Note. The above observations of Thetis and Leucothea are published on account of their near agreement with the Ephemerides of Schönfield and Schubert respectively, but from the continued unfavourable state of the sky, no other observations could be secured at Greenwich to compare with them.

Extract of a Letter from Prof. R. Wolf, of Zurich, to Mr. Carrington, dated Jan. 12, 1859. (Translation.)

"In my eighth communication on the subject of the solar spots now ready for the press, I intend partly to give in detail my observations during the year 1858, and partly to continue the researches commenced in the seventh number. I shall accordingly show, by employing, on the one hand, my own observations in the year 1849 to 1858; and on the other, extracts from the observations of Schwabe in the years 1826 to 1848, that the formula

M = 50°31 + 3'73 (1.68 sin 585°.26 t + 100 sin 360° t + 12:53 sin 30-35 t + 1.12 sin 12°•22 t

m

}

in which denotes the number of years elapsed since a period of mean spot-frequency, gives a curve very similar to the sunspot-curve; and therefore is very fit to be taken as the foundation of the more detailed research which I have now in hand. Now, as the coefficients of the four sines are the values which the fraction assumes, when for m and r are successively substituted the masses and mean distances of Venus, Earth, Jupiter, and Saturn; and the angles of the four sines are the 360° values of when for t are substituted the periodic times of the same planets, the conclusion seems to be inevitable, that my

t

conjecture that the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter, and Saturn, will not prove to be wholly unfounded. The preponderating planet Jupiter will in such case mainly determine the length and height of the wave of the spot-period; Saturn will cause small variations in the length and height; and, finally, the earth and Venus will change the smooth wave-line into a rippled one. Further investigation may decide this important question either affirmatively or negatively; but sketched out merely as it now is, I believe it will be found to have considerable interest.

"You will oblige me by bringing this contribution of mine to the knowledge of the Royal Astronomical Society. . . .

On the Visibility of Donati's Comet. By R. Hodgson, Esq.

Aug. 30th. The comet was barely visible with the naked eye, though easily found with an opera-glass.

Oct. 5th. Daylight, 11 A.M. Arcturus bright as a point; but the comet invisible, though the clock carried the telescope, (6 inches aperture; 7 feet 6 inches in focal length). Power used, low comet eye-piece, magnifying 25 times.

Covered my

Oct. 6th. Repeated the observation at II P.M. head with hood, and excluded all extraneous light from the eye, but could not see the comet. Arcturus brilliant; and Jupiter to be seen near the western horizon.

Oct. 9 and 10. Same time, telescope, and powers; but the comet was not to be seen.

Oct 17, 6 P.M. dark twilight. The comet visible in the finder, but invisible to the naked eye.

Note on a Method recently proposed by Lieut. Raper for Clearing the Lunar Distance from the Effects of Parallax and Refraction.* By J. Riddle, Esq.

If C represent the centre of the earth, O the place of the observer on its surface, S and M the places of the sun and moon (the figure is so easily conceived that it is hardly necessary to draw it). Then adopting the notation of the paper referred to, with the addition of d for the right line SM; the plane triangles SCM, SOM, CSO, and CMO, give the following symmetrical equations :—

*Monthly Notices, Vol. XVIII. p. 303.

If the last three of these be added and the first be subtracted from their sum, we obtain,

the leading equation of Lieut. Raper's paper.

m,

The third and fourth of these equations give at once the values of and m paper.

m

or II and II' as they are given in that

Nor is it more difficult to obtain equation (1) by spherical trigonometry, which is indeed a very convenient substitute for co-ordinate geometry in problems relating to the sphere (see solution in the note appended to this).

In a rigorous solution of the problem under consideration, it is necessary to consider the effects of parallax and refraction separately; and I suppose, that this special consideration of the effects of each is intended to be facilitated in the method proposed. In nautical practice the reasons for this separation are overruled on the ground of the simplicity gained in the solution of the problem, and the comparative insignificance of the error due to the neglect of them.

8. m

If they be neglected here also, then sm, for the determination of which special tables are suggested, is already tabulated in a sufficiently convenient form,

when N is the "auxiliary arc" of Table 25 of the first five editions of Riddle's Navigation.

A slight modification of the other terms only would be required.

With a careful estimation of the moon's parallax in altitude and a combination of the corrections, both the parallax and refraction may be allowed for, in the manner suggested for the refractions alone (known as Lyons' method). The first order of differences is not however sufficient for the larger correction (for the moon's parallax); a very concise formula for the computation of this little supplementary term, which I suggested, was printed in the Monthly Notices some years since.

I am under the impression that this mode of proceeding is as accurate and much more concise than the method proposed;

but open still to the objection of involving too many subordinate computations.

Equation (1) by Spherical Trigonometry.

Let true distance and d = apparent distance of sun and moon.
Let a, b, be the true zenith distances.
and a'b' be the apparent zenith distances.
Then cos d = cos a cos b + sin a sin b cos
and cos d
= cos a' cos b' + sin a' sin b' cos
And eliminating cos
sin a' sin b' cos - sin a sin b cos d'

=

Z

- sin (a' — a) sin b′ as b
cos, sin

cos &=

sin a sin b
sin a' sin b'

Z

Z

cos b cos b')

sin a' cos a sin
sin a cos a' sin b
+ sin (b' — b) sin a cos a'

Observations of Donati's Comet made at Haddenham, Bucks. By the Rev. W. R. Dawes.

The following are a few extracts from this paper, which the Council will, in all probability, order to be printed in extenso in the forthcoming volume of Memoirs, along with a few others on the same subject. The author states that his observations of the comet were made with an excellent objectglass of 74 inches aperture, by Mr. Alvan Clark, applied to his Munich equatoreal mounting.

"1858, Sept. 12. Sky remarkably clear. Comet found with the equatoreal at 6h 43m G.M.T., and was at that time well and easily seen. At 8h 32m the visible length of the tail was 3° 30'. A fine object to the naked eye. In the telescope

the nucleus appears quite planetary. Long after the head had set, the tail was visible, rising obliquely from the horizon, and might have been seen all night but for the intervention of trees in the northern horizon. The comet was a beautiful object in

the north-east at 15h."

66

Sept. 24. Visible in the finder of the equatoreal at 61 10m. The arc or sector round the southern, or sun-ward, side of the nucleus is finely seen to-night, though the sky is not perfectly free from haze. I cannot trace the arc round on the side opposite to the sun; it seems to come to a rather abrupt termination at about 40° beyond a semicircle, being visible to about that extent further into the tail on the eastern side than on the western. It looks like a hood set on awry, the tail resembling a fine gauze veil dependent from it. The narrow dark channel extending from the nucleus up the axis of the tail is very remarkable: its edges are surprisingly well defined, especially very near the nucleus. The comparatively sharp definition of

the eastern edge of the tail contrasts strikingly with the softness of outline on the western side."

"There is a second arc very close to the nucleus, and rather bright, and I think nearly uniformly so throughout its extent. The larger sector, on the contrary, is decidedly brighter towards its outer edge, and terminates rather sharply for such an object. A soft nebulosity or coma surrounds the larger arc, and appears to be concentric with it. Its outline is certainly not continuous with that of the tail, the apex of which falls within the arc of the sector.

"By measurement of a careful sketch, the middle radius of the sector (drawn from the nucleus to the middle of the arc) makes an angle with the direction of the dark channel in the tail of about 156°, reckoned round by the east side."

"Oct. 5. At 6h 30m G.M.T. Arcturus is just within the eastern boundary of the comet's tail, and about 20' north of the nucleus.

"The edge of the outer sector is much more indistinct tonight than it was some days ago, and so is also the edge of the eastern side of the tail. The inner sector is astonishingly enlarged since Oct. 2. There is in it an irregular dark spot on the western side of the nucleus; and a little to the north of that dark spot, and nearer to the nucleus, there is a bright spot softly defined and less bright than the nucleus.

"At 7h 11 Arcturus is judged to be in the middle of the tail.

"At 7h 15m Arcturus is in the dark channel.

"At 7h 56m Arcturus is just out of the tail on the western side.

"The following are measurements of angles of position and distances of the nucleus of the comet with respect to Arcturus, the comet preceding the star to the south:

·

O

D = 21 35.6

"Mr. Carrington having suggested to me to observe the angles of position of a series of tangents to the curve formed by the eastern edge of the tail, I endeavoured to do so; though my apparatus is not well suited to such an observation, for which a very low power and large field would be more appropriate than those ordinarily belonging to the parallel wiremicrometer. It is essential that the points at which the wire is made, a tangent should be pretty accurately determined; but this was not very easy to do. The mode which struck me as the most practicable was, to fix on certain differences of north polar distance from the nucleus. Having, therefore, brought