According to the calculations of Professor Encke, the comet's period is accelerated about 2 hours, 30 minutes, at each return, which he considers due to a resisting medium. May it not rather be owing to _the change of inclination of the major axis of the orbit, to the central plane of the vortex_? Suppose the inclination of the _plane_ of the orbit to remain unchanged, and the eccentricity of the orbit also, if the longitude of the perihelion coincides with that of either node, the major axis of the orbit lies in the ecliptic, and the comet then experiences the greatest mean effect from the radial stream; its mean distance is then, _ceteris paribus_, the greatest. When the angle between the perihelion and the nearest node increases, the mean force of the radial stream is diminished, and the mean distance is diminished also. When the angle is 90°, the effect is least, and the mean distance least. This is supposing the ecliptic the central plane of the vortex. When Encke's formula was applied to Biela's comet, it was inadequate to account for a tenth part of the acceleration; and although Biela moves in a much denser medium, and is of less dense materials, even this taken into account will not satisfy the observations,--making no other change in Encke's formula. We must therefore attribute it to changes in the elements of the orbits of these comets. Now, the effect of resistance should also have been noticed, as an acceleration of 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:
Date of Longitude of Longitude of Difference of Perihelion. Perihelion. nearest Node Longitude. 1822 157° 11' 44" 154° 25' 9" 2° 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.