of a hanging lamp. Trifles are full of meaning to them,
because their minds are already prepared to arrive at certain
conclusions by means of antecedent reflections. Simple and familiar
incidents, thus accidentally associated with the history of grand
discoveries, are the channels through which the accumulating waters at
length descend, rather than the rills which feed the swelling of their
floods. The orchard at Woolsthorpe, and the cathedral at Pisa, were
outlets of this kind, through which the pent-up tide of gathering
knowledge burst. If they had never offered themselves, the laws of
universal gravitation and isochronous vibration would still have
reached the world.

If the reader will hang up two equal weights upon nearly the same
point of suspension, and by means of two strings of exactly the same
length, he will have an apparatus at his command that will enable him
to see, under even more favourable conditions, what Galileo saw in the
cathedral at Pisa. Upon drawing one of them aside one foot from the
position of rest, and the other one yard, and then starting them off
both together to vibrate backwards and forwards, he will observe, that
although the second has a journey of two yards to accomplish, while
the first has but a journey of two feet, the two will, nevertheless,
come to the end at precisely the same instant. As the weights swing
from side to side in successive oscillations, they will always present
themselves together at the point which is the middle of their
respective arcs. This is what is called isochronous vibration--the
passing through unequal arcs in equal periods of time.

At the first glance, this seems a very singular result. The careless
observer naturally expects that a weight hung upon a string ought to
take longer to move through a long arc than through a short one, if
impelled by the same force; but the subject appears in a different
light upon more mature reflection, for it is then seen, that the
weight which performs the longer journey starts down the steeper
declivity, and therefore acquires a greater velocity. A ball does not
run down a steep hill and a more gently inclined one at the same pace;
neither, therefore, will the suspended weight move down the steeper
curve, and the less raised one, at equal rates. The weight which moves
the fastest, of necessity gets through more space in a given period
than its more leisurely companion does. The equality of the periods in
which two weig