E~PERIMENTAL VIOLATJON OF NEWTON'S THIRD LAW

Stefan JoIarinov

Institute f or FlA'ldaoren t~l Physics

Morellen feldgasse 16 A- BOlO C-ral, Austria

Nl..ml'l"(lus experilrents have shown that GrassFII:lnn's formula for tile force of inter­action of two curren t e\errents (which allegedly is accepted as the ri!t1t ooe by official physics) is wrong. Wrong are also the formulas of A~re , Whittaker lind NeUlMnn. Only Marlnov's formula, introduced recently by !te, resists ag.linst all ~nC/lO'n experioonts. Marlnov's formula preserves Newton's th i rd law . but not entire­ly, as the forces with wh ich two current elerrents interact are equal and opposi t el. directed but may not lie on the line connecting the elerrents. I report on an expe­rirrent carried out by !rE! . t he "rot ating AfI1)ere bridge with interrupted current", which violates the angular rromentum conservation Taw. Althou!tl giving rl~t predic tions to all known e>:perirrents. I show by the help of an original experirrent that even Marinov's fornATa is not perfect. I am howewr firmly coovi nced that II better fonnula can be never found.

1. MARINOV'S FORMULA

The force with which a current elerrent t dr ' ac t s on another current elerrent Idr,

to Which the ~ctor distance is r , is described by tile following fhe different for­

nlJhs, al1 of which seem t o be accepted by official physics as valid:

1. Al!pere's formula (1823)

df - (lIolI'/411r5 ){3( r .dr )( r .dr' )-21(dr .dr')lr . ( 1)

2. GraSSll\Clnn's fornsla ( 1845)

df . (fJoll'14'1r r3)dr x(dr '><r ) • (lIo !I·/4T1r3}{( r. dr )dr ' - (dr .dr ')r l. (2)

3. Neumann's forll'llla (tile middle of ~ I X- th century)

df . - (lIol! ·/4T1r3)( dr.dr ')r . (3)

This forlOOla. as a matter of fact . was introduced by me(l) and the narre "Neumann's

fornsla", rrort! precisely. "NeulI1I.nn's differential fornsh" was attached to it by me.

4. ~ittaker's formula (the end of nineteenth century)

df . (llo Jl'/411r3){(r. dr ')dr + (r .dr)dr ' - (dr .dr ') r l. (4)

The name of ~ittaker was attached to this formu la by !re(I), as Whittllker(2) consi­

<leNd it seriously as a contJ(! titor t o Ampere's and Grassmann's formulas.

5. Harlnov's formula (l993){1)

<If . (uo

ll'/4nr3)( r .dr ') ctr!2 + (r .dr )dr '/2 - (dr.dr' )r J. (5)

For the force of interacti on of two closed circui t s. Land L', the first te rms in

all above fo rmulas inte!lra:te to ze ro, and all of t hem lead to the following lnte 9ra1

Neumann's forlllUla

f " - {lIo/411)11'/S (dr .dr ')r /r3. L'

(6 )

- 2 -

Offici~l pllysics asserts that the force with which one current elenent acts on

another curr<en t elemerrt:cannot be observed and consequently it accepts tha t all above five fomulas II'1II)' be valid. This point of view was canonize d by Jeans(J).

It ;s t rue that one cannot observe the action of one cur rent elerent on anot her

current elemen t, but one ca n observe the ac t ion of a closed circuit on II current ele­

ment. And for such cases the formulas (1) - (5) may predict different results. Then,

if working with alternati ng cur rents , we can observe forces of interaction between

unclosed circuits. Offi cial physics, proceedi ng f rom the displacement current dogna

introdlJCed by Maxwell (4 ). asserts t hat there are not ' unclosed d n;ui t s', as between

the pla te s of the circuits ' condensers "displacement currents· f l ow which are

OI!!J'IetiClllly identical t o conduction cur ren t s, so that th@ circuits b@come comple t e.

I showed{l) by the he lp of nU!lerous experirrents thllt disphcerrent currents do not

@Jr.is t, as th@y n@ i th@r ac t wi th potential forces on o the r currents nor react wi th ki­

netic forces to the ~cti on of other curren t s. Th us "unclosed circuits· do exist. The

first experiment repor ted in th is paper i s carried out wi th such unclosed ci r cui t s.

1 pointed out to experiments{l), ca rri ed out by rre o r by other persons, Wh ich in­

validate all differential formulas (1) - (4). But t o the best of lIlY ~nowledge there is no eXllerirren t described in the literature which can invalidate formula (5). I have

however conceived and carried out such an e)(periment (see Sect. 7). Thus ne i the r M:l-

rinov's fonnl,da is perfect.

mula clln be neve r found , so

is the cardinal fonrula."

Nevertheless. accordi np to "lY f irm 0rlnion, a better for­

t ha t using the elqlression of Ma)(Well 4) we Cln say; "This

Thus, there are already too III/Iny experiments(l) which i nvalida te formulas (1) - (4).

As only one con tradic t ing experiment is sufficient to invalidate a fortrula, I shall

point out very brie f ly t o some of the basic falsifying experiment s .

First le t me no te that Lyness(5) showed t hat the force with wh iCh a closed cir­

cuit acts on II curr en t @l@ment is equal according t o A~re's and Q>assmnn's formu­

las.

According to GraSSmllnn'S f o rlrula th@ force wi th which II closed circuit acts on a

cur ren t element must al ways be perpendicular t o the latter. Thus both Ampere's and

Grassmann's formu las (1) and (2) are invalidated by the nl.llll!roU$ exper irren t s carried

out by Hering , Graneau, Nicolaev, Si~lov and Marinov where longi tudinal forces ac­

ting on a current eleTrent have been observed( 1).

According to NelMTlilnn's fo rnu la (3) t~ton's third law 11lIst be preserved at the

magne t ic in tera ctions . The first '.,periment reported in thh paper which viol E New­

ton's th ird l aw invalid;rteli thus Ne ulli'Inn 's fornuh ( t his experi ment i nva lidate; also

Ampere's fornula) .

Attordi ng t o htl\ ttake r ' S forlllJl a (4) a closed d rcui t cannot act \oI i t h I ongi tudi na 1

forces on a current elerrent as the first te rm i n (4) integrates t o zero and the other

two t enns give a force perpendicular t o the curren t elerrent. As lIlY SIBERI AN COllU ma-

- 3

chine demonstrlted(I,6-9 1. longitudi nal forces acting on the current elements c~n be

generated also by a closed circuit. Thl,l$ also lrt1ittaker's fornuh is falsified.

2. THE lORENTZ-IWUNOV EQUATICII

I showed t .... o decades ago PO) that if proceeding from the axioll'llt1cal lows of Cou­

~ and Neumann (the name of the last law Is given by ne(I)) for the electric and

IN.gnetic energies of two electric charges q. 'I' . separated by a distance rind -owing

with vel(H:jties 'I , 'I ' (we Qn always accept the equality qy • Idr)

U - (l/bto)qq'/r. W ,,- {llo/~,,)qq' v . v '/r. (7)

one cones, by the help of elementary cllcu1lt10115, to the following equiltion for the

(orce with whiCh the charge q' acts on the charge q

f " - qgradt ~/at + .,"rotA, (8)

• " (1/4mcJq'/r. (')

are the electric and f!la9'letic potentials which the cha r ge q' generates at the point

of location of tile chargE! q. If we have a system of n cllarges qi, the respective sums

are to be taken in for ... 1as (9). If t - 0, aA/at - 0, equation (8) gives fo .... ula (2).

FOnIILIia (8) is called by III! tile Lorentz-GraSSlllilnn equation.

I came to Marinov's fOl'lllUh by s)'nIlIetrizing GrnsBenn's fOl"nlh in the following

way: If denoting by df ' the Grassmann force with which the curnmt elel!l!nt Io:tr acts

on the cttrM!nt eluent I 'dr ', t hen I accepted that the actual force with which I'dr '

acts on Idr is given not by fo ... uh (2) but by the following fo .... uh (note that r -

- r ') or - (df - df ')/2, (10)

wtlidl leads to formula (5). Consequently the force with which Idr lIets on I'dr' will

y. - {df ' - df )/2 - - af'. (11 )

How the fOr'Ces with which two current eleaents IIct one on IIMlther will be equal

and oppositely directed (liccording to GrnsIMnn's fOl'1llUh theY ere not). Thus I

saved Newton's third law. But not totally! As one can easily see, tile two forces

(10) and (11) may not lie on tile line connecting bo t ll current elelTents , as 11 !!!Ust be

according to Newton's third hw.

In thfs paper I shall report on an experi .. mt carried out by ITe which violates

N!!wton's third law and the effect of which is calculated proceeding fro. Harlnov's

fOnllu\a (5).

I\fter the s)'lTmetr ization (10). tile fundllmental equation in electromagnetism is no

lION! to be written in the wrong fOrlll of the Lorentl-Grassmnn equation (8) but in the

fonn of the Lorentz-Marinov equation

f /q .. - gradilO - 3A/3t + v~rotA - vdivA/2 - (lIo/8lr~q'( r . v ) v '/r3. ( 12)

- 4 -

where V is the vol~ of location of the charges q' rooving with velocities y ' and

generating the electric and ma9'1eti c potentials t, A at the point of location of

the test charge q rrovlng with velocity ....

A, (r .Y) ... '. (yx(v '><v }( r.v ) t v (v ', v )(r.v )J/y2,

formula (12) can be written in the form, calling f /q global electric intensity.

f/q '" [glob " - grlld<l> -aAj at + . "rotA - vdivM2 +

(13 )

(llo/8'1f)y",q'{ V><Y ')(r .v1/v2r3 - (lJo/8~iq'(v. v' )( r . V )li r3.

[ coul + Etr + Errot + ~hlt + Evett-mar + Esc_mar' ( 14)

Thus the global electric intensity. [ glob' Is equal to the SlMII of six electric in­

tensities: the Coulonb, trans forrrer , rrotional. Itlittaker, vector-Marino .... and scahr­

I'Idrinov electric intensities. The reader sees thus that after making the childish - elemenhry IIss UllJltion (10).

I ClUTe t o the discovery that besides the well-known lorentz vector magnetic intensi-

!>'

there 3M! three other magnetic intensities;

The Marinov vector magnetic intensity

8mar .. (llo/8lT)'Q'(vxV')(r .V )/v'r3.

The htlittak.er scalar ma!1letic intensity

(l/2)divA z - (llo/8n}/Q'( r .v ')/r3. V

The Marinov scalar magnetic intensity

Sln/Ir " - (llo/81T)iQ'{v . ... ')( r . ... 1/v'r3.

If wri ti ng

8 .. 8lor + 8m.)r' s ~ \thit + Sln/Ir'

( 15 )

( 16 )

(17 1

( 18 1

(19)

ca11ing 8 the vector 1n/11ll!tic intl!nsity and S the scalar magnetic intensity. the La­

M!ntz-Marinov equation can be written in the fo11owing form

EgIOb

.. - gradO - <lA/3t + ,,' + ... S- E + E +E coul tr vett-m~gn ( 20)

where Evect-ma!J1 and Esc- ma !J1 can be called vector-malletic and scalar-magnetic elec­

tri c intensities. ()Ie rey pose the question: How was it possible that during two centuries of elec-

trol"llagnetism hlJllanity has not noticed the existence of the Whittaker. vector-Marinov

and scalar-Mar inov magnetic intensities?

5 -

The answer is the fol1()101ing: Only In "sophisticated" lIa!JIetic systeMS (such as Wi

SIBERIAN C!l.JU Illagnet(1.6.9~ un one reveal that besides the Lorentl vector ..... gnet ic

intensity. 810r ' there is also Marinoy vector _91ftic intensity. BNr . On the other

side, the scientific conmunity has not plid attention and lias Plit under the rug the

classical experiments of He r ing(Il) carrie<l out at the beginning of the century when'!

longitudinal forces acti ng on the curren t elements have been obse rved. And only such

forces give Indication for the uistence of the Whittaker and Marinoy scalar IMgnetic

intensities.

[verybO<ly knows tha t "l.J'Icomfortable" experiments Ire not to be put IofIder the rug.

Neither uncolllfortable fonnu1as. But silO'll !III! a textbook on electr(IIRlIgnetisll published

In the last years where Gnsslllllnn's (orlllll" is explicitly writtenl

I canrlOt abstain from the sedlK:tion to cite thf:o following lillf!s fro. Hering's ar· tlc1I!(I1) wtll!n its pl.blicatlon was twice declined:

In one cne pi,bllcatlon was at first refusl!d on thl! ground thllt if thl! uperi·

mental evidl!nce was correct , which was easily dl!lI'Onstrated, It was so serious

a matter to change one o f the oldl!r laws , that it ought to be kept secret! In

another case the refusal was beclluse It was "so si.bverslye of long established

principles · , the age of the law being considered IJI)re i~ortant than Its cor·

rectness.

And if it was difficult to throw the Lorentz eqU<ltion over bOlird at the beginning

of the century, which will be the difficulties lit the end of the century!

But Hering had not the equation whleh had to replace the lorentz equation. I have

it. And Hering had not the t'xeprilEnts which I have. Neither Kerlng sttlmtted a ~. per thirty times lMltll publishing it, as I ctJ.

My experiments produce miracles: they violate the laws of conservation. Tradi·

tions, established views, ' older laws' cannot resist a'}>linst miracles. Who would go

to hear the speeches o f Jesus O1rist and follow his teaching . had he not produced

wine of water. And I produce something from nothing!

The mst illtl'Ortant discovery to which I ca~ (this 'diScovery" Is the 1I)5t elemen­

tary result to which every logically thinking child can con! proceeding fro ..

equation (20» is that In the electJ'Ol\ilptic IIIiIchines worting with B-II!~etic inten­

sity (such are !!! Nchillf!s which hlllll!nity builds) the Lorentz and I4arlnov vector

_~etic intensities lead to a lenl effect . while in the electT"CBO.gnetlc I\iIctlfnes working with 5-IMgnetic intensi ty (such is .y SIBERIAN COllU NChine(1,6-9» the

IrIllttaker and Marinov scalar magnetic intensities Iud to an anti-Lenz effect. So

a B-generator brakes its rotation when producing electric current , while an S-gene­

rator supports its rotation "'-en producing electric curren t.

[ work IIctlvely to run my machine SIB ER INi CO!.IU as a perpetuul!I mobile(l.6-9).

the problems which I meet are only technic!!l, i.e . • financial. My financial possi­

bilities III"(! l1 .. ited. as J finance II\)' whole activity fl"Olll lIlY own pocket. and thus the

-. -roonlng of the SIBERIAN COliU generator as perpetuum 1OObi1@ n'B)' delay .

Let rre rlote that to UjHllln th e appu r,nce of 1te ant i-Lenz effect in lUI S-n'B chine

is IllUCh II'OI"e sl,."le than t o explain the appearance of the lent effect in a B-machlne.

Looki ng at the LDrenlz-Milrlnov equation (20). one sees il&ledhtely that for the eJ.­

planation of the fl¥l ctloning of a B-lI'8chine one needs ltlree ringen . willIe for the

elq)1anatlon Of the functioning of an 5-lI'fIchlne one needs one finger.

Let, for example. exphin the functioning of II B-generator and of an S-gener/ltor:

B-genera t or. Let us have before us a horizontal piece of wire going rl¢t-left which has at its

both ends sliding con tacts , building a closed loop with the. rest of the circuit. let

us sl4lllOse that the vector 1III9'll'tic intens i ty. B. is also horizonUI and points pay

fro_ us. If ~yi ng the wire eleRent upwu·ds. the third tern in equation (20) indica·

tes thH we h,ye to put the first fing!!r of our r ig,t h,nd along the direct i on of 110·

tioo (upwards) . the second finger , l ong the vector lM'71etiC intensity (ho r i zon t,ll y

<!Way from us) and we shall obui n that the induced current will flow along the wire

elerrent in the direction of our third f inger (to thll! lll!ft).

This induced current will interact with the lIIa'71etic field lind llgain according to

the third tenl in equation (20) we hllye to put now the first finger of our rig,t hlll'ld

along the induced current (to the left). the second finger along the Yector Q9'lll!tic

intensity (away fl"OlII us) ,nd the wire 's IIOtlon will be along the third finger .... ich is

at ri~t ,ngles with respect to th@ ffr$t two (dowfMards ). Which is thl.lS the result? •

We noved the wi re upwards but the induced current puslles it downwa rds, I.I! .• the i ndu·

ced current opposes the notion.

S·genera t or.

Here tile picture is even more si""le. Let us have again before us a horizontal pie·

ce of wire whicll has at Its both ends sliding contacts , buildin9 II closll!d loop with

the rest of the circuit. Let us suppose that the scah r 1IiI9'llI!tic in tll!nsity, S , is po.

sillve. If !roYing the wire II!lerrent to the left. the fourth tll!llII i n II!quation (20) in­

dicates th,t we have to put the first finge r (or the second , or the third) "long tile

direction o f notion (to the left) and tile Induced current will flow In the direction pointed by thll! finger (to tne left).

This Ino...ced current will interact with the positive scahr .. ~tic intensity and

again according to the fourth tena in equation (20) we hne to put now our finger

along the induced current (to tile left) and the wire's rotlon will be along the fin-

911!r (to the left) .... l1cll is thus the result? - we IIIDved the wire to the le ft Md the Induced C1.lrrent pushes it also to the left, I.e., the i nduce d current s upports the II!Otion.

This is the whole theory of lit.' perpetual lOtion IIIilchillll! SIBERIAN tOliU.

This paper will be dedicated. howeyer. to Iff e:tperi.rent wtJich hn deIIIonstrated

violation of thl! angular nJIIIentUIl conservlltion law and not of the energy conservation

- 7 -

law. As the forces with which biD current ele.rents interact are equa.l and opposfte~

ly directed but lMy not lie on the line connecting the elerrents, in electrolMgne­

tism the morrentum conse rvation hw cannot be violated but the angular RIlmentum con­

servation hw can be violated, what is a violation of Newton's third law for rotatio­

n~l mtion.

3. THE ROTATING .AJo1PERE BRIDGE WITH lNTERRUPTfO CURRENT

In fig. 1 (tal::en from Ma~11(41) the classical ~rl! bridge is shown which I call

the propulsive Anpe re bridge.

The rotiJting Al!pere bridge shown in fig. 2 is a set-up proposed by me(l); The cur­

rent carres from ~infinity· along the wire PO and going throu!ll the wires OA., AB, 66',

B'A~ A'O' and D'P' goes to "infinity". The wires f'O lind P'O' are called ·~:dal wires~

the wires OA lind 0'1\' lire called "rotating arltl!i". the wires AB and A'B' are ~alled

"propulsive arms', and the win:! BB' is called 'shoulder'.

Easily can be seen, taking into a~~oun t Molrinov's formula (5), that the net tor­

ques about the ~-axis produced by the intera~tion of the ~urrents in the following

wires are null: (i) axial wires and rotating arms, (ii) axial wires and shoulder,

(iii) shoulder and propulsive arms, (v) a~tion of propulsi~ arTIIS on axial wln:!s,

(iv) action of shoulder on rotating ar ms.

Different from zero are only the torques due: (i) to t he a~t1on of the currents in

the a~iaJ wires on the currents in the propulsive arms, (ii) to the interaction of

the currents in the rotating and prOj)ulsive arms, and (iii) to the action of the

currents in the rotating arms on the current in the shoulder.

All these to~ues are calculated in Ref. 1 and their SlKn gives zero. Thus the ro­

uting Anllere bridge cannot rotate.

Pappas(12 - 14) carried out a variation of the rotating /tnpere bridge experiment

(fig. J) by reduelng it only to its rotating and propulSive al"lll'5 011 and AS and by ad­

ding for symrretry a pair of "opposi te " rotating and propul sive arms OJ and JK and by

suspending thlS "l-shape antenna" on a string ( t he ... ires AS and JK are in the horizon­

tal pl<lone!) . Pappas feeded energetically his '~-shape <lon t enna" by indoction from a

radio frequency tr~nsformer (in his first experiment(12,lJ)) and from a micro-waves

generator (in his second experiment(14)j. Choosing the total length of the antenna to

be (3llP, where A " clv, and v is the frequency of the generated current, Pappas

could produce standing ... aves in the "antenna', as shown in fig. 3, where the intensi­

ties of the flO\oling alternating currents are indicated. As it C<lon easily be seen pro­

ceeding from Grassmann's fonnuJa (2), soch a "z-shape antenn~" has to rotate clock­

wise if looked from above.

Pappas observed no rotation and thus with this experiJrent he falsified (once rrore)

Grassmann's fonnul<lo.

The calculations ... ith Marinov's forllJ.lJa (5) shaw(l) that the net torque due to the

- 8 -

interaction of the currents in the rotating and propulsive ums Is null. Thus Pappas'

·z-antenna e~peri/rent· represents II con firmation (one mo re) of the validi ty of Ma­

r inov's fonnula.

I fIIolde t he ro tat ing A~re bridge rotating i ndeed by substi tut ing the currents

01\ and A'O' by "displacen-ent currefl ts", i.e., by putting condensers be tween the

points 0 an d A and the poi nt 0' and A', and by sending altemating current across

t he bridge. As the displacement current is no current (I use the tenn "displacerren t

current" only for historical reasons and for JOOre easy understandi ng ) , of the ~bove

mentioned torques tile following will be ze r o : (ill the torque due t o t he interaction

of the currents i n the ro t atin g and propul si ve arms and (ill) the torque due t o the

action of the currents i n the ro t at i ng ar ms on the currents in the shoulder, so that

only (i) the torque due to the action of t he curren t s in the axial wi r es on the cur ­

rents. in true propulsive arms will remain. 1 called such B bridge "the rotating Alr4Je re

bridge with in terrupted turrent". Now , shall t1lltulate its torque.

A tur rent elewent ' dr ' along the axial wire PO lIt t s on a turren t eleJll:'nt ldr along

the propulsive arm AB, t o wh ith t he ve t t or dist~nce is r , with tile following elerren-

tal f orce 9I!nerat ing torque about the z-a~is (in t he next three for mJlas the

tons t lln t factor lJo12fS1! is dropped out )

df .. (r .dr ')dr fr 3 .. cos( r .dr'jdrdr'iJr2 " Zdxdzi/ ( i + z2 + R2)3/2, (21)

\;"here R " OA " AB. The l\"Cnrent of this force about the z-a ~is will be

dM • (xi + Ri )><zd xdz i /(i + z2 + R2 j 3/2 ,. _ RZdxdyt! (i + z2 + R2 j 3/2. (22)

For tile z- compooent of the int egral torque we obtain, taking PO " "' ,

R " 2 M .. - J J Rzdxdz/(x

00

R2)3/2 ~ _ R,(i + R2)-1/ldx " _ RArsinh l. , (23)

If the shoulder SB' is long enou!tl, we can neglect the torque produced by the ac ­

tion of t he axial .... i re c urrent PO on the current in the prop ulshe arm B'A'. Thus

t aking into IIccolXl t also the t Orq ue due t o the act ion of the curren t O'P' on the cur­

rent B'A', we shall obtai n for the z-COPrfl<l nent of the net t orque , i nserting again

the omitted const1lnt factor \lo I2/SlI" .

~et " - (\l0,2/8lTj2AArsinhl " - (lJo I2/4lTj O. SS14R. (24)

The drawing of the rotating A~re bri dge with 4nterrupted current is shown i n

fig. 4 and its photograph i n fi g. 5 . The bridge was wi th two shoulders. The cur rent

conduc t i ng wires were loose and moch attention was paid so that their heating by the

current and the f ollowi ng elastic defonnatlon .... ould not IMr the effect which WftS to

be obser~ed. The bridge was suspended on a separate string wi th low t orsion constant

(thread). I gave to the bridge periodic pul ses of altemating current with the fre­

quency o f na tural oscilla ti ons of the system and co uld set the system i n oscil lations .

- , -Thus the bridge was oscillating but it is evident th<lt it can easily be transforwed

into a rotating one.

The hei\t1t of my rot<1ting Ampert' bridge (its tota l size in fig. 4) was 12 em and

all other sizes can be then taken from the drtIWing . Here I

length of the propulsive arm R • 5.2 Cn1, the heijlt of the

ternal and external cylinders L

shall rrention t he

dielectric between the 1n­• 3 em, the internal ta-

dillS of the external cylinde r Re~t • 1.9 em. the radius of the intemal cylin-der R

int " 0. 3 an and the external radius of the e.xtemal cylinder Ro ,,2.0 em.

The capacitance along a lengttl L of an infinitely long cylindrical condenser is

(25 )

where EO " 10-9/3611" F/m is the electric constant. e: is the permittivity of the die­

lectric, Rext ;s the internal radius of the external cylinder and Rint is the radius

of the intem~l cylinder.

I ordered the production of the c~p~titors ~t the c~p~citors plant Siemens in

Oeutschlillndsberg, Austria, which delivered to III'! the toroidal dielectrics covered

with two lretal rings representing the capacitors' electrodes lind these elerrents were

put in the space between the internal and external cylinders of my apparlltus. The

dielectric was the substance YSU 153 UL (lead-iron-tlIngstlinate) with t ; 1.5><104

which has been first pressed and t hen sint ered. The capacitance Which I measured for

any of the condensers WliS 16.4 nF.

The capacitance o f the whole circuit was C = 8.2 nF. For the freQl.I@nc), of 300 Hz

of the current used, I balanced thh capacitance with coils with thick enougJ wires,

the COPJll)n inductance of which was L" 34 H (thus the cwn frequency of the cil'(;uit

was \I ~ l/211(LC)1I2 • 301 Hz) and the ohmc resistance was R " 24 n . The alternating

current which I lTeasured by lIpplying tension of 220 V was I " 9 A. Ilith this current

I was able t o set the bridge in oscillations. The rotation was in clockwise direction if looked from above (for fig. 2, for fig .

S in anti-clockwise direction). as predicted by fo r mula (24). For m:lre sllJ'4lle calcula­

tions I assl,l!led R " Ro • 2 cm and obtained (with \10 ~ 41110-: HIm and I " 9 A) ~et • 0.142 \lNm. As there was R • 5. 2 cm, the actual torque was hlgJer but because of the finite length of the Shoulders it had to be reduced. The relevant calculations are

elementary.

4. THE GKAHAM ANO LAHOZ EXPERIMENT Graham and Lahoz(lS) carried out an e.xperinmt which seelll'!d to have violated the angu­

lar IIDmentum conservation law in electroma!TIetism. The scheme of their experirrent is

shown in fig. 6 which is taken from Ref. 15:

The two plates of the cylindrical condenser were connected with the wires!. and ~

to which an alternating tension was applied. A constant vector magnetic intensity B

was applied parallel to the nis of the condenser. As the wire a is longer than the

- 10 -

wlre~. the torqt.Oe due to the IIIiIgnetfc forces acting on the wire !.will be bigger than that acting on the wire ~ (use the third term in equation (IZ) putting Idr for

qv and integrllte). The whole system was suspended on a string and when altemating

electric tension was applied with the natural period of the mechanical system, the

system began to oscillate. Graham and Laho~ have not understood the essence of

their ell.perirrent, as they supposed that electromgnetic energy had to be radiated

and its angular oorentLlm had to balance the observed torque. First, they have not

ob5erved such radiated energy; second, to obtain theoretically the Poynting Yector

of this radiated energy, they multiplied the II\/Ignetic intensity, which is constant,

by the variable electric intensity appearing between the condenser plates. This is a

nonsensical calculation, as electromagnetic energy can be radiated only by II single

system but not by two. the one sypp\ying the vector 8 and the other the vector E.

For the people who assl.IIII! that a cin::ular current wire (the cylindrical !TIlgnet)

cannot be set in rotation about its axis by PIII!1letic force5, this ex.periment repre­

s!!nts a viohtion of the angular moment~ conservation hw. Let me cite Graham and

lahOl:

this result .. . leads inexorably to the acceptance of the physical real ity

of the Poynting vector, even though E and B arise from independent sources.

This can be seen by s!!ftl:ing the system on whicn the third law reaction torque

must act. It can be neither the external electric cin::uit, as the loop Is es­

sentially closed within the suspension, nor in the !TIlgnet, which, as a coil

cannot receive an axial torque (force parallel to its own current). For angu­

lar rmrrentll:1'l conservation , the loop Is an isolated system and ,the reactiv!!

torque can only be considered as a change in electromagnetic angular momentum

carried by the fields themsehes in the region of their co-existence. that is,

within the vacuum gap of the capacitor.

It is true that a cylindrical magnet cannot be set in rotation about its axis by

the action of closed currents, but by the action of non-closed currents it can be set in rontion. I ~hall show in the n!!xl section that Iotien proceeding from Marinov's

formula (5), one obtains tha~orqu!! with which a circular current acts on radial cur­

rent is exactly equal and oppositely directed to the torque with whiCh the radial

current acts on the circular current. Thus the explanation of the effect in th!! Gra ­

ham and lahoz exp!!rinent is elementary: The cylindrical magnet acts on the current

in the wire a-b with a tOl'qlle opposite to the torque with which the wire a-b acts on

the magnet.

••

S. THE MARINDV FORCES OF [~TERACTION BETWEEN A CIRCULAR ~D A RECTANGULAR CURRENTS To the best of Rtf knowledge, none has calculated the forces o f i ntera ction between

II circular and" ndh.l currents according t o sone of the known for~las (1) - (4 ) , alttJou!p this preble.;s IIIilthematically not at all di (fitult.

In t his section I shall clI1cl,l1ate the t orques gellerated by the forces of i ntel1l c­

tion betweel'l a t1 reuhr and a rllctangular currents proceeding froID l'lllrino~'s (onnuli!

(5) and in the nut section proceeding from Grassmann's formula (2).

I shall nsUft (fig. 9) that there are a rectangular loop lede in the :r.z-phne

along whfch current ] ' flows i n clockwise direction and a circular loop In the x:y­

plane along which current f flows In anti-clockwise direction. If we aS51m! that the

wires ae and ae are very long, the intera ction .... ith the currents fn the wfres cd and

de, as ..ery feeb le , can be neglected.

The problelll is: If both circuits <lre fh:ed one to <lnotl\er <lnd the system h<ls <l

rotational freedo. about the z·.Jds, will it be set in rotation or not. Both Nari·

nov's and Grassnnn's formula s leave thi s ql.lestion open , as there is no general thea·

!:!!!! de"l;mstrating that the net t orque generated by two interacting circuits IIlISt be

al ways zero according to Grassmann's (or !.'hittlker's ) forrrula (accordi ng to Aqlere's

and Helll'll1lnn's fOnallas the net torql.le oost be zero). Heither could I find such <l the­

are. for Harinov's f01"&l1l. Thll$ WI! have to give the answer i n any special case sepa·

rately by calculating the generated net to!"'qtll!.

I shall """ke now the calculations for the loops shown in ffg. 9 proceeding from

/oIarino~'s formula. For brt'~ity, in the following forl1ll1as the comnon constant factor

uoll'/BlI will be oraitted.

I. Action of the axial current on the circula r current.

Before starting with the calculations let n! note that the torque e)(l'rted by the

action of the circular current on the axh l current is zero , as the levers of the

forces are null.

The elenenta!"), ",:uren t of force about the z·axh due to the action of the axial

current e lenen t dr ' on the current elerrent dr of the circuhlr current will be given

by the formula • dill .. Ril ><df. (26)

Putting here (5), we obtain (fig. 9), denoting tl\@ torque with which the whole

axhl current acts on the whole circuh r c urrent by 111 1' 2 • •

"'1 • (R/ r jp><cos" t drdr', (Z7)

where ",' is the angl e between dr ' and r . We have fro m ffg. 9

cos,," ' • - zl r , (2B)

so that by 5,,*,51ltut1n9 (28) into (27) we obtain for the z·co~nent of the differen·

tlal terque

- 1Z -

The I-component of t~e inte9ral to rque will be

211 ... RZZdz ZII Idol> J Z _? 3/Z • - J Rd40 o 0(1 + Ir) 0

• - 211R .

2. Action of the internal radial current on the ci rcular current .

Putting (5) Int o (26), we obtain ( fi g. 10)

'"2 .. (R/r lp><{cos1J(- i ) + cos~'+ - 25in¢l{r /r)}drdr'.

We ~ave f rom fi g. 10

r /r " sinwP + c.os~, "" "AA" P"" .. - 51n91 , p,,* " z , dr "Rd¢ ,

50 that for t~e l- component of t~e differential torque we obtain

dM2 " (RZ/r2 )(_si n40cosljl + cos~' )d~#.

A9il in from fig . 10 we ~ave

C05i1' " (~/r)5iM , cosl/l' '" (~- RC05q,)/r, 50 t~at

d.., • (RZ/r3)(xcosZq, _ Rco~).

3. Action of t~e ci rcuhr current on the internal radial current.

(29 )

( 30)

( J 1 )

dr' "d~ , (32 )

( 33)

(J4 )

(35 )

To mke the calcuh.tion roore easy, let us exchange the letters ln~ica tin g t~e cur­

rents and let us c~ange t~eir di rect ions to t~e opposite ones ( fi g. 11). Wit~ these

changes t~e acting forces remain t~e saJre. but .. e shall have the angles"" and 1/1' less

t~an fI/Z. fi!.cl1itating th us t~e I1'3therratics.

Now t~e differential lII) .... nt of force about the z-a~is due t o the action of t~e cir­cular current elem;ont dr ' on t~e radial current element dr will be

eM " xXxdf . (36 )

Putting (5) into (36), we obtain (fig. 11)

dM3 " (x/ r2

)Xx{cos"'f-+) + cos",' i - Zsi nq,( r / r )Jdrdr'. ( 37)

We have from fig. II

r /r .. - Sin,' p - cos,' • • " , xxp .. 5 ir;tz , ,

.. C05q,Z. dr .. dx , dr' .. Rdq" (36)

so that for the I-co~onent of the differential mommt of force we obtain

""3 " (xR/r2:)(-cos40coslJI + Zsi n2q,sint ' + Zsinq,cosq,cos,.')dxdoj>. (39)

Again from fig . 11"e haVe

cosil' .. (x - Rcosoj>c)/r. sirJil"" (R - ~cosq,)/r, cos",' .. (x/r)sinq, . (40)

- 13 -

so that

(4 1)

4. Inte raction of the tl rcul.r current .nd the interml r.dial current.

The z-coqlOnent Of the integr.1 torque due to the inter.ction of the whole cIrcu­

lar current and the whole Inte",a l radial c urrent will be given by the sum of t he

torques (35) and (4 1) . in which we have t o put

r2. i · ZxRoost t i. (42 )

and then to integrate R2.. R2,. 2

Mz t H3 .. - R Jax J ,.2 cost dt t R fdx J 2xRsin .. dOl> o 0 ( - 2xRcos+ .. R2) 1/2 0 0 (>f - 2xRcost ..

If we i ntegrue the second inte gral p!'!r partes by the help of the

(42 ) ~)3/2·

s!,bstitutlons

u • sl nt .

u' • cost, I , . -.,..,----::-:-'----::.-:--;'" (x2 _ 2xRcos • • R2)1/2'

it obtai ns euctly the fonn of the first Integral (with opposite si!P'l).

(43)

Thus the torques ":1 and "3 e re equel and oppositely directed. This is true also if we take rlot the whole l nte",el radia l current but arlY part of it.

5. Interacti on of the circular current and the externel radial CUrrerlt .

Eu1ly can be seen that the differential torque, dM4, with which VIe external ra­

dial current eets on the circular current will be gi ven by forlllJla (35) end the dif­

ferenthl torque, dMS' with which the circular current acts on the exte",al ndh l

CUrrerlt will be shen by the formula (41 ). Thus the in tegral torque due t o the i nter­

acti on o f the whole circular current and the whol e external radial current will be

null and we un write

( 44 )

looking at fOl"lllUhs ( 30) Bnd (44 ) , one comes to the conclusion that the sys te .. o f

two fixed one to another circuits in fig. 9 will be set in rotation. The objection

thBt an oppos i te to"lue may .ct on the very far wi re ed is ~ten.ble as i ts lever is

r but the force is proporti onal to r-2 , so thet It r-- the torque tends t o zero. To c lear bette r the problell by eXcluding the avaihb1lity o f -very fir lying wires· let us

assu me that the wire de is equal to zero and let us ca lcuhte the torq ue due to the

i nteraction o f the circular current and the vertical cu r rent ed Which in this case

Cln be call ed with rrore precision "vertical circumferentill cu rrent~.

6 . Interacti on of the ci r cula r current and the vertical circ.ferenthl current.

Putting (5) into (26) . we ob tain for the di fferentia l to"lue with whidl the ver-

- 14

tlul current ilets on the circul"r current 2 - (-) _, 3 _

"\ .. (R/ r )p >< cos.'. elrdr ' .. (Zir/r )~dzi. (46)

lind putting (!l) into (Z61. we obtain for the differential torque with which the cir­

cular current acts on the vertical current . by exchanging the letters indicating the currents 6hd then the directions of the currents to the opposite ones,

ttl7 .. (R/i)i><{C051/1(-+:)}crdr' .. - (ZR2/r3)costdl>dzz. (47)

Thus for the z-coqlonent of the integral torque due to the lnterilctfon of these

two currents we obtain

.. 4R. (as)

hlt1ng lnto acco~t formula (30). the first fOmllla (44) and fol"ftlh (48) , we see

that the net torque acting on the Whole 51stI.''' of blo circl,llts will be different from Un). I showed, however, by the help of the experirrent reported in sect. 7, that

the lou,l tOrtlue acting on such a system 15 null. This experiment thus delll)ns t rated

that even ~rinov's formula is wrono. Nevertheless , according t o II\Y firm opinion (see

Sect. B) II better formuh can be never found.

6. THE GRASSMANN FORCES OF INTERACTION BETWEEN A CIRCUlAR ANO A RECTANGULAR CURRENTS [,sl1y can be seen that if work!n!;! with Grassll'8l'11\'s forwh (2), we shall have

cf4, • 0 , <I'Io!. 0, dM4 • O. (49 )

If the constant which"'Srllit in our fOT'IrAJlas will be not uoll' IBlI, but \.loll' /411, we

shall have by using fig. 11

'"3 • (x/r2)xx{cosl/I(-i) - sin¢>( r /r)Jdrdr', (50) .. , (51)

The Un! for .. uh will be obtained also for dl\. It is difficult (perhaps i!llpOs­

sible) to integrate th is forftJh. Using however another way, I shall now show that

(52 )

The IIIIIgnetic potential of a circular current " with radius II. flowing in

the IIY-plane generated at iI distance 0 from the center is(l)

~ pf 4 (11.2 _ J)112

(0 ( 1/:)

(53) (p > 11.).

The Lorentz I!\lIgletic intensity in the )I)'-phne is

. ! 3('&) Z • , "

- 1>

(p < R)

(0) R). (54 )

Thus for the differential force s elf ] and df S ";11 slllll1

king into account that for this figure A, is negative

have using fig. 11 and U-

df, . Idrx81'~ • )lf l' 2R2. p2 ~ , (RZ _ p2)3/2 y,

. - IlolI' 4

(55)

For the z-component of sl,nt J,!0Il'/4 ,

the integral t orque " J we obtain, omtting t o write the con-

"3 • '(P; XdfJ)z , and for the z-co~nent of the in tegrol t orque Hs we obtain

Ms • r RZodp • _ lim.. R2 II (aZ _ R2))/2 o-+R (p2 _ RZ)lIZ '

FOl"lWlas (56) and (57) give forl!JJh (52).

(56)

(57)

Thus the Grahn and LaIlDI elqlerilrent(15j in wil let! the Whole s)'5telll is suspended

on II string un serve as an u~ eAue.U. for Marinoy's and GrassrMnn's fol"nJ­

In. Acco l"din g to Jo\lrinov's fOrnlUla no roution is to be observed . while according

to GrassNnn ' s for.uh rotation @(jual to that when the cylindrical lIiI!JIel is fixed to the laboratory ;s to be obseryed. As there are already so IDIIny experl~nts whith haye i nyalidated Grassmann's fo~h(l), the outtO!re of such a yarihion of the Gra-

ham and Laho: e)q)eri!rent tan OI'\ly be thH one preditted by Harinoy's formula.

Easily ta n be seen that the elenoental torque .... ith .... lIlth the circular current acts on the current elewent dr of the Yflrtical circumferential wire .... ill be given by for-

mula (47) , lIkl1tiplied by 2 (the omi tte d constants in Sects. 5 and 6 are different!)·

Thus the net torqlA! attlng on the syste .. in fig. 7, at the assuq>tion be • O. will

b.

(58)

The cal culation of the second integral is difficult, but it is obvious that the SUI! of the integrals In (58) is not zero. As both these integrals

haye peculiarities, it is expedient to take in fig. 7 the wire ae less (or Imre) thlll

R and then to ca 1 cula t e 011 a co~uter the 1 ntegra Is gi vi n9 the torques 1'13 and " r I have not done th is calculation, as it is clear that the sum o f the Integrals .... il l be

not zero. Thus Grassrrenn's fOnlllh will predict rotation of the sys te .. of the circu­lar and rectan!!ular ci rcuits in f ig. 7.

- 16 -

1. THE EXPERIHENT WITH THE SUSPENDED CIRCULAR AND RECT~NGULAR CIRCU ITS ~ sil!lpliffed parthl dhgrUl of the "PI'"ratLt5 with which I falsified Harinov's fol"-

1lU1a is presented in fig. 10 "nd the photogr"ph in fig. 11.

~en looking ~t fig. 1 the diagru. of the ~pp~ratus presented in fi g. 10 and 11 be

cones self-e xplanat ory: it hu t\oIO rectangular loops for syrmetry reasons and to

make the to'fque two times larger. The reml III!chine (fig. 11) has, for further sym­

metry reasons and to Ir0ke the torque two times ..ore larger. a second circular loop

on the top where Ute current flows in II direction op!)osite to the direction of the

current flow in the lower circula r wire. hld instead of one winding there are I18ny.

The u14l wires 91 1I10ng the axis o f the plastic aroor and cannot be seen in the

photograph.

The wire in Iff IrBchine wu with thickness 0.6 II1II. The rectangular loop h"d n1 •

100 turns and the ci rcular loop hid n2 • 600 turns. The radi us of the circuh r

loop was R ·6 cm. The helcjlt of the rect"ngular loop was 28 CII. The ohmic resis­

tance of the whole ci rcuit was 50 Q. The current was sl4lPl1ed by ten slMII Cd-HI

accumulators connected In series , everyone of which sl4lplled tensi on g V. During

the obse nations the curren t flowing in the wires was about I • I A. Because o f the

small capacity o f the accumulators, they had to be o ften recharged.

The current was switched on and off by decreasing and increas1n9 the illuMi nat ion:

" shple electronic circuit with" I i~t diode actiy"ted and denctiy"ted "n e lectro­-edl"nical switch (see them fixed to the botto_ of the u-bor). At the botto. left

can be seen a condenser of 4.2 \IF connecttd ;n parallel to the roil for dll1inlshinq

the sparlt in the switch. A 9-volt accUl1ll.lJa.tor feeding the switch. clrcl/it (whldl is

behind the aroor) was attached~r dl$tached froll! the circuit by" rrechanical Swi t ch

to be seen at the bottom ri \til. The wei cjlt of the whole Mrotor" was about Z kg.

If "numing t~t the heicjlt of the rectangular loop is much larger than the radi­

us of the circ ular loop, the "cting t orque produced by one rectangular loop and

one circular loop only will be, according to forlllJlaS (30) "nd (4S),

H • (uOn1nzIZ/S.){Z. - 4)R. (59)

Putti ng here n l • 100, nZ

.600, I • I A, R • 0.06 _, we obt..tin M. 411 ",NIn.

Such" torque had to provoke pret ty powerful asci Ilations. Sut there were no oscil­

htlons.

I checked the sensitivity of the suspended syste", by I15king on the one side n _

10 reclangular windings IIDre. lihen the rectangular loops were in the plane o f the magnetic rreridlan , the torque wi th which the Earth's magnetic field acted on the cur­

rent In the addition~l vertical wi res could be calculated acco rding to the fonnula

Hearth

... here L • 0.3 !'II was the length of the

ma • RnIL8. l601 gn. thl! horizontal pro et on

vertical wires and 8 • 50 liT wasythe intensity

of the Earth's _gnetic field, so that putting in (60) these values and the values n •

10, I • 1 A, R. 0.06 III, 'ole obtain for the torque 9 1.lNm. Thh torque could be clearly

detected. Finally I sl4lplied the circuit by alternating current (50 Hz, 220V, about 3 A) con­

ducted via t.o bifila r .ires to its botto ... HooIabsolutely no IIlItlon was ooser Yl'd liS

the action of the Earth's magnetic field.as excluded.

8. COHCLUSIOHS

ThU'S the experiment In the previous section dem:mstrated that Ha.rinov's fOmlla is

wrong, too. It is 10giCill then to continue the search for the ri!jlt fonnulll descri­

bing the force .ith which II current elell'ent IICts on IInother current element. Joti 1000g­

year experience in electroN\rIetis .. tells me, howeYer, that a better for1llUla cannot

be found. This is ~ firm conviction. I 'oIrote on the pages of ~ DIVI NE ELECTROMAG­

HETISH(l); "the Divinity is not perfect". Now I shall add; or, permps. the Dhinit;y

is so sophistlCi1ted that _nklnd with its ri~}CH'OUS IIIolthelMticaJ apparatus is unable

to grasp the way in .hlch the Divinity has constructed our worl d.

\tIen calcihtfng the torques of interllctlon bet'lleen circular and radial currents,

the Divinity was perfect , indeed. as the torque with which IIny radial current eluel'lt

acts on the circular current is equal and oppositely di rti;ted to the torque with 'oIhich

the circular current acts on the radial current elelQ!nt (see formuhs (42) - (44)).

When, howeW!r. calcuhtlng the torques of interaction between circuhr .nd vertical

(u.ial and tircumferentlal) currents. wtJich 00 not lie In the sue plane, the Divinity

could not Rl1Ike Impeccable calcuhtlons , as here the elerentary torques cannot be eqUIII

and opposite. To save the angular romentur.. conservation hw . the Divinity had to ob­

ta in In fOrnJla (48 ) ~ + "7 .. 2d , as there is "1 .. - 211R. but at the nlculiltions the Divinity could arrive only at the value 4R .

The problem about the force of interac t ion between t'IIo current elen>n l s is pemaps

the n'Ost ~si~ le~ ooe ..mere the Divinity has disclosed His I~rfectlon or His puz­

zling sophistication. This problelll. I think, will relllllin unresolYl'd and I18nklnd , af­

ter many I6'Isuccesful years. will put it on the shelf where It has put the problem

about the trisection of the angle or the problem about the physical essence of the el@ctric current.

Nevertheless one Cdn only .onder thllt Klrinov's forRl!a .as "dl$covered" after al­

most two centuries of electrOIllll\rletism. And this fOnll.lh shwed that besides the al­

ready known l orentz vector miI\rIetic Intensity, there are three other intensities; the

Marinov vector lII/I\Ptlic intensity. the IIIittaker scahr III!Ignetic intensity and the

HIIrinov scaler lIIiI\rIetic intensi ty . all of which relllllined for t'IIo centuries unnoticed.

And there is the miracle that the scalar IJIIIgnetic intensities give possibilities for constructing perpetually woncing IJIIIchines.

If mankind has discovered Marinov's formula in the XIX-th centur)l, the history of

the XX~th century could be cOll9letely different and the world had not to COIIIi! to the bordt!r of an energetic and ecologic preteDice on Ifhidl it stllvc I'II'\W

- Jt:--

REFERENCES

1. S. l'\lrinov, Divine Electrolllil91etism (East-west, Graz, 1993).

2. E. T. ~ituker. A History of the Theories of hother .nd Electricity. Vol. I

(lonQlll.lns. Green .nd Co .• london. 191 0). p. 91.

3. J . H. Jeans. The Mathematical Theory of Electricity and JoIagnethlll (tarrOrldge.

19(0).

4. J. C. MII:.well, A Treatise on Electricity and Ma91etislfl (Clarendon Press, O:a:ford,

1891).

S. R. C. lyness , Con teqlOr. ry Physics, 3, 453 (1961) ; reprinted in: S. Haorinov,

6. 7. 8 •

••

The Thorny Way of Truth, Part VlIl (East-West, Graz. 1990) p. 88.

S. I'oIIrinov, DeutsChe Physik, 3(10). 8 ( 1994).

S. I'0Il ri nov, Deutsche Physik, 3(11).18 (1994).

S. Marino .... Deutsche PI'Iyslk, 3( 12 ).13 (1994).

S. Marinov. Deutsche Physik, 4 (13) ,15 (1995).

10. S. Harinov, Eppur si ~ove (C.B .O.S., BrU)(f!lles. 1971).

11. C. Hering , Trans. Am. Inst. [1. Eng., 42, 311 (1923); reprinted i n: Deutsche

Physik, 1(3) ,41 ( 1992 ).

12. P. T. Pap~s and T. V.u!1l.n: In S. Harlnov. The Thorny way of Truth. Part IV

(Eut-W!!st , Gru , 1989). p. 158.

13. P. T. Pappas and T. Vau!1l.n. Physics Essays. 3, 211 (199 0).

14. P. T. P.ppas: in U. 8artocc! .nd J. P. Wesley , Proceedings of the conference

"FolA'ldatlons of I'oIItheNtics and Physics", Perugia 1989 (Benj.nrin Wesley, D--78176

81 llIlDllrg , 1990) p. 203.

15. G. H. Grah'lII .nd D. G. Lahoz. H.ture, 285, 154 (1980).

FlGJRE CAPT IONS

Fig. I. The propulsive Ampere bridge.

Fig. 2. The routing Inpere bridge.

Fig. 3. Pappas' ·z - an tenna e:a:perillent".

Fig. 4. Drawin9 of the routing Ampere bridge with interrupted current.

Fig. 5. In the photograph the author holds the rotating A~re bridge with In terrup-

te<l current suspende<l on hh hands .

Fig. 6. Diagra. of the Grah.m and ll-hoz (lllperi"",nt.

Fig. 7. Rect.ngular an<l circula r circuits.

Fig. 8 . Action of i nlemal radfal current on circular current.

Fig. 9. Action of circular current on internal radial current .

Fig. 10. Diagram of the apparl-tus with circ ular and rectangula r circui t s.

Fig. n. Photograph of the apparatus with circular and rectangular circuits.

Fi g. 1

dr ' p

z

r

dr ' 0

y a

~ a

r dr

A

B

dr

0' A'

----B'

P'

B

J r--"; o ,

• Fl g. 3

~ Metal

(Ss:3 Plastic

c:==J Dielectri c Fi g. 4

Fig. 5

b •

,

,

,---------__________ , d

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