US1254118A - Signaling-circuit. - Google Patents

Description

3 G. A. CAMPBELL.

SIGNALING CIRCUIT.

APFJC YTION FILED AUG. 18. 1911 Patented Jan. 22, 1918.

INVENTOR. I Gd CampZmZZ BYMWMA ATTORNEY GEORGE A. CAMPBELL, 0F MONTCLAIR, NEW JERSEY, ASSIGINUIB T0 AMERICAN TELE- PHONE AND TELEGRAPH COMPANY, A CGEPORATION OF NEW YORK.

$IGNALING-CIRCUIT.

Specification of Letters Patent,

Application filed August 18, 1917. Serial No. 1863M.

To-aZZ whom it may concern:

Be it known that I, GEORGE A. CAMBBELL,

residing at Montclair, in the county of his sex and State of New Jersey, have invented certain Improvements in Signaling-Circuits, of which the following 1s a specificatlon.

This invention relates to circuit arrangements for signaling systems wherein signals may be either transmitted from or received at the same station. In its more specific aspects this invention is embodied in a subscribcrs telephone station, hereinafter termed, in accordance with common usage, a substation, and more particularly in. the combination of a'substation and a telephone line. Its object is to provide a signaling circuit arrangement which in cooperative combination with a similar and equal communicating arrangement or station shall deliver the maximum amount of energy to the receiving apparatus of said communicating station or arrangement. A further object is to provide an arrangement such that the receiving apparatus is protected from interference by the transmission energy originating at the same station. In other words its object is to provide signaling means characterized by the maximum possible ratio of received to transmitted energy and further characterized by the absence of side tone.

The object of the inventionis attained, in itsspecific aspect, by providing a substation consisting of transmitter, receiver, auxlliary resistance, and a transformer having a.plu.

rality of windings v ich, in combination with a telephone line,""'shall satisfy the following fundamental requirement Given two identical substations designed for invariable two-way communication, and connected by a line of given impedance and length, the

amount of energy absorbed by the receiver.

at the receiving station shall be the maximum part of the total telephonic energy developed by the transmitter at the trans mitting station consistent? with invariabletwo-way communication and, as hereinafter explained, cons1stent with a desirable amount of discrimination against disturbing line noise. lhis fundamental require ment may be stated in terms of the follow ing subordinate requirements which are necessary for its satisfaction: (1) The transmitter and receiver shall be conjugate, that is there shall be negligible side tone in the receiver in consequence of the actuation Patented Jan. as, rare.

of the transmitter by sound waves; (2) the line and auxiliary resistance shall be conjugate in order that none of the energy ab sorbed by the substation from the line shall be wasted in said auxiliary resistance; for a given line having a definite impedance the telephonic energy delivered by the transmitter shall be a maximum; (4) the amount of energy delivered by the line to the substation shall be a maximum, in other words the impedance of the substation as seen from the line shall be equal to the impedance of the line; (5) at a small sacrifice of efficiency it shall be possible toLdiscrimin-ate effectively agalnst disturbing line noise as distinguished from the telephonic signals from the communicating station.

A substation satisfying the above-mentioned requirements is ideal in that its overall efiiciency from transmitter of "one sub station to receiver of the communicating substation is a theoretical maximum which cannot be exceeded by any invariable sub stations whether satisfying the require mentof transmitter-and receiver conjugacy or not. It is further ideal in the sense that a minimum number of elements is employed since at least one auxiliary element is neces sary to secure freedom from side tone.

It might be interred that the addition of an auxiliary resistance element, necessary as it is to secure freedom from side tone, would at the same time necessarily reduce the elii ciency of the substation since energy is un avoidably wasted in said auxiliary resist. ance. That this is not the case and that the etiiciency of the substation of my invention 1 is a theoretical maximum which cannot be of substation for invariable two-Way com:

mnnication is that in which the receiver and transmitter are connected in series with each other across the line. In such an arrangement the over-all efficiency is a maximum 5 when the resistance of the receiver is equal to that of the transmitter. When this condition is satisfied obviously fifty per cent. of the energy delivered by the line to the substation is wasted in the transmitter and 1a fifty per cent. of the energy delivered by the transmitter is wasted in the receiver. Further such an arrangement labors under the disadvantage of full side tone. In the substation of my invention fifty per cent. of

' the energy delivered by the line to the sub dom from side tone. The foregoing consideration will serve to explain the desirability of having the line and auxiliary resistance conjugate as well as the transmitter and receiver.

In my present invention I provide a substation comprising transmitter, receiver, auxiliary resistance and transformer and so proportion said component elements and so relate them to a telephone line and to each other that, in combination with said tele- 44 phone line, said substation satisfies all of the foregoing requirements.

I have discovered that the above-mentioned requirements may be satisfied by a large number of arrangements employing 45 the minimum number of elements and all equally efficient and without side tone. While theoretically all these arrangements are equally good, practical considerations make certain arrangements preferable.

My invention will now be fully understood by reference to the accompanying drawing in which:

Figures 1, 5 and 9 are schematic diagrams of three forms of substations in accordance with this-invention, said diagrams being so arranged as to clearly indicate the equlvalenceof the different circuits. Figs. 2, 6 and 10 are circuit diagrams showing the arrangement of the several forms of substations in reater detail. Figs. 3, 7 and 11 are circuit diagrams indicating the relative direction of current flow in the several circuits shownin Figs. 2, 6 and 10, respectively, during transmisslon, the dotted lines indicating elesidered. The condition, then, that the subments through which no current flows. Figs. 4, 8 and 12 are similar diagrams indicating the relative direction of current flow during reception. i

In order to illustrate the scope of my 1n- Vention and elucidate the principles on which all specific embodiments rest, a general theoretical discussion will now be given which applies to all substations satisfying the requirements heretofore stated in this specification. In this discussion and the equations and formulae included in this specification the subscripts l, 2, 3 and 4 will refer to transmitter, receiver, auxiliary resistance and line respectively. Thusl 1 1,, L will denote the currents flowing in transmitter, receiver, auxiliary resistance and line respectively, while R, will denote the resistance of the transmitter, R, the resistance of the receiver, etc.

Consider a substation consisting of transmitter, receiver, auxiliary resistance and appropriate transformer windings, connected to a line of given impedance. In practice the line connects two similar and equal substations between which communication is 9.0 established. It is awell known principle that if a terminal impedance is connected to a source of electromotive'force through a line of impedance i Where R, is the resistance and R the reactance component of the impedance, the

terminalimpedance must be R,iR'., for maximum absorption of energy. In particular if the line impedance has no reactance component, the impedance of the terminal arrangement as seen from the line should be equal to the resistance component of the impedance of the line. The condition, then, that the substation shall have maximumv energy absorption from the line is that its impedance, as seen from the line, shall be equal to the line impedance. The significance of the foregoing statement may be explained by reference to Fig. 2, as follows: Let the substation be disconnected from the line and lot the impedance of the substation" be measured across terminals a and d. Then the impedance so measured shall be equal to the impedance of the line. With the line terminatedat each end by a substation satisfying this condition, the line may bc'replaced, as regards transmission from either substation, by an impedance element of resistance equalto-theimpedance of the line. Any reactance effect, which isin practice small, may be eliminated by neutralizing reactance and, therefore j need not be constation have maximum energy absorption from the line is that its impedance as seen from the llne be a pure resistance of value The total expressed by the formula inseam equal to the impedance of the line. This condition is evidently equivalent to the fol lowing requirement; let an electromotive force be impressed on the substation termr nals through a resistance equal to the im pedance oi the line; then the energy consumed in the substation shall be equal-to the energy consumed in said resistance,

Further, line and auxiliary resistance are conjugate by reqidrement (2), as hereinbefore stated, or in other words, the auxiliary resistance is connected to. points of equal potential with respect to an electromotive force applied to the line terminals. Moreover, the impedance of the substations as seen from the line should be equal to that of the line. Let, then, an electromotive force E, be impressedthrough a resistance ll, on.

a substation whose transmitter and receiver resistances are ll, and 3,, respectively, and let the resultant currents in line, transmitter and receiver be 1,, l, and l 'respectively;

the impedance across the substation termi na ls must be H, as seen froir' the line and the total r sistance in series with E, is 2H,, and since the current in the line is 1,, it follows that E energy consumed may then be lflt, L lt, +1 3, LE, '4 Since the energy consumed by the substation is equal to that consumed by the re sistance ll, and therefore one-halt of the total energy consumed, it follows that requirement lmay be formulated by the i'ollowing:

mi n

y This equation states that the, energy consumption in the resistance R, .qual to that in the substation, and that the substation is equivalent. as seen from the line, to a resistance of value R Similarly, if transmitter and receiver are conjugate the condition that the transmitter shall have its maximum output to line and auxiliary resistance may be :tormulated as follows: Let an electromotive force E, in the transmitter produce eurrei'its 1,, l, and.

l, in transmitter, line and auxiliary resist Equation (2) i the analogue of equation (1) and may be interpreted as follows by reference to l? 19;, 2: Let the transmitter be disconnected from, the terminals 5 and c and let the impedancebe measured across said terminals. Then. if equation (2) s sat1stied the mpedance so measuredis equal to the impedance of the transmitter itself. In

other Words, the impedance of the combination as seen from the transmitter is equal to station; then, by equation (2), l/EZ'W is the amount of energy delivered to line and auxiliary resistance. Let the amount of energy taken by the auxiliary resistance be m times that taken by the line, then the amount of energy taken by the line is so that the transmitting eiliciency is measured by Of the total energy delivered to the receiv ing substation, let the transmitter absorb 3 times that absorbed by receiver; then the reeeivinp; etticiency is measured by l (4) The over-all e'tliciency from transmitter of one station to receiver of communicating station is clearly proportional to the prod-,

not of the transmission efficiency and receivng eliiciency; therefore the over-all etliciency isby formulae and (4:)

(fi st If m and :I/ were independent, clearly the overall eliiciency would be a maximum for co y :0. For all substations embodying the principles of my invention it may be readily shown, howei'er, that a: and 3 are connected by the relation arr :1. Eliminating a: from the above formula by mcansof this relation, the expression for the over-all ellic'iency becomes la order to demonstrate the'above statement, namely that m c :1, designate the elements or branches '1, R, X and L by 1, 2, 3

1 by the transmitter at the transmitting sub 12 a4 Also by equation a 1 (8402B; (S42) 2R2 40 1 4R 4 and by equation (2) Now it is a fundamental principle which is deducible from elementary algebra, that That is the current set up in by a unit electrom'otive force in is equal to the current ""set up in by a unit 'electromotive force in 41 14' branch 1 branch 4 branch 4 branch 1. and equation (2') by R aii'd subtracting it follows that:

Now in accordance with the notation adopted in this specification, the energy consumed in branch 3 is w times that consumed inbranch 4 when an electromotive force acts 'in branch 1; therefore 40 Also the energy consumed in branch'l is 3 times that consumed in branch 2 when an electromotive force acts in branch t; whence 14) 1 z4) 2 Multiplying (b) and (a) (so am y/(se nt From (11) and (d) it follows "at once that m O b viously the expression given by formula (5) is a maximum when 3 :1. This means that for a given amount of telephonic energy developed in the transmitter at the transmitting substation a maximum amount' is usefully delivered to the receiver at the receiving substation connected by the line, when y: .Since the maximum amount of energy in the receiver is the prime desideratum of telephony, it would appear that the substation should be designed to make 3 :1. Another consideration, however, modifies this conclusion somewhat, namely, the effect Multiplying equation (1) by R,-

designated N of line noise. Since the line noise originates in the line the amount delivered to the receiver is proportional to A 1+y (see equation' l) while the amount of energy delivered from the transmitter of the communicating station is proportional to,

(see equation 5). The ratio of the latter to the former is 1 1+y and this increases as 3 increases beyond unity. It will be clear, then, that if .-y is made greater than unity the substation discriminates against line noise as compared with the signals it is desired to receive. The amount of discrimination desired depends of course on the amount of line noise present.

For conditions occurring in practice I have found by experiment that a desirable value value of 3 the over;

for y is 1.4. With this all efliciency is reduced 2.8% below the maximum for 1 :1, while the receiving efliciency alone is reduced 16.6%. It is thusseen that agood degree of discrimination against line noise is obtained with a small loss in over-all efliciency.

The above considerations as to over-all efliciency and discrimination against line noise may be formulated as for an electromotive force inserted in the line. In this equation y is to have a value lying between 1 and 1.5 preferably.

Proceeding now to a description of the specific circuits, one form of my invention is illustrated in Fig. 2 in which L represents a telephone line terminating in' a substation comprising a transmitter T, a receiver R, an auxiliary resistance X and a two winding induction coil,

nd N The line L, resistance X and re 'eiver-R are connected to a common terminal d, the remaining terminals he windings of which areb and c of the -esistance and receiver being inter-connected. by the windingsN and N of the induction coil, with the transmitter T connected in parallel therewith. The re maining terminal of the line is connected to the junction point a of, the two windings of the induction coil. A condenser may be provided in series with the winding N if desired, so that direct-current from a distant source will flow over the line to terminal a and thence through the'winding N to terminal b. At terminal b the current divides, part flowing through the transmitter and resent the direction of current flow at any giveninstant. When the transmitter T is operated, variations in the current flow are produced, the effect being equivalent to applying a variable electromotive force to the transmitter. At a given instant a current I fiows from terminal 6, through the transmitter and winding N to terminal a, where the current divides and a current 1, equal. to I flows over the line and through the auxiliary resistance X, to the terminal 5, while a current 1 -4,, flows in parallel therewith,

through the winding N Potentials are induced in the windings of the transformer of such value and direction that terminals 0 and d are brought to the same potential, so that no current flows through the receiver during transmission and consequently the.

substation is anti-sidetone.

The action during reception is indicated. in Fig. 4 and is as follows: Upon the application of a receiving potential to theline terminals, since no current flows through the auxiliary resistance, the line and receiver are in a series circuit and a current 1 equal to L flows from terminal a, through the re ceiver and over the line L, to terminal a. A current I, flows in parallel therewith from terminal 0, through the transmitter and the winding N,, to terminal a, where the two currents merge and a current L-l-I, flows from terminal a, through the winding N to terminal 0.

the same potential, so that no current is Wasted in the aux liary resistance during reception.

The proportloning of the arrangement of Fig. 2, to satisfy the fundamental requirements of the substation of my lnvent on, Wlll now be given. In deriving the deslgn formulae, the resistances of the transformershown that these simplifying assumptions are justified and that thdassumed conditions may be closely realized in practice by careful design.

To formulate the condit1on for conpigacy of transmitter T and receiver R, assume an electromotive force in the transmitter circuit and assume thatthe required condition of Potentials areinduced in the transformer windings of such value and direction that terminals 1) and cl are brought to conjugacy is satisfied. In other words,assume that the terminals of the receiver are at points of equal potential with respect to an electromotive force applied to the transmltter. Let 1,, I 1 and 1,; denote the currents flowing in the transmitter, the receiver, auxiliary resistance and line, respectively, and R R R and R denote the resistances of the corresponding elements. The conditlon of conjugacy of the receiver, with respect to the transmitter, requires that no current flow through the receiver during transmission and hence 1 :0. It 'isalso clear from Fig. 3 that 1 :1 Assuming that a potential is applied across terminals b and c, the potential drop through windlng N, must equal the IR drop through the line and auxiliary resistance. Consequently,

if at, denote the number of winding turns through windings N and N and the IR drop of the auxiliary resistance X must equal zero. Hence, f n, denote the number of winding turns in coil N Kn Kn -R L Also since the algebraic sum of the ampere turns of the transformer windingsmust equal zero, it follows that Referring now to Fig. 4 which shows the condition when receiving, since the trans mitter and the two transformer windings are in a series closed circuit, the algebraic sum of the drops through windings N and N and the IR drop through the transmitter must equal zero. Consequently l urthermore, since points I) and d are atthe same potential, the IR drop through the transmittermust equal the IR drop through the receiver and hence 5 Furthermore, the algebraic sum of the amere turns of the transformer windings must e zero, so that 1. Also Therefore E; -11 -1: R1" 2 4 V i 2) 11 z I4 I1 2 I 2 whence R n i 1 2 (9) il i $a Substituting equation 8 in equation 2 and remembering that during transmission 1 :1

we get I Substituting equation 10 in equation 6 we Collecting formulae 7, 9, 11 and 12, we have n ece) e Solving equations (6) and (d) we get ii 1-1 g r-l Simplifying we have I v 1 1-1= whence y+1 r= 13 v y From equations 13 and (a) From equations 13 and (b) we have From equations'l3 and (0) we have R3+B4=R12 Substituting equation 14 in the preceding, we get Collecting, we have as the design formula. for the substation of Fig. 2, the following:

It will be noted that in the above formulae q the impedances of the transmitter, receiver and auxiliary resistance are given in terms of the impedance of the line and the ratio 3 while the ratio of the transformer windings is given interms of the ratio 7 Consequently, having given the impedance of the line and having selected a suitable Value for 7 the remaining elements of the substation may be readily computed.

A modified form of substation is illus 'trated-in Fig. 6, which differs from that of Fig. 2, in that the transmitter is shunted only by the winding N while the line connected to the terminal of the winding i 41.

through the winding N instead of being connected to the common terminal of the two windings as in Fig. 2. A condenser may be inserted in series with winding N so that direct current will flow from the Zinc heeaaue ne through winding N to terminal 25, and thence in parallel through auxiliary resistance X, and through the transmitter T and receiver R to terminal d, from which point it flows back over the line.

The operation during transmission will be clear from Fig. 7. A variable potential applied to the transmitter causes a current I to flow in a local series circuit, including the transmitter T and the winding N An line causes a current I equal to 1 to flow from terminal a, through the receiver R and over the line L to termmal a, and thence through the winding N to terminal Z). A

current I flows in parallel therewith from terminal a, through the transmitter to terminal I), where the two currents comblne and a current I a-I flows from terminal b through the winding N to terminal (1. Potentials are induced in the transformer windings of such value and direction that terminals 6 and d are brought to the same the auxiliary resistance.

A comparison of Figs. 1, 5 and 9 shows that the several substations herein disclosed differ from each other only in the connec- -potential, so that no current flows through tions of the transformer windings. Refer- 1 ring to design formulae A for the substation of Fig. 1. it will be seen that the expressions for the impedance of the transmitter, receiver and auxiliary resistance as given in the last three formula: of the group are independent of the ratios of the transformer windings so that these expressions will hold true' for all of .lhe substations herein dis closed. Writing connecting terminals or and 7) and a and 0.,

respectively, may be expressed as follows: N 771 N n -n Substituting these values in equation 18,

We get as the corresponding equation for the substation of Fig. ti

lhe design formulae for the substation or Fig. 6 then become of the two windings so that direct current' from the line flows through the windings N and N and thence in parallel through the auxiliary resistance X. and through the transmitter 'l and receiver R to terminal at, from which point the current tlows back over the line.

During transmission. as indicated in Fig. 11, a variable potential applied to the trans mitter causes a. current 1 to How from ter minal 0, through the transmitter to terminal I), where the current divides and a current ll equal to L tlows through the auxiliary resistance K, orerthe line L, and through the winding; N as terminal a. A current I ll flows in parallel therewith from terminal Z), through the winding N to terminal c. Potcntials are induced. in the trans:

.the same potential, sothat no current flows through the receiver.

During reception, as indicated in Fig. 12,

since no current flows through the auxiliary resistance, the receiver and line are in a series circuit and a potential applied to the lineranses a current l; equaluto ll. to flow from terminal r through thereceivci' R, over the line L and through the Winding N back to terminal c. An induced current il flows in a local closed circuit, including the transmitter Taud the winding N Po tentials are induced in the transformer windings of such value and direction that points 0 and d are brought to the same potential so that no current is wasted in the auxiliary resistance.

Comparing Fig. 10 with. Fig. .2, it will be seen that the number of turns of the wind- The design formulae for the substation of Fig. 10 may then be written The type of substation disclosed above and illustrated in the accompanying drawing is but one of a large number employing only one transformer and one'auxiliary resistance and all of these are ideal in the sense that they satisfy the fundamental requirements for an ideal substation, as stated heretofore in this specification. It will be understood therefore, that my invention is not limited to the specific embodiments herein illustrated, but is broadly directed to providing a substation comprising a single transformer and only one auxiliary element, which is so proportioned with reference to. the line with which it is to be'cooperatively combined, that it is ideally efiicient and substantially without side tone. Furthermore, I do not desire to limit the design ofthe substations herein disclosed and illustrated to the accompanying design formulae. These formula: are derived on the assumption that ideal transformers are employed and that the component elements have no reactance, assumptions which are only approximately justified in practice. When particularly high precision is desired I may, therefore, proportion the substation more precisely by taking into account the fact that the transformer impedances are finite, and that the line and the various substation elements may have in general some reactance. The accompanying formulae however, give quite satisfactory results, and the methods by which they are derived will enable one skilled in the art, to compute more precisely the substation constants when desired. V

It will be understood that in the appended nals.

claims, Where certain elements are said to be conjugate, or certain impedance relations are said to exist, since in practice these conditions can in general only be approximated, these expressions .will be satisfied by structures substantially conforming thereto, es-

pecially where some compromise with respect to the rigid requirements is necessary in order to discriminate against line noise.

It will also be understood that while I have specifically illustrated and described m invention as embodied in a telephone su station it is capable of many and varied embodiments which render it applicable in other kinds of signaling systems and consequently my invention is not to be limited to the particular form and use herein disclosed. It will be further understood that in this specification the word substation is employed in its generic sense and that consequently its significance is not limited to a subscribers telephone station but embraces broadly a telephone station includin a repeater station for relaying telephonic sig- What is claimed is:

1. In a two way signaling system, the combination of a transformer having a plurality of windings, and fourlcomponent elements consisting, respectively, of a path for the transmission and reception of signals, .a

points of said closed circuit, and another winding joining the third junction point of said closed circuit with said series circuit.

2. In a two way signaling system, the combination of a transformer having'a plurality of windings, and four component elements consisting, respectively, of a path for the transmission and reception of signals, a path including transmitting apparatus, a path including receiving apparatus, and a path including a balancing resistance, said last three mentioned paths being connected in a closed circuit, a series circuit including said first mentioned path and one winding of said transformer connected to the junction point of said third and fourth mentioned paths and one of the remaining junction points of said closed cir cuit, and another winding joining the third junction point of said closed circuit with said series circuit, said elements being so proportioned and related-that the impedance of the combination comprising said transformer, and said first, third and fourth mentioned paths,'as seen from said second mentioned path, is equal path.

to the impedance of said second mentioned 8. In a two Way signaling system, the combination of a transformer having a plurality of wi'ndings,and four component elements consisting,.respectively, of a path for the transmission and reception of signals, a path including transmitting apparatus, a path including receiving apparatus, and a path including a balancing resistance, said last three mentioned paths being connected in aclosed circuit, a series circuit including said first mentioned path andone winding of said transformer connected to the junction point of said third and. fourth mentioned paths and one of the remaining junction points of said closed circuit, and another winding joining the third junction point of said closed circuit with said series circuit, said elements being so proportioned and related that the impedanceof the combination comprising said transformer and said second, third and fourth mentioned paths, as seen from said first mentioned path,-is equal to the impedance of said first mentioned path.

4. In a two wa y signaling system, the combination of a transformer having a plurality of windings, and four component elements consisting, respectively, of a path for the transmission and reception of signals, a path including transmitting apparatus, a path including receiving apparatus, and a path including a balancing resistance, said last three mentioned paths being connected in a closed circuit, a series circuit including said first mentioned path and one winding of said transformer connected to the unction point of said third and fourth mentioned paths and one of the remaining junction points of said closed circuit, and another winding joining the third junction point of said closed. circuit with said series circuit,

said elements being so proportioned and related that said third and second mentioned paths are con ugate.

5. In a two way signaling system, the

eoi'ubination of a transformer having a plurality of windings, and four component elemus consisting, respectively,of a pathfor the transmission and reception of signals, a

path including transmitting apparatus, a path including receiving apparatus, and a path including a balancing resistance, said last three mentioned paths bein connected in a closed circuit, a series circult including said first mentioned path and one winding of said transformer connected to the junction pointof said third and fourth mentioned.v

paths and one of the remaining junction points of said closed circuit, and another winding joining the third junction point of including transmitting apparatus, a path in-' eluding receiving apparatus, and a path in cluding a balancing resistance, said last three mentioned paths'bemg connected in a closed circuit, a series circuit including said first mentioned path and one winding of said transformer connected to the junction point of said third and fourth mentioned paths and one of the remaining junction points of said closed circuit, and another winding joining the third junction point of said closed circuit with said series circuit, said elements being so proportioned and related that the impedance of the combination comprising said transformer, and said first, third and fourth mentioned paths, as seen from said second mentioned path, is equal to the impedance of said second mentioned path, the impedance of the combination comprising said transformer and said second, third and fourth mentioned paths, as seen from said first mentioned path, is equal to the impedance of said first men tioned path, said third and second mentioned paths are conjugate and said fourth and first mentioned paths are conjugate.

, In testimony whereof l have signed my name to this GEORGE A. CAMPBELL.

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