example, of the first point of Aries, greater and greater longitudes come into that direction. Your beautiful remark on the longitude-drift of spots being opposite in higher and lower latitudes is therefore completely confirmed also in sign by my observations (at least as far as I see from the Table B which you mention). This remark seems to me of no little importance, disclosing a fact which (as a cause or as a consequence?) may have something to do with the two belts of spots situated at or near the border of the opposite currents. . . . In latitudinal sense, however, I cannot make agree my observations with what yours seem to indicate. Besides the latitudes of spots exhibited in my Table A (and these are all the spots observed during a whole, or rather, more than a half, revolution), which indicate, as it seems, an unexceptional drift towards the equator, I have just examined in this respect the individual positions of the totality of spots before me; and though, with more leisure, the single isolated spots ought to be discriminated from the participants of systems, I write, in the annexed paper, an abstract presenting a general survey of the motions in latitude. In drawing inferences from individual positions, a good allowance must be made for the mean error of the observations. But, on the whole, I do not recognise in the annexed conspectus a regular law depending on the distance of the spots from the equator... . Distracted in the latter years by other business, I have not done anything more upon solar spots. Your researches, however, as published from time to time, have kept up with me a lively interest for this subject; and I think I may take it up again, when the measuring apparatus for my refractor is in order; though, to be sure, the fine climate of Italy offers a much greater reward for this kind of work.”

Note.-I would remark that, in my paper printed in the Monthly Notices for January, when I spoke of a reverse current in the higher latitudes, I did not affirm the existence of advancing and retrograde motions in longitude absolutely, but as exhibited by the use of a mean period of rotation. I have not yet concluded that the drift of all spots is not in the direction of the general rotation, the drift being, in that case, most rapid in the region of the equator of the sun; and with respect to Dr. Peters's result of the drift in latitude being general towards the equator, I may here remark that M. Laugier came to the opposite conclusion, and that my own examination would seem to explain the possible origin of the difference between two observers so capable and so exact; for it may well be that the critical latitudes at which the directions of drift in latitude change sign may be different at different epochs. The question is rather a minute one, when the possible errors of observation are considered, and at present requires the expenditure of more labour and investigation.-[R. C. C.]

Hofrath Schwabe has recently communicated to the Astron. Nach. his customary abstract of his enumerations of spots for the previous year. From observations on 335 days in the year 1858, he recorded the passage of 188 groups of spots, and on no day found the disk free of spots. The increase of action over that of 1857 is very decided, and such as was anticipated. The next maximum may be predicted for the year 1860.

The first of these methods is that of Sir William Herschel, proposed by him when the number of known proper motions was very small. It consisted mainly in drawing upon a celestial globe a great circle representing the direction of proper motion of each star, and finding the point at which any two such circles intersect each other, which point, supposing the apparent proper motion of each star to arise entirely from a real motion of the sun, would be that to or from which the sun's motion is directed. This method was most happily adapted to the limited facts of observation then known, and the whole investigation considered one of the best specimens of Sir W. Herschel's enterprise and sagacity; but it is evidently insufficient for the discussion of proper motions of a great number of stars.

The second method, which is applicable to the discussion of the proper motions of larger catalogues of stars, has been in use up to the present time, and is of the following nature. A point is assumed as a probable approximation to the apex of solar motion; the direction of the arc of great circle drawn from the star's place to this point is ascertained as also the direction of the star's apparent proper motion; and the angle between these two directions multiplied by a certain factor is considered as the small residual errors in ordinary problems of combinations of observations; and all the equations thus formed are to be treated by the method of least squares.

In the author's opinion there are many objections to this method, of which the following are the most important:First, that it requires the point to be approximately known, since an error of its assumed position equal in amount to the smallest which could be probably assigned to Sir W. Herschel's determination causes great confusion in the change of direction of the great circle drawn from the star's place to the assumed point of direction of solar motion, when the star is not very distant from that point; and, secondly, that the proper motions of some stars are so nearly the opposite to those implied in the assumption of the point, that a small change in the place of the point will change the angle of errors per saltum from +179° to -179°.

On such grounds as these the author considers the method employed very imperfect, and proposes one totally different, of which the following sketch will give a tolerably correct idea:

Instead of using the apparent angular motions of the sun and stars, as exhibited on the surface of a globe, their linear movements are treated of by reference to rectangular co-ordinates, and the following advantages result from the adoption of this method. It is quite independent and complete, and does not require the assumption of a point determined by preceding investigations; and it gives exactly due weight to each observation subject to our antecedent judgment as to the general weight-multiplier to be attached to any class of stars defined by brilliancy or any other characteristic, with the exception of magnitude of proper motion.

In applying the method, the author takes for the origin of co-ordinates the centre of the sun at a fixed epoch, and for the plane of xy, the plane passing through the sun parallel to the earth's equator, the axis of x being drawn towards the first point of Aries, and that of y to the point whose right ascension is 90°; z is drawn parallel to the earth's axis and is positive towards the north.

Taking the sun's linear motion in a year or other definite time, and resolving it in the direction of x, y, z, it is not difficult to express the R. A. and N.P.D. of a star at the end of the year in terms of the initial values of R.A. and N.P.D., and of the sun's resolved motion in x, y, and z, multiplied into certain functions of R.A. and N.P.D. easily calculated. In fact, for a star at distance r, the expressions for its apparent R.A. and N.P.D., at the end of the year, will be respectively,

The author then proceeds to show that where a number of equations given by different stars, the elements of linear motion of the different stars must be considered absolutely as chance-quantities to be treated in the same way as chanceerrors of observation, subject, however, to one consideration (not treated of in this memoir) as to views which may be entertained respecting the probable inequalities of motion of the stars forming our nebular cluster, as measured in various directions. To this consideration he calls the attention of future inquirers, but as he has no means of forming a judgment on the nature of the motions of individual stars, he supposes that for every star the probabilities of movements of given magnitude in all directions are equal.

He next enters on the consideration of the effect of systematic errors which may have crept into the computations by which the proper motions have been determined. These proper motions are taken from Mr. Main's paper printed in vol. xix. of the Memoirs, and from another paper recently printed, and were deduced by comparison of the places of Bradley's stars as given in Bessel's Fundamenta, with the places given in the Greenwich Twelve-year and subsequent Six-year Catalogue, and therefore will be affected by any errors in Bradley's observations or Bessel's reductions. In addition, they will be affected by incorrect values of the constants of precession used in reducing the stars from Bradley's epoch to the modern Greenwich epochs. On the whole, they may consist, for right ascensions, in the error of equinox used in reducing Bradley's observations, together with errors of the constants of precession, and from north polar distances, in errors of the constants of precession, together with those arising from the defects of the Greenwich quadrants. To these systematic errors must be added the chance-errors of observation of each individual star not connected in any way whatever.

By comparison of the aggregates of the various terms before specified with the tabulated results of observations, equations of the following forms arise:

sin R.A.

and

--

+

+ Error in parallel

=

Proper Motion in parallel.

177, 178

M

"

Mn

where and are the real apparent angular motions in the directions of parallel and meridian, m' and n' are the possible errors of m and n, the constants that enter into the formula of precession in R.A. and N.P.D., and q is the possible error of Bradley's observations in N.P.D., arising chiefly from the defects of the Greenwich quadrants.

Equations may now be formed on two extreme suppositions; first, that the irregularities of Proper Motion are entirely due to chance-error of observation; secondly, that they are entirely due to peculiar motions of the stars. The author is inclined to think that the second supposition corresponds most nearly with the truth, especially when the stars to which the calculation is applied are taken from a catalogue of large proper motions; he, however, proceeds to show how the final equations for determination of X, Y, and Z, must be found, according to the rules of the Theory of Probabilities, on both these extreme suppositions.

For the values of r, Mr. Airy has been guided by the assumptions of Struve (Introd. in Cat. Nov. Stell. Dup.), the stars being divided into seven classes from the 1st magnitude to the 8th.

As it would have been a work of enormous labour to make use of all the stars in Mr. Main's catalogues, amounting to about 1200, those only have been used which have proper motions above a certain limit assigned by the author of the catalogues, but without any distinct motives of preference.

The author here makes a remark which is of great importance in the determination of the solar motion, and which it is best to express without abridgement in his own words:

"It appears to me that the propriety or impropriety of retaining the stars whose proper motions are extremely large will depend entirely upon our assumption as to the practical reference for zero of space. In void space, there can be no zero either of linear ordinate or of angle. Any person who endeavours to form a notion of such zero will find that his mind sinks under the effort. We are compelled therefore to adopt, as our zero of space, the place of one body, or the mean of the places of many bodies. And, to whatever extent we adopt a number of bodies in forming our mean, to that extent our deductions of all kinds will apply. Thus, if we include in our treatment the stars with very large proper motions (61 Cygni, Cassiopeia, &c.), we may expect to obtain the movement of the solar system, as referred to the mean of all the stars of which we treat, including 61 Cygni, μ Cassiopeiæ, &c.; if we exclude them, we obtain the movement as referred to the mean of all the stars except those. The retention or exclusion of those stars appears then to be quite arbitrary, provided that we give the proper interpretation to our final results. In the investigations of this paper, I retain these stars, so far as they are included in Mr. Main's catalogue."

The author then proceeds to the solution of the equations on the two suppositions before-mentioned, and obtains the following results; R being the sun's whole proper motion expressed in seconds of arc as seen from a star of the first magnitude, and A and D the right-ascension and north declination respectively of the point to which that motion is directed.

179, 180

The author considers the results of the second assumption to be more worthy of confidence than those of the first, and proceeds to give the numerical evidence of the probability that the motion of the solar system is not very different from that given by it, by forming the sums of the squares of the observed proper motions in parallel and in N.P.D., and then forming the sums of the squares of the residual errors of the proper motions after the application of the terms depending on the solar motion. The results according to the second supposition are,

"From these the reader may form an opinion on the legitimacy of the general conclusions. I do not believe that the fundamental suppositions are sufficiently certain to justify any investigation as to the probable range of error in the assigned position of the line of the sun's motion.

"The most remarkable feature in the result is, however, the very great difference between the velocity of the solar motion as found from this investigation, namely, 1"'912, and that found by M. Otto Struve in his Bestimmung der Constante der Pracession, namely, o" 339." This Mr. Airy attributes to the fact that the stars used in his own investigations are exclusively those having large proper motion, and enters largely into the explanation which depends, he considers, on the choice made in 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.

cos

rde

= 2 sin see p. 26 Lunar Theory, Part 1. de

2 R, cos 27 × - cos - 2 R, sin 2 + x 2 sin

de

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 strice 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

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.

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 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

*These drawings were exhibited at the meeting of the Society.

183, 184

184, 185

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 the ball. In both these respects the aspect was far less favourable at the epoch of Captain Jacob's observation in November 1852, from which his excellent picture is drawn. Captain Noble does not give the date of his own observation.* Haddenham, Thame, March 1859.

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 74-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 1 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

h m

S

3.6

21 I

92 43 16.8

19 47 46.2 From the three places above determined Captain Tennant computed the following parabolic elements, employing the method given by Sir John Herschel in his article on Astronomy in the Encyclopædia Metropolitana: