Page:Newton's Principia (1846).djvu/483

 equal to ⅓ of γδ, or a little less, as perhaps $5/16$ of γδ; and a perpendicular let fall from the star δ on the right line γY was equal to about $1/6$ or $1/7$ γδ. But the comet being then extremely near the horizon, was scarcely discernible, and therefore its place could not be determined with that certainty as in the foregoing observations.

Prom these observations, by constructions of figures and calculations, I deduced the longitudes and latitudes of the comet; and Mr. Pound, by correcting the places of the fixed stars, hath determined more correctly the places of the comet, which correct places are set down above. Though my micrometer was none of the best, yet the errors in longitude and latitude (as derived from my observations) scarcely exceed one minute. The comet (according to my observations), about the end of its motion, began to decline sensibly towards the north, from the parallel which it described about the end of February.

Now, in order to determine the orbit of the comet out of the observations above described, I selected those three which Flamsted made, Dec. 21, Jan. 5, and Jan. 25; from which I found St of 9842,1 parts, and Vt of 455, such as the semi-diameter of the orbis magnus contains 10000. Then for the first observation, assuming tB of 5657 of those parts, I found SB 9747, BE for the first time 412, Sμ 9503, iλ 413, BE for the second time 421, OD 10186, X 8528,4, PM 8450, MN 8475, NP 25; from whence, by the second operation, I collected the distance tb 5640; and by this operation I at last deduced the distances TX 4775 and τZ 11322. From which, limiting the orbit, I found its descending node in ♋, and ascending node in ♑ 1° 53′; the inclination of its plane to the plane of the ecliptic 61° 20⅓′, the vertex thereof (or the perihelion of the comet) distant from the node 8° 38′, and in ♐ 27° 43′, with latitude 7° 34′ south; its latus rectum 236,8; and the diurnal area described by a radius drawn to the sun 93585, supposing the square of the semi-diameter of the orbis magnus 100000000; that the comet in this orbit moved directly according to the order of the signs, and on Dec. 8d.00h.04′ P. M was in the vertex or perihelion of its orbit. All which I determined by scale and compass, and the chords of angles, taken from the table of natural sines, in a pretty large figure, in which, to wit, the radius of the orbis magnus (consisting of 10000 parts) was equal to 16⅓ inches of an English foot.

Lastly, in order to discover whether the comet did truly move in the orbit so determined, I investigated its places in this orbit partly by arithmetical operations, and partly by scale and compass, to the times of some of the observations, as may be seen in the following table:—