Page 31 - January 2009

[a Newton, The Mathematical Principles of Natural Philosophy (Principia), Book II (Of the motion of bodies), Section VIII (Of motion propagated through fluids), Proposition 50. Derham would have had the first edition published in 1687. There were two subsequent edi- tions (1713, 1726). The third edition gives two values for sound speed: 979 ft/s and 1142 ft/s. In the first edition and for the lower value in the third edition, Newton based his calculation on the static compressibility of air and its density; the higher value in the third edition was based on an imaginative and specious correction for the (then unknown) size of air molecules. The higher value was an attempt to reconcile theory with the overwhelming experimental evidence for a speed considerably higher than 968 ft/s. Another century passed before the calculation was done correctly (by Laplace).
b Francis Roberts, “Concerning the distance of the fixed stars,” Phil. Trans. 17, 101–103, 1694.
c Robert Boyle, An Essay of the Great Effects of Even Languid and Unheeded Motion, London, 1685, p. 24.
d Walker, “Some experiments and observations concerning sounds,” Phil. Trans. 20, 433-438, 1698. Well worth reading to illustrate the
nature of the pendulum timing devices but also contains an excellent description of two variations of the echo method for determining sound speed. In the simpler echo method, the observer adjusts his position with respect to a flat wall until the echo from a clap (Walker used two small boards) returned just as the pendulum completed a swing. A refinement consisted of repeated clapping – clapping each time an echo was heard – and dividing the total time by the number of claps to get the single round-trip time. A further refinement of the repeated echo technique was developed later: rather than trying to react instantly to a received echo, if the claps are interspersed even- ly with the echoes, the achieved timing precision is much greater. Perception of rhythm is much more accurate than instantaneous reac- tion to an event.
e M. Mersenne, Cogitata Physico-Mathematica, Paris, 1644, Ballistica, proposition XXXIX, p. 138.
f Essayes of Natural Experiments, Accademi del Cimento, 1634, translated by Richard Waller, FRS, 1667, pp. 140-142.]
considered in connection with the slowness of our senses, and of our perception or attention, may produce a great error, as is well known to those who have made experiments con- cerning these matters. This is especially the case if
B. The interval between the sounding body and the observer may have been small. It is manifest, however, that the most of these distinguished men made their experiments at the distance of only a few feet, and made their measure- ments by the return, or echo of the sound. For some of these observers scarcely extended their measurement beyond six or seven hundred feet, and others not beyond a mile. But I have always observed that an ambiguity arises in a distance so small, though the best apparatus may be used. Because the slightest error in distances so very small is to be consid- ered comparatively great for the pendulum, perhaps has passed through the half of its sweep or arc, from the last vibration when the sound may have been first emitted; but we count that beat as if it had been a full and complete vibra- tion; or perhaps we may anticipate the vibration. And after the sound reaches us, we may perhaps count more or less than is right.
Or, if the distance shall have been long enough, still an error may arise from that very circumstance, if
C. Account is not taken of winds—about which more hereafter. These are the certain, inevitable and perpetual inconveniences which accompany the measurement of the
progress of sounds – inconveniences which in small intervals, as I have said, especially if the instruments be bad, are able to produce great errors; and without doubt they have been the greatest cause of the disagreement among authors so eminent. But one can see how very near is the agreement among the dis- tances assigned by the last three observers in our table—a fact which doubtless arises from the circumstance that they were furnished with good automatic instruments, in the use of which the ear is simply occupied with catching the vibrations of the pendulum, while the eye marks the flash or some other indication of the sound. These observations, besides, were made at long distances, in which a petty error will not be of great account. For the observations of the very celebrated Messrs. Flamsteed and Halley were made at a distance of almost three miles, (a few perches [The perch is a surveyor’s rod 16 1⁄2 feet in length.] more or less being excepted), from the Royal Observatory on Shooter’s Hill, and the sound came to them in 13 1⁄2 seconds. The gentlemen of Florence, who were also celebrated members of the Accademie del Cimento, made their experiments at about the same distances and some exper- iments at the distance of only a mile. And finally, the very cel- ebrated Messrs Cassini, Picard, and Roemer made their exper- iments at a distance of 1280 French toises, which is more than one English mile and a half.
That the truth might be brought to light in the midst of the aforesaid disagreements, I have made very many exper-
30 Acoustics Today, January 2009