Part 3
This leads to the inquiry as to what magnetism is. We know that it can produce motion by its moving at a distance a piece of iron or another magnet. It will also sustain a mass of matter against gravity or some other contrary force. Through such mechanism as magneto-electric machines it produces electricity in great abundance, which again can be used to produce any of the effects of electricity,--moving bodies by attraction or repulsion, generating heat or light, or again making a magnet. But as all of these are but varied forms of motion, either of a mass as a whole, or molecular, can it be doubted for an instant, that what we call magnetism is but some form of motion? Must it not be either some form of matter, or some form of motion? If it were a form of matter, then a magnet would only be permanent so long as it was not used; for use implies consumption of the force; and, if this be matter in any form, then in a given mass of matter there can be but a definite quantity of such magnetic matter, and consumption must lessen that quantity. As a matter of fact, there is no perceptible lessening of the power of a magnet when it is properly used. It is also a matter of fact, that neither motion of a mass, nor electrical effects, nor any other, can be produced by the action of a magnet alone. It is only when some form of motion has been added to its own property, that we get any kind of an effect from it: hence all effects due to its action are _resultants_ of two forces, one of them being common motion of a mass of matter, and the other the energy of the magnet. Hence we infer that a magnet is a mechanism of such a structure as to change the direction and character of the motion which acts upon it. When the wheel of a common electrical machine is turned, the product is electricity,--a force very different from that which originates it. Ordinary mechanical motion _goes in_; electricity _comes out_, the latter being a modified motion due to the physical structure of the machine. In like manner, a magnet may be considered as a machine by means of which mechanical motion may be converted into some other form of motion. It is evident that molecular structure is chiefly concerned in this. If a bar of iron that exhibits no evidence of magnetism whatever be subjected to torsion, it will immediately become a magnet with poles dependent upon the direction of the twist. This developed magnetism will re-act upon a coil of wire, and so move a galvanometer needle. If the bar be permitted to recover its original condition, it will lose its magnetism, which will at once re-appear upon twisting the rod again. Now, when the rod is twisted, it is evident that there is a molecular strain in certain directions throughout the mass. The converse experiment illustrates the same thing. It has been found, that when a rod of iron is made magnetic by the action of a current of electricity circulating about it, and at the same time passing longitudinally through it, the rod is slightly lengthened and twisted in a direction that depends upon the direction of the current. Moreover, if a permanent magnet be heated to a red heat, its magnetism is destroyed; for such a heat allows the molecules to freely arrange themselves without any external constraint. Also, if a permanent magnet be suspended so as to give out a musical sound when it is struck, the magnetism will be much weakened by making it thus to vibrate. In this case, as in the other, the vibrations affect every molecule, and so enable them to re-adjust themselves to the positions they held before being magnetized. The same thing happens when a bar of iron is made magnetic through the inductive action of the earth. When this bar is held in the direction of the magnetic dip, it becomes but very slightly magnetized; but, if it be so held that when it is struck with a hammer it will ring, that is, give out a musical sound, it will at once become decidedly magnetic. Evidently the earth's action tends to set the molecules of the mass in a new position, but cohesion prevents them from assuming it. When the molecules are made to vibrate, they can assume such new positions more readily. The molecules of a magnet, then, are differently arranged from those in an unmagnetized piece of iron or steel; and, for every new arrangement of the molecules of a mass of any kind, we always have some new physical property developed. The same identical substance may appear as charcoal, coke, plumbago, anthracite coal, and diamond. Hence a magnet is a machine in which other forces acting upon it are transformed in character, and re-appear as attractions and repulsions of other kinds of matter: this transformation cannot take place, and hence magnetism cannot become apparent, only upon the condition of another force acting in concert with it; and, if at any time it may seem to be acting without such external force, it is done at the expense of the heat it has absorbed, and therefore the magnet must at such time be losing temperature proportional to the work done. This I have discovered to be true by making a magnet to exert its force in front of a thermo-pile, which uniformly exhibits a cooled face under such conditions. What the particular form of the motion may be that we call magnetism, is not yet made out; but that it is some form of motion, is very evident. The following experiments may throw some light upon it. Last August Mr. Kerr read a paper before the British Association of Science, in which was detailed the following experiment: The pole of an electro-magnet was nicely polished so as to reflect light like a mirror. A beam of sunlight was permitted to fall upon it, and be reflected to a convenient place for examination. A current of electricity was sent through the coil, which of course rendered the iron magnetic; and it was noticed that the light that was reflected from the pole was circularly polarized: that is, the motion of a ray, instead of being a simple undulatory movement, was now made to assume such a motion as the water from a garden-hose has when the nozzle is swung round in a circle while the water is escaping from it. After reading the account of it, it occurred to me that the converse experiment might be tried; that is to say, the effect of a circularly polarized beam of light upon a piece of steel. By concentrating a large beam of ordinary plane polarized light with a quartz lens, and passing it through a quarter wave-plate at the proper angle, a powerful beam of circularly polarized light was obtained. At the focus of this beam a fine cambric needle without magnetism was placed so that the light passed it longitudinally. Ten minutes' exposure was sufficient to make it decidedly magnetic. Hence I infer that the motions which we call magnetic attractions and repulsions may be quite analogous to such helical motions; also, that these motions exist in ether, and evidently may be either right-handed or left-handed. Wind up on a pencil a piece of wire twelve or fifteen inches long, making a loose spiral. Bring the two ends of the spiral together; and note first that one is twisted to the right, the other to the left. If they be twisted into each other, they will advance very easily; but if a right-handed spiral were to be interlocked with another like it, and both turned in the direction of their spiral, they would separate rapidly. Applying this conception to a magnet, we might suppose that such spiral motions will be set up in the ether by the magnet, and that such motions re-acting upon ordinary matter affect it as attraction and repulsion; and thus we should have at least a conceivable mechanical explanation of the phenomenon.
There are numberless experiments which might be given to further exhibit the relation of mass 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 pass 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 quantity. 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 passed; 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 deg. 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.
CONSTITUTION 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 shell 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.
Imagine a tuning-fork that is made to vibrate. Each of the prongs beats the air in opposite directions at the same time. Look at the physical condition of the air in front of one of these prongs. 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 prong 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 constituted 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
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 256x9/8=288. In like manner G is produced by 256x3/2=384, and C above by 256x2=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 384x2=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 Haendel'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. Koeenig 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, Koeenig 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 Zooelogical Gardens, and produced such high sounds near the ears of all the animals. Some of them would prick 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 prongs 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.