Galileo, redux

In the latter half of the 20th century, historians of science questioned whether, in fact, Galileo had carried out the experiments he cited as evidence for his theories of falling bodies.
This perhaps healthy skepticism was put to rest with the discovery of "a manuscript page obviously containing experimentat data."

Galileo's own description suggests that he used both his pulse and a clepsydra (water-clock) to measure time:

"... We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse-beat...
...
"For the measurement of time, we employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water which we collected in a small glass during the dime of each descent, wheter for the whole length of the channel or for part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results."

That seems to settle the matter: Galileo used a water-clock.

But wait! Modern attempts to replicate Galileo's results have been unsuccessful - the accuracy he asserts cannot be replicated. Now - it could be that the moderns are less adept at experiment than was Galileo. This is not altogether improbable - as noted previously, Galileo is the experimental physicist par excellence.
[For what it's worth: Galileo mentions repeating his experiments "a full hundred times". If he averaged the results of these hundred trials, his asserted accuracy could easily have been attained. Indeed - as a professional statistician, I rather like this explanation. Galileo himself, however, makes no mention of averaging, and seems to suggest that each individual reading met his standard for reliabilty/accuracy.]

Nevertheless, a second, plausible method for determining the inverses of the required time ratios has been proposed (... by these same moderns who failed to reproduce Galileo's water-clock accuracy!). That is, a method whereby only distances need be measured directly, the time intervals being held constant.

I happen to find the alternative plausible.

Think: train on track, or car on segmented pavement - click-clack, click-clack... if traveling at constant velocity, the click-clack providing a constant beat.

Suppose that moveable 'frets' could be introduced into Galileo's inclined plane - such frets sufficiently small as to not significantly impede the descent of the marble... say, thin threads strung across the track. By adjusting these frets so that, to the human ear, the resulting click-clacks were equally spaced in time, Galileo could easily measure the distances between successive click/clacks to arrive at his laws of falling bodies - essentially holding time constant.

The moderns used this technique to achieve Galileo's stated accuracy. They further note that Galileo, coming from a family of musicians, "may have used rhythms in order to measure very short time intervals."

For a much fuller discussion (with photos, footnotes, and all that jazz), see Reconstructing Galileo’s Inclined Plane Experiments for
Teaching Purposes.

Me - I like the rhythm method!