In the following table, the same comparison is made for Biela's comet:--
Date of Longitude of Longitude of Difference of Perihelion. Perihelion. nearest Node. Longitude. 1772 110° 14' 54" 74° 0' 1" 36° 14' 53" 1806 109 32 23 71 15 15 38 17 8 1826 109 45 50 71 28 12 38 17 38[43] 1832 110 55 55 68 15 36 41 45 19 1846 109 2 20 65 54 39 43 7 41
Between 1832 and 1846, the increase of the angle is twice as great for Biela as for Encke, and the angle itself throws the major axis of Biela 10° above the ecliptic, whereas the angle made by Encke's major axis, is only about 1°; the cosine of the first angle, diminishes much faster therefore, and consequently the same difference of longitude between the perihelion and node, will cause a greater acceleration of Biela; and according to Prof. Encke's theory, Biela would require a resisting medium twenty-five times greater than the comet of Encke to reconcile observation with the theory. Halley's comet can scarcely be considered to have had an orbit with perfect elements before 1835. If they were known accurately for 1759, we should no doubt find, that the angle between the node and perihelion _diminished_ in the interval between 1750 and 1835, as according to the calculations of M. Rosenberg, the comet was six days behind its time--a fact fatal to the common ideas of a resisting medium; but this amount of error must be received as only approximate.
No comet that has revisited the sun, has given astronomers more trouble than the great comet of 1843. Various orbits have been tried, elliptical, parabolic and hyperbolic; yet none will accord with all the observations. The day before this comet was seen in Europe and the United States, it was seen close to the body of the sun at Conception, in South America; yet this observation, combined with those following, would give an orbital velocity due to a very moderate mean distance. Subsequent observations best accorded with a hyperbolic orbit; and it was in view of this anomaly, that the late Sears C. Walker considered that the comet came into collision with the sun in an elliptical orbit, and its _debris_ passed off again in a hyperbola. That a concussion would not add to its velocity is certain, and the departure in a hyperbolic orbit would be contrary to the law of gravitation. This principle is thus stated by Newton:--"In parabola velocitas ubiquo equalis est velocitati corporis revolventis in circulo ad dimidiam distantiam; in ellipsi minor est in hyperbola major." (Vid. Prin. Lib. 1. Prop. 6 Cor. 7.)