# Патент USA US2408775

код для вставки@CL 3, 1946. w. M. GooDALL 2,408,773 ' POSITION DETERMINING SYSTEM Filed March 31, 1942 P ON IES. l1» J 4 Q Ii @ K /N VEN TOR ¿f2/_ M. 600ML; A TTOR/VEV Patented Get. 8, 1946 2,408,773 UNITED STATES PATENT oFFicE 2,408,773 POSITION DETERMINING SYSTEM William M. Goodall, Oakhurst, N. J .,v assìgnor to Bell Telephone Laboratories, Incorporated, Newl York, N. Y., a corporation of New York Application March 31, 1942, Serial No. 436,995 10 Claims. (Cl. Z50-11) 2 rI'his invention relates to radio position-deter mining methods and systems and particularly to methods and means for ascertaining the position of a mobile body relative to one or more ground stations. As disclosed in German Patent 546,000, M. Harms, March 8, 1932; United States Patents 2,148,267, E. A. I-I. Honore, February 21, 1939, 1,995,285, W, Al-bersheim etal., March 26, 1935, and 2,198,113, P. J. Holmes, Ap`ril 23 1940, the 10 change in location of a mobile body such as an airplane relative to a pair of spaced ground sta It is another object of this invention to elimi nate in a system utilizing a relay or repeater transmitter, interaction between the incoming and outgoing energies. It is still another object of this invention to secure and maintain, in a phase-integration posi tion-determining method and system, the proper frequency relations and the proper initial or absolute phase angle relations among the radio frequency waves transmitted from the ground stations. In accordance with the preferred embodiment of the invention, the various radio frequencies tions may be determined at the mobile body by emitted from the three ground stations in a posi integrating, during the entire travel or move tion-determining phase-integration system are ment of said body, the changes in phase angle of all derived only from a single source of energy; a detected low frequency “signal” current hav ing a non-uniformly changing phase angle rep and, in accordance with a modification, the above mentioned radio frequency and also the inter resenting at each instant the position of said mediate or low frequencies supplied to the phase body with respect to said stations. In at least one of the above-mentioned systems, the integra 20 integrators are all derived only from a single osciilator having a high frequency stability and tion is effected by continuously comparing the located at one of the ground stations. More par signal current phase angle with that of a “ref ticularly, the primary ground station A comprises erence” current having the same low frequency a crystal-controlled oscillator generating a fre and a uniformly changing phase angle which is independent, or substantially independent, of the 25 quency F equal, for example, of three megacycles, and thisstation emits a Wave nF, where n equals position of the body. The signal current is de any integer lbut preferably a large integer such rived from two waves having different frequencies as 8. At each of the relay ground stations B1 and received from different ground stations, one and B2, the wave nF is received, and waves are of which may be a relay station; and the refer ence current is obtained from a local low fre 30 obtained therefrom having frequencies (nfl-DF and (1L-DF which are emitted, respectively, by quency reference oscillator on the mobile body these secondary stations. The receiver C at the or from one of said incoming waves and a third aircraft includes separate detecting channels for wave of still another frequency emitted by one obtaining from waves 'nF and (n+1) F a iirst high of the ground stations or Áby an auxiliary ground station. For the purpose of securing a geograph 35 frequency signal current, from waves nF and ical position determination, a second relay station may be utilized. ' As is apparent, for successful operation of the system using the local low frequency reference (1l-DF a second high frequency signal current and from wave nF a reference high frequency current. The phase angle of the first signal cur rent contains a component or factor representing oscillator, the frequency of the reference current 40 the difference in distances between the aircraft must lbe maintained in exact synchronism with that of the received signal current and, in the other arrangements, the proper frequency rela tions and the absolute phase relations of the sev eral emitted beacon waves must -be preserved. ï Heretofore, completely satisfactory results have and stations A and B1 and another component representing the dis-tance between the aircraft and station A. Similarly, the phase angle of the second signal current contains two components, one representative of the difference in the dis tances of the mobile receiver from stations A and B2 and the other=representative of only the dis tance between the receiver and station A. The phase angle of the reference current includes a not been attained in practice in using the above systems primarily because of the difñculty of se curing a local reference low frequency oscillator which is highly stable as to frequency and also 50 component which yrepresents the distance between the aircraft and station A. At the mobile re in View of the difficulty of synchronizing or ex ceiver, a 100-k`ilocycle wave isobtained from a actly relating the frequencies of the various trans local beat oscillator and combined with the afore mitted waves. mentioned reference current toproduce a result It is one object of this invention to determine ant current, which is separately «combined or accurately the position of a mobile body. 4 o o modulator' 8, filter 9, power amplifier it? and non directional transmitting aerial II. rent for the purpose of obtaining a first detected Referring to Fig. 2, the receiving apparatus at signal current and a second detected signal cur the mobile station C comprises a non-directional rent corresponding, respectively, to the first and second high frequency signal currents. The in receiving antenna 5, common to the three receiv« ing branches or channels L, M, and N. Channels phase angle of each detected signal current in L and N each comprise a first detector I2, a ñlter cludes the component representing the difference i3, -a second detector I4. Channel M includes a in distances of the aircraft from the associated radio frequency amplifier I'5, the output of which stations A and B1 or B2, but does not` include the is connected to the input of the first detectors I2 component representing the distance between the in channels L and N, a subharmonic generator receiver C and station A, since the components i6, an intermediate frequency local beat oscillator representative of this variable distance mutually il, an auxiliary modulator-filter I8 having its cancel in the modulation process. Each of the input terminals connected to the subharmonic detected signals is supplied, together with an un `generator I6 and to the local oscillator Il and its modulated 100-kilocycle reference wave from the ~ output connected t0 the input of the second de beat oscillator, to a different combined phase modulated with each high frequency signal cur comparator-integrator. Each ‘comparator-inte tectors i4 in channels L and N. grator functions to determine during movement of the plane the total phase angle change in the signal current supplied thereto, the total change meral I9 kdenotes a phase comparator-integrator including a cycle counter, the integrator being connected between the output terminals of the intermediate frequency oscillator i-'l and the sec ond-detector It in channel L‘; and numeral 29 designates a simi-lar comparator-integrator con nected between the output terminals of oscillator I 'I and detector i4 in channel N. The compa rator-integrators each comprise a phase angle being a, measure of the change of position, both asr regards sense and amount, of the aircraft relative to the two associated stations. ThelOO kilocycle oscillator is not necessarily of a high frequency stability type. If desired, for economical or other reasons, the Reference nu meter equipped with a counter and may be of the above-described system may be modified to omit the 100-kilocycle oscillator and associated appa ratus. In the modiñed larrangement the ñrst electrical type illustrated by Patent 1,934,460, J. H. Bollrnan, November 7, i933, the gearbox 3E in the Bcllman system being replaced by a counter for counting the number of c'ycles of phase angle change. Alternatively, 'the integrator may be of high frequency signal current and a portion of . the high frequency reference current are sup plied to one combined phase comparator-inte« grator and the second high frequency signal cur rent and another portion of the reference high frequency are supplied to the other comparator integrator. In the case of each comparator integrator the phase angle components of the wave supplied thereto and representing the dis tance of the aircraft from station A cancel each other so that the integrated phase angle indica 40 a mechanical type comprising a differential gear assembly, such as illustrated by Patent 1,907,132, G. M. Thurston, May 2, 1933, a counter being attached to the crown gear 6I of the Thurston system. In operation, the crystal-controlled oscillator I at primary station A generates and Isupplies a wave having a constant frequency F equal, for tion represents the net change in the difference of the distances separating the aircraft from the associated stations A and B1 0r lâz. The arrange example, to three 'megacycles to the harmonic generator-amplifier 2, which functions to pro ment comprising the 100-kilocycle oscillator is more accurate than the modified embodiment since the integrated phase angle change in each quency nF where n «is any integer but preferably duce a wave having a large intensity and a fre - isy a large integer "such as 8. The wave nF is ra diated by aerial 3 and intercepted by receiving signal current is transferred or impressed upon antennas 5 at stations B1 and B2. t each of relay stations B1 and B2 the received wave 11F is supplied over different -paths to the input of >The invention will be more fully understood from a perusal of the following specification, taken 50 the subharmonic generator-amplifier 6 and the ampliñer ’.I. The subharmonic generator fi func in conjunction with the drawing on which like a lower frequency. ` tions to derive from the Ywave nF a wave of fre reference characters denote elements of a similar q_uency F which is combined inthe modulator 8 function, and on which: with the wave nF' from amplifier 'I for the pur Fig, l illustrates the transmitting apparatus used at the primary and relay ¿ground stations; 55 pose of producing among other components the side-band Yfrequencies nF-ì-F and 11F-F. The Fig. 2 illustrates the preferred receiving equip ñlter 9 connected to the output of the modulator ment used at the mobile station; 8 at station B1 passes only the upper side-band Fig. 3 illustrates the space patterns established frequency (1i-I- 1)F, whereas the corresponding ‘oy the transmitting stations; Vand filter at station B2 passes only vthe lower side«band Fig. 4 illustrates amodiñed receiver which may 60 frequency (n4-DF. At each relay station the be lused in place of the apparatus of Fig. 2. selected side-band is amplified by amplifier it! Referring to Fig. l, reference character A de and vradiated 'non-directionally by antenna II. notes a Vmain 0r primary ground transmitting As radiated, the phase angle of the waves emitted station and reference ycharacters B1 ‘and B2 desig 65 by antenna 3 and the two relay antennas I I may nate relayorre'peater ground stations each spaced ordinarily a distance of’25-50, or even 1D0-500 miles, from station A. The primary station A be represented as follows: From antenna 3,~s'tati'on A cos 21r(nF) (t+a1) includes a frequency Vstabilized crystal-controlled oscillator I which _is connectedthrough a com bined ¿harmonic ¿generator-'amplifier 2Y to a non (l) from antenna n, station B1 o ' eos 21r<a+1>F<t+a2> <2) directional antenna system comprising ’the aerial 3 and the Vgroundw'll. Each of relay stations B1 from antenna Il, station -Bz and B2 includes a receiving aerial 5, -a combined cos 21r(TL-1)F(t-I-a3) (3) where t denotes time in seconds, and on, a2 and amplifier-subharmonic generator 6, ‘amplifier l, 2,408,773 6 5 From Equation 15 itis apparent that the phase as are time factors which diiîer from each other. The diiîerences among a1, a2 and ce and the phase angle `variation is dependent on , two factors, namely, the distance h of station C from station A and the difference h-g between the> distances of station C from station-s A and B1. Similarly, in channel N, the filter £3 passes only the lower side-band current obtained by subtracting Equation 6 from Equation e and rep variations introduced in the equipment at relay stations B1 and B2, may be compensated if desired in accordance with the teaching of Patent 1,926,169, El. Nyquist, September l1, 1933. At the mobile station C the waves nF, {rt-HMP and (1t-'DF ir-oin stations A, B1 and B2, respec tively, are intercepted by antenna 5. Assuming resented by the following equation: a1, a2 and as have been compensated and, in et fect, eliminated by proper adjustments at sta tions B1 and B2, the phase angle of the waves, as received, may be represented as follows: Considering channel M, the subharmonic gen» erator i6 connected to the output or amplifier ~ From antenna 3, station A l5 functions to derive from the incoming wave, @es 2mF<i-%) from antenna l l, station B1 , cos 21r(7L-l~1)F<t--%) el) _ (5) ,(17) fic-g) 20 (18) and this wave is combined in the auxiliary mod» ulator nlter i8 with a heat wave from antenna al, station B2 cos 21r(n~ DFG-â) une) a wave (6) Cos 21rft <19) from the 10û-kilocycle oscillator to produce the side-band where c is the velocity of propagation in space of the Wave and, as shown in Fig. 3, h, o, and y' are distances, respectively, at any given instant , h cos 211-[E (t--ë > -l-ft] separating the mobile station C from the ground (20) stations A, B1 and B2. The factor “cos 2W” in The wave represented by Equation 20 is coin the phase angle expressions given above is a con~ 30 bined in detectors lll in channels L and N with stant and hereafter will be omitted for the salse the side-band currents represented, respectively, of clarity. by Equations 15 and 16 to produce in the output of the detector I4, channel L, the signal current, The received waves are supplied directly to the detectors l2 in channels L and N and are also supplied to these detectors through the ampliñer bij (21) i5 in channel M. Of the various modulation products present in the output of each of the and in the output of detector lil, channel N, the detectors l2 only one of the side-band currents signal current obtained by combining the waves received from 40 station A, Equation 4, and from station B1, (22) Equation 5, and represented by Equation i5, given below is passed through the lilter i3 in channel L. The sum and diiîerence currents obtained by combining Equations ¿l 5 may be repre sented: [tnenrë]¿womb-Q] The signal current from channel L and a por tion of the reference current from oscillator Vl are supplied to the cornparator~integrator I9, and the signal current from channel N and an other portion of the reference current from os c) cillator Il are supplied to the comparator-inte the lower side-band or difference frequency being: grator 2e. 50 It is apparent that Equation 2l represents a family or set of hyperbolic isophase curves for each of which the factor h-g C is a constant and that Equation 22 represents another set of hyperbolic curves for each' of which the factor ill 60 C is constant. Referring to Fig. 3, the curves 33 represent several of the hyperbolic courses cor responding to Equation 21 and the curves 3l il lustrate several of the hyperbolic lines corre sponding to Equation 22, the being at stations A and B1 and 3l being at stations A and B2. adjacent hyperbolic curves Si) foci of curves 3Q the foci of curves Considering two (or 3i) the dif 70 ference between the values of the factor so that the phase angle of the current in the out put of the iilter I3 in channel L is for the two curves mayV for convenience be taken 75 as one wave-length. ' . i ' " 2,408,773 '7 8 The phase angle given by Equation 21 and ln tegrated during the movement of the mobile body or airplane does not change when the airplaneV subharmonic generator *l5 >and ,the ñlter i3 in channel L; and integrator 20 ,is connected to the d moves along a path coinciding with one of the outputs of the subharmonic generator I6 and a filter I3 in channel N. Considering the receiv curves 30, but does change when the ,movement Ul ing system of Fig. 4, the high frequency current is not along oneof these paths. Similarly, the phase angle given by Equation 22 changes onlil when the airplane moves in a direction making an angle with the curves 3l. Considering the hyperbolic system established by stations A and B1 and assuming the airplane is at a location such as P1, Fig. 3, on the particular curve 3!) rep resenting the condition h-g=0, the rotation or angular speed of the vector Yof the detected sig nal current supplied ‘to the integrator 19,'which vector rotates in a counter-clockwise direction, is constant. As the plane moves toward the po sition P2 located farther away from station A and nearer to station B1, the factor C assumes a positive value and it increases'as the Equation 18, becomes the reference current. The high frequency signal currents utilized for inte gration in channels L and N are given by Equa tions 15 and 16, respectively. In the modiñed system the phase angles are measured and integrated at the very high radio frequency F(3,000,000), whereas in the system including the 100-kilocycle oscillator I'I the integration oc curs at the relatively 10W or intermediate fre quency of 100 kilocycles. Inasmuch as the in stantaneous phase angle change may be meas ured and integrated more easily and more accu rately at the intermediate frequency f=100 kilo cycles than at the radio frequency F='3,000,000 cycles, and since integrators designed to oper ate at intermediate frequencies are more easily plane moves toward position P2. Hence, the phase angle as given by Equation 21 continues 25 manufactured and maintained than those de signed to operate at a radio frequency, the sys to increase with movement of the mobile body tem of Fig. 2 comprising the auxiliary oscillator toward position P2. Since the phase angle of il, and in which the phase angle changes in the the reference current from beat oscillator l1 is radio frequency received wave are transferred to independent of the movement of the mobile body and impressed upon the intermediate frequency the counter in the integrator i9 records every 100-kilocycle wave, is >preferred over the modiñed S60-degree phase angle change. On the other arrangement-,of Fig. 4. hand, if the plane moves from position P1 tov/ard Referring again to Fig. 1, it will be observed P3 located near to station A and farther away that at relay stations B1 .and B2 the received and from station B1 than P1 the factor retransmitted waves differ by a multiple of the lily fundamental frequency F=3 megacycles. Thus `c at stationBi the received and transmitted >fre changes from a Zero to a `negative value and it quencies are 24 megacycles and 2'7 megacycles, re spectively, and at station B2 the received Yand 40 transmitted frequencies are 24 megacyc‘les and 21 gained or lost, as a result of the movement of megacycles, respectively. Because of the differ the mobile body and counted ,by the integrator ence in the order of several million cycles in the 19 is an indication, not of th'e actual distance received and transmitted frequencies at each re traveled, but of the change of location with re lay station, singing and =other interference phe spect to stations A andk B1. 'The indication is not nomena are, in accordance with one feature of in any Way affected by, cr related to, the speed 45 the invention, avoided at the relay station. of transit of the airplane or ,the timeconsumed Moreover, as already pointed out, since all fre in making a night or the geometrical nature, quencies utilized at the -three transmitted sta linear or tortuous, of the path or course followed tions, including the frequencies received andre by the mobile body. In a similar manner, the transmitted at ,each relay station, are derived continues to decrease until position P3 is reached. 'I‘he number of net degrees, radians, or cycles integrator 2li indicates the change of position of the plane relative to the line connecting .sta tions A and B2. By observing the registration on both indica tors at a known starting point P1, at which each counter has a predetermined reading, and ob serving the registrations on ‘Lboth counters ,at any given subsequent time, the position of ¿the plane with respect to the three stations A, B1 and B2 may be ascertained and the straight line distance separating the starting and termination points ,may be determined. If desired, a mech anism which may be set or yadjusted at t'h‘eiknown starting point prior to Vthe 'beginning `of travel may be utilized to operate a camera, bomb `re lease, etc., whenever one counter gives a pre determined registration and similarly the other counter gives another predetermined registra tion. If desired, the transmission from each sta tion may be camouflaged by voice broadcast 50 from the oscillator l at station A, the frequency difference at each relay station `between the re ceived and transmitted waves is maintained. Although the invention has been explained in connection with certain embodiments Yincluding a modified receiving arrangement, it should be vunderstood that it is not tto be limited to the em bodiment described inasmuch as other apparatus may be employed in successfully practicing _the invention. As is believed to be app-arent, the position of the mobile body may, in -accordance with the invention, be determined in a plane other than the azimuthal plane as, for example, a vertical plane. What is claimed is: l l. In a phase integration position determin ing system, means for transmitting from two spaced geographical points waves of different frequencies, means at a mobile body for securing modulation of the emitted radio frequency waves. a reference current having a constant phase angle and for obtaining from said ’waves a signal Referring to Fig. 4, the 100-kilocyc1e oscillator l1, auxiliary modulator 'i8 and the detectors I4, employed in the arrangement of Fig. 2, are in the modified receiving circuit. ‘In Fig. 4, -inte current having a vphase ¿angle variation 4depend ent upon only the Vdifference vin the distances of said body Ato said points, and a phase integrator at said mobile body for .comparing said currents. 2. In a phase integration position determining grator I9 is included between'the `outputs of the ‘ . 9- _ system, means for transmitting from spaced geo graphical points a pair of waves of different fre quencies, receiving means at a mobile body for obtaining from both of said waves a ñrst cur rent and from only one of said waves a second current, said currents having equal frequencies, signal current having vsaid given frequency„the instantaneous diñerence in the phase angle varia tions of vsaidsecond signal current and said ref erence current being related to the'instantaneous change of position ~of said body with respectï to said first station and said second relay station, and a second measuring means .actuated bysaid last-mentioned currents for integrating the last the phase angle of the first current being repre sentative of the difference in the distances be tween said mobile receiver and said stations and mentioned instantaneous differences , during the phase angle of the second 'current being in 10 dep'endent of said difference, and means con '7.' In combination, a first transmittingstation trolled by said currents for integrating during for radiating a vwa've'of a given carrier'frequency, movement of said body the relative phase Hangle a relay'sta'tion lspaced from the'ñrst stationV for travel of said body. changes in said currents. ` 3. In combination, a pair of spaced ground sta tions for radiating harmonically related frequen , . - . - i - . radiating ,a .waveof Vdi'iferent frequency, the ì fre quency of the last-mentioned wave being derived from the first wave and the frequency difference cies, a receiver on a mobile body for receiving said between said waves being a submultiple of each waves, said receiver including means for obtain radiated wave, and means at a mobile station for ing from said waves a signal current having a obtaining from the transmitted wave a signal cur frequency equal to a submultiple of each of said 20 rent having a phase angle related to the position waves and a phase angle representative of the of mobile station and a reference current having a substantially constant phase angle, and means distance between said mobile body and one of said stations andthe difference in the distances be controlled by said currents for integrating the relative changes in phase angle of said currents tween said body and both stations, means for ob taining from one of the received waves a reference 25 during the travel of said mobile station. current having the same submultiple frequency 8. In combination, a primary station, and two and a phase angle representative of the first relay stations spaced therefrom for radiating three different harmonics of a fundamental radio mentioned distance, and means connected to both frequency, receiving means atV a mobile body com of said means for integrating the phase angle change of the signal current during travel of said 30 prising a first channel for deriving from the har _ body. , monic received from the primary station a ref erence current of the fundamental frequency, a 4. In combination, means for radiating from two spaced geographical points different har second channel for deriving from the last-men tioned harmonic and the harmonic received from monic waves derived from a given fundamental frequency, receiving means on a mobile body for 35 one of the relay stations a first signal current of said fundamental frequency, a third channel for obtaining from said waves a signal current and a deriving from the first-mentioned harmonic and reference current both of said said fundamental frequency, the phase angle of the signal current the harmonic received from the other relay sta being representative of the position of said body tion a second signal current of fundamental fre with respect to said points and the phase angle 40 quency, said first signal current having a phase angle variation related to both the change in the of the reference current being representative of distance between said body and the primary sta the position of said body with respect to only one tion and the change in the difference in the dis of said points. and an integrator controlled by tances between said body and said primary sta said currents for ascertaining the net change in phase angle of the signal current relative to the ' tion and the first-mentioned relay station, said second signal current having a phase angle varia change in phase angle of the reference current tion related to both the change in the first-men resulting from travel of said body. said integrator being responsive to every instantaneous change tioned distance and the change in the difference in the distances between said body and the pri in phase angle. and a counter controlled by said integrator for indicating the net number of cycles 50 mary station and the second-mentioned relay station, said reference current having a phase of phase angle change. angle variation related to the change in said first 5. In combination. means at a first station for mentioned distance, means including a beat oscil securing a wave of a given frequency _F and lator for deriving from the reference current and transmitting a harmonic nF of said frequency to a relay station and to a mobile body, means at 55 the first signal current a ñrst intermediate fre said relay station for deriving from the received wave the harmonic (n+1) F of said frequency and transmitting said wave to said mobile body, and quency signal current having a phase angle varia tion representing the first-mentioned difference and for deriving from said reference current and the second signal current a second intermediate means on said mobile body for obtaining from said waves a reference current and a signal cur 60 frequency current having a phase angle variation representing the second-mentioned difference, a rent having` the same given frequency and an in stantaneous difference in their phase angle vari ations related to the instantaneous change of position of said body with respect to said stations` ñrst phase integrator actuated by the ñrst inter wave a harmonic (1L-1) F of said given frequency ting from one station a wave having a frequency mediate frequency signal current and an inter mediate frequency reference current of constant and a measuring means actuated by said cur 6 Ul phase angle from said beat oscillator, and a sec ond phase integrator actuated by the second in rents for integrating the instantaneous differ termediate frequency current and another inter ences during travel of said body. mediate frequency reference current of constant 6. A combination in accordance with claim 5. phase angle from said beat oscillator. i a second relay station for receiving the wave emitted by the first station and means at said 70 9. A method of position determination utiliz ing two spaced stations which comprise transmit second station for deriving from the received nF, where n is any integer, obtaining at the sec ond station from said wave another wave having taining from the 'nF and (1t-DF waves a second 75 a frequency (ni 1) F and transmitting said wave, and transmitting said (fri-DF harmonic to the mobile body, means at said mobile body for ob 2,408,773 11 12 obtaining at a mobilev receiver from both trans mitted waves a signal current F having a, varia tion related to the change in the difference. of the distances between said mobile receiver and said stations, obtaining from the first-mentioned wave nF' a'reference current F having a phase angle independent of said change, and continuously having one of the frequencies (niDF and trans mitting said last-mentioned Wave, obtaining‘at a mobile receiver for both transmitted Waves a, sig nal` current F having a phase angle Variation rep~ resentative of the change in the difference of the distances between said mobile receiver and comparing and integrating the phase differences Wave nF a, reference currentv F having a phase between said waves during travel` of the mobile angle variation independent of said change, changing the frequency of the reîerence and sig receiver. l0; 1A method of position determination utiliz ingv two spacedv stations which comprises trans saìdlstations, obtaining- from the ñrst-mentioned nal currents each to the same intermediate fre quency, and integrating the phase differences between said Waves during travel of the mobile lflîulttingV from one station a Wave having a fre receiver, quency 12F, Where n is any integer, obtaining at WILLIAM M. GOODALL. the second station from said wave another wave 15

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