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On Sir Christopher Wren's Cipher, containing Three Methods of finding the Longitude. By Sir DAVID BREWSTER, K.H., LL.D., F.R.S.

Sir David said that at page 263, vol. ii. of his 'Life of Sir Isaac Newton,' the following paragraphs would be found: -"The bill which had been enacted for rewarding the discovery of the longitude seems to have stimulated the inventive powers of Sir Christopher Wren, then in his eighty-third year. He communicated the results of his study to the Royal Society, as indicated by the following curious document which I found among the manuscripts of Newton :

"Sir Christopher Wren's cipher, describing three instruments proper for discovering the longitude at sea, delivered to the Society November 30, 1714, by Mr. Wren :— OZVCVAYINIXDNCVOCWEDCNMALNABECIRTEWNGRAMHHCCAW. ZEIYEINOIEBIVTXESCIOCPSDEDMNANHSEFPRPIWHDRAEHHXCIF. EZKAVEBIMOXRFCSLCEEDHWMGNNIVEOMREWWERRCSHEPCIP.

Vera copia. EDM. HALLEY.'

We presume that each of these paragraphs of letters is the description of a separate instrument. If it be true that every cipher can be deciphered, these mysterious paragraphs, which their author did not live to expound, may disclose something interesting to science."

Sir David Brewster went on to say that soon after the publication of 'The Life of Sir Isaac Newton,' he had received a letter from Mr. Francis Williams, of Grange Court, Chigwell, suggesting very modestly that as the deciphering of the cipher, as published, was so simple, he supposed many persons had already done so; but if not, he begged to say that the mystery could be solved by reading the letters backwards in each of the three paragraphs, omitting every third letter. He had, on the approach of the Meeting of the British Association, received permission from Mr. Williams to give an account to this Section of Mr. Williams's method of solving the enigma. In his letter conveying the permission, which Sir David read, he suggests that "Sir Christopher Wren's object was to make it too mysterious to be of use to any one else. It is possible he may have wished to delay for a time the publication of his inventions, perhaps till he had improved his instruments, but was afraid that in the interval another would hit upon and publish the same discovery. He would send this cipher, then, to the Royal Society as a proof to be used at any future time." Sir David had the following explanation then, in accordance with Mr. Williams's suggestion, written upon the black board, the letters to be omitted being written in small characters to distinguish them, and backwards :

WACCHhMArGNwETrICeBAnLAmNCdEWCOU¢NDxIN¡VAvCUzO. —Wach magnetic balance wound in vacuo (one letter a misprint). The omitted letters similarly read are-CHR. WREN, MDCCXIV.

FIcXHhEArDHwIPrPEeSHnANmDEdSPcOIcSEXTUiBE¡ONiEY¡EZ.-Fix

head hippes handes poise tube on eye (one letter a misprint). Omitted letters make— CHR. WREN, MDCCXIIII.

PICPEhSCrREwWErMOeVInNGmWHdEEcLScFRxOMIBEVAKzE.-Pipe

screwe moving wheels from beake.

MDCCXIV.

Omitted letters make-CHR. WREN,

The three last omitted z's occurring in the first part of each cipher to show that that part must be taken last.

On the Longitude. By Sir C. GREY.

On the Inclination of the Planetary Orbits.

By J. POPE HENNESSY, M.P., F.G.S.

The author stated that, on consulting a synoptic table of the planetary elements, some laws had been obtained for the other elements, but none hitherto for the inclinations of the several orbits. This he conceived arose from the inclinations being set down in reference to the plane of the earth's orbit; for he found that a very remarkable relation manifested itself when they were tabulated in reference to the plane of the Sun's equator. The author had written on the board two tables: one,

the ordinary table, in reference to the Ecliptic; the other, that to which he wished to draw attention, having reference to the plane of the Sun's equator. In the latter it was seen, as a general law, that the inclinations of the planetary orbits increased as the distances of the several planets from the sun increased. Thus, the inclination of the orbit of Mercury to the plane of the Sun's equator was but 0° 19′ 51′′, while that of Neptune was 9° 6′ 51′′,—the only considerable deviation from regular progression being found, as might be expected, among the asteroids; of which if we take Victoria as a type, her inclination is no less than 15° 42′ 15′′. The author considered that the fact that the orbits of the larger planets, Jupiter, Saturn, Uranus, and Neptune, are not more inclined, would seem to confirm a surmise of La Place, who, in his Exposition du Système du Monde,' speculates on the order in which the planets were thrown off from the Sun, and supposes that Jupiter, Saturn, &c. were thus formed long before Mercury, Venus, the Earth, and Mars. If so, the oblateness of the Sun would, in its condition at that time, have tended more powerfully than in its subsequent or present state to keep the planets near the plane of its equator. The discovery of this law regulating the inclinations of the planetary orbits appeared to him another addition to the class of facts which establish the analogy between the Solar system and that of Jupiter and his satellites, it being well known to astronomers that the inclination of the orbits of the latter to the plane of Jupiter's equator was a function of their distances and masses.

On Chinese Astronomy. By J. B. LINDSAY.

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The object of the present paper is to draw the attention of this Section to the fact, that much information may be derived from Chinese literature in order to perfect our astronomy. The Chun-tsiu,' written by Confucius, contains an account of thirty-six eclipses (several of them total), and several comets, falling stars, and meteorites. The first eclipse here recorded was in the year before our era 719, the last was in B.C. 494, thus comprising 225 years. Confucius was born in B.C. 550, and died at the age of seventy-three in B.c. 477. In a book lately published I have given an extract of the thirty-six eclipses; but the whole of the Chun-tsiu' deserves to be translated and published. I have myself made a translation of the whole verbatim, but should prefer seeing it published by another better acquainted with the Chinese. The Chun-tsiu' is a short chronicle of events; but there is an extended commentary on it entitled the Tso-chuen,' by Tso-kiu-ming, who was a contemporary and an intimate friend of Confucius. This work should, I think, be also translated, as it gives a detailed account of astronomical observations, and comes thirteen years further down than the work of Confucius. Another work, entitled the 'Kwo-yu,' supposed to have been by the same author, contains an Appendix by another person, bringing down the history to B.C. 453. The succeeding history was principally written, and the celestial phenomena recorded, by Szi-ma-tsien, who lived a century before our era. His work is entitled 'Shi-ki,' or Historic Memoirs. He was Imperial Historian, as was also his father; and his work is extremely interesting, as giving an account not only of Chinese affairs, but also of the Scythians and Turks who were then on the north-west borders of China. The 123rd chapter, recording foreign events, has been translated into French by Brosset, and is found in the Journal Asiatique for 1828. This chapter comprises the history of forty-three years, or from B.C. 140 to B.C. 97, shortly before the author's death. Small portions of the Shi-ki' have been translated into English, but the whole deserves to be so. A translation of the whole Chinese history and literature before our era would not be voluminous; but the Chun-tsiu,' the Tso-chuen,' and the Shi-ki' should, I think, be translated first. Extended notes would be necessary to render the whole intelligible, and the Astronomer Royal might append notes on the various eclipses. The ancient Chinese classics are nine in number,-five of the first class, and four of the second. The five of the first class are the Shu-king,' the Shi-king,' the 'I-king,' the 'Li-ki,' and the Chun-taiu.' The Shu-king' has been translated into French by Desguignes,; the Shi-king' into Latin by Lacharme; the 'I-king' into Latin by Regis, and others; the 'Li-ki' into French by Callery; but the 'Chuntsiu' has not yet been translated into any European language. The four books of the second class have been often translated into Latin and French. Their names are, the 'Ta-hio,' the Chung-yung,' the Lun-yu,' and 'Mang-tszi,' or Mencius, scarcely any of which have been translated into English.

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On an Improvement in the Heliometer.

By NORMAN POGSON, Director of the Hartwell Observatory.

The purpose of this communication is to suggest what I conceive to be a great addition to the power of any kind of micrometer used for measuring long distances on the double-image principle. It is therefore especially applicable to heliometers, and has indeed occurred to me chiefly from familiarity with the defects which have hitherto rendered this costly but magnificent instrument a comparative failure. It is well known to practical astronomers that the contact between two stars, however skilfully made, is a very unsatisfactory observation, even when the objects are pretty equal. But when one is a large bright star and the other a faint one, the difficulty and uncertainty amount to impossibility; for the faint star is invariably obliterated on approaching within two or three seconds of its superior. The alternative is then to diminish the aperture of that half of the object-glass through which the brighter star is viewed; but here again arises another evil; the disc is enlarged by diffraction, the value of the scale sensibly changed, and definition materially injured. Hence parallax determinations of first magnitude stars, such as Arcturus and a Lyræ, cannot be satisfactorily made; but when the object is a double star, as, for instance, 61 Cygni or Castor, the comparison star can be brought between the components of the double star, and a most exquisitely perfect and comfortable measure obtained. Now, from having used the rock-crystal prism micrometer when residing at Oxford last year, then kindly lent me, together with a five-foot telescope of surpassing excellence, by Dr. Lee,-the idea occurred to me of introducing a prism, or achromatized wedge of rock-crystal, into the heliometer, so as to double the image of the brighter star. By this means the dubious contact would be dispensed with; for the fainter object, by being brought midway between the two images of the bright star, would be precisely similar to the present easy observation of 61 Cygni previously referred The prism could be of such a constant angle as to separate the two images to a convenient distance; not too far, so as to render the estimation of distance difficult, but just wide enough to prevent the obliteration of a faint comparison star, before named as one of the evils to be avoided. The prism rather improves the appearance of a bright star than otherwise; and as the images are doubled, of course half the light of each is lost, equivalent to a considerable reduction of the aperture, thus obviating the third objection alluded to at starting. Armed with this addition to its strength, and taking the precaution never to observe on bad nights, when the atmosphere will not permit the use of powers from three hundred upwards-for I hold it as an absurdity to attempt to investigate tenths of a second of arc with anything less-the heliometer is doubtless yet destined to realize the highest expectations ever raised, as to its efficiency for grappling with that most minutely intricate and vastly important research, viz. the parallax of the fixed stars!

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On three Variable Stars, R and S Ursa Majoris, and U Geminorum, as observed consecutively for six years*. By NORMAN POGSON, Director of the Hartwell Observatory. (Communicated by Dr. LEE.)

[With a Plate.]

The periodical variation in brilliancy of certain fixed stars has now been known to astronomers for more than two centuries. The fact of simple change, apart from periodicity, has been recognized and recorded for nearly two thousand years; and while every other celestial phenomenon has been explained and reduced to intelligible methods of calculation, based upon theories as incontrovertible as the events they foretell in future or account for in past times, these changes of light and colour remain enshrouded in mystery, and their prediction as purely empirical as was that of eclipses by the Chaldeans of old, aided by their renowned Saros, or eclipse-period of 223 lunations.

It is not, however, for want of due thought and attention from the eminent astronomers of the past and present that such a reproach attaches to any branch of their science. Commencing with Fabricius, who first drew attention to the dis

* This paper was illustrated by large diagrams of the light curves of the above three variable stars, covering an area of more than sixty square feet. The portions most especially referred to by the author have been reduced to a suitable scale, and are given in Plate I.

appearance of the now well-known variable Mira Ceti, and the Dutch Professor Holwarda, who discovered its periodicity, the list of observers of these objects includes most of the greatest names that have figured in astronomy :-Hevelius, Bulliald, Montanari, Cassini, Maraldi, G. and C. Kirch, Halley, Koch, Goodricke, and Pigott-all contributed largely by discovery or observation to our knowledge of the variable stars. Sir William Herschel's first astronomical communications were upon the same subject, since most ably followed up by Sir John Herschel, the distinguished inheritor of his great name and lofty talents. Olbers paid great attention to the variable stars, as also Harding, Wurm, Westphal, Schwerd, and above all others, Professor Argelander, of Bonn. To him is due not merely the merit of arranging the labours of all that had preceded him, and more accurately investigating the elements of change of most of the old variables, as well as the discovery of several new ones, but that of training a band of young and able followers, who by their successive discoveries and patient researches have honoured both themselves and their great instructor. In England, besides the labours of Sir John Herschel, Mr. Hind has discovered no less than twenty-one new telescopic variable stars, two of which, S Cancri and U Geminorum, are especially remarkable. The writer of this paper has also contributed ten to the list, which now numbers more than eighty of these interesting objects. Mr. Baxendell of Manchester, Messrs Chacornac and Goldschmidt of Paris, as well as Drs. Winnecke, Schoenfeld, Luther, Auvers, Hoek, Oudemans, and Schmidt, are all devoting more or less of their time and attention to the same pursuit.

Why then, it may be inquired, have not all these combined efforts proved as successful as they undoubtedly deserved to be, in arriving at more satisfactory results? We can only regret the circumstance, and redouble our exertions to attain so important an object. Want of continuity is doubtless a most weighty objection to all previously published series of observations, and one which the observers could not help: for unless a star be circumpolar, there must inevitably occur a break in the records of its changes during the time that it is in conjunction with the sun, and therefore not observable. It is not enough merely to watch a star through its successive maxima; every stage of its variation should be remarked, and an unbroken record thereof kept for years, or at least through ten or twelve complete periods. The detection of four remarkably regular variable stars, suitably placed in the circumpolar region, has enabled me to secure this desideratum, and to supply data not previously available.

A brief summary of the principal features hitherto remarked in periodical stars, may be advantageously stated, before proceeding to the description of our illustrations. Some of them, from fine bright stars distinctly visible to the naked eye, fade away beyond the limits of the largest telescopes in use, and after remaining invisible a certain time suddenly regain their brilliancy. The increase in light is generally more rapid than the diminution, and about or after maximum such stars are frequently more or less red. Others, usually of short period and small variation, complete their changes in a few hours, and at all intermediate stages are of a constant magnitude. Most of the stars of this class are visible to the naked eye and pretty steady in their periods, which may be stated as between the limits, three and forty-six days; while those of the former class, or vanishing stars, range from 97 to 650 days in the interval between two successive maxima. In one instance the period cannot be less than seventy-three years; and it is even probable that some of the brilliant visitors, described as new or temporary stars in past ages, may be periodical, but returning only after the lapse of many centuries.

The largest of our three diagrams represents the light curve, or graphic history, of the circumpolar variable star R Ursa Majoris, since 1853, the year of discovery of its variability. Eight maxima, dependent upon 138 observations, and seven minima, resting upon 122 observations, making in all 260 nights on which the star has been examined, are here presented to the view. The Time co-ordinates, marked along the top and bottom of the projection, are on a scale of ten days to an inch. The other co-ordinate-magnitude or light-is marked at each extremity of the dia gram. The upper limit, which, however, this star has never attained, is the 6th magnitude, or faintest visible to the unassisted sight. The lower limit is 134, or the faintest magnitude discernible with a telescope of 7 inches in aperture. The

observation of every night is represented by a black spot. Thus, on 1855, September 19, the magnitude of the star was recorded 6'6; on November 8, it had diminished to 8.8; and on 1856, March 7, when only just discernible, it was noted 13.5. It appears therefore, that if R Ursa Majoris never becomes visible to the naked eye, on the other hand it never quite vanishes with an object-glass of 7 inches in aperture. A waved line, smoothly traced among these dots, so as to pass as nearly as possible through the mean of each three successive observations, is adopted as the curve which represents the variations of the star with the most probable exactitude. The general regularity and similarity of the different periods is strikingly evident, also the gradual descent of the curve corresponding to diminution of light, and its rapid ascent or brightening up before each maximum. The whole period being 302 days or ten months, the interval from maximum to minimum is 191 days, that from minimum to maximum only 111 days.

Closer inspection will bring to view some more interesting details. At the first observed maximum the star acquired only the 8th magnitude. At the next it became 0'6 of a magnitude brighter, or shone with half as much light again as on the first occasion. On the photometric scale adopted, which is an average of those employed by all the chief catalogue constructors who paid attention to the relative magnitudes of the fixed stars, and is in exact accordance with the notation of Professor Argelander, the highest authority on that point, one star is said to be a magnitude brighter than another, when it contains 2 times the actual light of the fainter star. Thus a 7th magnitude is 24 times as bright as an 8th. At the next three maxima, viz. 1854, November 22; 1855, September 15; and 1856, July 10, R Ursa Majoris was within O1 of the 7th magnitude. But at the next maximum on 1857, May 15, it reached the 6-7 magnitude—the brightest on record; a veritable maximum maximorum! On the last two occasions, viz. 1858, March 16, and 1859, January 5, it did not exceed the 7.6 magnitude. Owing to the extreme faintness of this star at its minima, less weight can be assigned to their determination, but similar fluctuations are manifested, especially by the first four. After reducing the fifteen equations afforded by this curve, by the method of least squares, the resulting elements of variation are:-period, 301.91 days; epoch of minimum, 1858, September, 15.9; and that of maximum, 1859, January, 6·6; which represent the original observations with surprising accordance. The mean difference between an observed maximum and one computed from the elements is 2 days; the extreme difference 5 days. For the minima, these differences are-mean, 4; extreme, 8 days. Strong evidence this, in favour of the regular periodicity of the star, and the sufficiency, both of the observations and their treatment by this simple but effectual method of projection, when for two of the oldest known variables, o Ceti and x Cygni, the most refined formulæ of calculation often disagree with observation to the extent of twenty-five and forty days respectively!

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29 30 31

Minutes of Right Ascension

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32 33 34 35 36 37

38 39 40

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10

6.8

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It must not be supposed that the observations here projected are mere estimations of the magnitude of the variable; neither are they photometric measures of 10 the actual light emitted by the star. In +69 either case, the changes in the atmosphere or in the sensibility of the observer's eye would materially affect the estimation, and the dots would stand out very unsatisfactorily from the interpolating lightcurve. The method employed is as follows:-A map of the neighbourhood of each variable is constructed, and a certain number of stars selected, if possible in the same telescopic field of view, as standards of reference. One of these maps, viz. that of the variable just de- +70° scribed, is here given for the purpose of

illustration.

North Declination

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29 30 31 32 33 34 35 36 37 38 39 40 41
Minutes of Right Ascension

30'

North Declination

50

+70°

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The comparison stars, nine in number, are lettered in order of brilliancy, and their adopted magnitudes, the means of careful estimations on twenty favourable nights,

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