n distance, and another
for the tangential current; but we are only considering here the general
effect. By diminishing the comet's proper velocity in its orbit, if we
consider the attraction of the sun to remain the same, the general
effect _may_ be (for this depends on the tangential portion of the
resolved force preponderating) that the absolute velocity will be
increased, and the periodic time shortened; but after passing the
perihelion, with the velocity of a smaller orbit, there is also
superadded to this already undue velocity, the expulsive power of the
radial stream, adding additional velocity to the comet; the orbit is
therefore enlarged, and the periodic time increased. Hence the necessity
of changing the "Constant of Resistance" after perihelion, and this will
generally be found necessary in all cometary orbits, if this theory be
true. But this question is one which may be emphatically called the most
difficult of dynamical problems, and it may be long before it is fully
understood.

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 90d, 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