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It may seem singular that the position of the Fundamenta for 1755, and Bessel's for 1820, should seem to differ at all from the Tabula Regiomontana, when the latter were calculated from the former. The numbers given above, for those Catalogues, are merely the corrections necessary, on account of the alteration in mutation, rendered necessary by more modern observations. Corrections have been applied also to Olufsen's reduction of Pond (-o"26), to Argelander (+0"40), and to Busch (-0" 39); these being the excess of the correction taken from Table IV. on p. xxvi. of Struve's Positiones Media for Sirius over the similar correction for the four stars compared.

Our table includes, then, the deviation from the Tabula Regiomontana of the Declination of Sirius, as observed by different observers, with (in general) different instruments, less the mean of the similar corrections for Spica, a2 Libræ, Antares, and a Capricorni; corrected in the cases above specified for error of mutation.

On referring to Dr. Peters' memoir, we shall at once find that, if his hypothesis be adopted, the numbers given above will be represented by the formula

b' + f' + c′ (t − 1800) + y′ cos u + h′ sin u,

where b' denotes the correction of the Declination for 1800 of the centre of gravity of the system, c' the correction of Annual Proper Motion; each of these quantities to be applied to the Tabula Regiomontane values for Sirius itself, to get declinations in general accordance with Bessel's other declinations; g', h', being constants depending on the elements of the orbit of Sirius around the centre of gravity, and f' =—g' e, where e is the excentricity; u being also the excentric anomaly of Sirius in its orbit.

If, then, we adopt Peters' Elements V.,

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Pond

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Piazzi

1805

(+0·8)

Pond

1813

(−0·6)

Bessel

1820

-0'6

Pond

1822 (Olufsen) +03

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1826

+0'4 (+0·8)

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There can be hardly any doubt, then, that Bessel's and Peters' hypothesis does actually represent the observed De clinations of Sirius, although the evidence on which it has been previously urged depends entirely on the Right Ascensions.

It may be noticed that Calandrelli's statement, that the Greenwich Twelve-Year Catalogue for 1845 (1844) is mate rially in error, is at once refuted by the almost perfect agree ment given above. The phenomena which Sirius presente about 1841, that being according to Peters (confirmed by th results above) the time of the passage of the lower apside, ar sufficiently remarkable; rapid variations both in Right Ascension and Declination were then taking place.

Extract of a Letter from Mr. A. Auwers to the Rev. R. Mais dated Königsberg, 1862, February 21, on the Irregularity of the Proper Motion of Sirius, and on a Missing Nebula. (Communicated by the Rev. R. Main.)

For some months I have been attempting to represent the observed Declinations of Sirius from 1755 to 1859, in which a periodical change of proper motion is very conspicuous, by a formula grounded on the elements of Peters; and I found the correction q' of the declinations of the Tabula Regiomontana, relatively to Orionis and a Hydra, from thirty-one equations, q′ = +0" 10 + o"·0158 (t — 1800) + 1"536 sin u - o".025 cos u,

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a satisfactory agreement with reference to the materials employed. This in fact is not unexceptionable, the probable error of a determination of declination being, according to Safford, o"-30, and according to me, o"32, while at the same time I have found for Procyon an orbit, which represents the observed places with the probable errors o"17. The reason of the lesser agreement of the Declination of Sirius arises plainly from the circumstance that this star for European Observatories culminates at too low an altitude. For a new determination of the elements of its orbit from all the observed Right Ascensions and Declinations, which I contemplate undertaking, determinations of southern Observatories would be very desirable. Is it known to you whether the observations of the Cape of Good Hope since 1834 are reduced?

I observed several times in February and March, 1858, the interesting Nebula found by Hind in 1852, and observed by D'Arrest and Breen in 1855 and 1856, and finally missed by D'Arrest in October 1861. In 1858 I found it to be fainter than it ought to have been, according to the description of D'Arrest in 1855. At that time I saw it with a telescope of 4 inches aperture, but, in January and September 1861, I could not find it with the 6-inch heliometer, nor have I been able to find it after repeated searches during the last five months. The variability of the accompanying star I remarked in November 1861, as I found it to be of the 11-12 magnitude, while in 1858 it was of the 10th magnitude. At present it appears to be getting somewhat brighter, and is of the 11th magnitude.

Extract of a Letter from Mr. A. Auwers to the Rev. R. Main, dated Königsberg, 1862, March 21, on the Orbit of Procyon, and on the Positions of the Radcliffe Catalogue. (Communicated by the Rev. R. Main.)

I am much obliged for your answer to my letter of the 21st of February. Learning from your letter that the results of my researches on variable Proper Motions may perhaps be interesting to you, I add to the formula for correcting the tabular Declinations of Sirius, given in my preceding letter, also the elements of the orbit of Procyon, derived from all available observations of Right Ascension and Declination, made between 1750 and 1860:

150, 151

Epoch of minimum in R.A. =T
Time of revolution
-U
Mean yearly motion
Radius of circle

1795 5676 Probable error ±0.4457

= n

= r

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There is not the least trace of ellipticity indicated by the observations. The corrections to be applied to the Right Ascension of Wolfers' Tabula Reductionum, relative to the mean of the stars Aldebaran, Rigel, a Orionis, Pollux, a Hydræ, and Regulus, and to the Declination of the same tables, relative to a Ceti, a Orionis, a Serpentis, y, a, ß Aquilæ, and a Aquarii, are the following:

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da = +0.0033-0001192 +00033 -0.001192 (t-1830) -0°0705 cos n (t−T), dd = +0·201 +0′00931 (t−1830) +1′′853 sin n (t−T). The mass of the dark companion of Procyon is probably not less than three-quarters of the mass of the Sun.

Variations have also been supposed to take place in the proper motions of a Virginis, a Hydra, and ẞ Orionis; but in all these cases the results of my researches are entirely negative, showing with evidence that there exist no variations in the motions of these stars.

The reason of my again taking the liberty to write to you is a paper "On the Positions of the Radcliffe Catalogue," in No. 9 of vol. xxi. of the Monthly Notices. It has not been before now that I have learnt that Mr. Safford calls attention by this paper to a rather large discrepancy between a formula, given by me in No. 1300 of the Astronomische Nachrichten, for correcting the Declinations contained in the vol. i.-xiv. of the Radcliffe Observations, so as to make them agree with Wolfers' Tabula Reductionum, and the corrections to be applied to these Declinations according to the late Mr. Johnson's investigation in vol. xv.

The formula has been derived, as it is stated in the Astronomische Nachrichten, from Mädler's comparisons (Dorpat Observations, xiv.), and represents them very accurately between the Declinations 40° and 80°. But now the definitive Declinations of the Radcliffe Catalogue having been substituted to the provisionally adopted ones of the Observations, I have thought it advisable to undertake a direct comparison of the first with some other Catalogues, the relations of which to the Tabula Reductionum are accurately known.

There occur 231 stars of the Radcliffe Catalogue in Argelander's Abo Catalogue reduced to 1845, and corrected for the difference between the constants of Nutation adopted in the construction of the Catalogue and the computation of the Proper Motions and the true value =9"223; the correction to be applied to the Declinations being +0" 244 sin (R.A.—oh36m), and to the Proper Motions o" 0081 sin (R.A. +055). Argelander's Declinations differ from Johnson's (corrected, where necessary, according to the introduction of the Catalogue) by the following quantities, A-R, to which I have also added the differences W-A between the Tabula Reductionum and the Abo Catalogue, reduced to the year 1845, and the differences W-R, resulting from the addition of the numbers A-R and W-A.*

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I

may also mention that the differences between the Rad cliffe Declinations and Argelander's in the hours 3-11 of R.A are on the whole smaller (about o" 5) than in the other hours; but in the comparisons with Struve, no such variation being shown, I have not had regard to it. The probable error of a difference A-R, by one star, is found from the circumpolar stars to be o"-622, and that of a difference S-R is found to be 0743. The probable error of a Declination of the Abo Catalogue beingo" 27 and that of the reduction to 1845 being o16, the probable error of a Declination of the Radcliffe Catalogue becomes, from the comparisons with Argelander, o"54.

Observatory, Königsberg, March 21, 1862.

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155, 156

155, 156

Mr. POGSON: Ephemeris of Variable Stars for 1862.

Ephemeris of the Long Period Variable Stars for 1862. By N. R. Pogson, Director of the Madras Observatory.

The initials in the last column indicate respectively, Messrs. Argelander, Baxendell, Krüger, Pogson, Schönfeld, and Winnecke.

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112 33 April 19.
106 52 August 5

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April. Uncertain
Oct. 24
April 22.

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B. &W.

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The preceding Ephemeris has been hastily prepared, chiefly from the elements of variation employed for the last two years. Mr. Baxendell has as usual favoured me with the maxima of the stars bearing his initial. The minima of the Short Period Variable Stars shall follow by the next mail.

One star, S Sagittarii, was discovered at Dr. Lee's Observatory shortly before my departure from England, and has been re-observed here this year. Time forbids further details in this letter.

Madras Observatory, 1861, Dec. 28.

On the Stars R Vulpecula and U Geminorum, and on an Appearance in Venus. By G. Knott, Esq.

R Vulpecula. A few months ago I had the honour of submitting to the Astronomical Society a short paper on an unexpected minimum of this star; further observation enables me to report a maximum, mag. = 8.7, on or about the 31st December last. It will be seen that this result does not accord with the predictions of Mr. Pogson's valuable Ephemeris; by reference, however, to a paper by Dr. Winnecke, in No. 1224 of the Astronomische Nachrichten, it appears that the period is subject to considerable irregularity, for while two observed maxima in 1859 gave a period of 129 days, one of 147.35 days was found more satisfactorily to represent the earlier observations, including two by Piazzi in the beginning of the century. It would be premature on my part to say anything decidedly on this point, I will merely add that my own light-curve seems to favour the shorter period.

U Geminorum. This remarkable star was due at maximum on Jan. 21; my own observations show that the maximum

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March 8, July 16, Nov. 23 July 26

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April 28
June 28
Nov. 15. Minimum (13) May 30

P.

actually occurred nineteen or twenty days earlier. On turning my Equatoreal to the spot on the evening of Jan. 3d, I found the star of the 94 mag., by the next evening it had fallen to 96, and on the 11th of the same month it shone as a star of the 112 mag. Bad weather and bright moonlight prevented further observation. Unfortunately the maximum was passed before my observations commenced, but we may probably assume the 1st or 2d of January as the date of its occurrence.

Readers of the Monthly Notices will remember an interesting paper by Mr. Pogson (Monthly Notices, vol. xx., p. 37) containing an account of a series of observations of this star by M. Goldschmidt in November 1859, from which, in combination with one of his own, he deduced a maximum on Nov. 12th, "full 27 days before the time indicated by computation." Starting from this date, and applying Mr. Pogson's period of 96.879 days, I find a maximum due on Dec. 25th, 1861, a result, which, compared, with my own observations, seems to show that, in the interval, the period has not been subject to any startling irregularity.

I take the opportunity of mentioning a recent observation of that curious phenomenon connected with the planet Venus, sometimes called the phosphorescence of the dark side. On the evening of Jan. 14th, my uncle, Mr. Berry of Liverpool, was examining the planet with a small but very perfect Gregorian reflector of 4 inches aperture, mag. power 160. The wind was high, but the atmosphere very clear, and in repeated intervals of quiet, when the cusps were sharply defined, the unillumined part of the disk shone with a faint light similar in appearance to the lumière cendrée in the crescent Moon. In proof of the independence of the observation I may say, that, at the time, it had entirely escaped Mr. Berry's memory that the phenomenon had been remarked by previous observers.

Woodcroft, Cuckfield, March 10th, 1862.

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