On Electrostatic Transformers and Coupling

Coefficients.1

BY F. C. BLAKE

Physical Laboratory, The Ohio State University, Columbus, Ohio.

Starting from the experimentally determined fact that the capacity of an air condenser is independent of the fre­ quency of electrical oscillation, it is shown by means of Lord Rayleigh's equations for the mutual reaction between two circuits each having inductance, resistance, and capacity, that for high-frequency conditions when the resistance is negligible compared to the reactance, the capacity reaction between the two circuits can be expressed best in terms of elast- ances. Definitions are given for self and mutual elastances as well as for self and mutual capacitances and the definitions are tested by our knowledge of spherical condensers. The coefficient of elastic coupling is shown to be the ratio between the mutual elastance and the square root of the product of the two self elastances, the analogy with the coefficient of inductive coupling being exact. The coefficient of capacitive coupling between two circuits each having capacity with a capacity in the branch common to both is shown to be a limiting case of the coefficient of elastic coupling, and thereby a condenser of the ordinary or close form is shown to be an electrostatic transformer with a coupling coefficient of unity. The true relationship between Maxwell's coefficients of capacity and the elastances or capacitances is pointed out in the case of the spherical condenser. The ideas developed are applied to the thermionic tube and thereby the behavior of the ultraudion and the experiments of Van der Pol are readily explained. Attention is called to the alternative view of the behavior of condensers toward alternating currents, viz., instead of being paths of low impedance, they are paths of ready yielding or low stiffness or elastance, as suggested by Heaviside and by Karapetoff.

N a paper presented before the American Physical wave-length of the harmonic under consideration, I Society in November 1919, the writer was able K the capacity of the condenser and k the capacity experimentally to verify the equations developed per unit length of the Lecher wires. In such systems by Lord Rayleigh1 for the reaction of one circuit upon equation (3) takes the place of Lord Kelvin's equation another, each circuit having both kinetic and potential for the discharge of a condenser, viz., energy as well as dissipation, i. e., inductance, capacity p2 L K - 1 = 0. (4) and resistance. If L L and L are the self and lh 22 12 In equations (1) and (2) all the self coefficients were mutual inductances, E , E and E the self and n 22 12 determined from geometrical considerations, the mutual mutual elastances, (see below) R , R and R the n 22 u coefficients being determined from the experimental self and mutual resistances, and p the generalized observations. For instance, En is the reciprocal of frequency, then the effective elastance, E and the e the capacity of the plate attached to the Lecher cir­ effective resistance, Re are given by the equations: cuit when it exists alone in space, E22 being the re­ 2 2 (E12-p L12) ciprocal of the capacity of the plate attached to the Ee = En-p'L, Ei P2 U receiver circuit under the same conditions. E12 on the other hand was determined by noting the difference in p2 [Ru (E - P2 L ) - R (E - p2 L ) ]2 (1) 22 22 22 12 12 frequency of the two fundamental tones as the coupling + (E - p2 L ) [ (E - p2 L )2 + p2 R 2} 22 22 22 22 22 between Lecher and receiver circuits was tightened. Similarly, Ln is the self inductance of half of the R = R ~ Rl22/R22 e n Lecher circuit and L22 is the self inductance of the

2 2 receiver circuit. Substituting these values of L and [Ru (E22- P2L ) - R (E V L ) } 22 22 12 12 (2) + R 2[(E - p2L )2 + p2R 2} E in equation (3) one can find the natural frequency n 2 22 22 22 of each circuit when alone in space. It is, of course, The verification was accomplished by working with this natural frequency n that must be used in equations Lecher and receiver systems, thus using short electric (1) and (2) for either primary (Lecher) or secondary waves. For such systems the distributed capacity (receiver) circuit when existing separately. Hence, of the Lecher wires has to be taken into account as equations (1) and (2) become well as the capacities of the condensers. Thus the generalized formula for the discharge of a condenser (E - P2L )2 E = E - n2 L 12 l2 e n n 2 was found to hold, viz., E22 — n L22

2wl . 2irl kl p2 [R (E - n2 L ) - R (E V2L ) ]2 (3) 12 22 22 22 l2 -Y-tan-x- K + (E - n2 L ) [ (E 2 2 2 2 22 22 22 n L22) + p R22 ] ' (5) where I is the length of the Lecher circuit measured from the exploring bridge up to the condenser, X the Re = Rll — R2

*Read before the American Physical Society, Feb. 28, 1920. 2 [ Rn (E - n L ) - g (Ei, - p2 Lu) ]2 1. Phil. Mag. XXI. pp. 369-381, 1886; Scientific Papers, M 22 22 + R22 [ (E - n* L )2 + v2 R™2\ Vol. II p. 484. 2i 22 (6) 23 24 BLAKE: ELECTROSTATIC TRANSFORMERS Journal A. I. E. E.

By causing the Lecher and receiver circuits to approach frequency currents. It is to be noted that equation

each other both Eu and R12 were made to vary, the (11) is the exact analog for reacting systems having

system being so disposed that L12 was practically zero stiffness or elastance, of the well-known equation for

always. Naturally E12 would be expected to increase inductively reacting systems, viz., and Ru to decrease as the circuits approached each other. This was borne out by observation. Calcu­ T - T Ll2* lation really showed that for the frequencies used Lie — Li\ 1 — j • L (12) (n > 108) the last term in (5) was negligible compared 22 Now inertia (inductance) is a measure of the re­ to the other terms so long as R was small. Because u sistance a body offers to a change in its condition of the currents are of such high frequency p2 jR 2 is 22 motion, and stiffness (elastance) is a measure of the entirely negligible compared to (E — n2 L )2 and 22 22 resistance an elastic body offers to its instantaneous con­ (5) and (6) reduce to dition of vibratory motion. If in (12) the coefficient of

2 inductive coupling k is equal to —^12 as is well- E.-En-n IN- E22-n L22

y/Ln L22 2 2 2 2 2 known, then (12) may be written L = L (1 — k ). (13) V [R12 (E22 - n L22) - R22 (E12 - p L12) ] e n 2 So also the coefficient of elastic coupling k is equal to + (E22 - n L22f (7) E 12 and (11) may be written J? - I? #2i2 /in ~ J5 JXe — s/Eu E22 JX22 2 Ee = En (1-k ) (14) 2 2 2 [Ru (E22 - n L22) - R22 (E12 - p L12) ] From the definitions of self and mutual capacitances 2 2 ^ R22 (E22 - n L22) * (g) given it is manifest that if in (10) we take Ln and L22 For distances between the circuits less than 15 per each zero the effective capacity of the primary cir­ cent of the diameter of the capacity plates it was found cuit becomes that Ru was practically equal to zero and (7) reduced r< _ n C122 w — On -p p , in this case to r 2 O12 — on o ^25) 22 C C and if we substitute k2 for —^ 22 (15) reduces to For electrostatic (elastic) coupling between the c — di circuits L12 is zero and we have e~ ^ ' (16) E. = E - n2 L - El2* . n n T which obviously may be made as large as we please &22— Wr L/22 ^ Thus for radio frequency currents the effective by making k approach unity more and more nearly. elastance of a circuit is apparently a function not This accounts for the capacity of a condenser being only of its own elastance, the elastance of a neighbor­ so enormous compared to the capacities of its com­ ing circuit and their mutual elastance but also of their ponent conductors when far removed from each other. self and mutual inductances. If now the self Just as in (13) the maximum value of k is unity so the maximum value of k in (14) is also unity. Thus (di and C22) and mutual (G\2) capacitances of the conductors forming the condensers between the Lecher just as the effective inductance of a coil is decreased and receiver circuits be defined as the reciprocals by the presence of a second coil so also the effective of the self and mutual elastances of these conductors elastance of a conductor is decreased by the presence of a second conductor. and if Ce be the effective capacity of the primary cir­ cuit, then In discussing two mutually reacting inductive cir­ cuits Lord Rayleigh derives the equation Ce — Cu

1 2 T — T — -4- (£12 R22 — L22 R12) , r n \ C22 1 e ~ 11 L22 ^ L22 (P2 L 2 + R222) 9 a 22 n L C ) ^5- • !_ 2 n u W LmCm (17) (10) If in (9) the inductances L and L are negligible or in which the second fraction is positive and with n 22 increasing p2 continually diminishes. Hence, Lord zero we have

Rayleigh remarks that Le continually diminishes with

V - V E^ increasing frequency tending ultimately to the mini­ & e — ^ 11 im , mum corresponding to the disappearance of the dissipa- E22 (H) tive terms. At radio frequencies this minimum has which is, of course, the effective capacity of a con­ been reached and (17) then reduces to (12). If in ductor in the presence of another conductor for high- Jan. 1921 BLAKE: ELECTROSTATIC TRANSFORMERS 25

(5) and (6) we have two mutually reacting elastic spherical condenser the capacity of the condenser

circuits the, taking L12 = 0, (5) and (6) become when the outer sphere is earthed is ,a ^ and when

2 2 0 — a El2 P (R12E22-R22EuY Ee = En • 2 2 + #22 (S222 + V R22 ) 2 E22 b the inner sphere is earthed its capacity is ^ _ • If (18) a

Ru (i?12 #22 — R22 Eu)2 the inner sphere is taken as the first conductor and

Re Rn — 2 2 2 the outer sphere as the second then we have E = 1/a i?2 + R22 CE22 + V R22 ) n (19) and E22 = 1/6 whence and Lord Rayleigh remarks for this case of the dis­ A=j£ _L a-abEu2), charge of condensers through high resistances that ab = a (20) as p2 increases the elastance increases and the re­

sistance diminishes. But here again at radio fre­ giving £12 = 1/6 and consequently Ci2 = 6. Thus quencies the resistance terms disappear compared to k = V a/b and when 6 = » k = 0 and for 6 = a, the reactance terms unless unusually fine discharge k = 1 as it should. If the conductors be reversed wires are used and accordingly the third term on the we get right-hand side of (18) becomes negligible and again the minimum given by the first two terms has been - 4" (1-abEu2), reached and (18) reduces to (11). In other words, beyond a certain frequency the effective elastance, giving E12 = 1/6 as before. The fact that for the spherical condenser E = E22 testifies most strikingly instead of increasing with increasing frequency as i2 Lord Rayleigh says, will in general decrease owing to to one of its fundamental properties, viz., that all the the ratio of the reactance to the resistance steadily lines of force leaving the inner sphere end on the inner mounting in value, the effective elastance ultimately surface of the outer sphere. reaching the minimum given by the disappearance of the dissipative terms.

Comparison of (11) with (12) and of (13)twith (14) leads to the following further considerations. Given two inductive coils each on closed circuit. Starting with them infinitely removed from each other, by causing the distance between them to decrease from FIG. 1 infinity to zero the coefficient of inductive coupling is increased from zero to unity. When alone in space It is customary to define the capacity of a con­ the self inductance of each coil is the magnetic flux denser as the ratio of the charge on one of the con­ from it (through it) when unit current is passing in it. ductors forming the condenser to the difference of So also for any given distance between the two coils potential between the conductors, all the lines of the mutual inductance is the magnetic flux through electric flux starting from one conductor ending on one coil due to unit current in the other. Similarly, the other. The last phrase of the previous sentence given two conductors infinitely removed from each shows that such a condenser is to be regarded as an other to start with. As the distance between them is electrostatic transformer whose coefficient of elastic decreased from infinity to zero the coefficient of coupling is unity. elastic coupling is increased from zero to unity. When It will now be shown that the coefficient of elastic each conductor is alone in space its self elastance is coupling as defined in this paper, viz., the ratio of the the electric flux from it due to unit charge upon it. mutual elastance between the two component con­ So also for any given distance between the two con­ ductors of a condenser divided by the square root of ductors their mutual elastance is the electric flux the product of their self elastances enables one at ending on one conductor B due to unit charge on the once to derive the coefficient of electrostatic coupling other A provided the conductor B has the induced between two circuits in each of which there is a con­ charge of like sign as that on A removed by being denser with a third condenser in the branch common to "earthed." both circuits. That the proviso in this definition of mutual elastance E. Bellini2 has shown that the coefficient k of what is necessary is easily shown from a consideration of the he calls the electric coupling fulfills for the most spherical condenser. It has been shown (equation 15) general case (see Fig. 1) the equation that the theoretical capacity of a condenser is the reciprocal of the effective elastance, E , where E k = V Gi G € e K K 2 fulfills equation (11). Now it is well-known that if a and X 2 (21) 6 are the radii of the inner and outer spheres of a 2. La Lumiere Electrique, 2, 33, p. 241, 1916. 26 BLAKE: ELECTROSTATIC TRANSFORMERS Journal A. I. E. E. where rdingly remembering the reciprocal relationship een elastances and capacitances we have 1 1 + 1 K, ~ K K + 1 1 2 2 1 f 2 1 1 K £2 _ Ei2 _ C 12 + t Gi Ki K{- En 2?22 1 1 Cn C and 22 1 1 1 K + - t Eil K K? = G2 2 (Ea + Ei) (Eb + Es) By taking 1

K12 = Ku' = 00, k reduces to VKnK22 2 c Ci2 (22) (~u7 + ~ur)(~u7 + ~cT) (23) ||/fc II If one redraws Fig. 2B as Fig. 5 by omitting the 1 inductances it is readily seen that the system consists I of four circuits, two of which are exact counterparts

FIG. 2A FIG. 2B of the other two. Viewed from the standpoint of a Lecher system, circuits 1 and 2 of Fig. 5 are equal, as where

1 1 , 1 A 1 Ku and

Kc = Ki + K2. FIG. 5 . In this case Fig. 1 obviously reduces to Fig. 2A, and are also circuits 3 and 4. But by comparing Figs. 4 Professor G. W. 0. Howe3 has shown that Fig. 2A and 5 we see at once that on account of (16) reduces to Fig. 2B wherein

a = 2 c = 2 an( b = 2 KC = K1 + K2 ^ 1 — k ' ^ 1 — k ' * ^ 1 —k ' Consider now Figs. 3 and 4. Now Ei of Fig. 4 is —J— of Fig. 5 as is also E of Fig. 4. The two figures are exactly alike except that in 2 C Fig. 3 the reaction is an inertia reaction while in Fig. 4, C it is an elastic reaction, hence the conductors Ei and Whence 1 E2 are represented as spiral springs while the Us may 2 C12 fc* = (1 - k2)2 — —

i±+-h)(-h+-h)

FIG. 3 FIG. 4 1 be thought of as masses if one chooses. Plainly the coefficient of magnetic coupling k in Fig. 3 is given by c (24) But k (Fig. 5) = -y=tw~ Ln L22 c whence where Ln = Li + La and L22 = L2 + Lb Equally plainly in Fig. 4 the coefficient of elastic 1 coupling k is given by 1^ Cc kc

En E22

where En = Ex + Ea and E22 = E2 + Eb _ Cc \/Kn K22 C\ k 1 3. Electrical World, 68, p. 368, 1916. 2 c Jan. 1921 BLAKE: ELECTROSTATIC TRANSFORMERS 27

circuits have been introduced into the equation to which is equation (22) provided may be taken allow for the distributed capacity of the discharge wires. The writer has proved by experiment that equal to unity, a permissible thing to do for ordinary the effective elastance of an air condenser is inde­ condensers, as has been shown. Thus it is proved pendent of frequency. For circular plates 5 cm. in that the coefficient of electric or electrostatic coupling diameter and 1 mm. thick the mutual elastance E12 is identical for very close couplings with the co­ was determined experimentally by observing the two efficient of elastic coupling. It is thus seen that just fundamental wave-lengths Xi and X2 that existed in as the auto transformer is the limiting case of the the Lecher system when the coupling became tight customary transformer (See Circular No. 74, B. S. enough to produce two. Thus k was equal8 p. 49, Figs. 33A and B) so also the auto condenser V + Xi2 _ , _ , , E transformer (Fig. 33c of B. S. 74 or Fig. 2 of this paper) to and this was set equal to 12 2 is the limiting case of Fig. 4 of this paper. W. 0. ^•i y/Eu E22 Lytle has recently4 verified experimentally equation and Eu thereby determined. It is possible to de­ (22). termine En theoretically from (11) or (14) in certain Several practical consequences follow from the above simple cases as has been done above for the spherical considerations. This paper gives, as it were, the condenser. In all such cases, however, the capacity modus operandi of the capacity coupling of a triode of the discharge wires has been ignored and any valve. It explains for instance the regenerative theoretical value of k or En could not be expected to action of deForest's ultraudion connection,5 for there agree with the value obtained by experiment. For is elastic coupling between the grid and plate and also instance for the plates mentioned above when separated between the plate and filament of a triode valve as 6.84 mm., k was found to be 0.2243 and since Eu = E22

= 0.6109 e. s. u. E12 was found to be 0.1371 e. s. u.,

and thus Ee was 0.3090 e. s. u. But if the Ee is inde­ pendent of frequency it is plain that what happens when one attempts by experiment to determine k is that the

Xi and X2 necessarily so change as to hold Ee inde­ pendent of n and thus the measured value of k and

hence E12 are lower than the theoretical value just in FIG. 6 proportion to the effect of the distributed capacity of the Lecher wires. Thus while E is not a function indeed between the grid and filament. Hence e of the inductance of the Lecher wires it is because deForest's explanation and that of Armstrong on the Xi and X are such as necessarily to compensate for action of this circuit do not differ so much after all. 2 what would otherwise appear to be the influence on That regeneration can occur under much simpler E in equation (9) of Ln and L , n being connected conditions than that given in the ultraudion has been e 22 with the inductances through equation (3). Thus proved lately by B. Van der Pol, jr.6 Indeed his what does change with the electrical constants of the circuits PBC and GAC (Fig. 6) may be thought of discharge wires is the coupling coefficient, being much as Lecher and receiver circuits respectively of a reduced from the theoretical value because of their Lecher system. Evidently many writers and ex­ distributed capacity. Should one attempt to de­ perimenters7 are conscious of the existence of a capacity termine experimentally, for instance, the coupling coupling between the grid and the plate of a triode coefficient between the grid and plate of a thermionic valve though no one seems to have attempted before tube he would findi t a function of the electrical con­ to explain the nature of this coupling. Van der Pol stants of the plate and grid circuits. Should one even remarks that varying the distance between the plates of the external condenser not only varies the , Eil represent ^ _ ^ ^ ^ _ ^ ^ capacity in the plate circuit but also the coupling L coefficient. In the light of this paper this is readily by k2, equation (9) could be written understood. E = (En-^Ln) (1- fci2), (25) It might at first sight appear from equation (9) e k2Eu - n2Ln that the effective elastance of a condenser is a function Whence kr = 2 of the electrical constants of the discharge wires with En-n Ln (26) 2 which it happens to be associated. The terms con­ For the plates mentioned above, kx would equal taining the inductances of the primary and secondary E -i e 0.144 whence k, = 0.338, and 4. Proc. Inst. Rad. Eng. 7, p. 427, 1919. En-tfLn 5. See Goldsmith's Radio-telephony, p. 91 , , also Proc. if one substitutes the value of £ eand!£nin (14) A: would I. R. E. 4pp. 264-6, 1916. 6. Phil. Mag. 38, p. 90, 1919. 8. See for instance Fleming's Principles of Electric Wave 7. Notably Hazeltine, Armstrong and Van der Pol, jr, Telegraphy, 2nd Edition, p. 262. 28 BLAKE: ELECTROSTATIC TRAINSFROMERS Journal A. I. E. E. 1 cordingly there is no justification for calling k and equal 0.702 instead of 0.224 and Eu would equal n

0.429 instead of 0.137. k22 coefficients of (self) capacitance and K12 a co- Future experimentation alone can determine underr efficient of mutual capacitance as is sometimes done. what conditions it is important to know the couplingy Of course the geometrical configuration of the system coefficients of a thermionic tube. Equation (26) shows, of two conductors must enable one to work out the

however, that kx equals k when both are equal tod exact relationship between Maxwell's coefficients and unity, or in other words when the distributed capacityj the elastances or capacitances for any particular of the discharge wires can be neglected compared t3o case, e. g., for the spherical condenser given above. the condenser capacity. In radio practise one gener­ ally employs condensers of large capacity and hence* For this condenser it is known that kn = 1 a ^— by masking the internal coupling coefficient of a 0 — a 1 thermionic tube by an outside coupling of unity one* b2 = — k and k = —r . And it has been shown reduces the need for knowing the internal coefficient. 12 22 b — a And yet in Van der Pol's experiments he found os­ that Cn = a and C = b = C . cillation set in when the plates of his external con­ X2 22

7, Cn C 7 — C12 Cn denser (10-cm. diameter) were 1 cm. apart. Sincei Tj „ _ 22 - Hence k = —p n— > = -p p— the ratio of the distance between the plates to their u diameter did not differ much from the experiments O22 — On O22 ~~ On of the writer, and the capacity and inductance of the external circuits were of about the same magnitude5 j 7 C222 > ana k =-• -p ^— as those of Lecher circuits used by the writer, it is 22

likely that the coefficient of coupling at the moment O?2 - On (29) 5 of oscillation in his experiments was not far from 0.25. E22

Certain types of thermionic tubes, e. g., deForest's 7 _ 1 7 E12

"laboratory oscillion," have the ratio of the distance Or Kn — 77? > #12 — -jFj ™ between the grid and plate to the mean diameter of £j 11 — Ei 22 11 — XV 22 plate not far different from 0.1 and hence their coup­, En f £i and fc = T, V ling coefficient must in general be distinctly less than 22 unity. Other types are still more open. Van del r Those interested have here enough to keep them PoPs experiments seem to call in question the state­' busy for some time. There is, however, one relation- ment made by Miller9 that the input resistance of a. ship for infinite distance between conductors that thermionic tube is always positive for a capacity1 deserves comment. Eliminating the g's and v's load, for Van der Pol with such a load actually hadr between (27) and (28) one obtains ' 1 - fellCn — fci Ci fenCi2 + kn c the tube working as an oscillation generator. 2 2 = 22 k\ Cn ~\~ ^22 C12 1 — ^i2 €12 — ^22 c It might be well to point out certain properties of 2 22 self and mutual elastances and capacitances of con­[ (30) If we now put ductors as compared with Maxwell's coefficients ofF

~ kn = k22 and Cn = c22 (30) reduces to potential and capacity. If qx and q2 are charges and Vi and v potentials then we have Maxwell's 2 5 ki2 = „ 1, k . (31) well-known equations n Cn + C12

qi = kxlVi + k12v2 ) With conductors infinitely removed from each other

1 #2 = ki2Vi + k22v2 j (27) Cn = -7^— = En = and ci2 = 0 = E12 where kn, k22 and k12 are capacity coefficients and kn Cn

Vi = Cn qx + C12 q2 1

= -J— hence ki2 = 0 also. v = C12 qi + c q j (28) 2 22 2 1 C12 Thus the mutual capacitance is infinity in this case, where cn, c22 and ci2 are coefficients of potential. Maxwell long ago pointed out that all the c's arej whereas Maxwell's coefficient of induction (sometimes . called the mutual capacitance) is (negative) zero. positive while kn and k22 are positive but k12 is nega­ tive. Now when the second conductor is absent: In many ways it seems more fundamental to ex- Cn is the self elastance, but in general Cn as well as C12 and c 2 in (28) changes as the two conductors 2 press k2 as JF1^— rather than as GllPl2 and to approach each other. So also in (27) all the &'s are l £j\i£j22 W2 functions of the distance between the conductors and^ this extent the idea of elastance is more fundamental so kn is the self capacitance of the first conductorr than the idea of capacitance. Hazeltine10 has pointed only when the second conductor is absent. Ac- out, however, one important difference between 9. Bureau of Standards, Sci. Paper 351, 1919. electrostatic (elastic) coupling and magnetic coupling. Jan. 1921 BLAKE: ELECTROSTATIC TRANSFORMERS 29 Magnetic couplings may be normal or reversed; Either statement is correct but there are some ad­ not so elastic couplings. If desirous one would vantages in favor of the latter statement; for a con­ be permitted of course to conceive reacting circuits denser is thought of by students, because of the method having both elastic and inductive couplings and hence of approach in alternating-current theory, as a store­ to extend the usual equations of alternating-current house of potential energy and they know that the theory. The extension will probably only prove greater the capacity of the condenser the more elec­ useful when the coefficient of coupling is other than tricity it will hold. Heaviside long ago11 pointed out unity, that is, whenever in the future open condensers that Maxwell's main notion of a dielectric was its are practicable for one reason or another, the triode ability to yield to elastic displacement. It will valve being already a case in point. probably be of advantage in training future students Telephone and radio engineers ordinarily say that of alternating-current electricity to stress more than a condenser offers a path of "low impedance" to the in the past the presentation of the ideas concerning passage of alternating current. This is of course, elastance contained in this paper. Professor correct according to the equation Karapetoff12 has shown the usefulness of the idea of elastance when condensers are joined in series and E has called attention to the hydraulic analog of the I =—, / 1 \ ' When the frequency is so electrostatic circuit. He has called the reciprocal of the farad the "daraf." Professor Kennelly13 has also found the idea of elastance useful. But neither high that the reactance outweighs the resistance, then of these writers mentions the idea of mutual elastance. as the frequency increases the impedance decreases Cordial acknowledgment is made of helpful sug­ and the current through the condenser accordingly gestions received in the preparation of this paper increases. Thinking in the terminology of elastance, from Dr. A. W. Smith of this laboratory and from Dr. it is plain from equation (9) that the effective elastance J. H. Dellinger of the Bureau of Standards. of a condenser decreases with increasing frequency, and hence the current through the condenser increases. 11. Electrical Papers, Vol. II, p. 328. 12. The Electric Circuit, Chapters 6 and 7. 10. Electrical Papers, Vol. II, p. 328. 13. Proc. Inst. Radio Eng. 4, 1916.. p. 47.

NEW BRIDGE ACROSS THE HAWANG-HO which, when received, will be available for consultation ON THE PEKING-HANKOW RAILWAY at its office, Washington, D. C. The Bureau of Foreign and Domestic Commerce ELECTRIC RESISTANCE OF THE has received a cabelgram from Commercial Attache HUMAN BODY Julean Arnold, dated at Peking, China, November 27, During the past few months some measurements have 1920 which reports that the Ministry of Communica­ been made by the Bureau of Standards of the electric tions is calling for bids for a new bridge over the resistance of the human body. In this work the mea­ Yellow River (Hwang-Ho) on the Peking-Hankow surements were made for the first time in such a way Railway, to replace the present bridge which has been as not to include the resistance through the skin where much criticized as not being of sufficient strength to current entered and left the body. By eliminating the carry properly the motive power that is being used. large and uncertain resistances through the skin, results The present bridge, which is by far the longest one on were gotten which are more consistent than any pre­ this line, is 9,875 feet in length, about 11 feet above viously obtained. These show that the resistance of high water, partly through trusses and partly deck the same part of the body of different individuals may girder construction, all supported on very elaborately differ by a ratio of 3 to 2 or even more, the resistance of placed screw piling. One-half of the superstructure a person changes from day to day and often by small was fabricated in Belgium and the other half in France, amounts in an hour, also the resistance depends to and the floor system is all of the stringer type with the some extent upon the position of the body and the openings filled in with metal plates. It was stated extent to which the muscles are relaxed. that the permissible loading is very little, if any, in There is reason to think that a part of the difference excess of "Cooper E-35", and the appearance of the found between different persons and some of the changes structures would seem to warrant this statement. observed in the same persons depend upon patho­ It is understood that the specifications for the new logic conditions. Such measurements may, therefore, bridge will call for a permissible loading of "Cooper be of interest to the pathologist. E-50." The length of the new bridge will approximate A knowledge of the resistance of different parts of 10,000 feet and will probably cost between $15,000,000 the body exclusive of the skin may also be of interest to and $20,000,000. The Ministry of Communications those concerned with life hazards from high-voltage reports that the specifications will be ready sometime circuits, since when accidental contact is made to such this week. circuits the skin is burned at the point of contact and The Bureau has cabled for a set of the specifications therefore largely loses its protecting property.