Dr. LEE, President, in the Chair.

Col. T. Schaffner, Kentucky, U. S. A.,

was balloted for and duly elected a Fellow of the Society.

Extract of a Letter from Professor Hansen to the Astronomer Royal, dated Gotha, 1861, Oct. 18.

My principal labours advance progressively, and I work at them with pleasure. Events in the last summer have indeed occasioned some delay, and my other various avocations also often create cessations, but nevertheless I proceed. The working out of the new terms depending upon the planets, which I mentioned in my last letter, has occasioned a considerable addition to the labour of the calculation of the secular variation of the Moon's mean longitude, which I have not yet quite completed. I must in fact execute in regard to these terms as great a labour as in the calculation of the lunar perturbations themselves. I must carry on the approximations until the values at last substituted come out again. These terms are far greater than I suspected at first, and the circumstance that here the coefficients of the terms which have very small divisors become remarkably large particularly increases this labour. In the lunar perturbations themselves the analogous terms have only small coefficients. I am, I may say, perfectly convinced that the value of the secular variation which I have before calculated from theory and assumed in the Lunar Tables must again come out, although I have considerably changed the method of calculation.

In the calculation of the secular variation of the mean longitude, I have set out with the proposition that the element which I have always denoted by has no influence over it. This proposition I have already proved, even to the cube of the disturbing forces, in my third memoir upon the perturbation of the small planets, and the proof holds also for the Moon. Further, the numerical equations of condition have shown me that this proposition is true even for the higher powers of the disturbing forces, at least to a considerable extent.

I have calculated anew the principal part of the perturbations of the longitude, of the radius vector, and of the latitude, and obtained such an agreement with the coefficients used by me in the Lunar Tables, and derived from the previous theoretical

calculations that the differences in the individual coefficients amount only to a few hundredths of a second of arc. A new calculation of the secular variation of the motion of the perigee is also finished, and the deviation of the coefficient thus found from that of the Lunar Tables scarcely amounts to o"4. Now this coefficient, multiplied only by 2 e, enters into the longitude; and as 2 e is nearly, this difference is of no greater significance than o"04 in the coefficient of the secular variation of the mean longitude.

As I have brought such accuracy into my theoretical determinations of the various parts of the Lunar Theory, it of course follows that I do not need to deem the cry which some have raised concerning empiricism finding place therein deserving of the least notice.

In order, however, as much as possible to comply with every reasonable desire concerning the early publication of my theoretical determination of the coefficients of the Lunar Theory, I have occupied myself, for some short time past, with putting together and sending to the press my calculation of the principal perturbations, which, as stated above, has been executed afresh. As soon as possible will follow, also, the publication of the calculation of the smaller coefficients. You will ask perhaps why I then do not publish the first calculations, which were finished long ago, before the completion of the Lunar Tables? and I answer, that I executed the last approximations in that calculation by substitution of the differences with the preceding approximation, and that therefore, by the publication of these calculations, a complication would arise which could only be made intelligible with great difficulty.

In the publication the result must proceed from one fountain; and it was necessary, therefore, that a new approximation should be calculated, with the full values of the coefficients. Only in this manner can I make myself clear, and place every one in a position to be able to examine with ease the individual parts of my calculation.

With regard to the two small errors in the Lunar Tables which you communicate to me, they have arisen in this manner-Page 86, Arg. 37 and (a) have, according to my present re-calculation, been calculated by my former computer, who has made so many errors, with an incorrect coefficient of (c-18). The influence of this error, however, is so insignificant that it can, even in the year -800, produce an effect, at the most, of 18 upon the Moon's longitude, and, as a matter of course, still less in subsequent centuries. I consider, therefore, its correction to be superfluous. Page 77, Arg. 10, Year -500, 56.619 was written by mistake instead of 56.691.

3, 4

On a Result deduced by M. D'Abbadie from Observations of the Total Solar Eclipse of 1860, July 18. By the Astronomer Royal.

In the Compte Rendu of the French Academy for the meeting of 1860, November 12 (tome li.), M. Antoine D'Abbadie has given an account of his observations of the eclipse of July 18, and in particular of his measures of the height of a certain red prominence A, to which my present remarks are confined. The telescope employed had an aperture of 72mm.5 (2.9 inches nearly), a focal length of 800mm (32 inches nearly), and was used with a magnifying power 47. The micrometer consisted of a glass plate in the field of view, bearing a net of equal divisions, which divided the whole field into squares of 51" each side.

Omitting all observations except those which I have specified, M. D'Abbadie's record is as follows::

5, 6

The conclusion of M. D'Abbadie regarding the discordance between the observed decrease of the prominence and the computed change in relative positions of the Sun and Moon, rests entirely upon his arbitrary correction of the first observation; where his recorded measure was 13, which measure he has changed with the simple remark "probablement 2'3", and has used so changed in the subsequent computations. There is nothing to lead to the supposition that any circumstance attending the observation itself called for a change. It has been made, as far as we can judge, simply because the progress in the measured height of the protuberance between and 3 is 5 inconsistent with that between 5 and 7: it has, in fact, the wrong sign.

But if we are permitted to make such changes, where shall we stop? Why not alter the measure 5 instead of 3, which would have led to a discordance in the opposite direction? I conceive that it is much safer to use the observations as they stand, to extract from them the best result which mathematics enable us to draw, to form the numerical values of the residual errors, and to judge whether these can properly be attributed to error of observation.

Adopting, then, for observation 3 the original value 13, and considering the diagonal measure in observation 5 as 14, we have the following measures of the height of the promi

dont une en diagonale.

Hauteur de A, 0*7 division.

"Ici, la decroissance observée est plus de deux fois celle qui serait produite par le simple mouvement relatif des deux astres."

We owe it entirely to the candour of M. D'Abbadie and to the completeness of his published statement, that we are in any way enabled to criticise his conclusions. I trust, therefore, that, in expressing my inability to agree with M. D'Abbadie as to the method of treating his observations and as to the results to be drawn from them, I may be understood as offering to him my thanks and those of other persons interested in this discussion, for the clear and full account of his original observations, from which we are all enabled to frame our own deductions.

X- y x 2'45

Treating these by the method of Probable Errors, we obtain the equations

y × 4.63

3 x x × 463-y x 8.60

6, 7

Observations of the Solar Spots. By Rev. F. Howlett.

Mr. Howlett presented to the Society a further series of drawings of solar spots. The following is extracted from the letter, dated St. Augustine's Parsonage, Hurst Green, Sussex, Nov. 5th, 1861, which accompanied the drawings:

"The present series, continued from Nov. 15th, 1860, and brought down to Oct. 31st of the present year, consists of about seventy-three drawings of the whole solar disk, as magnified about 30 diameters, besides upwards of 200 separate spots, grouped or single, as amplified from 120 to 150 diameters.

"I may be permitted to remark that the wonderful commotions exhibited on the solar surface during the years 1859 and 1860 have scarcely, I think, been equalled at any period during the year which is now drawing to a close. These commotions, indeed, would appear to be now calming down-consistently, so far, with the much-discussed eleven-year cycle of maximum and minimum of spots.

"At no time, however, this year have I ever observed the Sun to be entirely devoid of spots: the two barest days might, I think, be stated as the 1st Feb. and 9th Oct. last, as may be inferred from the condition of the disks when respectively depicted on the 2d Feb. and 10th Oct. (as shown in sheets Nos. 37 and 58); whilst the spots of the latter part of March, and of the last half also of April and May, were very grand (as see sheets Nos. 41, 43, 44, and 47, especially the last).

"The preponderance of spots occurred, as usual, in the Sun's northern hemisphere; indeed, during the ninety-nine days upon which I made records of these appearances, I found, as nearly as I could judge, that a northern preponderance obtained on

7,8

47 days, and a southern one on 28; the spots on the remaining 24 days of recorded observation being nearly equally distributed in both hemispheres.

"The longest series that I have been able to depict of the changes undergone by any one individual spot is that exhibited in nine separate drawings of the spot v (see sheets 43 and 44), between the period of its first being observed by me on the 16th April and the condition it was in on April 26th, including the alteration suffered even between the hour of 7'30 A.M. and 30 P.M. on April 17th.

"A peculiar eddy seems to have strongly characterised the spot numbered 2, in group x (sheet 54), as observed at 6·20 A.M. on July 29th, but which had nearly ceased, judging from appearances, at 2:15 P.M. on the same day.

"I may also, perhaps, be allowed to call attention to the manner in which I have endeavoured to represent, approximately, the inclination to the horizon, at different hours of the day, of the line of junction of two spots on the Sun's surface, as recorded also on July 29th. The subject is interesting, as far as the matter of spherical geometry is concerned; and not less so, perhaps, as regards the best time for drawing the solar disk -in the way, at least, with which I am obliged at present to content myself, as alluded to in my last communication to the Society.

"The absence of penumbra on the north-east side of so large a spot as 3 (see Aug. 19th, sheet 56) is, I should imagine, very unusual.

"I would only desire to remark, further, the impression which is increasingly felt by me of the extreme shallowness, by comparison, of the photospheric stratum in which is sunk the penumbra of spots generally, and even of the penumbral stratum itself; inasmuch as the nuclei commonly remain visible to almost the very edge of the disk, the penumbral border of a spot very seldom presenting much appearance of foreshortening, either; so far, at least, as I could perceive, though armed with a Dawes's solar eye-piece, by Dollond, with a magnifying power of 200 diameters, and with an ordinary astronomical eye-piece, of about 300 diameters, appertaining to one of the Society's Sheepshanks Equatoreals, by Simms.

"This assumed shallowness of the photosphere, indeed, seems proved by Mr. Nasmyth's most interesting discovery of the thin layer of luminous lenticular bodies, of which that observer asserts the solar surface to consist.

"On the other hand, the nuclear stratum, or perhaps strata, appears to be of prodigious thickness, as may be inferred from the evidently vast depths into which the nuclear orifices descend, and as the varying intensity of blackness in different parts of the same nucleus seems also to bespeak. See series of large spot throughout sheet 41, and series also of the grand spot v in sheets 47 and 48, where the idea scems forced upon one, of chasms descending through cloudy strata, dozens or perhaps rather scores of thousands of miles in perpendicular depth."

Description of a portion of the Lunar Surface seen at Dr. Lee's Observatory at Hartwell, on the morning of July 31, 1861. By W. R. Birt, Esq.

The Roman numerals refer to the accompanying sketch which is taken from Beer and Mädler's map of the Lunar Surface.

I. Cichus. A deep crater on the south-west extremity of