to grow larger,
until at length they had presented the appearance of two pairs of mighty
arms encompassing the planet. If Galileo had reasoned upon these changes
of appearance, he could not have failed, as it seems to me, to interpret
their true meaning. The three forms under which the rings had been seen
by him sufficed to indicate the true shape of the appendage. Because
Saturn was seen with two attendants of apparently equal size and always
equi-distant from him, it was certain that there must be some appendage
surrounding him, and extending to that distance from his globe. Because
this appendage disappeared, it was certain that it must be thin and
flat. Because it appeared at another time with a dark space between the
arms and the planet, it was certain that the appendage is separated by a
wide gap from the body of the planet. So that Galileo might have
concluded--not doubtfully, but with assured confidence--that the
appendage is a thin flat ring nowhere attached to the planet, or, as
Huyghens said some forty years later, Saturn '_annulo cingitur tenui,
plano, nusquam cohaerente_.' Whether such reasoning would have been
accepted by the contemporaries of Galileo may be doubtful. The
generality of men are not content with reasoning which is logically
sound, but require evidence which they can easily understand. Very
likely Huyghens' proof from direct observation, though in reality not a
whit more complete and far rougher, would have been regarded as the
first true proof of the existence of Saturn's ring, just as Sir W.
Herschel's observation of one star actually moving round another was
regarded as the first true proof of the physical association of certain
stars, a fact which Michell had proved as completely and far more neatly
half a century earlier, by a method, however, which was 'caviare to the
general.'

However, as matters chanced, the scientific world was not called upon to
decide between the merits of a discovery made by direct observation and
one effected by means of abstract reasoning. It was not until Saturn had
been examined with much higher telescopic power than Galileo could
employ, that the appendage which had so perplexed the Florentine
astronomer was seen to be a thin flat ring, nowhere touching the planet,
and considerably inclined to the plane in which Saturn travels. We
cannot wonder that the discovery was regarded as a most interesting one.
Astronomers had heretofore had to deal with solid masses