ke a note more than 10 or 12 times in a second. It is only
in case of recurring phenomena that we can make personal observations
more accurate than this by taking the mean of a large number of
observations, and allowing for personal error. For the purpose of
determining longitude at sea accuracy to 1/30 of a second of time would
find the place to about 20 yards. It seems to follow that the extent to
which astronomical clocks can be made accurate, viz. to 1/30 of a second
average variation from their mean daily rate, or one two-and-a-half
millionth of 24 hours, is a degree of accuracy sufficient for present
purposes, and it seems rather doubtful whether mechanical science will
in the case of clocks be likely to reach a much higher figure.

In the 17th century it was a favourite device to make a clock show
sidereal time as well as mean solar time. The length of the sidereal day
is to the mean solar day as .99727 to 1, and various attempts have been
made by trains of wheels to obtain this relation--but all are somewhat
complicated.

_Magical clocks_ are of several kinds. One that was in vogue about 1880
had a bronze figure on the top with outstretched arm holding in its hand
the upper part of the spring of a pendulum, about 10 in. long. The
pendulum had apparently no escapement and the puzzle was how it was
maintained in motion. It was impossible to detect the mystery by the aid
of the eye alone; the truth, however, was that the whole figure swung to
and fro at each oscillation of the pendulum, to an amount of 1/400 of an
inch on the outside rim of the base. A movement of 1/400 of an inch per
half second of time is imperceptible; it would be equivalent to
perception of motion of the minute hand of a clock about 6 in. in
diameter, which is almost impossible. The connexion of the figure to the
anchor of the escapement was very complicated, but clocks of the kind
kept fair time. A straw, poised near the end on a needle and with the
short end united by a thread to the bronze figure, makes the motion
apparent at once and discloses the trick. Another magical clock consists
of two disks of thin sheet glass mounted one close behind the other, one
carrying the minute hand and the other the hour hand. The disks rest on
rollers which rotate and turn them round. The front and back of the
movable disks are covered by other disks of glass surrounded by a frame,
so that the whole looks simply like a single sheet of glass mounted in a
fr