US2852453A - Control of cellulose precipitation bath concentrations - Google Patents

Description

p 16, 1953 J. K. HAUSNER 2,852,453

CONTROL OF CELLULOSE PRECIPITATION BATH CONCENTRATIONS Filed Oct. 21, 1955 2 Sheets-Sheet 1 \Qnb WEIYZZI/f JoHA KARL HAUSNER CONTROL OF CELLULOSE PRECIPITATION BATH CONCENTRATIONS Filed Oct. 21. 1955 Sept. 16, 1958 J. K. HAU SNER 2 Sheets-Sheet 2 United States Patent T CONTROL OF CELLULOSE PRECIPITATION BATH CONCENTRATIONS Johann Karl Hausner, Chicago, Ill.

Application October 21, 1955, Serial No. 541,898

3 Claims. (Cl. 204-131) This invention relates to the control of precipitation baths in cellulose product manufacture, and more particularly, to an improved method and apparatus for the precipitation of cellulose products in a bath.

This application is a continuation-in-part of my copending application Serial No. 327,404, entitled Control of Precipitation Baths in Cellulose Product Manufacturer, filed December 22, 1952, now abandoned.

As is well known, in the formation of the so-called regenerated cellulose products crude cellulose is first treated with aqueous sodium hydroxide so as to ultimately obtain a solution of cellulose material that is strongly alkaline. This solution is known in the art as viscose and the viscose is then fed into a strongly acid bath wherein the cellulose product is precipitated. In the formation of films of regenerated cellulose the viscose is cast into the acid bath through a very thin slot. In the formation of rayon the viscose is fed through a spinning means which provides a plurality of fine apertures for feeding the viscose into the acid bath. In either case precipitation of the cellulose product takes place and the sodium hydroxide in the viscose is neutralized by a portion of the acid in the bath, which is sulfuric acid. It is important to maintain a substantially constant concentration of sulfuric acid in the bath in order to have constant precipitating conditions therein. The bath ordinarily contains from about 12% to about 26% sulfuric acid and from about 4% to about sodium sulfate, depending upon the precipitation conditions desired. As used herein, the terms parts and percent mean parts and percent by weight unless otherwise specified.

Preferably, the spinning or precipitation baths contain about 13 to 15% sulfuric acid and 6 to 9% sodium sulfate, with the balance water. and other size-hardening agents may be used in the spinning baths in minor amounts. In the spinning bath the tendency is for the amount of sodium sulfate to be constantly increased and the amount of sulfuric acid to be constantly decreased because of the continuous addition of sodium hydroxide in the viscose. For this reason the baths are circulated in commercial practice and there is a constant removal of a small amount of bath with a replacement therefor of concentrated sulfuric acid. This results in an obvious loss of material in the form of sulfuric acid and sodium sulfate.

British specification No. 215,851 (accepted May 20, 1924) has suggested the use of electrolysis to effect a continuous removal of sodium hydroxide from the bath, with consequent regeneration of sulfuric acid from the sodium sulfate, but it has not been possible to develop this process commercially in accordance with the teachings of the British specification. In the instant invention, in contrast, certain high frequency fields are imposed upon the D. C. field ordinarily employed in electrolysis so as to provide a unique and practical solution to the problem. In this way the precipitating bath concentrations are maintained substantially constant during the continuous precipitation operation. The bath is subjected to an elec- On occasions, tannic acid 2,852,453 Patented Sept. 16, 1958 trolysis while superimposing on the D. C. field a high' to resonance effects which bring the molecules or colloids,

into disintegrating oscillations, as a result of the ion pressure of the applied direct current, so that they follow the operating D. C. current with the least requirement of energy, effecting a complete decomposition of the resulting sodium sulfate immediately upon its coming into existence. There is, in elfect, an immediate decomposition of the sodium sulfate into sulfuric acid and sodium hydroxide (actually first into the sulfate anion and the sodium cation, followed by migration to the respective electrodes). The spinning or precipitation proper is carried out in an anode compartment defined by an electrolysis diaphragm positioned between the anode and the cathode; and the sodium hydroxide or sodium cations migrate through the diaphragm to the cathode compartment.

Such a superimposing of a high frequency alternating current on the operating direct current makes it possible not only to decompose the salts which form in the bath into their components immediately upon their production, but furthermore also makes it possible to decompose and carry away the colloids which collect, thereby making it possible to continuously keep the bath substantially at its original composition. Therefore, it is not necessary, as was previously customary, to continuously supplement the bath, and further the loss is avoided of valuable constituents of the bath, such as the sodium sulfate or Glauber salt, present in large quantities in the waste water in the manufacture of cellulose products.

By way of further explanation, the spinning or precipitating bath in a spinning plant is sub-divided, for the purposes of the instant invention, by a diaphragm (of the well known type employed for electrolysis) into an anode compartment and a cathode compartment. The spinning nozzles (or in the case of films, the casting hopper) are located in the anode compartment. The sodium sulfate forming in the anode compartment is decomposed by the applied direct current so as to cause formation of sulfuric acid from the sulfate anions when they reach the anode and the formation of sodium hydroxide from the sodium cations when they have passed through the diaphragm to the cathode. The very high, so-called threshold value for sodium sulfate is to a very far reaching extent reduced by the superimposed high frequency field. In this way, a very slight current consumption is obtained.

It is, therefore, an important object of the instant invention to provide an improved method for the treatment and control of a precipitation bath for cellulose products.

It is another object of the instant invention to provide an improved system for obtaining a cellulose product in a precipitation bath.

It is a further important object of the instant invention to provide an improved process of treating a precipitation bath for cellulose products containing sulfuric acid and sodium sulfate, which comprises imposing a D. C. field on the bath and superimposing on the D. C. field a high frequency field whose frequency is of a magnitude of 1.8 to 16 meters, expressed in wave lengths in air.

Still another important object of the instant invention is to provide an improved system for obtaining a cellulose product in a precipitation bath, which comprises an,

anode and a cathode in the bath, a pair of conductors for connecting a direct current source to the anode and cathode, means introducing cellulose material into the bath adjacent the anode to precipitate the product, means withdrawing liquid from, the bath adjacent the cathode,

3 and means superimposing a high frequency field between the anode and the cathode.

Other and further objects, features and advantages of the present invention will become apparent to those skilled in the art from the following detailed disclosure thereof and the drawings attached hereto and made a part hereof.

On the drawings:

Figure l is an essentially diagrammatic view of a spinning tank embodying the instant invention, shown in vertical cross-section;

Figure 2 is an essentially diagrammatic view of the embodiment of Figure 1, shown in top plan view;

Figure 3 is essentially a diagrammatic view showing a wiring diagram and the tank of Figures 1 and 2 connected thereto; and

Figure 4 is a wiring diagram of high frequency generator which may be employed in the practice of the instant invention.

As shown on the drawings:

In Figures 1 and 2, the instant device, indicated generally by the reference numeral 10, comprises a container 11 having a front wall 11a, a back wall 1117, end walls 11c and 11d and a bottom wall 11a. Means are provided in the front Wall 11a for feeding viscose into a bath within the container or tank 11, and such means are here shown in in the form of spinning nozzles 12 which are fed through inlet lines 12a connected to a main header 13 (all of which is shown diagrammatically). A diaphragm 14 extends the full length of the tank 11 from top to bottom so as to divide the tank into an anode compartment A and a cathode compartment C. The spinning nozzles 12 are in the anode compartment A. Electrodes in the form of an anode 15 (extending along the backside of the front wall 11a in the anode compartment A) and a cathode 16 (extending along the front side of the back wall 11b in the cathode compartment C) are provided. A pair of condoctors or leads 17 and 18 are provided for the anode and cathode 15 and 16, respectively, to supply direct current thereacross.

The anode 15. is made of a suitable metal or alloy, such as lead, which may be used effectively in sulfuric acid baths of the concentrations here employed and the anode 15 extends along the sidewall for substantially the entire length and height thereof so as to have a maximum surface of contact with the bath. The cathode 16 also extends along substantially the full length and height of the back wall 11b to afford maximum surface of contact and the cathode 16 may be made of iron or steel (in the form of grating or wire to alford additional surface of contact).

The diaphragm 14 is an electrolysis diaphragm, which is a well known type of diaphragm having fine porosity (i. e., a micro-porous diaphragm) so as to reduce the speed of diffusion through the same in both directions. In the instant device the anode is made of lead, and the cathode of steel and the diaphragm is formed of a sintered powdered glass commercially available as an electrolysis diaphragm. It will be appreciated that the electrolysis diaphragm may also be made from clay. mixed with saw. dust and fired, or parchment. In general, the diaphragm is a micro-filter or colloid filter with pore sizes in the range of 1.2 to 14 microns, and preferably 5 microns.

It will also be noticed that the diaphragm 14 mounts screens or grids 19 and 20 on opposite sides thereof. The grid 19 is mounted in the anode compartment A and it covers the exposed surface of the diaphragm 14 in the anode compartment A, being substantially commensurate in area with the height and length of such exposed surface; and the grid 20 is positioned in the cathode compartment C covering the exposed surface C, covering the exposed surface of the diaphragm 14 in a similar manner. The metal grids 19 and 20 may be made of any-suitable electrical conductor that is also substantially non-corrosive in the present environment. Platinum is preferred, but stainless steel may also be used. The grids 19 and 20 have openings therein of substantial size as contrasted to the micro-porosity of the diaphragm 14, so that no interference with the free flow of ions or colloidal material is presented by the grids 19 and 20, but rather that the grids 19 and 20 may function solely (in conjunction with the high frequency source to be described) to avoid buildup of electrically charged particles, colloids, ions, etc. at either surface of the diaphragm 14. A pair of conductors 21 and 22 areconnected to the grids 19 and 20, respectively, to'provide electrical connection between the grids 19 and 2t) and a source of electrical energy to be described.

As indicated in Figure 2, the solution in the anode compartment A is constantly recircled through a recycle line 23 and a pump 24 positioned therein and make up sulfuric acid may be fed in limited amounts from a source 25 through a makeup valve 26. As will be appreciated, only minor amounts of sulfuric acid need be fed into the system because of the manner in which sulfuric acid is regenerated therein. In the cathode compartment C the sodium hydroxide is generated and drawn off in aqueous solution through a drawoff line 27 (as indicated by the arrow). Water is continuously fed through an inlet line 28 and a pump 29 into the cathode chamber C. In this way, excessive amounts of water may be used to continuously dilute the sodium hydroxide in the cathode chamber so that the water passing through the line 27 will contain such a small amount of sodium hydroxide that it will not cause excessive pollution and can be handily discarded as waste water. In such situations, it is preferable to flow a sufficient amount of water into the cathode chamber to maintain a pH therein of about 8. In contrast, it will be appreciated that water may be fed slowly into the cathode chamber so as to take oif a relatively concentrated sodium hydroxide solution and this may be used in the process, in the initial step of treatingthe crude cellulose material. In any event, material from the liquid within the cell 11 is drawn off from adjacent cathode so as to continuously remove sodium hydroxide from the system.

As will be appreciated, filters may be mounted in the recycle line 23 and/or the caustic outlet line 27 in orderto remove any colloidal material or other material which may be caused to precipitate during the treatment in the anode or the cathode compartments.

Heretofore, one of the problems in carrying out electtrolysis (and particularly electrolysis using a precipitation bath of this type) was that of keeping the diaphragm sufliciently open to permit economic operation. There is a great tendencyfor colloidal material particularly to build up on the surfaces of the diaphragm, because of the tendency for an electric charge to be built up on the surfaces. In the instant case, however, the high frequency fields to which the system is subjected tend to prevent this buildup and permit economic and practical electrolysis. A plant operating in accordance with the process of the instant invention (using the instant apparatus) has been operated successfully and economically. Moreover, the savings in electric power were supplemented by savings in material and improvements in quality because of the possibility of maintaining substantially constant concentrations in the bath at all times.

Although the details of the Wiring diagram will be described hereinafter, it will be noted that the high frequency fields employed in the practice of the instant invention, expressed on the basis of Wave lengths in air, are of a magnitude within the range of 1.8 meters to about 16 meters, and preferably about 2 to about 8 meters. The wave lengths of each diflFer from one another by a magnitude offrom 2 to 75% of their average wave length (i. e., the average wave length for the 2 or more high frequencies), and preferably the wave lengths differfrom about 20- to about 50% of their average wave length.

The frequency of the high frequency field used is determined empirically inasmuch as a particular effect desired will control the frequency to be used. The novel result is obtained by the superimposing of the fields of different wave lengths on the D. C. field. Controlling factors are, on the one hand, the composition of the bath and, on the other hand, the dimensional extension and capacity of the bath container. Also, it will be appreciated that a different plurality of high frequencies may be used across the electrodes and across the grids.

For example, continuous spinning or precipitation of viscose is carried out ina bath in the anode compartment A containing 14% sulfuric acid and 8% sodium sulfate maintained at 70 C., with a D. C. current density of 12 A. S. F. (amperes per square foot) for both electrodes (and without application of the high frequency fields) using 0.6 to 1 volt (or about 12 watts) per cubic meter of bath. After a short time, electrolysis is substantially discontinued and the sulfuric acid content in the anode compartment A falls off noticeably to substantially below the desired 14%.

If the same procedure is employed except that high frequencies of 3.5 and 7 meters Wave length magnitude are used across the electrodes, it is noted that the electrolysis is not discontinued in a short period of time as in the case when the high frequency fields were not applied. Moreover, it is noted that if a second plurality of high frequency fields is used across the grids 19 and 20, using high frequencies of 2.5 and 3.5 meters wave length magnitude, the unit can be operated indefinitely, while maintaining a substantially constant sulfuric acid concentration in the bath. The output power for each of the transmitters employed in imposing the first plurality of high'frequency fields (across the electrodes) and the second plurality of high frequency fields (across the grids) is 1200 watts.

In the practice of the instant invention the electrode current density may vary over a wide range of, for example, 5 to 200 A. S. F., but preferably it is within the lower region of the range at 5 to 50 A. S. F.

Referring now to Figure 3, reference numeral 30 generally designates a direct current source which has a positive terminal connected through an ammeter 31 and a conductor 32 to the anode 15, and a negative terminal connected through a conductor 33 to the cathode 16. The source 30 may be any source of steady or pulsating current. Batteries may be used or where standard 25, 50 or 60 cycle alternating current is available, it will ordinarily be preferable to provide rectifiers to convert the alternating current to direct current.

To apply high frequency fields, points 34 and 35 of the conductors 32 and 33 are respectively connected through capacitors 36 and 37 to terminals 38 and 39 of a high frequency generator 40. Points 41' and 42 of the conductors 32 and 33 may be connected through coupling capacitors 43 and 44 to terminals 45 and 46 of a second high frequency generator 47.

Although a high frequency field of a single frequency may be used to substantial advantage in many circumstances, greatly improved results are obtained by using a plurality of fields of different frequencies. For this purpose,.the generators 40 and 47 may each have a single frequency output to apply fields of two different frequencies. Preferably, however, the generator 40 is of a special construction (to be described) such that it applies two different frequencies. Hence, when only two different frequencies are needed, only the generator 40 is required and by providing the second generator 47, an additional frequency or plurality of frequencies may be applied. It will, of course, be apparent that additional high frequency generators may be used to advantage in some circumstances.

In order to achieve more efiicient application of the high frequency fields to the precipitation bath, the terminals 38 and 39 of the high frequency generator 40 are connected through capacitors 48 and 49 to the conductors 21 and 22 connected to the grids 19 and 20, and the terminals 45 and 46 of the high frequency generator 47 are similarly connected through capacitors 50 and 51 to the conductors 21 and 2.2. The capacitors 4851 are preferably variable so that they can be adjusted to obtain optimum coupling to the precipitation bath.

It will be noted that the high frequency generators are connected in parallel relation to the direct current source. A series coupling could be used but such would necessitate that the direct current source have a very low internal impedance to the high frequency currents to obtain efficient operation, which would be difficult to achieve particularly with the relatively long conductors usually used to connect the direct current source to the electrodes. In addition, it would not be possible with a series coupling to obtain the proper field distribution, but such can be accomplished through the use of the parallel connection and the coupling to the screens 19 and 20 through the capacitor 48-51.

With a parallel coupling such as illustrated, the impedance of the high frequency current path through the precipitation bath should be much less than the impedance of the path through the direct current source. With conductors of substantial length as are usually used to connect the direct current source to the bath, this is achieved to a certain extent by placing the points 34, 35, 41 and 42, at which the high frequency generators are connected to the conductors 32 and 33, relatively close to the anode 15 and cathode 16. If desired, in addition, choke coils may be provided between the terminals of the direct current source and the points at which the high frequency source is connected to the conductors 32 and 33.

A further specific feature of the invention is in the adjustment of the position of the points 34, 35, 41 and 42 to obtain optimum coupling of the high frequency currents to the bath. With frequencies in the ranges previously specified, the conductors 32, 33 can form a transmission line of substantial length as compared to one wave length, and by moving the points 34, 35, 41 and 42, resonant and anti-resonant point (or nodes and anti-nodes) may be found and by using such resonant points, optimum coupling can be achieved. In many cases, points can be found at which the high frequency current path through the bath is resonant with the high frequency path through the direct current source being anti-resonant so that the ideal coupling can be obtained.

When a plurality'of high frequency sources, such as the generators 40 and 47, are used it is desirable to prevent direct coupling between the two sources. This may be readily accomplished in the illustrated arrangement, by proper positioning of the points 34, 35 relative to' the points 41, 42.

Figure 4 is a circuit diagram of the high frequency generator 40 and it will be understood that the high frequency generator 47 may use the same circuit. In this circuit, the output terminals 38 and 33 are connected to the terminals of a coil 52 which may have a variable tuning capacitor 53 connected in parallel therewith. The coil 52 is inductively coupled to a tank coil 54 of an oscillator which comprises a triode vacuum tube 55 having a plate or anode 56, a control grid 57 and a directly heated cathode or filament 58. The oscillator may be a series-fed Hartley type with the plate 56 being connected to one end of the tank coil 54, with the grid 57 being connected to the other end of the tank coil 54 through a direct current blocking capacitor 59 and with a source of plate supply voltage being connected between a tap 60 on the coil 54 and the filament 58.

A source of direct current may be used for the plate supply but preferably, to eliminate the need for rectifiers, an alternating current supply is used. In particular, the filament 58 is connected to one terminal of a high voltage secondary winding 61 of a transformer 62 and the tap 60 7 is connected through a choke coil 63 to the other terminal of the winding 61.

To heat the filament 58, one side thereof is connected to one side of a secondary winding 64 of a transformer 65, the other side of the filament being connected through an ammeter 66 and a rheostat 67 to the other side of the winding 64. The transformers 62 and 65 have primaries 68 and 69 connected in parallel in terminals 70 and 71 which may be connected to a suitable source of alternating current, such as a source of 60 cycle, 220 volt current.

Grid-leak bias is preferably used for the oscillator to insure self-starting, the grid 57 being connected through the parallel combination of a resistor 72 and capacitor 73 to the filament 58.

With the coil 52 being tuned by the capacitor 53, it is not necessary to tune the coil 54. However, it may in some circumstances be desirable to tune the coil 54 by means of a variable capacitor 74 connected thereacross.

It will be appreciated that with the oscillator circuit as thus far described, a high frequency field of one frequency may be readily applied to the precipitation bath. As previously indicated, a high frequency field of a ditferent frequency may be applied from a separate oscillator, but the oscillator is preferably of a special construction by which two different frequencies may be simultaneously applied.

It has been found that this highly advantageous result is achieved by using a relatively high degree of coupling between the coils 52 and 54. It is believed that a high degree of coupling results in the generation of two frequencies because of the fact that when two resonant circuits are coupled together with a coefiicient of coupling greater than a certain amount, two resonant peaks will exist at frequencies respectively above and below the frequency to which the circuits are tuned (which hereinabove is referred to as the average frequency). The oscillator circuit may thus have the greatest degree of amplification at two ditferent frequencies and can operate simultaneously at both frequencies.

If the oscillator output is viewed on an oscilloscope, for example, the wave will have the same general form as is produced by the addition of two sine waves. As is'well known, beat frequencies may be produced from waves of two different frequencies and such beat frequencies are produced by the oscillator described.

It should be noted that the greater the degree of coupling, the more prominent are the pair of resonant peaks and the greater is the spacing or frequency difference therebetween. Thus the relation of the two frequencies can be adjusted by adjusting the coupling between the coils 52 and 54.

In practice, the coupling is generally adjusted until optimum performance is achieved. In any case, the coupling should be such that the mutual inductance in henrys is substantially greater than where R is the resistance of one coil in ohms, R is the resistance of the other coil in ohms and w equals 21rf, f being the frequency to which tuned in cycles per second. A coupling of such value is generally termed critical coupling and hence the coupling should be substantially greater than critical coupling.

By way of illustrative example and not by Way of limitation, the capacitor 53 may have a maximum capacitance of 125 micro-microfarads; the capacitor 59 may be constituted by two vacuum capacitors each having a ca- 8 pacitance of 250 micro-microfarads; the capacitor 73 may have a capacitance of 100 micro-microfarads; the resistor 72 may have a value of 10,000 ohms; the voltage devel. oped across the secondary 61 may be 5,000 volts R. M. S.; and the tube 55 may be an air-cooled high vacuum type with 2,000 watts maximum power output.

It will be understood that modifications and variations may be effected without departing from the spirit and scope of the novel concepts of this invention.

I claim as my invention:

1. A process of treating a precipitation bath for cellulose products containing sulfuric acid and sodium sulfate, which comprises passing an electric current through the bath between a cathode and an anode to create a D. C. field therein, carrying out precipitation adjacent the anode with consequent addition of sodium base to the bath, removing sodium base from the bath adjacent the cathode and superimposing on the D. C. field at least two high frequency fields whose frequencies, expressed in Wave lengths in air, are of a magnitude of 1.8 t016 meters and which diifer from one another by a magnitude of 2 to 75% of their average wavelength.

2. A process of treating a precipitation bath for cellu-.

lose products containing sulfuric acid and sodium sulfate,

' which comprises passing an electric current through the bath between a cathode and an anode to create a D. C. field therein, interposing an electrolysis diaphragm between the cathode and the anode, carrying out precipitation on the anode side of the diaphragm with consequent addition of sodium base to the bath, removing sodium base from the bath on the cathode side of the diaphragm and superimposing on the D. C. field at least two high frequency fields whose frequencies, expressed in wave lengths in air, are of a magnitude of 1.8 to 16 meters and which differ from one another by a magnitude of 2 to 75% of their aver-age wave length.

3. A process of treating a precipitation bath for cellulose products containing sulfuric acid and sodium sulfate passing an electric current through the bath between a cathode and an anode to create a D. C. field therein, interposing an electrolysis diaphragm between the cathode and,

the anode, carrying out precipitation on the anode side of the diaphragm with consequent addition of sodium base to the bath, removing sodium base from the bath on the cathode side of the diaphragm, superimposing on the D. C. field between the anode and the cathode a first plurality of high frequency fields whose frequencies, expressed in wave lengths in air, are of a magnitude of 1.8 to 16 meters and which differ from one another by a magnitude of 2 to 50% of their average wave lengths, and superimposing on the D. C. field across the diaphragm a second plurality of high frequency fields whose frequencies, expressed in wave lengths in air, are of a magnitude of 1.8 to 16 meters and which differ from one another by a magnitude of 2 to 75% of their average wave length.

References Cited in the file of this patent UNITED STATES PATENTS 1,162,213 Bloom Nov. 30, 1915 1,980,873 Niederreither Nov. 13, 1934 2,341,356 Briggs Feb. 8, 1944 FOREIGN PATENTS 843,625 France Mar. 27, 1939 215,851 Great Britain May 20, 1924 629,099 Great Britain Sept. 12, 1949 905,360 Germany Mar. 1, 1954 516,237 Belgium Dec. 31, 1952

Claims (1)

1. 2. A PROCESS OF TREATING A PRECIPITATION BATH FOR CELLULOSE PRODUCTS CONTAINING SULFURIC ACID AND SODIUM SULFATE, WHICH COMPRISES PASSING AN ELECTRIC CURRENT THROUGH THE BATH BETWEEN A CATHODE AND AN ANODE TO CREATE A D. C. FIELD THEREIN, INTERPOSING AN ELECTROLYSIS DIAPHRAGM BETWEEN THE CATHODE AND THE ANODE, CARRYING OUT PRECIPITATION ON THE ANODE SIDE OF THE DIAPHRAGM WITH CONSEQUENT ADDITION OF SODIUM BASE TO THE BATH, REMOVING SODIUM BASE FROM THE BATH ON THE CATHODE SIDE OF THE DIAPHRAGM AND SUPERIMPOSING ON THE D. C. FIELD AT LEAST TWO HIGH FREQUENCY FIELDS WHOSE FREQUENCIES, EXPRESSED IN WAVE LENGTHS IN AIR, ARE OF A MAGNITUDE OF 1.8 TO 16 METERS AND WHICH DIFFER FROM ONE ANOTHER BY A MAGNITUDE OF 2 TO 75% OF THEIR AVERAGE WAVE LENGTH.

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