Supposing the Trajectory of this Comet to be parabolic, I collected from the foregoing observations, that its motion round the sun is direct, and that it was in its perihelion October the 21st, at 7h 55' mean (or equated) time at Greenwich. That the inclination of the plane of its Trajectory to the ecliptic is 12° 50' 20"; the place of the descending Node ♉ 4° 12' 50"; the place of the Perihelion ♄ 2° 58' 0"; the distance of the Perihelion from the descending Node 88° 45' 10"; the Logarithm of the Perihelion distance 9.528328; the Logarithm of the diurnal motion 0.667636.
From these Elements (which are adapted to Dr. Halley's general Table for the Motion of Comets in parabolic Orbits), I computed the places of this Comet for the respective times of the foregoing observations, as in the following table; which contains likewise the longitudes and latitudes deduced from the observed right ascensions and declinations, and also the differences between the computed and observed places. These differences (no-where exceeding 40") shew, that the elements here set down will be sufficient to enable future astronomers to distinguish this Comet upon another return; but as they do not correspond with the elements of the orbit of any other Comet hitherto taken notice of, we cannot determine at present the period thereof.
| Greenwich, 1757. Mean Time. | Comet. Long. Observ. | Latit. Observ. | Long. Comp. | Latit. Comput. | Diff. Long. | Diff. Latit. | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| d. | h. | ' | S. | ° | ' | " | ° | ' | " | S. | ° | ' | " | ° | ' | " | " | " | |||
| Sept. | 12 | 16 | 2 | ♊ | 29 | 34 | 13 | 11 | 32 | 16 | No. | ♊ | 29 | 34 | 11 | 11 | 32 | 20 | No. | -2 | +4 |
| 13 | 12 | 37 | ♋ | 2 | 35 | 34 | 11 | 12 | 13 | ♋ | 2 | 35 | 47 | 11 | 12 | 11 | +13 | -2 | |||
| 14 | 14 | 0 | 6 | 27 | 45 | 10 | 44 | 3 | 6 | 27 | 42 | 10 | 43 | 43 | -3 | -20 | |||||
| 17 | 13 | 0 | 17 | 49 | 40 | 9 | 3 | 31 | 17 | 50 | 16 | 9 | 3 | 11 | +36 | -20 | |||||
| 19 | 15 | 17 | 26 | 6 | 8 | 7 | 36 | 49 | 26 | 5 | 50 | 7 | 36 | 30 | -18 | -19 | |||||
| 23 | 15 | 57 | ♌ | 11 | 19 | 18 | 4 | 33 | 38 | ♌ | 11 | 19 | 4 | 4 | 33 | 32 | -14 | -6 | |||
| 24 | 15 | 21 | 14 | 44 | 19 | 3 | 49 | 37 | 14 | 44 | 3 | 3 | 49 | 39 | -16 | +2 | |||||
| 28 | 16 | 22 | 27 | 23 | 43 | 1 | 3 | 44 | No. | 27 | 23 | 32 | 1 | 3 | 52 | No. | -11 | +8 | |||
| 30 | 16 | 24 | ♍ | 2 | 45 | 43 | 0 | 5 | 30 | So. | ♍ | 2 | 45 | 39 | 0 | 5 | 17 | So. | -4 | -13 | |
| Octob. | 2 | 16 | 48 | 7 | 37 | 43 | 1 | 5 | 50 | 7 | 37 | 42 | 1 | 5 | 32 | -1 | -18 | ||||
| 3 | 16 | 45 | 9 | 51 | 36 | 1 | 32 | 22 | 9 | 51 | 29 | 1 | 31 | 55 | -7 | -27 | |||||
| 4 | 17 | 0 | 12 | 1 | 4 | 1 | 56 | 42 | 12 | 0 | 25 | 1 | 56 | 23 | -39 | -19 | |||||
| 7 | 16 | 54 | 17 | 51 | 3 | 2 | 56 | 48 | 17 | 51 | 6 | 2 | 56 | 24 | +3 | -24 | |||||
| 8 | 16 | 53 | 19 | 39 | 45 | 3 | 13 | 7 | 19 | 39 | 33 | 3 | 12 | 28 | -12 | -39 | |||||
| 11 | 16 | 52 | 24 | 47 | 22 | 3 | 48 | 49 | 24 | 47 | 47 | 3 | 49 | 29 | +25 | +40 | |||||
| 17 | 17 | 12 | ♎ | 4 | 38 | 58 | 4 | 15 | 42 | So. | ♎ | 4 | 38 | 36 | 4 | 15 | 2 | So. | -22 | -40 | |
LIII. The Resolution of a General Proposition for Determining the horary Alteration of the Position of the Terrestrial Equator, from the Attraction of the Sun and Moon: With some Remarks on the Solutions given by other Authors to that difficult and important Problem. By Mr. Tho. Simpson, F.R.S.
Read Dec. 22, 1757.
SINCE the time, that that excellent Astronomer, my much honoured friend Dr. Bradley, published his observations and discoveries concerning the inequalities of the precession of the equinox, and of the obliquity of the ecliptic, depending on the position of the lunar nodes, mathematicians, in different parts of Europe, have set themselves diligently to compute, from physical principles, the effects produced by the sun and moon, in the position of the terrestrial equator; and to examine whether these effects do really correspond with the observations.
Two papers on this subject have already appeared in the Philosophical Transactions; in which the authors have shewn evident marks of skill and penetration. There is, nevertheless, one part of the subject, that seems to have been passed over without a due degree of attention, as well by both those gentlemen, as by Sir Isaac Newton himself.
This part, which, upon account of physical difficulties, is indeed somewhat slippery and perplexing, I shall make the principal subject of this essay.
General Proposition.
Supposing an homogeneous sphere OABCD ([Fig. 1.]) revolving uniformly about its centre, to be acted on at the extremity A of the radius OA, in a direction AL perpendicular to the plane of the equator ABCD, and parallel to the axis of rotation Pp, by a given force, tending to generate a new motion of rotation at right angles to the former; It is proposed to determine the change, that will arise in the direction of the rotation in consequence of the said force.