mission length of 394-55 met. [431-184 yds]. At this distance the length of 451 yards. time of transmission through air would be 1158" by calculation, supposing the temperature still 11° [51.8° F.]. The interval between the two sounds, deduced from 64 Interval. experiments, was found to be 0-81". The differenee Time of transtherefore, or 0.348", was the time of transmission through through the the solid. This appears much too great, if we com- solid. pare it with the preceding experiments, and on those This apparent ly much too that follow, which were made on nearly triple the length. great. The latter would not permit us to suppose a longer time than 0.125" for the transmission through the solid, which would give an errour of 0.223" in the observation. But, beside that it is extremely difficult to answer for such quantities, when the instaut of observation does not coincide exactly with a beat of the watch, it must be remarked, that the whole length of the pipe might be far from being at the same temperature, which might occasion currents of air, that would influence the velocity of the sound. For instance, in the present case, if we were to admit the transmission of sound through air as it results from the observations of the chronometer made by Messrs. Martin and Bouvard at the points of departure and arrival, it would be found equal only to 1.07′′, or 0.088" less than the truth, which gives 0.26" for the time of the transmission of the sound through the solid; and the excess of this result over those that follow, being no more than 0.135′′, is more easily reconcilable with errours of observation. Finally, the experiments now to be related were made by 3d set of expeMr. Martin and myself, on a series of 376 cylinders, which, riments, on a length of 1040 with their joints, formed a length of 951-25 m. [1039.575 yds] yards nearly. of which the joints alone occupy 5.61 m. [6.131 yds]. I satisfied myself at different times, and by more than 200 experiments, either with the hammer or the bell, that the interval between the two sounds transmitted by the metal and by the air, was exactly 2.5"; and I found no sensible variation in this quantity. I made Mr. Martin observe the interval also, without letting him know my results, and he found the same.. Now, at the distance of 951.25 met. Interval. [1039-575 yds], the temperature being 11° [51-8° F.], the Velocity calculated. As this indie time of transmission of the sound through the air would be from calculation 2.79": and if we substract from this 2.5′′, the interval observed between the two sounds, there will remain 0.29′′ for the time of transmission through the me tal to this distance. From the care with which I repeated these observations, and from the exact coincidence of the five beats, of the half-second chronometer with the interval between the two sounds, I believe, that this result may be considered as a very near approximation. Still however it may be objected, that the velocity of the sound in air deduced from calculation might differ a little from what really took place in the pipe, owing to variation of temperature. This would leave some uncertainty with might be ques- respect to the result, and particularly as to the precise quantigned, tity. I sought therefore to verify it directly in another way, and accomplished it as I shall relate. rect method the velocity was measured directly. I stationed Mr. Martin at one extremity of the pipe with a half-second watch, while I remained at the other with a similar watch, which was carefully compared with the former at the beginning and end of the experiments: though this comparison could have no influence on the results, as will soon appear. When Mr. Martin's watch was at 0" or 80", he struck with a hammer on the last cylinder, near which he was stationed; and when my watch was at 15′′ or 45", I answered him by a similar stroke. We each watched the arrival of the sound transmitted to us, and noted down the time. We were very attentive to strike precisely at the appointed second; and this, with a little practice, we could readily do, as the series of our observations will show. Now, whatever the difference of the watches might be; and even if it were variable, provided there was no sensible change in 30"; it would be reduced to nothing by taking the mean of two consecutive observations, and the result would be independent of it. For, let us suppose the first watch to be the quantity r before the second, and put p for the time in which the sound is transmitted by the solid body. When the first observer strikes on his watch at 0", the other reads on his o"-r; and consequently pr indicates, before or after o", the time at which he hears the the sound. On the other hand, when the second observer strikes at 30", the first observer reads 30′′ +r; and conse quently p+ indicates, beyond 30", the time in which the sound is transmitted to him. The quantities p— and pr therefore are given by these isochronous observations; and half their sum immediately shows the time of transmission p, independant of the differences between the watches, and more exactly than by direct observation. In the experiments I made, the series of the quantities pr and p+r were as in the following table. This differs only 0.03" from what we found above from This nearly the difference of the transmissions: but the last method, as the last calcu agrees with it gives double the quantity to be deduced, deserves the lation. preference. If we add 0-26", the time of transmission through the Velocity in cast iron more as great as in than 10 times air. Other pheno. mena observed. Conversation easy through a pipe of 215 yards. Speaking loud heard 431 yards. At 1040 yds. loud shouting scarcely audible, and the sound of the bell or the hammer not solid, to the difference 2.5′′ constantly observed between the arrival of the two sounds, we shall have the whole time of the transmission through the air equal to 2.76". This time, calculated from the length of the pipe, would have been 2.79", as has just been seen; and the agreement between these numbers, which differ only 0′03′′, appears calculated to inspire some confidence in the results. The time of transmission through the metal being 0.26", while that through air is 2·79", it follows, that the transmission of sound through cast iron is 10.5 times as quick as through air. If this estimation be not sufficiently exact to determine with precision the ratio of the velocities, it is at least enough to show of what kind this ratio is, and what idea we ought to form of it. In making these experiments we had an opportunity of observing several phenomena worthy of remark with respect to the power with which sounds, even the faintest, are preserved and transmitted in tubes, to distances at which we could scarcely suppose they would be perceptible. In our first experiments at the distance of 197 met. [215 yds.] we heard each other so well through the length of the pipe, that it was an inconvenience in the commencement, as the slightest noise was transmitted from one extremity to the other. It was not necessary to speak into the pipe to be heard, as common conversation two yards from the end was transmitted through it clearly; and in writing down my observations I asked Mr. Martin what it was o'clock by his watch, as I would have done a person only two paces from me. This mode of conversing with an invisible neighbour is so singular, that we cannot avoid being surprised, even though acquainted with the cause. In the experiments made by Messrs. Malus and Bouvard at the distance of 395 m. [431 yds.] they still heard each other, but with much more difficulty. It was necessary to speak very loud, and frequently to desire a repetition of what had been said. Finally, in the last experiment, which we tried at first together on a total length of 951 m. [1040 yds.], the voice was scarcely to be heard when shouting as loud as possible. The sounds of the bell and of the stroke of the hammer were no longer audible through the the air. air. The sound through the metal alone was perceptibly at all through transmitted. Lastly, though we could still hear the sound of the voice, it was not sufficiently clear for us to distinguish words, or to transmit the necessary information after our observations. From the great difficulty, which Messrs. Malus and Bouvard had already experienced at a much shorter distance, we were all inclined to suppose, that we had attained a distance, at which the human voice, even the loudest, ceases to be distinguishable in pipes. However, the extreme facility with which we heard each But this imother at 200 metres seemed to me to render so great a di- probable from the 1st experlminution altogether inexplicable. Besides, in the mathe- ments, matical theory of the motion of air we find nothing to indi- and from the. cate, that sound should be diminished in cylindrical pipes. ory. It appears on the contrary, that it ought to be transmitted to an indefinite distance with the same intensity, deducting merely the diminution, that the friction of the air against the pipe might perhaps produce. To decide the question, and know positively whether sound were weakened in such an extraordinary degree, I resolved to remove or diminish all the causes of foreign and neighbouring noises, that might drown the sound I sought to hear. I went to the The experi place of experiment only with Mr. Martin and two intelli- ments repeat gent workmen, and chose for these experiments the stillest of night, bours of the night, those from one to four in the morning. ed in the dead the bell and the lowest whisper was I then discovered, that my conjectures were well founded. when not only We not only heard the two sounds of the hammer and bell the sounds of so distinctly as to observe the intervals such as I have re- hammer, but ported them; but even the lowest voice was heard so as perfectly to distinguish the words, and to keep up a con- heard. versation on all the objects of the experiments. I wished to determine the point at which the voice ceases to be audible, but could not accomplish it: words spoken as low as when we whisper a secret in another's ear were heard and understood; so that not to be heard there was but one resource, that of not speaking at all. From this experiment there can be no doubt, that words may be transinitted so as to be distinctly heard at a more considerable distance. Between a question and answer the interval was not greater, than was necessary for the trans mission |
