if it could be
admitted that the exterior envelope of the nebulosity were not permeable
to the ether; but this difficulty seems insurmountable, and merits our
sincere regret; for M. Valz's ingenious hypothesis has laid down the law
of variation of the bulk of the nebulosity, as well for the short-period
comet as for that of 1618, with a truly wonderful exactness." Now, if we
make the calculation, we shall find that the diameter of the nebulosity
of a comet is inversely as the force of the radial stream. This force is
inversely as the 2.5 power of the distances from the axis, and not from
the sun: it will, therefore, be in the inverse ratio of the cosine of
the comet's heliocentric latitude to radius, and to this ratio the
comet's distance ought to be reduced. But, this will only be correct for
the same plane or for equal distances above the ecliptic plane,
considering this last as approximately the central plane of the vortex.
From the principles already advanced, the radial stream is far more
powerful on the central plane than in more remote planes; therefore, if
a comet, by increase of latitude, approaches near the axis, thus
receiving a larger amount of force from the radial stream in that plane
than pertains to its actual distance from the sun, it will also receive
a less amount of force in that plane than it would in the central plane
at the same distance from the axis. Now, we do not know the difference
of force at different elevations above the central plane of the vortex;
but as the two differences due to elevation are contrary in their
effects and tend to neutralize each other, we shall make the calculation
as if the distances were truly reckoned from the centre of the sun.

The following table is extracted from Arago's tract on Comets, and
represents the variations of the diameter of Encke's comet at different
distances from the sun,--the radius of the orbis magnus being taken as
unity.

Times of observation, Distances of the Real diameters
1828. comet from the sun. in radii of the earth.
Oct. 28 1.4617 79.4
Nov. 7 1.3217 64.8
Nov. 30 0.9668 29.8
Dec. 7 0.8473 19.9
Dec. 14 0.7285 11.3
Dec. 24 0.6419 3.1

In order the better to compare the diameters w