USA > Maine > York County > Parsonsfield > A history of the first century of the town of Parsonsfield, Maine > Part 14
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There remains a whole department in the domain of heat, which is of the great- est interest both for its theoretical and for its practical applications. This de- partment is called thermo-dynamics. The first law of thermo-dynamics has been mentioned when speaking of the notions which have prevailed concerning the nature of heat. It may be stated again thus: When heat is expended to perform work, the amount of work derived is mechanically equivalent to the heat which disappears. A second and no less important law is: Heat cannot, of itself, be made to pass from a colder to a hotter body; nor can it be made to pass from a colder to a hotter body by means of any inanimate material contrivance; nor can any mechanism whatever be made to move by the simple cooling of any body below the temperature of surrounding bodies.
A moment's consideration of these laws will make it clear that there are nar- row limits which the steam engine and other heat engines cannot pass as re- spects their efficiency. This depends, as is evident, on the difference in temper- ature between the in-going and the out-coming steam or hot air or gas. Now, we cannot make this difference as great as we please; for this would compel us to construct boilers of unlimited strength (for which no materials are available), or to make a region of indefinitely low temperature for the exhaust steam to escape into (which is impossible). It is common to assume a point of absolute zero of temperature 273 degrees below our practical zero C., for purposes of cal-
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culation, but no such removal of heat as this requires can be effected. The rea- son for assuming this particular point for the absolute zero is found in the beha- viour of a perfect gas. It is found that such a gas expands or contracts one 273d part of its volume, at zero, for every degree of change in temperature reckoned from that point. If, therefore, 273 degrees of heat could be withdrawn from a gas at zero, and the same law should hold continuously, the entire motion of the particles of gas would cease, and the gas as a gas would be destroyed. This view offers some peculiar advantages for purposes of calculation.
At present, only a small percentage of the theoretical value of the fuel expend- ed can be made available for driving an engine. All energy besides that de- rived from the tides is found, in the last resort, to have its origin in the solar radiations; this statement includes the energy of wind, falling water, muscular contraction, etc. This being so, the inquiry is at once raised, how the energy of the sun is maintained. The reply is that it is not certain that it is maintained. For aught we know, the sun may be growing cooler as the ages go by. Some . evident means, however, may be pointed out, which, doubtless, contribute to keep upthe supply of heat. It would only be necessary for the sun to contract in di- mensions by an amount which would be wholly imperceptible to us, in order to maintain its present rate of radiation. The meteorites, which, no doubt, are constantly falling into it in much larger amount than they strike the earth, must supply very great amounts of heat, and thus prevent the sun's temperature from falling off. The activities at present operating are having the effect, apparently, to reduce the universe to one common temperature. Such a state of things may, in the remote future, be reached, but the doctrine of the conservation of energy will not be contravened thereby, for the whole amount of energy will remain constant, though none of it will be available as at present. Heat is the lowest form of en- ergy, and consequently it is the form to which all others tend. Illustrations of this remark are seen in the generation of heat by collision, friction and mechan- ical action generally; also in the equalization of electrical accumulations, and in chemical action. The great generalization of the century-the statement of the doctrine of the conservation of energy-asserts that the sum of the energy of the universe remains constant through all the changes which it may experience, and it may be added that it appears to be certain that heat is to be its final form.
With the countless practical applications of heat which have come about dur- ing our century, we need not deal, for they are on every hand, and are observed by all.
SOUND.
Sound evidently presents two different provinces for exploration-acoustics, which deals with the phenomena perceived by the ear, and music which has to do with the sensations thus excited as they affect our æsthetic nature. While these two provinces are in some sense distinct, they are yet so related that dis- course concerning the one would be difficult without reference to the other.
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Concerning the nature of sound, the ancients had, of course, only the most imperfect notions. Empedocles (B. C. 490) taught that the sensation of sound is caused by the streaming of fine particles from the sounding body into the ear- a notion similar to that which prevailed respecting smell and taste. Aristotle, with better reason, held that it is produced by motions in the air correspond- ing to those of the sounding body. Vitruvius compared the action of the air in conveying sound to that of water when the waves spread out in circles from a point of disturbance. The Arabs, to a certain extent, cultivated music, and had some exact knowledge concerning its production by means of musical instru- ments. During the middle ages music was extensively developed under the in- fluence of the church. In the 11th century a musical staff, with notes to desig- nate the pitch of sounds, was introduced by a Benedictine monk, Guido von Arezzo. He it was who virtually gave the names to the notes as we have them. They are taken from a song of praise to St. John, in which is a prayer that all impurity might be removed from his voice:
" Ut queant laxis resonare fibris, Mira gestorum famuli tuorum, Solve polluti labii reatum, Sancte Ioannes ?"
That bodies emitting sounds are themselves in motion, must have been ob- served at an early date, but Galileo was the first to undertake an investigation of the relative frequency of the vibrations producing the octave, the fifth and the fourth referred to the fundamental of the natural musical scale, though the an- cient Greeks knew the relative lengths of a stretched cord or organ pipe corre- sponding to these several pitches. When Galileo ascertained that the number of vibrations producing the octave, the fifth and the fourth, were in the ratios 2, 3:2, 4:3, respectively, the fundamental being 1, he discarded the intangible physiolog- ical method of estimating pitch, and laid a foundation for a proper mathematical treatment. By accident, he came upon a beautiful confirmation of his results. As he was cleaning a brass plate with an iron scraper, he repeatedly heard tones of definite pitch, and he noticed minute indentations on the plate over which the scraper had passed. Measurements showed that the intervals between these inden- tations corresponded to the known ratios of frequency in vibration to which the notes were due. He made similar observations respecting the water waves in glasses which were made to sound by rubbing with the wet finger. Thus he was the first to observe the so-called "standing waves " produced by a sounding body. He did not neglect the physiological importance of the ratios he discov- ered. He believed that the ear had the power of combining easily those tones whose ratios of frequency can be expressed by simple numbers, and thus he en- deavored to find a basis for the sensations of concord and discord.
Aristotle taught that the velocity of acute sounds is greater than that of grave ones, but Gassendi, born in 1592, showed that this is not so. He caused a mus- ket and a cannon to be fired at a distance, and, by observing the intervals be-
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tween the flashes and the reports, he found that the two sounds had the same velocity. He obtained, as a result, about 1473 ft. per second-somewhat too high. Mersenne published a work on harmony, in 1636, in which he gives the velocity 1380 ft. per second. He had noticed that a vibrating string produces other notes than its fundamental-overtones, as we now call them.
In 1686, the " Principia " of Newton appeared, in which is given a masterly mathematical treatment of the problem of the propagation of a pulse through an elastic medium. The special problem of the velocity of sound is considered, and the result obtained is 906 ft. per second. This is too small, as Newton well knew, for the various experimental determinations had made it certain that the true velocity must be between 1,000 and 1,100 feet. Newton proposed unsatis- factory explanations of the discrepancy, but it was reserved for Laplace to point out the real source of the disagreement, and to amend the formula of Newton so as to make it conform to the truth. Newton's formula, so far as it went, was perfectly correct, but he failed to take into account the fact that, as a sound con- sists in condensations and rarefactions of the medium, say the air, and that, as these traverse every portion of the medium disturbed, there must be a development of heat and cold at every point successively, so that, on the whole, there is no alteration of temperature. The effect is that the rate at which both the condensation and the rarefaction proceed is accelerated. This grows out of the fact that when a gas is heated suddenly its elasticity is increased suddenly and conversely when it is suddenly cooled. The ratio of these two elasticities is the same as that of the two specific heats, which, in the case of air, is 1.41 : 1. This factor, 1.41. is the one which Laplace introduced into Newton's formula, and thereby made it conform to the truth. Of course there is a factor de- pending on the temperature of the air at the time of the experiment. This is the one which expresses the expansion of air for one degree of temperature reckoned from zero, 0.003665. Thus the problem is completely solved and the theory fully established.
There are other methods of determining the velocity of sound, one of which should here be mentioned, on account of the light which it casts upon other branches of physical inquiry. It can easily be shown by experiment that a sound wave emitted by an open organ pipe is twice the length of the pipe. If, therefore, we can determine how many such waves are produced in a second, we have only to take the product of this number by twice the length of the given pipe in order to find the velocity of sound, since all sounds travel with the same velocity. Moreover, if the pipe be made to sound in any other gas than air, it will give a pitch depending on the density of the gas and on the ratio of its two specific heats. Thus, by observing the pitch of a pipe of known length, and the density of the gas under examination, we can find the ratio of its two specific heats. But this is immediately connected with its molecular constitution, and hence we get an idea of simplicity or complexity of its molecu- lar constitution. Reference has been made to this matter under "Heat."
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HISTORY OF PARSONSFIELD.
The labors of Galileo, Mersenne and others relating to the laws governing the vibrations of strings may be passed over with the remark that, important as they were, Dr. Taylor, in 1713, presented the results of experiment and dis- cussion in a simple mathematical formula, which shows the relations of the length, diameter, density and tension of the string to the number of vibrations which it can execute, or, what is the same thing, to its pitch.
In all the discussion to which allusion is here made, reference was had only to the so-called transverse vibrations, such as are produced when a guitar is plucked or a piano string is struck. In 1701, Sauveur described the " over- tones " which accompany the lowest or fundamental tones given by the string, though he was not the first to observe them. An account of them was given in 1677, by Wallis, whose pupils, Noble and Pigot, had discovered them, and also a means of making evident the behaviour of the string to which they are due. It had long been known that when two strings, in unison, are near each other, and one of them is made to sound, the other is set in vibration so as to sound also. This was ascribed to some action of the air, by means of which the mo- tion of one string was transferred to the other, but no reason could be given why the second string does not sound when it is not in accord with the first. Noble and Pigot stretched several strings in pairs, and so tuned them that one pair gave a certain fundamental and its octave, while the second pair gave the same fundamental and its twelfth, and the third pair gave the same fundamental and the second octave. On making the fundamentals sound, they found, on placing .small paper riders on the corresponding strings, that the middle point of the first, two points dividing the second into thirds, and three points on the third, dividing it into fourths, were at rest. Thus the fact that the string can vibrate as a whole, and at the same time its parts can vibrate by themselves, was demonstrated.
Sauveur called the stationary points nodal points, and the intervening vibrat- ing portions, ventral segments-names which they still retain.
Some notion of these overtones had been formed by Mersenne, for he had noticed that when a string is struck at random so as to produce its fundamental tone, other faint tones are heard as the fundamental vibration dies away. Des- cartes, to whom he communicated his observation, rightly explained the origin of them, but fell into the error of supposing that they did not occur except when the string is made to give a false note. The fact is that the overtones are produced by all stringed instruments as well as by most others, and it is to them that the peculiar quality of each kind of instrument is due.
These results do not appear to have had much effect in making clearer the cause of the characteristic sound of different musical instruments, nor were they made subservient to music as an art. As late as 1779, Funke, Professor of Physics at Leipzig, held that the " character" of the sound produced by a reed or a string is due to the motion of the molecules of which the reed or
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string is composed. Lagrange, however, in 1772, showed that a string may be so set in vibration as to produce its fundamental tone only, or it may be plucked so as to develop certain overtones Passing the labors and disputes of others concerning the cause of overtones, it may be noted that in 1800 Dr. Young gave a full and complete explanation of them by referring them to the reaction of the portions of the string on either side of the point of disturbance (the point of plucking or bowing) on each other. A similar explanation applies to the col- umn of air in the organ pipe and to the reed, etc. But, besides the fundamentals and their overtones, others are heard when two strings, pipes or reeds are sound- ed together, there being a difference of pitch between them. These tones corre- spond in frequency of vibration, to the sum or to the difference of the vibration frequencies of the primaries. Lagrange, in 1759, referred them to the same cause which produces the well known beats when two strings or pipes, not quite in accord, are sounded together. Helmholtz has, however, shown that a dis- tinct sound wave results from two waves simultaneously produced, and that the resultant tone in question is due to this, and not to the production of beats by interference.
Strings and rods, besides the transverse vibrations thus far considered, can also execute longitudinal vibrations, giving rise to musical sounds. If with the hand, armed with a glove on which a little powdered rosin has been strewn, friction be applied along the surface of a smooth rod of glass, metal or wood, the rod being firmly held by its middle point, a clear musical note will be produced. In a sim- ilar way, friction applied along the surface of a stretched string will produce a musical note. These facts were discovered by Chladni, and published in 1787-96. They have very important bearings both as respects the theory of acoustics and that of the elasticity of solids. The laws which pertain to the vibration fre- quencies, and so to the production of tones and overtones, are very similar to those which prevail in relation to organ pipes. But, since the tones given by rods, say of steel or iron, have vibration numbers which are directly as the square roots of their elasticities, it is clear that advantage may be taken of this relation to ascertain the relative elasticities of different samples of such metals. Thus the engineer may safely decide on the fitness of any proposed materials for his purpose in the construction of bridges, roofs, etc. So two arts, which, at first sight, seem to have nothing in common, are found to be so closely related that the data of the one are made the criteria for judgments in the other. Though out of place, it seems convenient to speak here of another simple test which is applied in determining the fitness of materials for a given use. If a uniform rod of iron or steel, or an indefinite length of wire, be made to pass in a constant direction and constant velocity near a freely suspended magnetic needle, the latter will assume and retain a fixed position so long as the metal remains homogeneous. But if the least flaw or imperfection pass before it, the needle will be disturbed. Thus, by means of magnetism, is the builder warned of local
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împerfections, while acoustics assure him of the general fitness or unfitness of his materials. Other similar applications of the data obtained by the study of acoustics might be given. As the density of a gas alters regularly with its tem- perature, it is easy to determine the latter by causing the gas to sound an organ pipe of convenient form and size. The experiment may easily be so conducted that we may determine the temperature of any highly heated region, say a fur- nace. It is only necessary to sound a small pipe of refractory material, as plati- num, porcelain, etc., after introducing it into the region to be tested, and to note the pitch of the sound. An easy calculation gives the temperature. The chem- ist can determine the density of a gas by merely noting the pitch of a pipe when blown with it, etc.
It has been assumed that the pitch of every sound can be ascertained. It will be of interest to point out some of the ways in which this can be done. The simplest is that of Duhammel, inventedi n 1840. He attached a small" style to the vibrating body, so that its point could trace a path on a prepared surface, such as smoked glass or smoked paper, which was made to move uniformly at right angles to the direction of vibration. When the vibrating body is set in mo- tion, a sinuous path is traced on the surface. It is only necessary to note the time during which the experiment lasts, and to count the number of undulations recorded on the surface, to know the number of vibrations made in a unit of time. The siren is also much used for the same purpose. It consists, essentially, of a revolving disc, having a number of equi-distant holes arranged in a circle about its axis of revolution. When a jet of air is directed through a small tube so as to pass through each of the holes as they revolve past the tube, there is produced a musical note depending for its pitch on the number of revolutions which the disc makes in a second, and on the number of holes in the disc. Since we can know both of these, it is easy to determine the number of puffs of air, or the number of sound waves constituting note heard. Other sounds may be compared with those produced [by the siren, and thus their vibration frequencies may be found. There are still other methods' which are frequently employed for the purpose in question, but they must be omitted.
When, instead of a current of air, a blast of steam, at high pressure, is em- ployed to operate a suitably constructed siren, the sound produced is very loud. For this reason such a device is employed in the service of the Govern- ment for danger signals along the coast. A steam siren should be able to give a sound which can be heard a distance of 25 miles under favorable circumstances.
A very striking effect is produced when the relative distance between the listener and the source of sound is rapidly changing. The principle involved is known. as Doppler's principle. It was investigated by Buys Ballot, in 1845, on the rail- road between Utrecht and Maarsen. A trumpeter was placed on the locomotive, who blew his trumpet both when the locomotive was approaching and when it was receding from the listener, who was stationed by the road side. The loco-
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motive was moving with a speed of about 16 metres a second, and an alteration of the pitch, amounting to about a half tone, was produced. This alteration made the tone higher when the locomotive approached the listener, and lower when it receded from him. The same results were observed when the listener and the trumpeter exchanged places. The mathematical formula expressing the relations between the velocity of motion and the change in pitch produced thereby is a very simple one, and is of great use in determining the velocity of motion of the so-called fixed stars; for the same principle applies to light as to sound. In the case of light, we have to observe the resulting change in the color.
When two sounds, having the same wave frequency and the same intensity or loudness, are so produced that the condensation of the one coincides with the rarefaction of the other, the air particles remain at rest and both sounds are destroyed completely. This result is easily produced by means of a common tuning fork. On striking the fork so as make it sound, a clear tone will be heard if it be presented to the ear; but if it be twirled between the fingers, intervals of silence will be observed alternating with the sound. This phenomena is called interference. There are various methods of producing it more satisfactorily than that just pointed out. They are made use of in investigating problems in sound as well as in light. In the latter case, two rays produce darkness.
Our references to progress in the science of acoustics would be incomplete without a brief consideration of the physiological aspect of it. This can best be done after considering a little in detail the matter of resonance. It has been mentioned on a former page that if one of two strings (or sonorous bodies in general) be set in vibration, the other string, placed near it, if in unison, will also be set in vibration. The principle may be so extended that any number of strings will be set in vibration when one is sounded which is in accord with them. Moreover, if a single string be so set in vibration as to produce not only its fundamental, but its overtones, any strings which are in accord with the overtones will be set in vibration. Such cases may be called cases of free resonance. It was suspected early in the century that there existed in the coch- lea of the ear some arrangement of sonorous bodies which could respond, by such resonance, to any audible sound. Thus Dr. Young, in a course of lectures, published in 1807, speaks as follows :-
" It has also been supposed that a series of fibres are arranged along the .cochlea, which are susceptible of sympathetic vibrations of different frequency, according to the sound which acts upon them; and, with some limitations, the opinion does not appear to be wholly improbable." More recently Corti has discovered an anatomical basis for this action. In the middle compartment of the cochlea, he found arranged, side by side, like the keys of a piano, a great number of microscopic plates communicating, by one of their extremities, with the filaments of the acoustic nerve, and by the other with a stretched mem- brane. When a sound the vibration frequency of which is nearly the same as any
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HISTORY OF PARSONSFIELD.
one of these plates could produce if it were set in vibration, is conveyed to the ear cavity, this particular plate will be disturbed, and so the nerve fibre connected with it will convey to the seat of consciousness a sensation which will be asso- ciated with that particular rate of vibration. Thus is the pitch of one sound dis- tinguished from that of another. There may be needed some modification of the brief statement here given, but that it is in the main correct, seems hardly doubtful.
Modern research concerning the exceeding minuteness of the motions which may constitute audible sounds, has surprised all who are familiar with it. The actual displacement of the air particles by an audibly sonorous body is much too small to be conceived of, and must not be thought of as comparable with the dis- placement of the masses of air which are thrown out from our lungs in speaking. It was the failure to appreciate this fact which constituted one of the chief hin- derances to the development of telephony in its early days.
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