= 6610,

The

possible value of c. For these we have S 10° and p and as far as c is concerned the following considerations. 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 expression,

The large values of e and c above found give

ec= 3561.6 seconds

and the greatest value of cot p. sin 1" = '000001, and therefore

and may be dismissed as of no appreciable value in practice. There remains still

Or, since sin2 p varies only between the values I and 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 1"= '000009

And hence the final value of (4) is 2035; or nearly f 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.

NOTE.

The following are the reductions referred to in this

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

paper:

... differentiating,

dh

1=0

sin p. cos + cos p. sin l. cos h - sin p. sin l. sin h.

dp

Results of the Observations of Small Planets, made with the Transit Circle, and of Donati's Comet, made with the Altazimuth, at the Royal Observatory, Greenwich, from July to October 1858.

(Communicated by the Astronomer Royal.)

The observations of Nysa in N.P.D. have not been corrected for parallax.

21 33 11*14