Chapter 8

Now a wave length in the red is about 1/40000 of an inch, and a little calculation will show that these particles are well within the necessary limits. Prof. Tyndall has delighted audiences here with an exposition of the effect of the scattering of light by small particles in the formation of artificial skies, and it would be superfluous for me to enter more into that. Suffice it to say that when particles are small enough to form the artificial blue sky, they are fully small enough to obey the above law, and that even larger particles will suffice. We may sum up by saying that very fine particles scatter more blue light than red light, and that consequently more red light than blue light passes through a turbid medium, and that the rays obey the law prescribed by theory.

I will exemplify this once more by using the whole spectrum and placing this cell, which contains hyposulphite of soda in solution in water, in front of the slit. By dropping in hydrochloric acid, the sulphur separates out in minute particles; and you will see that, as the particles increase in number, the violet, blue, green, and yellow disappear one by one and only red is left, and finally the red disappears itself.

Now let me revert to the question why the sun is red at sunset. Those who are lovers of landscape will have often seen on some bright summer's day that the most beautiful effects are those in which the distance is almost of a match to the sky. Distant hills, which when viewed close to are green or brown, when seen some five or ten miles away appear of a delicate and delicious, almost of a cobalt, blue color. Now, what is the cause of this change in color? It is simply that we have a sky formed between us and the distant ranges, the mere outline of which looms through it. The shadows are softened so as almost to leave no trace, and we have what artists call an atmospheric effect. If we go into another climate, such as Egypt or among the high Alps, we usually lose this effect. Distant mountains stand out crisp with black shadows, and the want of atmosphere is much felt. [Photographs showing these differences were shown.] Let us ask to what this is due. In such climates as England there is always a certain amount of moisture present in the atmosphere, and this moisture may be present as very minute particles of water--so minute indeed that they will sink down in an atmosphere of normal density--or as vapor. When present as vapor the air is much more transparent, and it is a common expression to use, that when distant hills look "so close" rain may be expected shortly to follow, since the water is present in a state to precipitate in larger particles. But when present as small particles of water the hills look very distant, owing to what we may call the haze between us and them. In recent weeks every one has been able to see very multiplied effects of such haze. The ends of long streets, for instance, have been scarcely visible, though the sun may have been shining, and at night the long vistas of gas lamps have shown light having an increasing redness as they became more distant. Every one admits the presence of mist on these occasions, and this mist must be merely a collection of intangible and very minute particles of suspended water. In a distant landscape we have simply the same or a smaller quantity of street mist occupying, instead of perhaps 1,000 yards, ten times that distance. Now I would ask, What effect would such a mist have upon the light of the sun which shone through it?

It is not in the bounds of present possibility to get outside our atmosphere and measure by the plan I have described to you the different illuminating values of the different rays, but this we can do: First, we can measure these values at different altitudes of the sun, and this means measuring the effect on each ray after passing through different thicknesses of the atmosphere, either at different times of day or at different times of the year, about the same hour. Second, by taking the instrument up to some such elevation as that to which Langley took his bolometer at Mount Whitney, and so to leave the densest part of the atmosphere below us.

Now, I have adopted both these plans. For more than a year I have taken measurements of sunlight in my laboratory at South Kensington, and I have also taken the instrument up to 8,000 feet high in the Alps, and made observations _there_, and with a result which is satisfactory in that both sets of observations show that the law which holds with artificially turbid media is under ordinary circumstances obeyed by sunlight in passing through our air: which is, you will remember, that more of the red is transmitted than of the violet, the amount of each depending on the wave length. The luminosity of the spectrum observed at the Riffel I have used as my standard luminosity, and compared all others with it. The result for four days you see in the diagram.

I have diagrammatically shown the amount of different colors which penetrated on the same days, taking the Riffel as ten. It will be seen that on December 23 we have really very little violet and less than half the green, although we have four fifths of the red.

The next diagram before you shows the minimum loss of light which I have observed for different air thicknesses. On the top we have the calculated intensities of the different rays outside our atmosphere. Thus we have that through one atmosphere, and two, three, and four. And you will see what enormous absorption there is in the blue end at four atmospheres. The areas of these curves, which give the total luminosity of the light, are 761, 662, 577, 503, and 439; and if observed as astronomers observe the absorption of light, by means of stellar observations, they would have had the values, 761, 664, 578, 504, and 439--a very close approximation one to the other.

Next notice in the diagram that the top of the curve gradually inclines to go to the red end of the spectrum as you get the light transmitted through more and more air, and I should like to show you that this is the case in a laboratory experiment. Taking a slide with a wide and long slot in it, a portion is occupied by a right angled prism, one of the angles of 45° being toward the center of the slot. By sliding this prism in front of the spectrum I can deflect outward any portion of the spectrum I like, and by a mirror can reflect it through a second lens, forming a patch of light on the screen overlapping the patch of light formed by the undeflected rays. If the two patches be exactly equal, white light is formed. Now, by placing a rod as before in front of the patch, I have two colored stripes in a white field, and though the background remains of the same intensity of white, the intensities of the two stripes can be altered by moving the right angled prism through the spectrum. The two stripes are now apparently equally luminous, and I see the point of equality is where the edge of the right angled prism is in the green. Placing a narrow cell filled with our turbid medium in front of the slit, I find that the equality is disturbed, and I have to allow more of the yellow to come into the patch formed by the blue end of the spectrum, and consequently less of it in the red end. I again establish equality. Placing a thicker cell in front, equality is again disturbed, and I have to have less yellow still in the red half, and more in the blue half. I now remove the cell, and the inequality of luminosity is still more glaring. This shows, then, that the rays of maximum luminosity must travel toward the red as the thickness of the turbid medium is increased.

The observations at 8,000 feet, here recorded, were taken on September 15, at noon, and of course in latitude 46° the sun could not be overhead, but had to traverse what would be almost exactly equivalent to the atmosphere at sea level. It is much nearer the calculated intensity for no atmosphere intervening than it is for one atmosphere. The explanation of this is easy. The air is denser at sea level than at 8,000 feet up, and the lower stratum is more likely to hold small water particles or dust in suspension than is the higher.

For, however small the particles may be, they will have a greater tendency to sink in a rare air than in a denser one, and less water vapor can be held per cubic foot. Looking, then, from my laboratory at South Kensington, we have to look through a proportionately larger quantity of suspended particles than we have at a high altitude when the air thicknesses are the same. And consequently the absorption is proportionately greater at sea level that at 8,000 feet high. This leads us to the fact that the real intensity of illumination of the different rays outside the atmosphere is greater than it is calculated from observations near sea level. Prof. Langley, in this theater, in a remarkable and interesting lecture, in which he described his journey up Mount Whitney to about 12,000 feet, told us that the sun was really blue outside our atmosphere, and at first blush the amount of extra blue which he deduced to be present in it would, he thought, make it so. But though he surmised the result from experiments made with rotating disks of colored paper, he did not, I think, try the method of using pure colors, and consequently, I believe, slightly exaggerated the blueness which would result.

I have taken Prof. Langley's calculations of the increase of intensity for the different rays, which I may say do not quite agree with mine, and I have prepared a mask which I can place in the spectrum, giving the different proportions of each ray as calculated by him, and this when placed in front of the spectrum will show you that the real color of sunlight outside the atmosphere, as calculated by Langley, can scarcely be called bluish. Alongside I place a patch of light which is very closely the color of sunlight on a July day at noon in England. This comparison will enable you to gauge the blueness, and you will see that it is not very blue, and, in fact, not bluer perceptibly than that we have at the Riffel, the color of the sunlight at which place I show in a similar way. I have also prepared some screens to show you the value of sunlight after passing through five and ten atmospheres. On an ordinary clear day you will see what a yellowness there is in the color. It seems that after a certain amount of blue is present in white light, the addition of more makes but little difference in the tint. But these last patches show that the light which passes through the atmosphere when it is feebly charged with particles does not induce the red of the sun as seen through a fog. It only requires more suspended particles in any thickness to induce it.

In observations made at the Riffel, and at 14,000 feet, I have found that it is possible to see far into the ultra-violet, and to distinguish and measure lines in the sun's spectrum which can ordinarily only be seen by the aid of a fluorescent eye piece or by means of photography. Circumstantial evidence tends to show that the burning of the skin, which always takes place in these high altitudes in sunlight, is due to the great increase in the ultra-violet rays. It may be remarked that the same kind of burning is effected by the electric arc light, which is known to be very rich in these rays.

Again, to use a homely phrase, "You cannot eat your cake and have it." You cannot have a large quantity of blue rays present in your direct sunlight and have a luminous blue sky. The latter must always be light scattered from the former. Now, in the high Alps you have, on clear day, a deep blue-black sky, very different indeed from the blue sky of Italy or of England; and as it is the sky which is the chief agent in lighting up the shadows, not only in those regions do we have dark shadows on account of no intervening--what I will call--mist, but because the sky itself is so little luminous. In an artistic point of view this is important. The warmth of an English landscape in sunlight is due to the highest lights being yellowish, and to the shadows being bluish from the sky light illuminating them. In the high Alps the high lights are colder, being bluer, and the shadows are dark, and chiefly illuminated by reflected direct sunlight. Those who have traveled abroad will know what the effect is. A painting in the Alps, at any high elevation, is rarely pleasing, although it may be true to nature. It looks cold, and somewhat harsh and blue.

In London we are often favored with easterly winds, and these, unpleasant in other ways, are also destructive of that portion of the sunlight which is the most chemically active on living organisms. The sunlight composition of a July day may, by the prevalence of an easterly wind, be reduced to that of a November day, as I have proved by actual measurement. In this case it is not the water particles which act as scatterers, but the carbon particles from the smoke.

Knowing, then, the cause of the change in the color of sunlight, we can make an artificial sunset, in which we have an imitation light passing through increasing thicknesses of air largely charged with water particles. [The image of a circular diaphragm placed in front of the electric light was thrown on the screen in imitation of the sun, and a cell containing hyposulphite of soda placed in the beam. Hydrochloric acid was then added; as the fine particles of sulphur were formed, the disk of light assumed a yellow tint, and as the decomposition of the hyposulphite progressed, it assumed an orange and finally a deep red tint.] With this experiment I terminate my lecture, hoping that in some degree I have answered the question I propounded at the outset--why the sun is red when seen through a fog.

* * * * *

THE WAVE THEORY OF SOUND CONSIDERED.

By HENRY. A. MOTT, Ph.D., LL.D.

Before presenting any of the numerous difficulties in the way of accepting the wave theory of sound as correct, it will be best to briefly represent its teachings, so that the reader will see that the writer is perfectly familiar with the same.

The wave theory of sound starts off with the assumption that the atmosphere is _composed of molecules_, and that these supposed molecules are free to vibrate when acted upon by a vibrating body. When a tuning fork, for example, is caused to vibrate, it is _assumed_ that the supposed molecules in front of the advancing fork are crowded closely together, thus forming a condensation, and on the retreat of the fork are separated more widely apart, thus forming a rarefaction. On account of the crowding of the molecules together to form the condensation, the air is supposed to become more dense and of a higher temperature, while in the rarefaction the air is supposed to become less dense and of lower temperature; but the heat of the condensation is supposed to just satisfy the cold of the rarefaction, in consequence of which the average temperature of the air remains unchanged.

The supposed increase of temperature in the condensation is supposed to facilitate the transference of the sound pulse, in consequence of which, sound is able to travel at the rate of 1,095 feet a second at 0°C., which it would not do if there was no heat generated.

In other words, the supposed increase of temperature is supposed to add 1/6 to the velocity of sound.

If the tuning fork be a _Koenig C^{3}_ fork, which makes 256 _full_ vibrations in one second, then there will be 256 sound waves in one second of a length of 1095/256 or 4.23 feet, so that at the end of a second of time from the commencement of the vibration, the foremost wave would have reached a distance of 1,095 feet, at 0°C.

The motion of a sound wave must not, however, be confounded with the motion of the molecules which at any moment form the wave; for during its passage every molecule concerned in its transference makes only a small excursion to and fro, the length of the excursion being the amplitude of vibration, on which the intensity of the sound depends.

Taking the same tuning fork mentioned above, the molecule would take 1/256 of a second to make a full vibration, which is the length of time it takes for the pulse to travel the length of the sound wave.

For different intensities, the amplitude of vibration of the molecule is roughly 1/50 to 1/1000000 of an inch. That is to say, in the case of the same tuning fork, the molecules it causes to vibrate must either travel a distance of 1/56 or 1/1000000 of an inch forward and back in the 1/256 of a second or in one direction in the 1/512 of a second.

I might further state that the pitch of the sound depends on the number of vibrations and the intensity, as already indicated by the amplitude of stroke--the timbre or quality of the sound depending upon factors which will be clearly set forth as we advance.

Having now clearly and correctly represented the wave theory of sound, without touching the physiological effect perceived by means of the ear, we will proceed to consider it.

We must first consider the state in which the supposed molecules exist in the air, before making progress.

The present science teaches that the diameter of the supposed molecules of the air is about 1/250000000 of an inch (Tait); that the distance between the molecules is about 8/100000 of an inch; that the velocity of the molecules is about 1,512 feet a second at 0°C., in its free path; that the number of molecules in a cubic inch at 0°C. is 3,505,519,800,000,000,000 or 35 followed by 17 ciphers (35)^{17}; and that the number of collisions per second that the molecules make is, according to Boltzmann, for hydrogen, 17,700,000,000, that is to say, a hydrogen molecule in one second has its course wholly changed over seventeen billion times. Assuming seventeen billion or million to be right for the supposed air molecules, we have a very interesting problem to consider.

The wave theory of sound requires, if we expect to hear sound by means of a C^{3} fork of 256 vibrations, that the molecules of the air composing the sound wave must not be interfered with in such a way as to prevent them from traveling a distance of at least 1/50 to 1/1000000 of an inch forward and back in the 1/256 of a second. The problem we have to explain is, how a molecule traveling at the rate of 1,512 feet a second through a mean path of 8/100000 of an inch, and colliding seventeen billion or million times a second, can, by the vibration of the C^{3} fork, be made to vibrate so as to have a pendulous motion for 1/256 of a second and vibrate through a distance of 1/50 to the 1/1000000 of an inch without being changed or mar its harmonic motion.

It is claimed that the range of sound lies between 16 vibrations and 30,000 (about); in such extreme cases the molecules would require 1/16 and 1/30000 of a second to perform the same journey.

It must not be forgotten that a mass moving through a given distance has the power of doing work, and the amount of energy it will exercise will depend on _its_ velocity. Now, a molecule of oxygen or nitrogen, according to modern science, is a _mass_ 1/250000000 of an inch in diameter, and an oxygen molecule has been calculated to weigh 0.0000000054044 ounce. Taking this weight traveling with a velocity of 1,512 feet a second through an average distance of 8/100000 of an inch, the battering power or momentum it would have can be shown to be in round numbers capable of moving 1/200000 of an ounce.

Now, when the C^{3} tuning fork has been vibrating for some time, but still sounding audibly, Prof. Carter determined that its amplitude of stroke was only the 1/17000 of an inch, or its velocity of motion was at the rate of 1/33 of an inch in one second, or one inch in 33 seconds (over half a minute), or less than one foot in one hour.

Assuming one prong to weigh two ounces, we have a two-ounce mass moving 1/17000 of an inch with a velocity of 1/33 of an inch in one second. The prong, then, has a momentum or can exercise an amount of energy equivalent to 1/200 of an ounce, or can overcome the momentum of 1,000 molecules.

It would be difficult to discover not only how a locust can expend sufficient energy to impart to molecules of the air, so as to set them in a _forced_ vibration, and thus enable a pulse of the energy imparted to control the motion of the supposed molecules of the air for a mile in all directions, but also to estimate the amount of energy the locust must expend.

According to the wave theory, a condensation and rarefaction are necessary to constitute a sound wave. Surely, if a condensation is not produced, there can be no sound wave! We have then no need to consider anything but the condensation or compression of the supposed air molecules, which will shorten the discussion. The property of mobility of the air and fluidity of water are well known. In the case of water, which is almost incompressible, this property is well marked, and unquestionably would be very nearly the same if water were wholly incompressible. In the case of the air, it is conceded by Tyndall, Thomson, Daniell, Helmholtz, and others that any compression or condensation of the air must be well marked or defined to secure the transmission of a sound pulse. The reason for this is on account of this very property of mobility. Tyndall says: "The prong of the fork in its swift advancement condenses the air." Thomson says: "If I move my hand vehemently through the air, I produce a condensation." Helmholtz says: "The pendulum swings from right to left with a uniform motion. Near to either end of its path it moves slowly, and in the middle fast. Among sonorous bodies which move in the same way, only very much faster, we may mention tuning forks." Tyndall says again: "When a common pendulum oscillates, it tends to form a condensation in front and a rarefaction behind. But it is only a tendency; the motion is so slow, and the air so elastic, that it moves away in front before it is sensibly condensed, and fills the space behind before it can become sensibly dilated. Hence waves or pulses are not generated by the pendulum." And finally, Daniell says: "A vibrating body, _before it can act_ as a sounding body, must produce alternate compressions and rarefactions in the air, and these must be well marked. If, however, the vibrating body be so small that at each oscillation the surrounding air has time to _flow round_ it, there is at every oscillation a local rearrangement--a local flow and reflow of the air; but the air at a distance is almost wholly unaffected by this."