[Ill.u.s.tration: FIG. 5.]
There are numberless experiments which might be given to further exhibit the relation of ma.s.s motion to magnetism, but a single one more must suffice. No rotation of a magnet upon its own axis can produce any effects upon a current that is exterior to it; but if a loop of wire be kept stationary adjacent to a magnet, as in Fig. 5, while the magnet revolves, a current of electricity is produced; and if the magnet be kept stationary, and the loop revolves, a current will also be produced, but in the opposite direction. Here, as in all the other cases, no electricity is originated, save when motion is imparted to one or other of the parts. This experiment is due to Faraday.
From all these cases we can come to but one conclusion, that both electricity and magnetism are but forms of motion; electricity being a form of motion in ordinary matter, for it cannot be made to pa.s.s through a vacuum, while magnetism must be a form of motion induced in the ether, for it is as effective in a vacuum as out of it; electricity always needing some material conductor, magnetism needing no more than do radiant heat and light.
VELOCITY.
Measurements have been made of the velocity of electricity; both that of high tension, such as the spark from a Leyden jar, and also that from a battery. The former was found to have a velocity over 200,000 miles a second, while the electricity from a battery may move as slowly as 15,000 or 20,000 miles a second; but this is very largely a matter of conductors. Its velocity is seldom above 30,000 miles a second on ordinary telegraphic lines. If the electricity be used to give signals, as in ordinary telegraphy, the time required varies nearly as the length of the line, and in any case is a much greater quant.i.ty. Prescott in his work on the telegraph states that "the time required to produce a signal on the electro-magnet at the extremity of a line of 300 miles of No. 8 iron wire is about .01 seconds, and that this time increases in a greater proportion than the length of the line; for example, on a line 600 miles in length it amounts to about .03 seconds." He also states that it varies much with the kind of magnet used, some forms of magnets being much more sensitive than others for this work.
Wheatstone proved a good many years ago that the duration of the electric spark was less than one millionth of a second. When a swiftly moving body can only be seen by an electric spark, or flash of lightning, it looks as if it were quiescent. Thus a train of cars rushing along at the rate of forty or fifty miles per hour appears sharply defined,--even the driving-wheels of the locomotive can be seen in detail, which is impossible in continuous light,--and all seems to be standing still. In like manner will the sails of a windmill, which may be turning at a rapid rate, be seen apparently at rest. This is because in the short time during which they are illuminated they do not appreciably move.
I am not aware that any attempt has been made to measure the velocity of magnetism. If, however, it be a form of motion in ether, it is probable that the velocity is comparable to the velocity of radiant energy, light, which is equal to about 186,000 miles a second.
SOUND.
BEFORE explaining the relation that sound has to telephony, it will be necessary to make quite plain what sound is, and how it affects the substance of the body through which it moves. If I strike my pencil upon the table, I hear a snap that appears to the ear to be simultaneous with the stroke: if, however, I see a man upon a somewhat distant hill strike a tree with an axe, the sound does not reach me until some appreciable time has pa.s.sed; and it is noted, that, the farther away the place where a so-called sound originates, the longer time does it take to reach any listener. Hence sound has in air a certain velocity which has been very accurately measured, and found to be 1,093 feet per second when the temperature of the air is at the freezing point of water. As the temperature increases, the velocity of sound will increase a little more than one foot for every Fahrenheit degree; so that at 60 the velocity is 1,125 feet per second. This is the velocity in air. In water the velocity is about four times greater, in steel sixteen times, in pine-wood about ten times.
CONSt.i.tUTION OF A SINGLE SOUND-WAVE.
If a person stands at the distance of fifteen or twenty rods from a cannon that is fired, he will first see the flash, then the cloud of smoke that rushes from the cannon"s mouth, then the ground will be felt to tremble, and lastly the sound will reach his ear at the same time that a strong puff of air will be felt. This puff of air is the sound-wave itself, travelling at the rate of eleven hundred feet or more per second. At the instant of explosion of the gunpowder, the air in front of the cannon is very much compressed; and this compression at once begins to move outwards in every direction, so as to be a kind of a spherical sh.e.l.l of air constantly increasing in diameter; and, whenever it reaches an ear, the sound is perceived. Whenever such a sound-wave strikes upon a solid surface, as upon a cliff or a building, it is turned back, and the reflected wave may be heard; in which case we call it an echo. When a cannon is fired, we generally hear the sound repeated, so that it apparently lasts for a second or more; but when, as in the first case, we hear the sound of a pencil struck upon the table, but a single short report is noticed, and this, as may be supposed, consists of a single wave of condensed air.
[Ill.u.s.tration: FIG. 6.]
[Ill.u.s.tration: FIG. 7.]
Imagine a tuning-fork that is made to vibrate. Each of the p.r.o.ngs beats the air in opposite directions at the same time. Look at the physical condition of the air in front of one of these p.r.o.ngs. As the latter strikes outwards, the air in front of it will be driven outwards, condensed; and, on account of the elasticity of the air, the condensation will at once start to travel outwards in every direction,--a wave of denser air; but directly the p.r.o.ng recedes, beating the air back in the contrary direction, which will obviously rarefy the air on the first side. But the disturbance we call rarefaction moves in air with the same velocity as a condensation. We must therefore remember, that just behind the wave of condensation is the wave of rarefaction, both travelling with the same velocity, and therefore always maintaining the same relative position to each other.
Now, the fork vibrates a great many times in a second, and will consequently generate as many of these waves, all of them const.i.tuted alike, and having the same length; by length meaning the sum of the thicknesses of the condensation and the rarefaction. Suppose a fork to make one hundred vibrations per second: at the end of the second, the wave generated by the vibration at the beginning of the second would have travelled, say, eleven hundred feet; and evenly distributed between the fork and the outer limit, would be ranged the intermediate waves occupying the whole distance: that is to say, in eleven hundred feet there would be one hundred sound-waves, each of them evidently being eleven feet long. If the fork made eleven hundred vibrations per second, each of these waves would be one foot long; for sound-waves of all lengths travel in air with the same rapidity. Some late experiments seem to show that the actual amplitude of motion of the air, when moved by such a high sound as that from a small whistle, is less than the millionth of an inch.
PITCH.
The pitch of a sound depends wholly upon the number of vibrations per second that produce it; and if one of two sounds consists of twice as many vibrations per second as the other one, they differ in pitch by the interval called in music an octave, this latter term merely signifying the number of intervals into which the larger interval is divided for the ordinary musical scale. The difference between a high and a low sound is simply in the number of vibrations of the air reaching the ear in a given time. The smaller intervals into which the octave is divided stand in mathematical relations to each other when they are properly produced, and are represented by the following fractions:--
C D E F G A B C 1 9/8 5/4 4/3 3/2 5/3 15/8 2
[Ill.u.s.tration]
These numbers are to be interpreted thus: Suppose that we have a tuning-fork giving 256 vibrations per second: the sound will be that of the standard or concert pitch for the C on the added line as shown on the staff. Now, D when properly tuned will make 9 vibrations while C makes but 8; but, as C in this case makes 256, D must make 2569/8=288.
In like manner G is produced by 2563/2=384, and C above by 2562=512, and so on for any of the others. If other sounds are used in the octave above or below this one, the number of vibrations of any given note may be found by either doubling or halving the number for the corresponding note in the given octave. Thus G below will consist of 384/2=192, and G above of 3842=768.
During the past century there has been a quite steady rise in the standard pitch, and this has been brought about in a very curious and unsuspected way. The tuning-fork has been the instrument to preserve the pitch, as it is the best available instrument for such a purpose, it being convenient to use, and does not vary as most other musical instruments do. But a tuning-fork is brought to its pitch with a file, which warms it somewhat, so that at the moment when it is in tune with the standard that is being duplicated it is above its normal temperature; and when it cools its tone rises. When another is made of like pitch with this one, the same thing is repeated; and so it has continued until the standard pitch has risen nearly a tone higher than it was in Handel"s time.
The common A and C tuning-forks to be had in music stores, often vary a great deal from the accepted concert pitch. Such as the writer has measured have been generally too high; sometimes being ten or more vibrations per second beyond the proper number. The tuning-forks made by M. Koenig of Paris are accurate within the tenth of one vibration, the C making 256 vibrations in one second.
LIMITS OF AUDIBILITY.
Numerous experiments have been made to determine the limits of audible sounds; and here it is found that there is a very great difference in individuals in their ability to perceive sounds. Helmholtz states that about 23 vibrations per second is the fewest in number that can be heard as continuous sound; if they are fewer in number than that, the vibrations are heard as separate distinct noises, as when one knocks upon a door four or five times a second. If one could knock evenly 23 times per second, he would be making a continuous musical sound of a very low pitch. But this limit of 23 is not the limit for all: some can hear a continuous sound with as few as 16 or 18 vibrations per second, while others are as far above the medium as this is below it. The limits of sound in musical instruments are about all included in the range of a 7-octave pianoforte from F to F, say from 42 to 5,460 vibrations per second. But this high number is not anywhere near the upper limit of audible sounds for man.
Very many of the familiar sounds of insects, such as crickets and mosquitoes, have a much higher pitch. Helmholtz puts this upper limit at 38,000 vibrations per second, and Despraetz at 36,850. The discrepancy of results is due solely to the marked difference in individuals as to acoustic perception.
For the production of high musical tones, Koenig of Paris makes a set of steel rods. A steel rod of a certain length, diameter, and temper, will give a musical sound which may be determined. The proper length for other rods for giving higher tones may be determined by the rule that the number of vibrations is inversely proportional to the square of the length of the rod.
The dimensions of these rods when made 2 c. m. in diameter are as follows:--
Length. Vibrations.
66.2 m. m. 20,000
59.1 " " 25,000
53.8 " " 30,000
50.1 " " 35,000
47.5 " " 40,000
These rods need to be suspended upon loops of silk, and they are struck with a piece of steel so short as to be wholly beyond the ability of any ear to hear its ring. Nothing but a short thud is to be heard from it when it strikes, while from the others comes a distinct ringing sound.
In experimenting with such a set of steel rods I have not found any one yet who could hear as many as 25,000 per second, my own limit being about 21,000. But it has been experimentally found that children and youth have a perceptive power for high sounds considerably above adults.
Dr. Clarence Blake of Boston reports a case in his aural practice, of a woman whose hearing had been gradually diminishing for some years until she could not hear at all with one ear, and the ticking of a watch could only be heard with the other when the watch was held against the ear.
After treatment it was discovered that the sensibility to high sounds was very great, and that she could hear the steel rod having a tone of 40,000 vibrations.
Last year Mr. F. Galton, F.R.S., exhibited before the Science Conference an instrument in the shape of a very small whistle, which he had devised for producing a very high sound. The whistle had a diameter less than the one twenty-fifth of an inch. The length could be varied by moving a plug at the end of the whistle. It was easy to make a sound upon such an instrument that was altogether out of hearing-range of any person. Mr.
Galton tried some very interesting experiments upon animals, by using these whistles. He went through the Zoological Gardens, and produced such high sounds near the ears of all the animals. Some of them would p.r.i.c.k up their ears, showing that they heard the sound; while others apparently could not hear it. He declares that among all the animals the cat was found to hear the sharpest sound. Small dogs can also hear very shrill notes, while larger ones can not. Cattle were found to hear higher sounds than horses. The squeak of bats and of mice cannot be heard by many persons who can hear ordinary sounds as well as any; sharpness of hearing having nothing to do with the limits of hearing.
EFFECTS OF SOUND UPON OTHER BODIES.
If a vibrating tuning-fork be held close to a delicately suspended body, the latter will approach the fork, as if impelled by some attractive force. The experiment can be made by fastening a bit of paper about an inch square to a straw five or six inches long, and then suspending the straw to a thread, so that it is balanced horizontally. Bring the vibrating tuning-fork within a quarter of an inch of the paper. In this case the motion of approach is due to the fact that the pressure of the air is less close to a vibrating body than at a distance from it; there is therefore a slightly greater pressure on the side of the paper away from the fork than on the side next to it.
If a vibrating tuning-fork be held near to the ear, and turned around, there may be found four places in one rotation where the sound will be heard but very faintly, while in every other position it can be heard plainly enough. The extinction of the sound is due to what is called interference. Each of the p.r.o.ngs of the fork is giving out a sound-wave at the same time, but in opposite directions, each wave advancing outwards in every direction. Where the rarefied part of one wave exactly balances the condensed part of the other, there of course the sound will be extinguished; and these lines of interference are found to be hyperbolas, or, if considered with reference to both entire waves, two hyperbolic surfaces.
SYMPATHETIC VIBRATIONS.
When it is once understood that a musical sound is caused by the vibrations more or less frequent which only make the difference we call pitch, it might at once be inferred, that if we have a body that is capable of vibrating say a hundred times a second, and it receives a hundred pulses or pushes a second, it would in this way be made to vibrate. Suppose, then, that we take two tuning-forks, each capable of vibrating 256 times a second: if one be struck while the other is left free, the former one will be giving to the air 256 impulses per second, which will reach the other fork, each pulse tending to move it a little, the c.u.mulative result being to make it move perceptibly, that is, to give out a sound. The principle is just the same as that employed in the common swing. One push makes the swing to move a little, upon its return another is given, in like manner a third, and so on until a person may be swung many feet high. If a gla.s.s tumbler be struck, it gives out a musical sound of a certain pitch, which will set a piano-string sounding that is tuned to the same pitch, provided that the damper be raised. It is said that some persons" voices have broken tumblers by singing powerfully near them the same note which the tumblers could give out, the vibrations of the tumblers being so great as to overcome cohesion of the molecules.
There are very many interesting effects due to sympathetic vibrations.
Large trees are sometimes uprooted by wind that comes in gusts timed to the rate of vibration of the tree. When troops of soldiers are to cross a bridge, the music ceases, and the ranks are broken, lest the acc.u.mulated strain of timed vibrations should break the structure; indeed, such accidents have several times occurred. There is not so much danger to a bridge when it is heavily loaded with men or with cattle, as when a few men go marching over it. "When the iron bridge at Colebrooke Dale was building, a fiddler came along, and said to the workmen that he could fiddle their bridge down. The builders thought this boast a fiddle-de-dee, and invited the musician to fiddle away to his heart"s content. One note after another was struck upon the strings, until one was found with which the bridge was in sympathy. When the bridge began to shake violently, the workmen were alarmed at the unexpected result, and ordered the fiddler to stop."
Some halls and churches are wretchedly adapted to hear either speaking or singing in. If wires be stretched across such halls, between the speaker"s stand and the opposite end, they will absorb the pa.s.sing sound-waves, and will be made to sympathetically vibrate, thus preventing in a good degree the interfering echoes. The wire should be rather fine piano-wire, and it should be stretched so tightly as to give out a low musical sound when plucked with the fingers. In a large hall there should be twenty or more such wires.