but, with a full value for the talent and zeal of that astronomer's process, I was still anxious for Sir John Herschel to return to his own field, and meet the apparently unaccountable informalities which still remained. Having made a request to this effect, he replied:

66

Maugre I cannot yet send you any finalities about y Virginis, yet to prove that I have not been quite idle, I will state one or two general conclusions that a projection of all the observations has led me to, preparatory to exact numerical computation. 1. We are all wrong, Mädler and all of us, and it is the early observation of Bradley in 1718 which has misled us. That observation is totally incompatible with any reasonable ellipse, and must be absolutely rejected. Had it not been for my respect for that single observation, I should have got very near the true ellipse in my first approximation. 2. The period is short of one hundred and fifty years. My conjecture, antecedent to any exact calculation from my projection, is one hundred and forty-three, which is considerably less than the least of Mädler's, and beyond his assigned limits of error. 3. I suspect Mädler's perihelion to be half a year too early, and that the true perihelion passage took place at 1836.6 or thereabouts. We shall get on better now that we have found out the black sheep.”

Thus duly authorised, I attacked the orbit again, rejecting, with some regret, Bradley, Pound, Cassini, and Mayer, and assuming 's observations of 1780 as the point of departure. Taking, therefore, the epochs from that date to 1843 for abscissæ, and the observed angles for ordinates, a fresh set of periods was obtained, through which the interpolating curve was led on a very large scale.* From the interpolated positions corresponding to the assumed dates between 1780 and 1843, the intervals being first decennial, then quinquennial, and afterwards more rapid still, the angular velocities were concluded, and by their aid the distances as radii vectores. These positions and distances were laid down from the central star as an origin of polar co-ordinates.. Now, though this is a simple and merely graphic process of obtaining the elements of both the apparent and true ellipse, and is liable to shakiness, it undeniably shows the physical fact of a highly-elongated orbit; and several of the conditions prove that, notwithstanding the present anomalous differences, we are arriving near the mark. It is singular how all the determinations of the eccentricity have agreed, thus:

As the ellipse projected by Sir John Herschel, under all the epochs, has been given, the reader may like to see the figure produced by the Bedford observations, which yields a period of about one hundred and eighty years.

* Sir John Herschel informs me, that he has disused the method of drawing tangents for the angular velocities. The substitute is a closer reading off of the curve, equalising the differences on paper, and thence deducing the angular velocities by first and second differences (if needed); but first will generally suffice.

In order to bring this very important condition under one view, I will here subjoin some of the determinations since arrived at, namely