First method.-1. Find x' an approximation to x by this formula.

tan (x' – $x) tan %.

- e

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2. Find y such that

ite tan (4 r-—y)= tar X

tan d x'. 3. Find c, the correction of x', so that

sin sin 1 sin (y - c) =


sin xl • expressing x' – z in seconds of a degree.

4. Then the eccentric anomaly, x = x + c.

Second method.—Find x' an approximation to the value of x in the given equation, z = x – e sin x, and form a successive series of angles connected by the following equations; they will be closer and closer approximations to the true value of x at every step.

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In these solutions, Professor Wallace suggests, that as in each planet,

ite and sin 15

are constant quantities, they may be conveniently ta

1 bulated for each of the several orbits.


VII. Sixth Catalogue of Double Stars, observed at Slough in the years 1831

and 1832, with the twenty-feet Reflector; containing the Planes, Descriptions, and measured Angles of Position of 286 of those Objects, of which 105 have not been previously described. Reduced to the Epoch of 1830*0.

By Sir John Frederick William Herschel, K.G.H. This is a continuation of a former series published in these Transactions. It is arranged in columns of No. | AR. 1830:0 | N.P.D. 1830.0 | Posit. | Dist. | Magn. | Remks. | Sweep. | Ref.

Of course no particular description can be given. The value of the paper consists in its determination of the position and character of the several objects contained in it. Only two observations occur of general interest beyond that which arises from a determination of the places. One is, that an observation in sweep 425, an observation of n Coronæ, was made with personal hazard; and the other that the triple star in sweep 392 appears to have changed since sweep 172 was made, including the same stars, they being in the first (172) in a straight line, but in the latter (392) no longer so.


VIII. Some Particulars respecting the principal Instruments at the Royal

Observatory at Greenwich, in the time of Dr. Halley. By S. P. Rigaud,

Esq., A.M., F.R.S., Savilian Professor of Geometry at Oxford. The Royal Observatory owes its existence to the indefatigable Sir Jonas Moore. It was placed under the direction of the Ordnance Department, with which Sir Jonas was so intimately connected; the salary of the Astronomer Royal was paid at the Ordnance Office; and all supplies for that institution were always made through the same medium, till very recently, when it was transferred, we think judiciously, to the governance of the Admiralty Board. The Master-General of the Ordnance has seldom been a man of science, or a man of right feeling in respect of science, (the Marquis Townshend is, indeed, a splendid exception, and, in more recent times, Sir James Kempt, during his short occupation of the post, is another:) and hence it has happened, that, for a national establishment, the Royal Observatory has been most inadequately provided for, both in actual payment to its labourers, and in respect to the supply of requisite instruments. The Admiralty Board, besides being the most natural guardian of astronomy, is also better fitted on several accounts, for carrying on the superintendence of the appropriate' business of such an institution, both on account of its interest in the results, and its particular constitution. It is nominally under the direction of men who know little of science, and care for it as little; but generally under the actual direction of one man, chosen because he is acquainted with the details of its business, and, consequently, fully impressed with a sense of the necessity for the results which are only to be obtained from such a source, and, therefore, deeply interested in its being supplied with all the requisite means for carrying it on successfully. The Board of Visiters, also, exercise a salutary influence, both upon the Government and the Astronomer Royal of the time being.

None of these advantages were attached to its connexion with the Board of Ordnance; and yet, by degrees, after the most painful and almost degrading solicitations, the Observatory became supplied with a tolerably good set of instruments, of almost every kind. Still the British Observatory was generally behind most of the continental national ones; and, in the essential instruments, was often behind more than one corporate, or even private, establishment devoted to the same objects. It is only very recently that science has been admitted to be of national importance: and, even now, it is little more than half-admitted. This, however, is not the place for amplifying the discussion of the causes of this unhappy trait in the mania of the day.

This very interesting paper of Professor Rigaud contains an account of the instruments which Bradley, the successor of Halley, and third Astronomer Royal, found in the institution upon his appointment to the office. Our readers will recollect that the learned Radcliffe observer published the miscellaneous works of Dr. Bradley, in three quarto volumes,

few years ago; and in these he gave a general account of those instruments at the period of 1742. No opportunity of printing the several distinct notices found amongst the papers of Bradley, relating to the time of Halley, presented itself till the present. Mr. Baily's Life of Flamsteed Vol. II. 2 D



contains ample accounts of the state of the Observatory during the lifetime of the first Astronomer Royal; and Professor Rigaud has, from the papers above mentioned, and from other sources, filled up the chasm, so far as Halley's occupancy of the office is concerned.

The instruments of the Observatory in Flamsteed's time were his own private property; and the jealousy subsisting between Halley and his predecessor, was an unconquerable difficulty in the way of any fair arrangement between the widow of Flamsteed and the man whom, from her husband, she had learned to hate most cordially. Halley was in his sixty-fourth year when he was appointed; and, upon his appointment, found the Observatory “wholly unprovided of instruments; and, indeed, of everything else that was moveable.”

The descriptions themselves cannot be well abridged. The paper itself is, however, full of interest, not only to the practical astronomer, but also to every one who takes the slightest interest in the history of science.

IX. Observations on Halley's Comet. By Captain W. H. Smyth, R. N.,

F.R.S., 8c. Captain Smyth appears to be the first who saw the Comet, on the present appearance of that remarkable body, with the naked eye. This was on the 19th of October, 1835, in crossing the great quadrangle of Trinity College, Cambridge, and it even appeared with “ a much finer effect" than through the telescope on the summit of the principal gate-tower of the College which he had just left.

These observations will be embodied in a paper which we are preparing, and which will appear in an early number, containing a condensed account of the appearances of the Comet on its several apparitions, so far as they have been recorded. It is sufficient to state here that they were made at Bedford, with the usual instruments and precautions, and, in addition thereto, with an excellent annular micrometer, which was lent to Captain Smyth by Mr. Francis Baily for the purpose.

The analytical difficulty of the problem, resulting from the very rapid motion of the comet, is very neatly solved by the “worthy assistant-secretary of the Society, Mr. Epps ;” and “the beautiful cometary ephemeris furnished to the astronomical world by Lieutenant Stratford has afforded the means of computing, to satisfactory exactness, the hourly velocities, èquating for second and third differences.”

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X. Astronomical Observations. These are of a miscellaneous kind, both as to objects and observers ; and very judiciously thrown together in a tabular form. We shall merely state them generally.

i. Observed transits of the moon, and moon-culminating stars, at the Observatories of Greenwich, Cambridge, and Edinburgh.

2. Observed occultations of the fixed stars and planets; by Messrs. Rothman, Henderson, Snow, Fisher, Sheepshanks, Hartnup, and Wrottesley.

3. Observed eclipses of Jupiter's satellites; by Messrs. Rothman, Henderson, and Sir Everard Home.

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4. Observations on the Solar Eclipse, November 30, 1834; by Sir E. Home, and Mr. Byron Drury, in Jamaica.

5. Observations on the Solar Eclipse, May 15, 1835; by thirty-nine different observers.

6. Observations of Halley's Comet. At South Kilworth, by Dr. Pearson; at Blackheath, by J. Wrottesley, Esq.; and at various places at sea, by Captain R. Owen, R. N., and officers of II. M. S. Thunderer.

7. Results of Lunar Observations made at Edinburgh, in the years 1834 and 1835. By Professor Henderson, Astronomer Royal for Scotland.

Of the address of the Council, or the President's speech on the delivery of the medal, though they enter somewhat into the history of the labours of the Society, we do not feel ourselves called upon to offer an opinion. Every one who looks to the labours of the practical astronomer as bearing upon the decision of the structure of the universe, will be interested in the brief but comprehensive discourse delivered by the President on that occasion, respecting nebulæ and multiple stars : still we cannot persuade ourselves that so fertile a topic might not have been more efficiently treated than he has done. We must confess, however, that we infinitely prefer the manly and subdued tone of the Astronomer Royal of England, to the laboured splendours of the Astronomer Royal of Ireland. If Professor Airy sometimes says too little, Professor Hamilton scarcely ever fails to make atonement for him by saying a great deal too much : if the one does not say all that might be said, the other says a great deal more than a philosopher ought to say. We prefer the former error to the latter: the philosopher injures his own respectability, and degrades his science itself, when he becomes a special pleader for Philosophy.



Biot and Newton.

shall, without doubt, admit that such

an acquisition was one of the finest A MEMOIR on astronomical refraction works of his immense genius, and one was lately read at the Académie des which, beyond all others, best demonSciences, in which the distinguished strates the sagacity with which he seized author, M. Biot, successfully proved all the constituent elements of the comthat there was one honour, not hitherto plicated phenomena which he submitted supposed to belong to him, yet due to to investigation." the illustrious Newton, namely, that of That this act of justice to the dehaving discovered the theory of astro- parted English mathematician should nomical refraction. M. Biot having bave been neglected by his scientific perused with close attention the letters countrymen is, to say the least, reof Newton to Flamsteed, published in markable ;-that it should have been the past year by Mr. Baily, found in rendered by a Frenchman, and by a them the complete series of ideas that philosopher so eminently qualified to Newton had followed out in order to appreciate the discovery, and that he calculate the table of refractions which should have deduced it from a correwas subsequently published in his name spondence supposed, by some persons, by Halley, in the Philosophical Tran- slightly to tarnish the lustre of a sactions, 1721, without the slightest splendid reputation, is one of the most reference to the means employed to striking and gratifying events in the form it. It is thus certain that Newton progress of modern science. was in possession of differential ex Is there no academy of either nation pressions of astronomical refractions (for both countries are now equally insimilar to those used at the present terested in the commemoration of this day, and that he had deduced from glorious event,) patriotic enough to offer them, theoretically, his table for the case the following subject for a prize in of an uniform temperature. M. Biot, in painting ? Bior announcing to the order to exhibit them in a simpler form, ACADÉMIE DES SCIENCES, a century went through the calculations of New. after the death of Newton, the diš. ton, and by them arrived at the same covery by the illustrious Englishman of numerical results as those which are the theory of Astronomical Refraction. furnished by the methods now in use.

“Thus," remarked M. Biot, “we have Apparent Connexion of Aurora Boyet to add to the vast number of other realis with Rain, Wind, and decreasdiscoveries made by this great man that of the theory of astronomical re

ing Atmospheric Pressure. fraction. If we reflect that he was An examination of our Meteorological obliged, as his correspondence shows, to Journal for October will show that an discover for himself, one after another, unusual quantity of rain fell during all the physical bases, and all the that month, particularly in the early meteorological elements, of this theory, part of it, and that it was in this wetter and that at a time when no person but period that the auroras were of conhimself suspected that the indications siderable splendour, and most numerous. of the barometer and of the thermo- The first aurora observed, occurred on meter had the slightest relation with September 30th. On the following these refractions, and that he at length day there was a decreasing barometric attained, approximatively it is true, but column, a strong south-west wind, and by a method direct, and due to himself torrents of rain. On October 4th alone, the same numerical values which another aurora occurred, and on the the mathematicians of the following age regarded as one of the grandest results fall of rain amounting to nearly an inch

next day a decreasing column, and a of the improved integral calculus, we and a half.

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