the apparent evidences of proximity of the stars, that is between brightness and magnitude of proper motion.

To the memoir is attached an appendix containing the elements of every sort used in the calculations, including the values of the functions of R.A. and N.P.D. which are necessary in the formation of the equations of condition.

Note on the Development of the Disturbing Function in the
Lunar Theory. By Sir J. W. Lubbock, Bart.

Mr. Cayley, in a paper recently published, has pointed out some errors in the development of R given by me in my work on the Lunar Theory, and amongst others in the numerical coefficient of the term of which the argument is 2 5 + § — 3 %', which I called + 45

64'

but which should be

rdR dr dR da

a being the true longitude.

845 64

If we consider the term of which the argument is 2 7 + §, in order to have the part multiplied by e, it is sufficient to take,

When the term only involves the first power of e, as in this

instance,

dR

de = de

R, or the coefficient of the term in R is

d R

the same as that of the corresponding term in de

The preceding result is entirely independent of ', and, moreover, would have been the same whatever multiple of had accompanied 27, so that as

so also the coefficient of cos (2+%+ %') = coefficient of cos (2+) cos (2 +++ng') =

whatever n may be.

=

cos (2 ++ng')

Many other similar equations of condition obtain. When I published the development in question I was not aware of the extent to which this means of verification may be carried in the lunar theory, but, as owing to Mr. Cayley's recent work, no uncertainty can exist with regard to the numerical order of any coefficient in this stage of the approximation, it is unnecessary to give any further examples.

March 14, 1859.

Note on a Group of Solar Spots observed on the 23d of
February, 1859. By W. R. Birt, Esq.

Mr. Birt's observations were made with Mr. Slater's refractor of 15 inches aperture, which was liberally placed at his disposal for the purpose. They were accompanied with a sketch exhibiting the details of the phenomena seen by him.

The nucleus of the principal spot presented a striated appearance, the direction of the striæ being that of the longest diameter of the spot. The illumination of the cloudy stratum was of a varied character, conformably to Mr. Dawes' observations (Monthly Notices, vol. xii. p. 168). It also exhibited unmistakeable traces of a striated formation, which seemed to be connected with the jagged or uneven edge of the nucleus. In this respect the observations of the author do not accord with those of Mr. Dawes.

The author thus proceeds :

"The most interesting feature of the nucleus consisted in two luminous patches presenting nearly if not quite the same intensity of light as the surrounding penumbra. These patches during the time of observation exhibited a somewhat fluctuating character, not so much in respect of luminosity as of position. They were confined to the upper part of the nucleus, but underwent changes of configuration.

“The Penumbra manifested the striated or ridged appearance spoken of by Mr. Dawes in a most characteristic manner. I am strongly disposed to regard the penumbra of this particular spot as radiated. Mr. Dawes' sketch before alluded to exhibits very distinctly the kind of radiation which I noticed in the spot now under consideration; the edges of the penumbra were notched, jagged, and uneven, and the outline was not coincident with the outline of the nucleus. I particularly remarked that the luminosity of the penumbra was nearly uniform, and broken only by a bright spot near the horns, forming the upper

angle of the nucleus, and by a brighter space between the nucleus and largest detached spot within the penumbra: the latter, however, might have resulted from contrast."

220.

The observations were made with a magnifying power of

On some Indications of Rotation in a Solar Spot.
By W. R. Birt, Esq.

Finding that a somewhat large spot had entered on the visible hemisphere of the sun on February 22, I availed myself of Mr. Slater's kindness, and obtained two views, one shortly before its passage of the centre, and one exactly three days after the first. The two drawings accompanying this communication indicate the nature and extent of the changes that occurred during the three days.* Power employed, 220; aperture, 15 inches, reduced to 4 inches for subduing the light.

h m h m

2 30 to 4 o G.M.T.

Sketch No. I
Sketch No. 2

February 28
March 3

2 45 to 3 45 G.M.T.

The two sketches are strictly comparable, having been executed about the same time of the day.

Nuclei.-The nuclei of the two principal spots in the group presented a more or less uniform appearance. I did not remark the peculiar striated appearance so distinctly apparent in the spot of the 23d of February, an account of which I communicated to the Society. It will be seen from the drawings that the nuclei of both spots underwent external configuration of form.

Penumbra.-The radiated appearance of the penumbra, as seen in the spot of February 23, was not detected in the penumbra of the two principal spots of this group. In Sketch No. 1, Feb. 28, three well-marked luminous patches were discernible near the left-hand upper edge of the penumbra (as seen in the telescope); also an intense luminous space between the principal nucleus and the smaller one in the largest spot.

On taking the second sketch, the penumbra around the two nuclei of the large spot appeared to be quite uniform in its luminosity; the smaller nucleus had increased considerably in size, and the intense luminous space between it and the principal nucleus had increased in brilliancy. It appeared to me that between the two nuclei the penumbra, properly so called, was absent; or this increase of brilliancy might have resulted from contrast.

The penumbra of the smaller spot underwent, in the three days, a marked change of form; the direction of the longer * These drawings were exhibited at the meeting of the Society.

diameter, on the 3d March, was nearly at right angles to its direction on the 28th February. The change of form of the nucleus during the same interval is considerable; it is, however, possible, by means of the angular points, to determine somewhat of the nature of the change of shape; and if we take the principal projecting point to the left, in Sketch No. 1, to be the same as the principal projecting point on the upper part of the nucleus in Sketch No. 2, then we have a somewhat similar disposition of the penumbra in both sketches, from which it would result that during the interval this spot had shifted its position about a quarter of a rotation.

The smaller Spots.-Numerous changes appear to have taken place among the smaller spots in the neighbourhood. Most of the spots below the large one, on Sketch No. 1, had disappeared on March 3. A small triangle only was visible, and it is somewhat difficult to ascertain if the spots forming it, and seen on March 3, were any of the smaller spots seen on February 28. While these spots had mostly disappeared, a somewhat considerable chain of small spots had formed below the smallest of the principal spots, and in the line of prolongation of the two principal spots. The nearly rectilinear division of the penumbra of the smallest of these is interesting; the same kind of arrangement was detected on Feb. 28.

Indications of Rotation of the largest Spot.-In order to exhibit in the clearest light the indications, afforded by the chinagg

Feb. 28. on

March 3.

two sketches, of rotation in the largest spot, I have placed views of them in juxtaposition. The change in the direction of the longer diameter of the penumbra, the alteration of place of the principal angular point of the larger nucleus, the new locality of the secondary nucleus, and other interesting features, bear testimony to a change of position of the spot itself apparently of the nature of rotation. This mode, however, of dealing with the subject may not be quite satisfactory. The spot itself has advanced considerably on the sun's disk in the interval between the sketches. It will therefore be important to compare the positions of the principal points of the largest spot with those of the spots surrounding it. A glance at the two sketches will

at once show that the longest diameter of the largest spot occupied two different directions, on the two days, with regard to the smallest of the two principal spots; in point of fact, that the largest spot had so moved in the interim as to bring its longest diameter into a line with the smallest spot, this having apparently changed its position by an independent rotation of its own.

The variations among the smaller spots appear to have been so rapid as to preclude the detection of any rotation among them.

March 4, 1859.

Note on Saturn's Ring. By the Rev. W. R. Dawes.

In the Monthly Notices for January last are some remarks by Captain Noble on the appearance of Saturn's obscure ring as seen with his excellent 4.2-inch refractor. He describes it as seeming to dip under ring B; "having never been able satisfactorily to trace the junction of those portions of it in the ansæ with the part crossing the ball." This seems obviously to arise from the want of more illuminating power than an object-glass of only four and a quarter inches aperture can afford, however perfect its defining power may be. I have on several fine nights during the present apparition of the planet been able, with the 7-inch refractor I now have in use, to trace the perfect elliptic outline of the inner edge of the ring C in the ansæ and across the ball, without the slightest break or irregularity but with a telescope of considerably less illuminating power (only as I to 3), the narrow portion of it which is inclosed, as it were, between the ball and the ring B might very probably be overpowered by the incomparably brighter objects in contact with it on each side.

With reference to the curvature of the shadow of the ring on the ball, it may be remarked that when the altitude of the sun above the plane of the ring considerably exceeds that of the earth, the shadow of the ring on the ball is curved in the opposite direction to the edge of the ring, and especially near the edges of the ball. This is most remarkable when the minor axis of the outer ring is not much less than the polar diameter of the ball. The edge of the shadow then falling near the pole the visible curvature is very considerable; but I have never seen it greater on one side of the ball than on the other. The circumstances existing during the earlier part of the present apparition were particularly favourable for the display of this phenomenon, the sun's elevation exceeding that of the earth by considerably more than two degrees, and the edge of the outer ring being only about three seconds from the northern edge of