When? What method did he use? How accurate was he?
Here is a site on the speed of sound. According to this author,Mersenne was the first in 1640. There isn’t any data on his accuracy. The speed of sound can be computed quite accurately from the physical properties of the medium.
I would think that thunder and lightening would make it pretty easy if you see a lightening strike hit am object of known distance away. That doesn’t mean that someone did it scientifically but people must have had a rough idea anyway. Guns fired from ships would be another way.
Or even someone chopping wood in the distance, especially in winter when it’s cold.
Obviously you’d have to know the speed of light in order to do it this way if you wanted it to be pretty accurate.
Oh, I dunno. You could assume the speed of light was infinite for any observations up to several miles (i.e. watch someone fire a cannon way in the distance and wait for the sound of the boom). Light only takes 1/60,000th of a second to travel ~3 miles, which is well within the margin of error of any but the most accurate instruments.
Heck, in 1/60,000th of a second, sound (in calm dry air at sea level at 20[sup]o[/sup]) only travels about half a centimeter.
In fact, the speed of light only becomes significant for speed-of-sound experiments that are larger than any practical test. Even at 100 miles (at which the curvature of the Earth gets in the way), light only introduces an error of about 0.0005 seconds.
But I suspect that the “calculation from the properties of the medium” method is a lot more recent than the “time it with a stopwatch” method. (In fact, I wonder if some of the “properties” aren’t determined by the equivalent of stopwatch methods.)
Well, stopwatches are more recent than all of them. 
Robert Boyle worked out a lot of the properties of air, elasticity, density as a function of temperature, pressure, etc. and Newton had done the mathematical determination by 1660.
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Newton did not do his calculations until later. In 1660 he had not even gone up to Cambridge.
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Yes, the light travel time is negligible… But did Mersenne know that?
And didn’t Galileo do some experiments on the subject before Mersenne?
I think everyone assumed the speed of light was either infinite or so great as to make time delays resulting from it insignificant.
I think Galileo tried to measure the speed of light but went about it wrong. Using his telescope had he timed the occultation of Juptier’s moons as did What’s His Name? he could have done it.
And now that I’ve posted I realize you didn’t mean Galileo did the Jovain moon occultation thing. Amazing what we realize 10 seconds after the “Submit Reply” button, isn’t it? Sorry, David Simmons, I already knew you were smarter than that…
It’s exactly like putting in golf. The instant you stroke the ball, but not one microsecond before, you know you haven’t hit it hard enough-or too hard.
According to Isaac Asimov Gallileo set an assistant with a lantern on one hill while he was with a lantern on another hill. He uncovered his lantern and when the aide saw it he uncovered his lantern and Gallileo timed from his uncovering to the reply. Of course, all he timed was reaction times, although the experiment was correct in principle. The fact that he tried it would indicate that he believed the speed of light to be finite. After I typed this whole paragraph I see that your cite tells the same story. It’s catching.
And in my original post substitue Roemer for ** What’s His Name.** I couldn’t come up with it on the spur of the moment and wasn’t about to go look it up.
Interesting that you mention Asimov… That’s where I started, with the essay “The Figure of the Fastest”. I wonder how many of us here owe the start of our interest in the world around us to him.
Probably quite a few. I first encountered Azimov in Astounding Science Fiction when I was a teenager and he wasn’t a lot older than that.