Note 227, [p. 360]. In fig. 74 the hyperbola H P Y, the parabola p P R, and the ellipse A E P L, have the focal distance S P, and coincide through a small space on each side of the perihelion P; and, as a comet is only visible when near P, it is difficult to ascertain which of the three curves it moves in.

Fig. 74.

Note 228, [p. 363]. In fig. 75, E A represents the orbit of Halley’s comet, E T the orbit of the earth, and S the sun. The proportions are very nearly exact.

Fig. 75.

Note 229, [p. 382]. Fig. 74 represents the curves in question. It is evident that, for the same focal distance S P, there can be but one circle and one parabola p P R, but that there may be an infinity of ellipses between the circle and the parabola, and an infinity of hyperbolas H P Y exterior to the parabola p P R.

Note 230, [p. 387]. Let A B, fig. 26, be the diameter of the earth’s orbit, and suppose a star to be seen in the direction A Sʹ from the earth when at A. Six months afterwards, the earth, having moved through half of its orbit, would arrive at B, and then the star would appear in the direction B Sʹ, if the diameter A B, as seen from Sʹ, had any sensible magnitude. But A B, which is 190,000,000 of miles, does not appear to be greater than the thickness of a spider’s thread, as seen from 61 Cygni, supposed to be the nearest of the fixed stars.

Note 231, [p. 389]. Stars whose parallax and proper motions are known.

Name of Star.Proper Motion.Parallax.Observers and Computers.
α Centauri3ʺ·7640ʺ·92Maclear.
„..1ʺHenderson.
61 Cygni5ʺ·1230ʺ·374Bessel.
α Lyræ0ʺ·3640ʺ·207Peters.
Sirius1ʺ·2340ʺ·230Henderson.
Arcturus2ʺ·2690ʺ·127Peters.
Pole Star0ʺ·0350ʺ·106Peters.
Capella..0ʺ·046Peters.
La Chevre0ʺ·4610ʺ·046Peters.
ι Great Bear0ʺ·7460ʺ·133Peters.