On Sep 12, 2011, at 10:59 AM, Stephen A. Lawrence wrote:
On 11-08-25 10:33 AM, Abd ul-Rahman Lomax wrote:
At 06:55 PM 8/24/2011, Jed Rothwell wrote:
Here is an interesting footnote to history. I believe the speed
of sound was not established with this much precision until
later. This was done by assuming for simplicity that the speed of
light is close to infinite over short distances, and firing a
cannon. The time delay from the flash to the sound of the
explosion gave the speed of sound. This was done in 1826 at Lake
Geneva to establish a value to within 1% of the modern figure. I
don't know how they recorded it. I guess by pressing buttons to
start and stop a timer. You would think this would mainly record
human reaction time but I suppose it depends on how far away the
cannon was.
The reaction time would affect both start and stop timing,
probably about equally. Only if the interval were short such that
variation in reaction time would be a major chunk of it would
reaction time be a serious problem.
Since the human reaction time is added to the clock reading at both
ends, and you're taking the difference, the error it introduces
should be essentially random, due to variation in the reaction
time. And in that case, you can just repeat the test a dozen times
and average the results. Noise which is largely random will tend
to cancel out, leaving you with something very close to the true
"noise-free" result. (That assumes, of course, that the same
person notes both the bang and the flash -- if two different people
record the two events, using two different nervous systems, you've
introduced a possible source of systematic error!)
Errors in reading a sweep hand should also be random, and hence
should also cancel out when averaged over many trials.
And after that, the biggest source of error may be the accuracy of
the clock itself. Clock technology was driven by the need for
accurate navigation, and was pretty good pretty early. So it seems
reasonable they could have gotten a very good result with that
technique.
The main problem for anyone trying to precisely replicate the
result, of course, will be the limited availability of really good
cannons. (Maybe try Ebay...)
Visible paths over Lake Geneva can be very long, especially if the
observer is on a hill or mountainside, and a telescope is used. For
example, the path between Nyon and Montreux is about 48.6 kM. Using
340 m/s as an estimated speed of sound, the delay is about 143
seconds. A 1% error thus represents 1.43 seconds. Variations due to
humidity and temperature would be large compared to human reaction
time error.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
