e mind, which finds
something altogether mystifying about abstract mathematics, this was a
feat savoring of the miraculous.

Stimulated by this success, Leverrier calculated an orbit for an
interior planet from perturbations of Mercury, but though prematurely
christened Vulcan, this hypothetical nursling of the sun still haunts
the realm of the undiscovered, along with certain equally hypothetical
trans-Neptunian planets whose existence has been suggested by "residual
perturbations" of Uranus, and by the movements of comets. No other
veritable additions of the sun's planetary family have been made in our
century, beyond the finding of seven small moons, which chiefly attest
the advance in telescopic powers. Of these, the tiny attendants of our
Martian neighbor, discovered by Professor Hall with the great Washington
refractor, are of greatest interest, because of their small size and
extremely rapid flight. One of them is poised only six thousand
miles from Mars, and whirls about him almost four times as fast as he
revolves, seeming thus, as viewed by the Martian, to rise in the west
and set in the east, and making the month only one-fourth as long as the
day.

The Rings of Saturn

The discovery of the inner or crape ring of Saturn, made simultaneously
in 1850 by William C. Bond, at the Harvard observatory, in America,
and the Rev. W. R. Dawes in England, was another interesting optical
achievement; but our most important advances in knowledge of Saturn's
unique system are due to the mathematician. Laplace, like his
predecessors, supposed these rings to be solid, and explained their
stability as due to certain irregularities of contour which Herschel
bad pointed out. But about 1851 Professor Peirce, of Harvard, showed
the untenability of this conclusion, proving that were the rings such as
Laplace thought them they must fall of their own weight. Then Professor
J. Clerk-Maxwell, of Cambridge, took the matter in hand, and his
analysis reduced the puzzling rings to a cloud of meteoric particles--a
"shower of brickbats"--each fragment of which circulates exactly as if
it were an independent planet, though of course perturbed and jostled
more or less by its fellows. Mutual perturbations, and the disturbing
pulls of Saturn's orthodox satellites, as investigated by Maxwell,
explain nearly all the phenomena of the rings in a manner highly
satisfactory.

After elaborate mathematical calculations covering many pages of his