Page 20 - January 2009

other members of the Royal Society—including Derham— would have looked for it.]
Measurement of the speed of sound
How was sound speed measured at the turn of the 18th Century? Often by the obvious method of observing both the flash of a gun or cannon and the subsequent report. Timing was accomplished by observing the oscillations of a simple pendulum. The natural decay of the pendulum amplitude limited the usable propagation time.
Derham opens his paper on sound with an analysis of the work of previous investigators. When confronted with the wide range of values for sound speed presented by others, he isolates two critical issues: (1) the difficulty of watching the oscillations of a simple pendulum while at the same time watching for the flash of the gun to start the timing, and (2) the uncertainty inherent in using a short distance from gun to observer for a speed measurement.
Derham understood that using a clockwork pendulum would yield better results than a simple pendulum for two reasons: each half-cycle produces an audible “tick” so the observer can concentrate on watching for the flash of the gun; and the oscillations do not decay so longer measure- ment times and distances can be used. With his background in clock mechanics, Derham equips himself with a state-of- the-art pendulum clock that he himself tuned. Realizing that the error associated with a short baseline contributed to the wide variation in sound speed values in the past, Derham made the measurements over as long a distance as he could.
The location and elevation of his church tower at Upminster allowed a clear line of sight to the artillery training ground at Blackheath 12.5 miles distant and Blackheath provided a ready source of cannon discharge.
But there were other clever methods of sound-speed measurement. Joshua Walker (1698) gives fascinating insight into echo methods:
“...and standing over against a high Wall I clapt Two small pieces of Boards together, and observed how long it was e’re the Echo returned, and I removed my Station till I found the Place whither the Echo return’d in about half a Second. But that I might distinguish the time more nicely, I clapt every Second of Time Ten or Fifteen times together; so that by this Means I could the better discov- er whether the Distances betwixt the Claps and the Echoes, and the following Claps were Equal. And though it be very difficult to be exact, yet I could come within some few Yards of the Place I sought for, thus: I observed the Two Places where I could but just discover that I was too near, and where I was too far off...”
In Walker’s account, clapping pieces of wood together gave a sharp sound with a distinct echo. By adjusting the distance to a wall, the experimenter can find a point of coincidence between the clap-and-echo time and the period of a simple pendulum. Rather than timing the echo over an arbitrary distance, the dif- ference between the echo-return time and the pendulum oscil- lation time is adjusted to be as close to zero as possible.
Derham’s De Motu Soni 19