Pursuant to a Resolution of the Council submitted to the Society and approved of by them at the Annual Meeting in 1859, the Monthly Notices are printed with the Memoirs, as well as in the accustomed octavo form. : Monthly Notices OF THE ROYAL ASTRONOMICAL SOCIETY. The paging of the octavo edition is repeated. VOL. XIX. Dr. LEE, V.P., in the Chair. Cyril C. Graham, Esq., Grand Cairo; and November 12, 1858. John Nichol, Esq., LL.D., Professor of Astronomy in the University of Glasgow, were balloted for and duly elected Fellows of the Society. On the Distribution of the Solar Spots in Latitude since the Beginning of the Year 1854; with a Map. By R. C. Carrington, Esq. I had fully hoped that by the time when the Society would meet again in the month of November I should have been able to present the members with a tolerably complete discussion of the series of solar spot observations which I have now kept up at Redhill for nearly five years; but a family loss by the hand of death has for the last three months deprived me of the leisure I had counted on, and compels me to confine the present paper to the publication of a single feature which the assembling and comparison of results has brought to light. It will be found to be another and instructive instance of the regular irregularity and the irregular regularity which, in the present state of our knowledge, appear to characterise the solar phic nomena. In the briefest form of statement, the result is, that throughout the two years preceding the minimum of frequency in February 1856, the spots were confined to an equatoreal belt, and in no instance passed the limits of 20° of latitude N. or S.; and that shortly after this epoch, whether connected with it or not, this equatoreal series appears to have become extinct, and in seeming contradiction to the precept, Natura non agit per saltum, two new belts of disturbance abruptly commenced, the limits of which in both hemispheres may be roughly set at between 20° and 40°, with exceptions in favour of the old equatoreal region. The tendency at the present time appears to be to contraction of the parallels. The method of reduction employed having already been explained and sufficiently illustrated in these pages, it is only necessary on this occasion to explain the arrangement of the accompanying map. In a mean solar day the sun rotates through an angle of 14° 11' very nearly, and the heliographical longitudes of spots, as compared with that of the centre of the disk, increase by No. I. the synodic quantity corresponding. If an observer plots down on each day the positions reduced to noon of the spots recorded ' on the 180° viewed, and lays the successive sheets so as to superpose the positions of the same spot, his plotting sheets will advance daily to the left by 13° 12' nearly. And if he then agrees to adopt one figure of a spot as typical, to be laid down on a single continuous sheet, he will obtain a result such as I have deduced by computation (with the exception that for convenience my map is reversed left for right), and such as might be supposed to be produced by imagining the sun to be the central cylinder of one of Applegarth's printing-machines. In this state the graphical result would be of too extreme dimensions in length for the eye to take it in as a whole; and, accordingly, in the map lithographed the scale in longitude is reduced in the proportion of 72 to 1, as compared with the scale in latitude, and the delineations of spots compressed to mere vertical lines. The uncertainty of the exact period of rotation affects the result only in this way, that if the true period be somewhat longer than that adopted, the vertical lines which indicate the commencement of successive rotations, should be drawn somewhat wider apart, and vice versâ; a matter of no importance, obviously, for our present purpose. The variation of the limiting parallels being established, the inquirer next desires to turn back to such past records as may throw light on their changes and their relation to epochs. In this respect I would call attention to a short, but very condensed and important paper, communicated to me by Dr. C. H. F. Peters, formerly of Naples, and lately of Albany, and published, I believe,* by the American Association for the Advancement of Science. Dr. Peters observed the sun with an object and purpose very similar to my own, from September 1845 to October 1846 inclusive, and obtained 813 places of 286 spots, which he subsequently reduced with a skill and exactness in which I place great confidence. He has given a plate exhibiting the gross distribution in latitude during the period of his labours, in which I find the limits laid down as 40° N. and 30° S. with a desolate region from 8° N. to 5° S., and with, on the whole, a preponderance of action in the north hemisphere. We know now that at that time the sun was passing from a period of minimum activity to a maximum, as The distribution is very similar to that which now holds, excepting that at the present time there appears an excess of activity in the south. The records of Dr. Peters are not all which leisure and research may make available in this branch of the history of solar action, there are those of Sommer* I have by me only the sheets of the volume containing this particular paper, sent by post. b now. 3, 4 Mr. POGSON: New Variable Star.-Mr. RIDDLE: "Equation of Equal Altitudes." ing and others; nevertheless, it is difficult to express the degree of regret which a student of the sun feels when evidence such as the present meets him of the state of maturity his subject might have attained ere this, had not the opportunities of two centuries been neglected, by his predecessors condemning the research as one of idle curiosity, fit matter for a University thesis, but below the level of Philosophy. The most cursory consideration will show that success in educing such conclusions in the case of the sun depends mainly on the continuity of the labours of the observer. The con clusion which an observer would have arrived at from a discussion of the observations made during the years 1854 and 1855 would have been exceedingly imperfect, though apparently borne out by a tolerably extensive experience; and the conclusion which I draw from the four years' results now accumulated is, that our knowledge of the sun's action is but fragmentary, and that the publication of speculations on the nature of his spots would be a very precarious venture. I am very anxious to know what the magnetic observers have to produce, corresponding or not corresponding with the results of my map; and I would take the opportunity of remarking that the question of the correspondency of the solar and magnetic disturbance phenomena is in the curious and imperfect state of a correspondency established in the aggregate, but not for particulars. I shall shortly offer some conclusions on the independent movement of spots, and on the divergence of neighbouring nuclei, a very singular and marked action, in the detection of which I find, however, that Dr. Peters has anticipated me. New Variable Star (R Sagittarii). By Norman Pogson, Esq. (Communicated by Dr. Lee.) On the night of August 7th, 1849, Professor Argelander observed a star of the 85 magnitude, south preceding a fine but widely-spread group, which has recently proved to be variable. In August 1856, when commencing my chart of Hour 19, the star in question was missing; but supposing an erratum in the published zone, no suspicion was entertained of its variability. However, on July 3d of this year, while planet-seeking with the Smythian telescope, I was struck by finding it in the position assigned by Argelander, and a full 8th magnitude. Since that date the following changes have been recorded, not simply by estimation, but by the more certain and satisfactory plan now usually adopted of comparing with adjacent stars of assumed magnitudes: 1858, July 3, 8.2 magnitude 1858, Aug. 8, 9.6 magnitude 4, 5 On the Value of the neglected Terms in the Ordinary In order to elucidate what follows it will be necessary to refer for a moment to the expression erroneously used in the calculation of the correction, known under the designation of the "Equation of Equal Altitudes,” viz., = (1) -ec cotp cot h - c cot l cosech Where p = polar distance of the sun, = colatitude of the place of observation, h half the elapsed time between the A.M. and P.M. observations of equal altitudes of the sun, c the change of the sun's declination in the time h, and e the equation of equal altitudes. This expression (1) is obtained directly by the differentiation of the fundamental one in Nautical Astronomy. dh dp . cos z = cosp cos + sin p sinl.cos h z = zenith distance: and h = hour-angle or meridian distance. Š Considering p and h only to change, it (1) is in fact only the value of c, or the first term in the total difference which the change of the sun's declination produces in the hour-angle h. And this, in all our elementary treatises on Astronomy, is employed as a sufficient correction of the middle instant indicated by the chronometer, between the A.M. and P.M. observations of equal altitudes of the sun, to deduce the time shown by the chronometer at noon; and this, too, without any allusion to the value or no value of the neglected terms. If, however, the next term be required, dh dp cot S = sin p Oct. 5, 12.8 It appears most probable that if the variation be tolerably regular, seven maxima have occurred between the years 1849 and 1858; in which case the period will not differ much from 465 days, and the next maximum will fall due in September or October, 1859. The position of R Sagittarii, as determined by micrometrical comparison with A.Z. 227.120, are found to be, when reduced to 1860, R.A. 19h 8m 285.62; South Dec. 19° 32' 59" 2. That given by Argelander, reduced to the same epoch, being R.A. 19h 8m 28.49; and South Dec. 19° 32' 57"4. 2 South Parade, Oxford, Nov. 11, 1858. 6,7 MR. RIDDLE: Value of the Neglected Terms in the Expression for the " Equation of Equal Altitudes.” And this multiplied by sin 1" will be the value of the second term of the difference when c and e are estimated in seconds. In attempting to seek the largest values of the expressions (1) and (3), we are at once forced to consider the practical limits of the application of the problem. For at the poles cot, and therefore e, are infinite; and this points, however vaguely, to a limit of latitude beyond which the problem is not fairly applicable. I am disposed to fix this limit at 70°, as being quite high enough, at any rate, for ordinary navigation, leaving the higher latitudes for a special polar legislation. (Even though I have been informed by an indefatigable observer that he has used this method several degrees farther north.) This limitation of latitude also includes a maximum limit of h. A second and inferior limit of h is pointed out in the expression (1); for as cot h enters into it h ought not to be very small, 2 or 30°, I think, would be an extreme limit here. But a third, and for the present purpose, an infinitely better limiting condition, is furnished by equation (2) which is the second form of equation (1), viz., S For if the angle S, between the zenith distance and the polar distance be very small, it will give rise to an "ill-conditioned" triangle, which is at all times to be avoided. should hardly be less than 10°. This condition has also the advantage of including those before mentioned. We are now prepared to enter upon the discussion of the values of terms (2) and (3). cot 8 For the first, viz., ce, to find its largest value we sin p must take the smallest values of S and p and the largest possible value of c. For these we have S: = 10° and p = 6610, and as far as c is concerned the following considerations. The greatest hourly change of the sun's declination is about 60" in March and September; and taking half the elapsed time, or h, between the A.M. and P.M. observations as 6h (a large value in actual practice), we have c = = 360": 24 seconds of time. These values of S, p, and c give e = 148.4 seconds of time, or about two minutes and a half, certainly an excessively large value for the equation of equal altitudes. Next for the examination of the several parts of the ex pression, sin 1" 7,8 Here again (c2 + e2), with the large values found for c and e, amounts to 22598.6 seconds, and taking h at 15° (only one-half of the inferior limit which I am disposed generally to assign to it), cot h. sin "= '000009 And hence the final value of (4) is 2035; or nearly seconds of time is found for an excessively large value of the second term of the difference, or secondary correction, and it may therefore also be safely neglected in nautical practice. The large values of e and c above found give ec = 3561.6 seconds P |