Primary Sources for Measurement of g

[brainpushups]

I have read, and seen it claimed in another old thread, that Galileo was the first to measure the free fall acceleration near Earth's surface. I have not found any source that explains how he did so or what his result was. I've skimmed through most of his Discorsi and have not seen it there. In K. Simonyi's A Cultural History of Physics the author claims that Galileo's measurement was 5m/s², but does not give the explicit source for this (only saying that "in his single surviving note, the numerical value for the terrestrial acceleration is quite far (5m/s²) from the correct value, which is difficult to reconcile with his painstaking process of measurement."

Does anybody know what 'note' that might be or know of any other resource that gives more information? If it is somewhere in the Discorsi and I have overlooked it would you please direct me to the page number?

 

[BiGyElLoWhAt]

Read 'The 10 most Beautiful Experiments' by George Johnson.

In that book, he doesn't give his numerical measurement, but goes into detail about how he discovered that g was inversely proportional to s^2. It was quite neat. If what you're after is the number details, this book doesn't have it. It is a great book, however.

The initial experiment they describe is essentially a ball on a ramp, with bells on sliders that could be moved around freely and locked into place. He then moved the bells around so that they sounded evenly as the ball hit them. This gave him an even time interval to work with. I believe, however, that there is doubt about his measurement process, as they provided (to my recollection) an alternative method that he may have used, which consisted of a continuous stream of water that poured into a cup, then by weighing the water, he would have known how much time had passed.

 

[brainpushups]

Thanks for the reply. I'm not after the details of the experiment. I have several sources (including the primary source, Galileo's Discourse and Mathematical Consideration of Two New Sciences) that describe them. His methods and arguments for determining that free fall motion is uniformly accelerated is well documented. I want to know if he actually measured g as is claimed Simonyi's book (and other sources) or if this was actually done later.

 

[BiGyElLoWhAt]

Ahh, I'm not familiar with that, sorry. I would assume that he did, but you know what happens when you assume...

 

[brainpushups]

Indeed. I think most of us make that assumption, and I'm suspicious.

There is no doubt that he could have calculated g based on his experiments with incline because he correctly worked out how the time it takes a ball to roll down an incline is related to its vertical height. Of course, his result would have been off by 5/7 due to the rotational kinetic energy of the sphere meaning that he could have gotten a result around 7m/s². But, as I said above, Simonyi claims he measured it to be 5m/s² (and only mentions this vague 'note' where it came from) and also speculates that Galileo was not so much concerned with the numerical value (which is entirely plausible).

Furthermore, if Galileo was using a water clock to make the time measurement he would have had to calibrate it to a time standard and I'm not sure how that would have been done accurately seeing as there were no mechanical clocks (though Galileo did write about the isochronism of the pendulum, he apparently did not use it to keep time).

I'm starting to think that g wasn't measured until later. If I find a reliable source I'll update the thread.

 

[SteamKing]

This article cites a reference for Galileo's reported measurement of g:

http://www.scientus.org/Galileo-Predecessors.html#ref1

When converted into modern units, Galileo's measurement of g was 467 cm/s².

Other scientists before and during Galileo's time performed free-fall experiments. There is even one experiment reportedly performed by Jesuits using a pendulum swinging from a tower in Italy (not the Leaning Tower of Pisa, though) The Jesuit experiment reportedly yielded a much more accurate figure for g (914 cm/s²) than did Galileo's own experiment.

 

[brainpushups]

This article cites a reference for Galileo's reported measurement of g:

Good find. Having two sources claiming Galileo calculated g at about half its accepted value is reassuring. Though I'm still interested in how he did it.

From page 82 of Holton and Brush's text, Physics, the Human Adventure - "The distinguished French philosopher-historian Alexandre Koyre, surveying Galileo's published works suggested that he was really a Platonist rather than an experimental physicist and that the results of several of his thought experiments did not agree with the actual behavior of objects in the physical world. The American historian of science Stillman Drake, on the basis of close scrutiny of Galileo's unpublished manuscripts, concluded that Galileo actually did do experiments even though he didn't publish his numerical results."

I guess that explains why I wasn't finding anything in the Discorsi! Perhaps the calculations appear in Galileo's 'folios,' many of which can be found here at the Max Planck Institute for the History of Science. And perhaps Drake has written about the details, but I don't have access to a library where I can access academic journals so I can't delve into those.

I remembered seeing an article in Physics Today some years ago about Riccioli and I looked it up. He is often credited with the first accurate measurement of g (within 5% by dropping objects, and better than this later with a pendulum). The article is by Christopher Garney and titled Anatomy of a fall: Giovanni Battista Riccioli and the story of g:
Physics Today 65(9), 36 (2012); doi: 10.1063/PT.3.1716

I think I'll share Riccioli's story with my students when we cover free fall next year.