WHY EUROPE? WHY THEN? 211Masters of Precision
All studies of change and rates of change have to measure elapsed
time. To do this, one needs a standard unit of measure and an
instrument to count the units; we call that a clock. In the absence of
a clock, one can substitute approximate equivalents. The seamen of
the fifteenth and sixteenth centuries who wanted to count the time it
took for a float to go from bow to stern by way of estimating the
speed of the vessel, might use a sandglass; but if they did not have
one, they could always recite Hail Mary's or some other
conventional refrain; and today any practiced photographer knows
that one can count seconds by reciting four-syllable expressions: one
one thousand, two one thousand, three one thousand...
Needless to say, such idiosyncratic improvisations will hardly do
for scientific purposes. For these one needed a good clock, but it
took four centuries to make one. Still, scientists are ingenious
people, and they found ways to enhance the precision of their pre-
pendulum, pre-balance spring timepieces. One way was to use clocks
with very large wheels with hundreds and even a thousand or more
teeth. Tycho Brahe did this, and instead of reading the single hour
hand of his clock (these early machines were not accurate enough to
warrant the use of minute hands), he counted the number of teeth
the wheel had turned and got much closer to the exact time elapsed.
He did so to track star movements and locate these bodies on
celestial maps (time was one of the two coordinates). Galileo needed
even closer measurements for his studies of acceleration. Ever
ingenious, he used small, hand-held water clocks rather than
mechanical clocks, opening and closing the outflow hole with his
finger at the start and end of the run. He then weighed the water
released as a measure of time elapsed, for in those days, the balance
scale was the most precise measuring instrument known.
The invention of the pendulum clock changed everything. This
was the first horological device controlled by an oscillator with its
own intrinsic frequency. Earlier clocks used a controller (swinging
bar or circle) whose frequency varied with the force applied. After
improvements (all inventions need improvements), a good
pendulum clock kept time to a few seconds per day. Watches were