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mainly consisted in using the angle as the independent variable, and interpolating and calculating t (the time) from it; by which means the solution of the transcendental equation, nt = u e. sin. u, is avoided, as u is given by tan. 1⁄2 u = √¦±. tan. § 6. The obtained elements of this searching investigation are



Inclination to the plane of projection
Position of ascending node

Angular distance of perihelion from node

on the plane of the orbit, or true angle between the lines of nodes and apsides Epoch of perihelion passage

Periodic time

e = 0.87952
Y = 23° 35′ 40′′
၁၇ = 5° 33'

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Sir John judiciously sums up by saying,-"Comparing the orbits which seem entitled to most reliance, it appears certain that the eccentricity lies between 0.855 and 0.880, the inclination between 23° and 27°, the perihelion epoch between 1836-20 and 1836-45, and the period between one hundred and forty and one hundred and ninety years."

In the meantime Virginis had again become an object of very easy measurement; and the results now obtainable are likely to be as trustworthy as our present micrometric power will admit of. And indeed it is in good keeping, being closely attended to in several parts of Europe and America; while the zealous Captain Jacob will not allow it to pass unobserved in India. These are my own additional data

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Having thus watched this extraordinary system for upwards of twenty years, and observed it pass through so important a phase of its entire revolution that I have actually measured the companion in each quadrant of the

circle, I prepared to close my telescopic observations upon it with the angle and distance of 1850. But, as the occasion was one of great interest to me, I wrote to several friends possessed of powerful instrumental means, begging of them to obtain sets of measures and oblige me with the results, in order to afford evidence, that the opinion I had expressed of all present observations approximating near to each other, might be tested. Urania, however, does not always command her votaries properly; and, at the due season of apparition, those scenes redolent of mortality and gas were unhappily preferred by one or two to the fresh air of the observatory. Moreover, Mr. Hind had overworked himself, and was unwell; while the instrument of one of our very best astrometers, the Rev. Mr. Dawes, was lying dismounted. Two of my correspondents responded cheerfully to the call, and I append their fruits:-those of Mr. M. I. Johnson-from a mean of six evenings-were taken with the new Oxford Heliometer, although it was then but just mounted, and the manipulation of it hardly attained; and those of Mr. Arthur Kett Barclay were observed under powers of 277 and 300, with a fine six-inch refractor of above eight feet focal length on a German mounting, driven by clock-work

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While gazing at the small companion which follows nearly on the parallel, I have more than once been struck with a sensation that another minute star was in the field; but even the idea was evanescent. To settle the question indisputably, I requested of both Lord Rosse and Mr. Lassell to search for me, with their gigantic reflectors: and the result of their kind examination is, that no star exists between the binary pair and the little follower.

Having again weighed an orbit from my own measures brought up to 1850, with special care in leading the curve through the epochs of the projection, I obtained a period of one hundred and sixty-eight years. From the sectors produced, the prediction angle for 1851.5-176°, to test which I again

applied for comparing observations to some of my astrometric friends, whose replies, being very illustrative of this portion of the Story, I subjoin. The first in date (Wateringbury, 25th March, 1851) is from the Rev. W. R. Dawes :

I fear you will think I have quite forgotten your request that I would send you a measure of Virginis as soon as practicable. You will see however that this is not the case: but at the same time, I must put your faith in my veracity to the stretch by affirming that the measures now sent are the first, and the only ones, I have been able to procure this year! After I saw you a tremendous cold confined me for some time to the house; and being accompanied by unusual oppression on the chest, I found it necessary to be cautious of long exposure to the cold or night air. Then a series of bad starlight nights occurred, several of which clouded over early; and two or three tantalized me with a view of y Virginis, more like a great oval nebula, or rather a silkworm's cocoon, than any object measureable as a double star. I really thought it would be insulting to put on record, by attempted measurements, the appearance of the elegant creature when suffering from such an awful shivering fit as produced a horrible deformity; completely amalgamating all her features into one shapeless mass. So I very unwillingly closed my eyelids (shutters) against so sad a spectacle. Last Friday night however, after watching the formation and partial dispersion of hazy clouds for several hours-feeling assured that the air ought to be fine if the cloud would but take itself off-while looking at y Leonis, I was amazed and delighted with a rather sudden tranquilizing of the image, which left nothing to be desired in the way of definition. I was using at the time a wheel of double convex lenses, and was aware I had got a pretty high power on; but having been turning the wheel about, I did not know which lens was in use. I thought, however, it was the highest but one, No. 5, power 641; so exquisite were the discs, with a single almost quiet ring round each, that I thought I would give the wheel one more click, and try No. 6, power 903. When behold, on giving the aforesaid click, I found I was already using 903! I instantly detached the eye-piece and applied the micrometer; and being duly pinned and loaded with power 500, levelled at the other 7; when lo! before I could get her fairly in focus, a cloud began to form over her; and, being determined not to be cheated if I could help it, I employed about an hour in getting three angles, and four distances, as the star appeared by glimpses in the chinks between large masses of cloud. It was worth while, however, for the results are good; and therefore I have pleasure in offering them as follows::

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Though I have recorded, or rather given you, the angle as south following, the northern star was noticed as being certainly the smaller: which I observed to be the case also throughout the apparition of 1848.

The next is from Lord Wrottesley (Wrottesley Hall, 18th April, 1851):


Having at last succeeded in getting ten more very capital measures of y Virginis on a very

favourable night, I no longer delay sending the results to you, and, as I promised, I send you the original entries of the observations, as read off from the instrument. The general result is,-

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The third letter is from Mr. Isaac Fletcher (Tarn Bank, Cockermouth, 17th June, 1851), describing the instrument with which he obtained the measurements

1851-401, POSITION 175° 58'; DISTANCE = 3"-047.

I have much pleasure in embracing the earliest opportunity to reply to thy note of the 14th


The telescope employed in procuring the measures of y Virginis, which appear in the May No. of the Notices, and which I employ in all my double-star operations, is an achromatic refractor of about 6 feet focus with a clear aperture of 4·14 inches.

The mounting is almost precisely similar to that of thy 8 foot equatorial, illustrated and described in the "Cycle."

The polar axis is 9 feet long, 9 inches square at the middle, and 7 inches square at the ends. It is made of 4 planks of mahogany, screwed together and bound internally. The hour and declination circles are each 20 inches in diameter, and read by verniers, the former to 2 of time and the latter to 10" of space.

The defining power of the object glass is first rate; it brings out the 5th star in the great nebula of Orion, and shows with distinctness the companions of Herculis and & Cygni. The power employed in measuring y Virginis is 300.

And, finally, Mr. J. F. Miller, of Whitehaven, having watched y Virginis

into daylight, and gained the last measures of her present apparition, favoured me with the following communication, dated July 19th, 1851

I have not long put my instrument to micrometer-work, and, being desirous to get an observation of Virginis before it is lost for the season, I have secured two sets of measurements, which I send you, as I know you are particularly interested in this remarkable star. I do not suppose you will consider them of any value, but you will see how they correspond with those of other observers. The observations in position I believe may be relied on as trustworthy. Micrometrical measures of y Virginis taken at the Observatory, Whitehaven, with a six-foot achromatic equatorial, 4·1 in. aperture, driven by clock-work. Micrometer by Simms; position circle 5 inches diameter:

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The telescope is exactly the same size as Mr. I. Fletcher's, Tarn Bank, Cockermouth; the two have been tried together side by side, and no difference in performance was perceptible. I readily saw the comes of Herculis on the 26th June. A Ophiuchi is comparatively easy even at this season. My instrument is mounted precisely like that of Ross in the Great Exhibition.

Meantime Mr. Hind had kindly consented to undertake another orbit from my observations only, by a proceeding modified from his last and it was somewhat satisfactory, to have the discoverer of four new planets at work in cooperation. On the 8th of last April he wrote to me in these gratifying terms:"I forward the results at which I have just arrived, from a discussion of your observations of 7 Virginis; but, not having yet been able to compare them fully with the data, I must ask you to regard them with some indulgence. For my own part, I am really astonished at the very close resemblance between these elements and those obtained from a discussion of all the observations, including Bradley's and the elder Herschel's. It speaks volumes for your admirable measures, and is the more remarkable, as I have not used any others or looked at any others for this purpose; in which, I believe, I was carrying out your wish."

Here, to my great satisfaction, I found a retrograde annual motion of 20.0987 at the epoch, coinciding exactly with elemental deductions; which,

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