hemisphere. We know now that at that time the sun was passing from a period of minimum activity to a maximum, as now. 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 Sommering 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 8.5 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 :

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.

On the Value of the neglected Terms in the Ordinary Expression for the "Equation of Equal Altitudes." By J. Riddle, Esq.

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.,

Where p = polar distance of the sun, l = 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 equation of equal altitudes.

e the

This expression (1) is obtained directly by the differentiation of the fundamental one in Nautical Astronomy.

{

cos z = cos p cos + sin p sin l. cos h

z = zenith distance: and h = hour-angle or meridian distance.

}

dh

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 dp 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,

d2 h c2
dp2

dh dp

it is by no means so easily obtained, in a practicable form, by a second differentiation of the already determined value of ; a convenient mode of attacking it has therefore some interest. There is not much difficulty in reducing the value of

dh

dp

to the

(2)*

(for S and h are the two angles of the spherical triangle ad

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 l, 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).