h the revolution of the
planet Uranus around the sun. Taking the earth's distance as unity, the
radius of the orbit of Uranus is about nineteen, and Uranus takes
eighty-four years to accomplish a complete revolution. We have no planet
in the solar system at a distance of twenty-one; but from Kepler's third
law it may be shown that, if there were such a planet, its periodic time
would be about ninety-nine years. We have now the necessary materials
for making the comparison between the mass of Sirius and the mass of
the sun. A body revolving around Sirius at a certain distance completes
its journey in fifty-two years. To revolve around the sun at the same
distance a body should complete its journey in ninety-nine years. The
quicker the body is moving the greater must be the centrifugal force,
and the greater must be the attractive power of the central body. It can
be shown from the principles of dynamics that the attractive power is
inversely proportional to the square of the periodic time. Hence, then,
the attractive power of Sirius must bear to the attractive power of the
sun the proportion which the square of ninety-nine has to the square of
fifty-two. As the distances are in each case supposed to be equal, the
attractive powers will be proportional to the masses, and hence we
conclude that the mass of Sirius, together with that of his companion,
is to the mass of the sun, together with that of his planet, in the
ratio of three and a half to one. We had already learned that Sirius was
much brighter than the sun; now we have learned that it is also much
more massive.

Before we leave the consideration of Sirius, there is one additional
point of very great interest which it is necessary to consider. There is
a remarkable contrast between the brilliancy of Sirius and his
companion. Sirius is a star far transcending all other stars of the
first magnitude, while his companion is extremely faint. Even if it were
completely withdrawn from the dazzling proximity of Sirius, the
companion would be only a small star of the eighth or ninth magnitude,
far below the limits of visibility to the unaided eye. To put the matter
in numerical language, Sirius is 5,000 times as bright as its companion,
but only about twice as heavy! Here is a very great contrast; and this
point will appear even more forcible if we contrast the companion of
Sirius with our sun. The companion is slightly heavier than our sun; but
in spite of its slightly inf