Halley's comet in
1835, yet the period was prolonged. To show, that our theory of the
_cause_ of these anomalies corresponds with facts, we subjoin the
elements in the following tables, taken from Mr. Hind's catalogue:

THE ELEMENTS OF ENCKE'S COMET.

Date of Longitude of Longitude of Difference of
Perihelion. Perihelion. nearest Node Longitude.
1822 157d 11' 44" 154d 25' 9" 2d 46' 35"
1825 157 14 31 154 27 30 2 47 1
1829 157 17 53 154 29 32 2 48 21
1832[42] 157 21 1 154 32 9 2 41 52
1835 157 23 29 154 34 59 2 48 30
1838 157 27 4 154 36 41 2 50 23
1842 157 29 27 154 39 10 2 50 17
1845 157 44 21 154 19 33 3 24 48
1848 157 47 8 154 22 12 3 24 56
1852 157 51 2 154 23 21 3 27 41

In this we see a regular increase of the angle, which ought to be
attended with a small acceleration of the comet; but the change of
inclination of the orbit ought also to be taken into consideration, to
get the mean distance of the comet above the plane of the vortex, and,
by this, the mean force of the radial stream.

In the following table, the same comparison is made for Biela's comet:--

ELEMENTS OF BIELA'S COMET.

Date of Longitude of Longitude of Difference of
Perihelion. Perihelion. nearest Node. Longitude.
1772 110d 14' 54" 74d 0' 1" 36d 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
10d above the ecliptic, whereas the angle made by Encke's major axis, is
only about 1d; 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 elem