I T1:~,_..4TI(),_.AL

ELAS~~SIJeU~~4L~~ IUIII)AMI:NI I>~ICI

EDITORIAL POLICY AND INSTRUCTIONS TO THE AUTHORS

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- 3 - No . 21

E D I T D R 1 A L

J:l fu.rrrapi1SI llll1BCWI' He OCeM MHJD10H8 6'1>.!1-

r·apMI!(l,, TYP1.fi1Ha H L\IH'rurrora, a oce~1 MM­mrorra OlPb.lltlt:fiOElll\.

11saH ,ll-IJIOB, 6J>JJrapc!GI 4umocoQ)-croHK, PeQJOPMa7.0p 1-1a eJJCI<'rpoMameTHs-la n II:I>P9HOJ;<O>l CI<C!lep!i:>teHT a"TOp, npe;li10K.IIl1 H OBiil'a fiYMa 11 6 bll r apci<ID! es~n< "Cf!P'h:IHCOOeU", TbH KaTO TOH , sae.QH 0 C 0Cl'3118Jl l:l'l'C pO!J)JI1 Cllp1¥1Re60iiufl, OT ~ CXm rrpaB», 11 rrpv. TODa 6oih«> H YCileDJHO . A t.f;):Ee C'biiiO 1-1 01" 60J'! .o,a npaBI:I 6all rrp'b,!J,Hl!: .

Le t Newton be again! 'J'Bopcmrr meeHo petre . 11 CHC'l'8 )13'1pe3HR C!IE\4 J:MRHCTI.lO'l'O

fla ~l,5!,l:la EBK.JnW.a B npOC'JPaHC'I'Ii01'0.

PaHren Kll'IE01H , 6eneJllm' m.nrapcKJl

KOCM<l!lOr I! af1Hmc5opel;.

Die Wahrheit ist Tochter der Zeit, nicht de r Autoritat.

Franci s Bacon

In this issue, with which DEUTSCHE PHYSIK enters i nto its sixth year, t he repor t i~

given on the negative effec t demonstrated by my SIBERIAN COLIU machine with eccen t r ic

permanent r1ng magnet as r otor . My conviction that such a machine wi 11 rotate as a

~e~~ mobiLe was so firm that I announced {see DP-19, p, 3 and DP-20, p. 3i the

nachine was already constructed. This announcement was done also at the free energy

conference in Denver a t the end of April 1996. •· · The ring magnet s which I needed for the machine with one,' or two, pai rs of SIBERIAN

• J • • •

COLIU magnets ( see pp. 33 and 34) were t o he ordered at t he ·i:OITP~·ny VACllJMSCHMELZE in

Hanau, Gennany . However , s i nce the price was '.'ery high, i dec ided to orde r thel!'· in the

People 's Republic of China. The neodymium magnets produced in China are of a ve-r;;: high

quality and can be obtai ned from the Austrian company MAGNETTECHNIK Or. SIEGFRIED

HEISS, Waidhofnerstr. 11, A-3333 Bohlerwerk, Tel+Fax~ 0043~7442~52643 for a price·

about an order lower than from Germany. However the de live ry time for these ring mag­

nets, which were manufactured according to s i zes given by me , was pretty long and the:;

arri ved in Graz in November 1996 . Much to my sur erise; the machine with t he eccentric permanent r i ng magnet did not

demonstra t e a preferred direction of rot ation ( see p . 33) and consequently di d not -rotate as a perpetua·l motlon machine. When the null e ffect was undoubtfully bef ore my

eyes, soon the explanat ion for th is null effect was found (see p. 34).

Th is null effect was , however, a heavy stroke for me, as already half a yea r r went

to my bed with the excel'i ent fee li ng that the runn ing of rqy SIBERIAN COLIU macl1ine as - --·-a peJt.peA!wm mob.<..tc 1 s imminent.

- 4 -

Fortunately. I never forget the etemal words: AUu, ~ .U.C.h ni.eh-t umb!Wtg.t,

nach.t mich b.taA~~! And the batt l e for t he realization of eternal motion goes furth

!ln.

The publication of No. 21 was delayed, as I awaited for the results of the exper ment with t he eccentric pe nmannet ring magnet. Since in th is time I prepared enough mt erial, issues 21 and 22 appea r together and will be dispatched together t o the subscribers.

AOOf:A Tl ON OF RELATIVITY

Note that the white circle around the he~d of the rel at ivi stic mi screature ls not a holy light but the m on.

- 5 - • Vwt4 c.lt~ Phy&-ik 6 ( 21 :

[1991

SIBERIAN COLl lJ r4ACHINE ~!ITif ECCENTRie .tC!RCl:JL·AR WRRI?NT ROTO!;

Stefan 'JVla r-lnov .

Inst1t ~:~.te for f'undall\ent..:al .Phys ics '~o:·e 1 ~ er. t t 'l dCia sse 16 P.->JOl'O Graz, · Aus"tri.o

Q~~c.r ibed is c. o.i rect cul·•·er• t e1~ctromagn¢t i'= mot.or without commutation whose rotor· h a ·circ•Jhr co·il r·v~. ilt~r. g about its axi s. It i s well known tha.t such a motor cann9t be const <'uc.te t: . ~>.v the· 11.e1 p of t ne conmonly known vector magnet ic. field. As ·a matter of fact \.f v1o~l<~ by, the he lp of the scalar· 116gnet .i c fi e ld discovered by Marinov . The theory of 'the .macnine and i'ts fJractical reali.zat ioh are pres en terl .

1. l NTROD uCTI 0 f<l

f·jumerous exper1,ments deme oy Mar-inov· and b,y othet· ~rs.ons nave shown that .t he well

known fljndamenta 1 e.ouation .in e "Ject romaBnet i.s 1~, c~ 1'1 eel further the Lorentz -Gr·assman r· ·

eoua ti on, ts wron~(l-J) Mari,t~ov ~ymmg.;,.rized thi s equat ion by taki ng .for t h.e oote~t~a~ force ~ti th wtvic,h il" electr-i.c char!¥:! ·a~t:. on another ::ha rg# .the half sum of the pc't·:r!· ...

tial force with which the fir~t r.ni\r.ge, a,:;t.s on th'i! ~ec.ond one pnd th~ potent ial for ce

ttaken with negative sign) l•t i t~, wh ';ch the second cnarge act·~ or. tne first o,ne. So '·~­

rinov obtained th~ Loren:tz .- ~larinov eouat1 or. acc.qr<lin,g to wnic:p the. for.ce ,; wit r. v.1hr.r.

two charges int.era~t are eoua.l anc op;)O:itel.y di rec.ted.(l -:3} The Lorentz-Marinov equation · gives thi:!' for ce with which· g· ~y~tem of r. ct:larj)-e:: ·,··:

(i = l ,2, . . . n) movi ng with velpci ti es v·; act.s ol'l· ~ te$1' . . F~~.rge \1 movi ng wi tr. e ve :, .•• '

city v at a distance r i from ct 1

f = ""Q ~l"adil' ·- (Q/c}aA/at + (q/c,}v-*B + (q.fc}vS,

A = i'q .v1/ cr. .. , , <.re tMe el ectric and magnetic potentia l s .{;lenerat e d by ti<le c~,.a:--~e~

po int of location of the test charge, and

• . ' . .. , .· .

•.•

-.;~ . ... ...

,B = ~lor + 8ma "' .S = 5~th it. + Smar (.:S.i

a-re. the vector a~- ~calar magpetic intens ities ge·nerated by the SY·Stem.

The vector magnetic intensity is the s~m of th~ Lorentz 'lllli)Tlet ic itJter.sity e.~ r. ';•f'f.·

Mari noY vector .magneti c i nten sj tv

B1 = ~" q 1 v .xr .f.cr~ " rotA, or L 1 1 1

The scalar magnetic intensity i s t he sum. or the ~~ttak~ ~gneti~~~~s i ty and

the _tl~!i nov s~a l a .r..:..~.~!!t ·i c i n:t.ensJ..::¥

Swhit = /. qi wi .r/2cr~ • - '( l /2 }divA, Smar = -( 1- 3)

According to t he best of our knowled~ . '

, .. \ .. ' . ; .

t he re is neJ ex,perinent contraa~ctin !) .. - ' '•

- 6 -•

the Lorentz-Marinov equation: Until the day when some fal s if1ing experiment should be presented t he physical community is impelled to accept the Loren t z-Marinov equa­t ion as the fundamental equat ion in electromagneti sm . .

The man ifestation of Bma r ts very simila r to that of Blor and for this reason no-body has not iced the presence of Bmar· If, however, exact measurements of t he vector magnetic field around a coi l shoul d be carri ed out, one must notice t hat the distribu­tion of t he f ield wi ll not correspond to .this one which is calculated proceeding only

·. from the fi r st formul a (4) .

Obviously the Whittaker magnetic intensity ·is equal t o zero for a system consisting of closed currents. For such a systemS is equal to Smar·

By tile help of the firs t three fingers of one's hand one can immediately conclude when looking at t he third term in equ. (1} that if a piece of wi re moves in a direc­tion perpendi cul ar to its length in a field B perpendicular to the plane of motion, the force with Which the f ield acts on the current induced in the wi re i s opposite to the motion. Because of this Lenz effect the electric power Pel generated in an electro­magnetic generator i s equal to the mechanical power Pmechinvested for setting it in motion (negl ecti n~ t he inevitable friction power}. Marinov, however, showed(l) that this is true only when the phase angle between the induced in the wire tension and the flowing . current is ,equal to zero. When the phase angle t ends to "1/2 there is

P mech/P e 1 ... 0. By the h<! 1 p of this null Lenz effect Mari nov con~tructs his over -unity generators called by the general name VENETlN COLI U machines< ) .

By the help of only one finger of one 's right or left hand one can imned iately conclude when looking ct t he fourth term in equ. (1) that if a piece of wire moves in the direction of i ts length in an S f ield, the force with which t he fiel d acts on the current induced in the wi re i s along the motion. By the help of t his anti-Lenz effect Marinov constructs hi s self-accel erating generators called by the general name SIBER IAN COLIU machines(l·3l.

2. THE CONCENTRIC SIBERIAN COLIU MACHIN£ The magneti c syst em in a SIBERIAN CDLIU machine is a cylindrical magnet cut i n two

pieces along an ax,ia l plane, the one .'of which is rotated up-down '(the magnetic forces themselves make t hi s rotation}. Such a SIBERIAN COLIU magnet generates a strong sca­lar magnetic i ntensi ty near the vertical cutting line, at the one side posit ive and at the other side negative. At 90° of the cutting 1 i nes S is zero. .

M!calculated<4l t he Marinov vector and scalar rilagnetic intensiti es generated by an infinitely l on~ SIBER IAN COLIU magnet with axis along the z-axis and current I ' on a unit of l ength flowing in the pos itive direction in the fir st and second quadrants.

Bmar acting on a t angential tes t current element, i .e., perpendicular to the rad i­us (qv : Idr i s called cu rrent element where I i s t he current and dr its oriented

length), with rad ius p and az imuth angle ~ generated by a SIBERIAN COLIU magnet with radius R ; s

• - 7 -

(Bmar)z [' p2 -R2

arctan2pRs i ncp - 2Rs in¢) + c -( c (:.2 n2-R2 p

I' sind>cosd>(lnR2+2cRcos¢ +P2 2cOS<l> arctan2PR s indi ) -c · R2 -2pRcos"' + , 2 sin9 r} 2 .

- R

Bmar act·i ng on a radial t est cu~rent element, i.e., along the radius, i s

I' c2+R2 2 R . 2R . ¢ = - ( arctan P Sln<P + _s ln .) -c P2 02 -R2 p

I' 5

. ..... .. , 1 R2+2pRcos~ + ,::2 + 2 sin£

- 1 • .,-cos .. , c R2- 2pRCOS$ + :!z COS'il

an a tangenti a 1 test current _element is

1 R2+2nRcosd> + r} 2Rcosd>) n-:: - ·+

R2-2oRcosm + ,::2 P

s in~ 2 }.

- R

2,...R s~n.± co54'arctan ,. ;:

2 ) .

CL - R

No. 21

(6)

( 7)

In fornulas (6)-(8) the first terms a re caused by the currents i n the cy1 i ndrica1

surface and the second terms are caused by the currents in the splitting plane. The

x- and y-components of Bmar are equal to zero and Smar acti ng on a radial test cur­

rent elelll@nt is null. (NB . We established (DP-22) t hat Sr,~ar acts on a ra dia 1 <!lemer.t.}

The most simple SIBERIAN COLIU motor can. be done if taking as ro~or a me t a l nng

encircling the magnet in its middle horizontal plane. If supplyi ng current via s1 i ­

ding contacts at the ooints of the ring which are at 90c of t he c~tt ing lines, the

ring begin s to rotate . If rota"ting the ring by one' s fi nger, current i s induced in

the two halves of the r ing, in the one half clockwi se and in the other one anti-clock·

wise, whi ch via the sliding contacts makes a closed ci r cui t. The torque produced by

the interaction of the induced current and Smar _2UP£2rts t he rotation (ant i-Lenz ef­

fect!) . If the self-propel ling torQue is equal to the fr i -;tion torque , the initid '!

mechanical driving torque can be reduced to zero and the machine will rotate as a

perpetuum mobile. If the self-propell ing torque will always be stronger than the

frict i on torque (at a higher rotational velocity the self-propell ing torque is hi gher

the machine wil l accelerate its rotation until destroyi ng itself because of tne a;:>ea­

ring centrifugal forces.

In fig. 1 is presented the most simple SIBERIAN COLIU m41chine where instead of a

metal ring t here is a trough filled with mercu~y. If sendin!) current, mercury begins

to rotate i n the trough. If sett i ng mercury in motion by on~ ' s finge r, current is in­

duced in t he circuit. The i nduced current f loo.,:s ·ir. the directi on in which. if curren~

from a battery is sent , mercur y obtains the sarre rotation (anti- Lenz effect). This

experiment can be carried out by every child in hal f an hour, if a SIBERIAN COL!U

" 8 -

magnet (preferably of neodymi um}, a t rou·~h wtth me rcury , u car bat tery and a sensi -, . tive galvanometer are available (a chil d is mo re adapted for ca rry ing out t he e xperi -

ment as hi s finger i s t hinner} . 11-:, the currents induced i n t he SIBERI.'N COLIU mtch i ne':, con~ t ructed by Ma r inov 1\Cre

too feebl e. and the fri ction too high, espec ia ' ly if there v1ere sJi.:l i ng contact s tc

a solid met a l r i ng, it was not possi bl e to make a perpetua l rrot ion machine i n t he forrr.

s hown in fig. 1. Thus 'Marinov began to construct rotors without s l idi ng contacts (S}.

The most .s impl e SIBERIAN COLIU machine without sliding contact s i s the machi ne in

f ig . 1 i f we remove the ci r cuit which i s,f i xed to the l abor atory and if t he t r ough

~lith mercury will be sus~ended the whol e, or i f we suspend a me tal ri ng. Tf 11e wil l

begin t o rotate t he r i ng , e lectr i c tensions wi II be induced 1n bOt 1 its halves. Hc~l ­

ever. as the tension i n t he one half ~1 il l be equa l and oppos ite ly di rected to t he tension in the othe r ha l f,~ current will f low.

3. THE ECCENTRIC SIBERIAN COLIU MACHINE

If, however, we shall put the c ircul ar metal ring eccentr1ca ll ,Y w1 t h respect tc

t he magnet' s aKi s, the t ension induced in t he one half wh ich is more neoar to t he rllag­

net wi ll be higher than the tension indu:ed, in t he ot her half and current will fl ow.

We can cal culate the torque with whi ch an inf init ely long SIBERIAN COLIU magnet ac t s on curren: fl o~1ing ln an eccent r ical ci rcular r i ng rotor by t ne he lp of f ig . 2

R

p

Fig . 1. The SIBERIAN COLfU MACHINE with ro tor of mercury .

• No. 21 - 9 -

showil)g the horizcntai cross-section of the machine ro r the case Ylhere the rotor has

!..~ circular currents 1•:ith r.adii di.ffering b.Y rand flowing in opposite directions ,

so that the drawing can be used for calculating the torque acting on a permanent r·ing

magnet.

When c:om;iciPring <1 sin!)le circular cur rent, we have to take i ·nto account onl y the

i nward current taking its direction not i n t he negative but in the positi ve direct ion.

The eccentricity distance of the centre of t he ci rcular current with respect to the

axis of the SIBER IAN COLIU magnet i s p. The mi ni ma l d~ stan~ between the surface of

the magnet and the current is q. The radi u~ of t he curcul ar currert is kR , where R is

the radius of the magnet and thus k "' 1 + p/R • q/ R. T"he azimuth c.ngle of the test

current element with respect to its cer.tre is f.l and :b with l"!!Spect to the magnet 's

axis to which its distance is :J. The right half of the SIBERIAN COLIU magnet w!Jic!'; is

i n the first and "econd quadrants ha s a north pole up.

The fanes elf 1 and df2 will act .• respect i vely, on the nearest and fertne>t ~:i:~~"'!i!

elements. Obviously df1

will be larger than df 2, howev~:r now the scal ar magneti~ i!'lte~

s ity wi ll be equal to ze ro not for ~ l = '11/2 and \>2 = 3'11/2, but for &1 < To /'2. and

df4

/ df

2 [ I

// ' I ' , ' I

I \

I I \ I I \ \ !

I \ •

I \ '

\ \ • ' I '•

I • \ ' \ ' I ' I ' i I

I I • I ' t •

i

t ' I h I

\ ; .

\ !

' \ j ' ' .,

\ ' J ·, I \ !

\ ' .. ·/ ' \ I

\"" ' \ '

" . ~'-..... df ---._: r

df3

Fig. 2 · Circular currents eccentric with respect to a SIBERIAII COL!U magn€t.

- 10 -

e2

> 3or/2, as t he scalar magnetic intens it y is equal t o zero ,for 9 = li/2 and ql = ~'1o/Z .

Thus we are not sure 1\tlethEr t he torque acting on t he whole circular cur rent will be di f ­

fe r ent from zero.

No~' we sha 1; show that th is torque is dtfferent from 7P. ro.

1<e have

cos:P = (R+g)2 + t>2 - {2kR;in(8/~ - .

2(R+q)p (9)

We see thus t hat p is obtained as a fJncti on of 0 . Tc obtain al so cos~ as a furc ­

t ion of e onl y , we have to put t he val ue for~ from the fi r st formula i nto the second

one. Then P and cos9 are t o be put i nto fo rmula (8: and so S = Smar will be obtained

a:; a functi on of 6 (we repe·at , for a closed circu it, as the c irco.rit nf 7-hf' S :BER II:N

COLIU ma gnet , there is Swhit = 0). The c ur rent e lement of the circular current at a g1ven an£le e h inJ i~.;dte d in r;g.

3 by dr (Ne re,eat, dr is the l ength of the current element). This current e· ement is

tangent ial to the circular current wi th radius kR. But the scal ar magnetic i ntens ' ty

S refers to c ur rent elements which are perpen:Jicular to the respect ive radii 1> f rom

the cent re (i.e ., the axi s ) of the SIBERIAN COLIU nagnet. ThLs S acts on cur rent el e -

ments

1 I

6 R

~ s 11 ft - -f • 0

Fig . 3. Diagrilm ;;n~bl ing t h<! calculat ion of the tangential force witt. which S ~ne­rated by a SIBERIAN COLIIJ magnet acts on a current element of eccentr ic

ci r cular current.

- 12 -

2 . Case p: l, q • 2.

P2 = i7 - Scose, cos.P = 4cos9 - 1 ( 17 -s~ose ) 112'

· cos? (~t- e ) (4 -c: n~fl ) 2 = , 17-Scose

S.,. " 1 {(9-4cos9 - 16sin2e)ln 4 - 2(4cos9-1) 17-Scose 5-4cosa

• s i n !/> = --'4;.:;s..:.;i n""'e'--• ( 17-Scoso) 1/2'

..

+ 8si ne(4cose-l)arctan s ine }, 2-cosa

M"' /rad .. 2

165•(4-cose) . ( 17) 17-Scosa

3. Case p • 1' 9 • 3.

4. Case p • 2, .9 = 1.

5. Case p = 3, 9 = 1.

The formulas for the cases 3, 4 and 5 wer e obtained exact ly in the same way as the formulei s for the cases 1 and 2 .. In the same way can be obtoined the form•Jlas fo r CI'\Y

other combination of the parameters p and .q, where p and q can also be ~on i ntegers . The net reduced torques for the f ive different cases, calculated on a computer ac­

cordi ng to fo nnul a ( 15 ), were:

1) M• = 2. 3127, 2) M• = 1.1760, • 3) M "' 0. 7207, 4) M• " 3.5520, 5) M* = 4.E703 . (18) . . ' The pl ots for S and H /rad for the f irst case (P =1, q • 1) are given , res pectively,

in fig s . 4 and 5 . · Now we shall show that bes ides the Mar inov sca l ar magnet ic intensi t y, Smar• al so t he

0.4 r---------~---------.---------,----------,

0.3

0.2 •

0.1

0 .. " .. "" ............................... -................... .............................. -............ ..._ ... ,.,_ .............. "'

-0.1 0 0.5 1 1.5

9/'JI 2

F: g. 4. The reduced Marinov scal a r magneti c intensity s* as function of the azimuth angle e for the case p = 1, q "' 1.

- 13 - • Ho .• 21

Mari nov vector ·mag'net ic ; ntensity Bmar 9e11era'tes a torque on· an ec~·entric c1 rtul ~t cur­

rent. This torQuE: can be n.et only cOJnpa rab·l e with the terque· ,generated by Smar·• but

eyen 1 a.rger. Bmar acts wi th a force which. alwa,ys is peYpend.i~ular to the t·est current el~nt

(see tile third term in. equ-at i91l .( ~.)) and 1 t .~~ems th~t Bma, cannot generate fqrce along the curre'l,t. elements (onJy such forces .c-an set a c1rcular current in ro~ation

about .the axis of the latter!). As it is we.ll known, this i s the case with the Lorentz

magnetic intensi ty, Bl or· However (8n,8~ .altl)ough hav ing the ~arne ·magnitude~ .• has££­pos1te signs for tangential and r.adi-~1 currliht ele~~~ents. 'Th1s, can ·.be seen ~ lllilediately

. \ . . . if taking the su!J\. o.f the formulas (.6) and· (7) : This sum gives zero . for !!!l ~.The res-pective graphs of the functions '(6) and (7) are g.iven in the first Ref. 4.

Now·,. by the l}~lp of fig. 6, we shan ·eltplain. why a SIBERIAN COLJU magnet acts on

an eccentri c circular cu.rrent with a torque generated by t:he af;t1on, of Bmar· When cons3der.ing the action Qf Bmar• beside~ the tangential component ,.(10) of the

current element dr, we have to tali.e into aet;:ount a:lso lts radial component

dr r " drsin(~·-·e y, (19)

as B~r act s with a force also on the radi·al companent (let us remi nd that the force

with which Smar a.cts on a radi a 1 current element i ; nul 1) . ( M. B .L~.st asse)'tt)n not. tT\Ie l ! ! Formulas (6) and (7) show that in the f i rst and second quadrants (·i.e., for

0 ~ ~ ~ w) (8marlz acting on a tangential curr.ent element is negati ve , while (Bmar)z acting on a radia l current element i s pos.itive. Thus the- force f t acting on thi:! tangen

tial current el~ment drt will point to the axi ~ of t he SIBERIAN COLIU magnet , w·hile·

the force fr actilig on the radial cu.rrent element drr wil l poi nt into a direction op­

POSite to the di'rection in which the elemeAt drt points.

Fig. 5.

4 ~---------.-----------r----------~--------~ r .

3

2

1

,• . ......... " ........................................ !.......... . . ....... .

' • J

0 c. s 1 1.5 2 6/'lJ

T.he reduced torque for t~n i't "rad1.an, · M41 /r.ad, p.rod.uced by S, a·s · funct l Gn .of

t .he azimuth angl e e for the c-ase· p = 1; q . • 1.

- 14 -

The forcesacting on the tangential and radial current elements will be, according to the third term in formula (1),

(20)

but a tor~ue will be caused only by the tan9ential components of these two forces (tangential with respect to the circle with radius kR described around the centre of

the circular current). For the magnitudes of these two components we shall have

( 21)

and they both will point into a direction opposite to dr. We have not put the nota­

tions (ft)t and (fr)t to these two forces in fig. 6, as tne figure will become ille­gible.

Let us now, as above, give the formulas for (B~arlz and for M~/rad as functions of the angle e. Fig. 6 shows that the torque with which (Bmarlz acts on the circular current is negative for 0 lii <1> ~ 11 as ~<ell as for 11 ~ a~ 211. Thus we shall give on· ly the formula for ((Bmarlzlt by putting formulas (9) into formula (6), wtlich will

I I

dr S N

Fig. 6. Oiagram enabling the calculation of the tangential force with which Bmar generated by a SIBERIM COLIU magnet acts on a current element of eccentric

circular current.

• - 15 - No. 21

be negative for 0 ~ s ~ rr and positive for n ~ e ~ 2n. Then M•/rad will be obtained with its f_isht sign if multiplying ((Bmarlzlt by 2k2R2 (the factor 2 is taken to ob­tain also the torque due to ((Bmarlzlr!)and by sin(4>-9)cos(cP-e). The last product is positive for 0 ~ cP,e f. nand negative for 11 ~ 4>,e ~ 2n, so that M"trad is obtained negative for any 4>,6, as it must be according to fig. 6.

The net torque acting on the whole circular current will be obtained after integ­rating M~/rad along the whole circular current

.. Zn~ 22 b., M = f (M /rad)d6 = 2k R f (Bmarlzsin(4>-9)cos(4>-~)de, (22)

~ 0 . 0

and here and beneath, for brevity, we do not attach to Here are the formulas for the first case. 1. Case p = 1, q = 1. FUNDAMENTAL CASE.

o2 = 10 - 6cose, cos<t> = 3cose - 1 ,

( 10-6cose) 112

the index "t".

s; ncP = --..:3;-::s..:..:i n~~-· --,.....,. { 10-6costl) liZ·

COS{4>-El) = 3 - cose , { 10-6cos e) 1/2 .

sin(¢-e) = sine ' ( 10-6cos6) 1/2

• 1 {(7+6cose-18cos2e)arctan Zsine 10-6cos6 3-2cosoS

- 6sine + 3sin€1(3cosCi-1)1n-......:.9-- ! ' 13-1~tOS ;.:

M* /rad = 18sin6 J-cose (8"" } . 10-6cose mar z:

The net reduced torque for the first case, calculated on a conputer according to formula (22) was

1) M* = - 2.2544. o.2r---------~--------~----------.---------~ .

•

0.1

0

-0.1

-0.2

\l '-I \ . ' . \I v • ..... ...................................................................... .. ··::..·· ..... -················ ····-·········· ....................... . .............. .. .. ·- .. -{ I

j l -.. I . . •

~--------~--------~--------~---------0 0.5 i 1.5 9/or 2

(24)

Fig. 7. The reduced Marinov.vector magnetic intensity <S:ar)z acting on tangential test current ·element as function of the azimuth angles for the case p = q a 1

- 16 -

The plots of (B~rlz' i.e. , of ((B:ar>z>t• ;:~nd cif M"'/rad i«lr the first case (p = 1,

q = 1) are given, respectively, in fig~ 7 and 8.

Comparing ( 24) with the f irst fonmul a (18) , we see tha t for the f i rst case t he

torque produced by S is larger than the torque procuced by Bmar and thus in thi s case

the circul ar wire will rotate in the positive direction.

The first case is presented in fig. 9, if taking into consideration the external

circular current, i.e., for the case q = q' . In the figure two Sl BERIAN COLIU magnets

are taken for i ncreasing the effect, as this was the case in our second experime nt

(see Sect. 5) .

If, however, we shall consider in fig. 9 the internal circular current which has

the same parameter p = 1, but whose parameter q = q" is much smaller than unity, we

see that the angles (op-e) " will be larger than the angles (~ -e} • . l hus if f or the

same angle 4> the relation iSI/ I lBmarh l remains constant, i.e., lS'I/i(Broarlz l =

IS"I/I(Bffiarlz 1. we shall have

(25)

wher~ MS i s the ton;ue produced by the $- i ntensity and M6 is t he torque producen hy thP

the Bmar- intensity . Thus one may expect that for a certain q = q0 less than unity it

will be IM~ 1 = 1M~ I. i .e., the net torque will become zero. and for q < q0, when

IMs!fiMs l <1, the torque will change its sign becor~ing negative.

The assumpt ion I S (~) I / I ( Bmarl~)) 2 1 = Const does not correspond to real i t y, however:

if lookinq at forli'IJlas (6) and (8), we see that for p .. R, i.e., for q ... 0, we have

(S)\¢=o .. "' • S<' that also IMsl -? "'• wh ile ICBmarlzllj)~o does not tend to infinity and

-0.25

-0.5

-0.75

-1 0 0.5 1 1.5 2

Fig. 8. The reduced t or que for uni t rad i an, M11

/ rad, produced by Bmar• as funct i cn

of the azimuth ang l e e for the case p = 1, q = 1.

- 17 - No . 21

,consequently :M8; does not tend to infi11i ty, too. As the cal culation of the integral s (15) and (22} on a computer is a simple task ,

one cart search f or values of p and Q which lead to consi derable torques acting on the eccentric circular current (most probabl y i n the positive dir~ction) .

As already mentioned, ~ rotati on can be real i zed if tak ing not a circular current but a ring magnet . It is wel l known t hat a ring axi al ly magnet ized magnet is equiva­

lent to two circular (as a matter of fa ct , cylindrical ) currents flowing into oppo­s ite directi ons . This case was presented in fig. 2 . The forces df1 and df3 in fig . 2 refer to t he case when only t he act ion of S is taken i nto account. In such a case the net t orque acting on t he whole ri ng magnet will be l ess than t he torQue acting only on the internal circular current.

However, if we take into account also the action of Bmar• then, at a suitable cho1c of the paramete rs p and q, it would be perhaps possibl e to realize a geometry when both torques wil l point i nto the same direct ion . This wi ll be the most effecti ve cas; when us ing as a rotor a permanent ring magnet.

Obviously, a SlBERIAN COLIU machine with an eccentr i c permanent ring magnet wiii t~ a perfect perpetual motion machine.

~-;I' /

'

Fig . 9, Two eccentric ci rcular currents wi th different q parameters.

- 18 -

4. INCONCLUSIVE EXPER IMENTS

In this section we shall report on three experiments whose results were inconclusive.

A •. P.ERIIANENT RING MAGNET SUSPENDED BV THE KELP OF BALL~BEARINGS.

Similar experiment was shown in figs. 4 and 5 of the last Ref. 5. The new experi­

ment of this kind is presented in fig. 10:

Two SIBER1AN COI..lU nagnets with radii R = 15 nwn and height H = 100 mn were mounted

one over the other. A ring Nd megnet,which can be seen at t he middle height of t he up­

per SIBERIAN COL11J lllilgrtet, was f i xed to the upper r im of cylindrical ring of PVC whose

lower rim was fhed to the outer race of a ball -bearing. The inner race of t he ball­

bearing was fixed to another s~~e ller ring of .PVC and the 1 a tter was fixed to the 1 ow­er SIBERIAn COLIU nlllgnet .

The ball-bear1ng was eccentric with respect to the SIBERIAN COLIU magnet. By the help of three pairs of screws (one of these pairs are the white plastic screws, the

other pair looks to the reader) such a position could be found that the ring magnet could t·reely rotate. The small ring magnet fixed by scotch to the upper SIBERIAN CO­

LIU magnet, which repulsed the part of the ring magnet in its neighbourhood, served

to balance the llli!gnetic force with which the big ring magnet was attracted to the SI­

BERIAN COLIU· magnet. The ring magnet wa s mounted so far from the ball-bearing for eva­

ding the induction of eddy currents in the balls of the bearing. At a small distance

between ring magnet and ball-bearings the eddy currents were extremely strong and to overwhelm their braking action a huge torque was necessary .

The internal radius of the ring magnet was 20 mm and the external radius 30.5 mm.

Its height was 10 mm. T~e distance between ring magnet and SIBERIAN COLIU nagnet was

about 1 m:n. Ttus the parameters of the system were p ,= 0.333, q = 0.066, r = 0.700.

To see whether there was torque in a preferred direction, we rotated the PVC cyl i n­

drical ring by an electromotor in the positi ve and negati ve directions and measured the coast:-down t imes. No reliable t ime differences have been registered. As the mecha­

nical friction was considerable and the coast-down times were short (some 20 seconds), the conclusion was to be drawn that the effect was less than the sensitivity of the

measurements. If the ring magnet encircling the SIBERIAN COLIU magnet was taken in the hand (see similar experiment in fig. 18), no torque could be sensed. The force of

•

interaction was ~lways pointing to t .he axis of the SIBERIAN COLIU magnet.

B. PERMANENT RING MAGNET SUSPENDED BY THE HELP OF PER~NENT MAGNETS AND WATER.

To reduce the friction as much as poss tbleJ we decided to suspend the same ring

magnet by the help of permanent magnds,which had to govern the position of the ring magnet in the horizontal xy-plane, and by the help of the forces acting on a body im-

mersed in water, whkh had to ~ovem the position i~ the vertical z-direction. The drawing of the machine ·s shown in f ig. 11 and the photographs in figs. 12 and

13. The diagram and the photographs are sel f-explanatory.

19 Nc. 21

Fig lC. : ccen tric penraren t. r l n ;~ ~ac,gnr-t '>l•~pnndPd or :>o', he <! r i ng r, or ~ cy· l nar1ca' Slc~lM COLLL ,-ague:.

- 20 -

Because of the i mperfec t i on of the experiment ( no absolutely i dent i cal magnets

and no e~act geometry}, we were unable to suspend t he swimmer wi th the magnet in t he water and consequentl y we coul d not observe whether there would be rot ation i n a pre­

fe rred di.r ect1on . This wi 11 be the last suspens1on with 1 imited number of permanent

magnets wh ich Ma rinov has done. Such a suspension can be successful only i f many per­

manent magnets s houl d be used.

s s

Magnet. PVC Iron

fig. 11. Diagram of the eccentric perma­

nent ring magnet suspended by t he hel p

of magnets and wate r on a cylindrical

SIB£RIAN COLIU magnet.

- 21 - No. 21

C. COIL SUSPENDED ON CLOCK-MAKER BALL-BEARINGS IN A RING SIBERIAN COLIU MAGNET.

A kind of such an experiment when using permanent cylindrical magnet was presented 11, figs. 7 and 8 of the last Ref. 5.

Now instead of permanent cyli ndr ica l magnet, we suspended eccentrically a cyli ndri­cal coil in a ring SI BERIAN COL IU magnet wi t h the aim to see whether currents wi ll be induced at rotat ion of t he coi l . In the case that such current s will be induced and they will be $-currents, then, if t he self-accelera t ing torque (ant i -Lenz effect !) wi l l overwhelm the fri ction torque , the machi ne wil l become a~ mob~e. We have however to keep i n mi nd that in an eccentric coil Smar· and Bmar·tensions are induced (see Sect. 3) into o·pposite directions , and i f the latter tension is greater, the in­duced currents will be B-currents which will brake the rotation (Lenz effeet!).

It is to be noted that we have not analysed analytically the case with a ring SIBE­RIAN COLILJ magnet, as we did this for a cylindrical SIBERIAN COLIU magnet in Sect. 3, but it is logically to assume that al so for the case of a ring SIBERIAN COLIU magnet Smar· and Bmar·torques will act on an eccent ric circular current and consequently Smar· and Bmar·tensions will be induced if rotating the coil by external force.

The experiment is shown in figs. 14 and 15. Two coils with radii 15 mm and heights

Fig. 12. The "pot " and the swilMler from fig. 11 ..

- 22 -

36 mm were manufactured. The eccentricity of the suspensiofll wa~ 10 mm. The geometry

of the ring SIBERIAN COLIU magnet is 1~e 11 known from previous papers.

The coast-down times wer e measured when suspending the co11 in t he machine and "in air". The a rrangement for the suspension "in air" is shown in fig. 15, noting that

the ball-bearings for the sus pensions " in the machi ne " and "in air" were differen t.

The coast-down times for the same starti ng velocity are gi ven in Table 1.

Table 1 ---------------------------------------------- ----- - --- - -~----------- - -- ----------- -- -

Coast-down times for eccentrica lly suspended cylindri cal coi l s ------------------------- - -- - ---~----------------------------------------------~ ---- --

Firs t rotor: we ight 132 g {more copper) Second rotor: w~ight 56 g ( 1 ess copper) ------------ --------------------------------------------------------------------------

In t he machine In air In the machine In air ·---------~------------------------------------------ - - ----------·------------------- -

-------------~-------------------------------------------- ----------------------- -----

Fig. 13. Photograph of the machine from fig. 11 (in the photograph the eccentrically placed SIBERIAN COLIU magnet is mi ssi r.g) .

- 23 - No. 21

We see that the coast-down· times in t he machi ne were less than "in air" and if

discarding the tlighly speculative concept about common action of induced Bma r and

Swar currents, the most simple explanation is the follow ing:

Since a Blor- intensi t y cannot induce tens ion in a cylindrical coi l rotating about

its ax is, we have to conclude that the brak i ng torque was generated by B1 or -currents

induced in the ball ~bearings whi ch were made of ferromagne t i c mater ial.

5 . CONCLUSIVE EX PERfMENTS

In this section we shall report on fou r e«periments whose r esults were conclusive.

A. COIL SUSP£NOED ON A SINGLE SIBERIAN COLIU ~1AGNET .

The experiment is shown in f igs . 16· and 17. The cylindrical coil had 1000 windings

of copper wire of thickness 0.45 mm and resistance 16 Q. This coil was fixed to a

plastic "bell" which could rotate on a vertical axle with pcil'tted ends. The 1ower bea­

ring was on the upper half-sphe rical cap of soft iron which covered the SIBERIAN COL1U

magnet whose radius was R = 15 mm. The i nternal . diameter of the coil was 36 mm. and tr~

eccentricity was 3 l!lll, so that ther e was p ~ 0 .2. The weight of the rotor 1-1as ba1anced

in the usual way by the repul sive act i on of two small cylindrical magnets (see the

Fig. 14. The ring SIBERIAN COLIU magnet i n whose inner space an eccentric cylindric;~ l

coil is susoended.

- 24 -

lower repul si ng magnet i n fi gs. 17 and 18). Five batteries (Cd-Ni accumulators) of 9 v.any connected in serie~ supplied the

current. A s ixth battery feeded a 1 ight diode electronic breaker which was ON at dark. A llilnnual contact breaker was OFF when t uning t he elect ronic breaker. In fi g. 16 the electronic breaker i s fixed to the coil and in fig. 17 to the t op of the plastic bell .

At charged accumul ators the current sent to the rotor was 1.7 A and quickly dropped down, so t hat the accumul ators ha d t o be charged very often.

Since at dif ferent azimuths relatively strong torques acted on t he r otor. due to t he geometrical imperfection of the const ruction, when sending t he current a whole ro­tation could not be observed . Al so if sendi ng therotor i n rotation and switching then the current by making "dark", a continuous rotation could not be realized as t he fric­tion t orque overwhelmed the dri ving torque .

The availability of driving torque was t hus observed by measuring the coast-down t imes: For the case when the rot or was set in rotation i n t he directi on of the driving torque , the coast -down t ime was with about 20~ larger than for the case when the rotor was set i n rotation agai nst the direction of the driving torque. The sense of the ro­tation indicated that the torque due to the S-currents overwhel med that one due to the

Bma r -current s.

Fig. 15. Arrangement for suspE: nding the heavy (at t he left) and the light (at the r ight ) cylindrical coil s "in air'' .

He . 2l •

-- . --

Fig. 16. Eccentric circular coil feeded by co-rotating batteries and suspended on a sinqle SIBERIAN COLIU maqnet.

Fig. 17. The rotor frun f1g. 16 dismounted from the SIBERIAN COLIU magnet.

F1g. 18. The preferred driving torque sensed by hand.

- 27 - • No. 21

Before doing the experiment by supplying the current from co-rotating batteries, we sent current of 4-5 A by very thin and loose wires and observed the respective torque, but in this case, of course, a whole revolution could not be realized.

If rotating the rotor by hand, current was induced. Current was induced in the di­rection in which, if current was sent, the rotor obtai ned the same sense of rotation (.anti-Lenz effect!).

The torque in the preferred direction could be sensed even by hand as it is shown in fig. 18 but the feeling of the available torque was extremely feeble.

B. COIL WITH SLIDING CONTACTS SUSPENDED ON TWO SIBERIAN COLIU MAGNETS. With the aim to obtain a larger torque, we decided to suspend a coil on two SIBERIAN

COLIU ·magnets, as shown in the principal diagram in fig. 9. Now the coil had a larger diameter and the parameter p was larger. The radii of the

two cylindrical SIBERIAN COLIU magnets were again R = 15 mm. The eccentric displace­ment was also 15 mm, so that we had p = 1. The repulsive lower ring magnet now was placed exactly between the axes of the SIBERIAN COLJU magnets. The rotor's axle was suspended on clock-maker's ball-bearings to have very low friction in the bearings.

The coil had 370 windings of copper wire with thickness 0.6 mm and resistance 5 n. The photograph of the first variation where the current was supplied via thin and

loose wires is shown in fig. 19 (the two wires supplying the current are seen extremely faintly behind the rotor from the left) •

. , Fig. 19. Eccentric coi 1 feeded by thin and 1 oose wires and suspended 01'1 two SIBERIAN

COLIU magnets (in the photograph the rotor is dismounted from the magnets) .

- 28 -

Now by sending current of 4-5 A pretty powerful torques~ere observed, but for dif ­ferent alimuths of the rotor the torques were not into the same direction. Also at -different azimuths the induced current at the same sense of rotation was not into the

same dire-ction. These se~mingly "strange" effects were due to the imperfection of the construction: The axle of the rotor was very thin (thickness 1.2 mm), the clock-maker ball-bearings which we~~ppropriated for such a heavy rotor soon became loose and the rotor wobbled at rotation, the two SIBERIAN COLIU magnets had not the same magnetiza ­tion, etc. When imitating the wobbling by oscillating the rotor by hand without rota ­ting it, the induced tension was due only to the change of the Blor magnetic flux across the coil. Thus the side effects marred the effects due to Smar·

We could establish that the ~ torque was an Smar-torque and the average induced ten­sion was an Smar-tension by supplying the current via sliding contacts which allowed to make a continuous rotation (see figs. 20 and 21).

The variation with the sliding contacts was done as follows: Two troughs were made in a PVC cylindrical ring which then were filled with mercury. To the initial and fi­nal coil's wires two "knives" were welded which at rotation were immersed into the mercury and in this~ sliding contacts have been realiled.

Current until 10 A could be sent to the coil for short times (at higher currents the coil became too quickly hot). Howe~er as the net torque was feeble, it could not overwhelm the friction torque. By measuring the coast-down times at two opposite ro­tations and the same direction of the current (or at the same sense of rotation and two opposite directions of the current) the sense of the driving torque was establi-

'

Fig. 20. Eccentric coil feeded via sliding contacts and suspended on two SIBERIAN COLIU magnets (in the photograph the rotor is dismounted from the magnets).

j

Fig. 21. The machine from fig. 20 in working state.

- 30 -

shed which turned out to be an Smar-tor.Que. ~!hen rotat1n~ the rotor by one' s f ingers, t he induced current f lew i nto the direction in whi ch if sendi ng current we obse rved the same sense of rotation (anti -Lenz effect!), i.e., t he induced. current was an Smar­current.

To reduce the friction caused by the electrodes immersed into the mercury, we put the mercury t roughs near the rotational axle, as shown in fig. 22, and for electrodes thin wires were used. Now, finally, when sending current of some 10 A a con ti nuous

rotation was observed, when givi ng an initial push to the rotor. We have to note, however, that as t he suspension was substant ially deteriorated the

tuning of the maclfiJe, bEcame very difficult and much t ime was to be spent. until t he right posi t ion was found using also magnets around t he lower rim of the coil which had

to balance t he appearing disbalancing forces (see above).

C. COIL FEED ED BY CO-ROTATING BATTERIES ANO SUSPENDED ON TWO SIBERIMI COLIU MAGNETS

Aiming t o reduce further t he friction and the necessary current, we mounted two batter ies (Cd-Ni accumulators) on t he rotor in t he way al ready used in Sect . SA. To have the rotor as. ·l i ght as. poss ible, a light diode el ectronic breaker was not used (fig. 25}.

However, when the accumulators supplied current of about 1.5 A, even by giving to the rotor a·n initial push in the direction of the oriving torque, a continuous rotation cou ld not be realiz.ed . There was only difference in -the coast-down t imes for opposite ro tations.

Fig. 23. The machine from fig. 22 i n worki ng state

N e l..\1 ' .... ~ .C.OI ' • • ,_a

J •

Fig. 24. Eccentric coil feeded by co-rot~ting batteries ~nd suspended on two SIBERIAN COLIU magne t s.

- 33 - No. 21

0. PERMAMNENT RING MAGNET StlSPENDEO ON TkQ AND FOUR SIBERIAN COLIU MAGNETS .

As a per!llilnent ring magnet represents actually two equal circular (cylindt·i cal) cul'rents wi th different radii flo1~ing into opposite direct ions and we calculated {com­pare formula s (18,1), (18 ,2) and (18,3)) t hat the net t orque generated by two such currents i s different from zero , we dec ided to repeat the inconclusive kind of expe­riments reported i n Sect. 4A and 4B with a higher precision to see whetller t here will. be a net preferred torque. Our con~iction t hat such a preferred torque must exist was Yery firm .

Our neodymi um ring magnet (see figs. 25 and 26) had inner radius 40 mm , outer ra­di~s 50 mm and height 10 mm. Now we used not clock-maker bal l-bearings but steel bail­bearings for an axl e with thickness 4 mm. The bearings were mounted in t he brass co­l umn placed between the two SIBERIAN COLIU magnets (fig . 25). The rotati on was per­fectly stabl e and because of the very careful construction and the non-avai lability of sliding contacts, the fri ction ~1as very lo~1. However ~ prefert·ed torque was ob­served.

Wilen setti ng t he rotor into rotation with relatively low velocity, its cc.a~t-dtw<r• times were in t he l imits from 2ffiS6S to 3~4s for both senses of rotation and butt. ori ­entations of t he ring magnet (once the nor th pole up and once the south pole up).

Then the experiment was repeated with the same null result when acting on th"' rif;g

~agnet with four SIBERIAN COLIU magnets (see figs. 26 and 27) .

· Fig. 25. The permanent ring magnet and the two SIBERIAN COLIU magnets 1n dismounterl state.

- 34 -

First this h1gh-precision (uncertainty! 2%) null resuHnJas perplexing for us, as

according to the theory and the measurements 1~ith circular (cylindrical) currents a

preferred torque was to be exEected. Bowever, soon we found the explanation for the

null effect:

A permanent ring magnet can be replaced by two circular (cylindrical) currents flow­

ing into opposite directions when we act on it w1th a vector magnetic intensity 11hich

generates forces perpendicular to the fictitious two circular currents. When, ho~,oever,

we act on the permanent magnet with a scalar magnetic intensity which generates forces

parallel to the current elements of the magnet, we act, as a matter of fact, on milli­

ards of concentric currents, any two of which flow into opposite directions and are

very near one to another. Obviously the net torque on those milliards of pairs of cur­

rents must be null, what we actually observed.

We carried out also the inverse experiment by making the rotor in fig. 26 stator

and the stator rotor. Again the coast-down times for both senses of rotation were

equal within an accuracy of t 2%. The explanation of the lack of torque acting on the

SIBERIAN COLIU magnets which had a rotational degree of freedom is the same as above;

on these magnets act milliards of concentric currents any two of which flow into oppo­

site directions and are very near Qne to another.

We, however .• have not the slightest doubt that if suspending excentrica lly two equal

currents with different ~adii flowing into opposite directions, a driving torque should

Fig. 26. The permanent ring magnet and the four SIBERIAN COLIU magnets in dismounted state.

Fig. 27. The permanent r ing magnet suspended on four SIBER IAN COL IU magnets in worki nq state.

- 36 -

appear acting into t he direct ion in which a t orqw wn 1 u.w <tel in·~ onl y on the inner

current. Of cour se, the torque acting on the h;o oppos itely flowing cur rents will be

lllore fee ble (see once more the f i rs t three t ormulas (18)).

Our hopes that an eccentr ica lly suspended permanent ring magnet w111 be rot ated by

the SJBERJM COLIU magnets were very firm, and as in such a case t he frict ic·n can be

nade ext r emely l ow, our convi ·; t ion that a per petual motion SIBERIAN CCI.IU machine wi ll

:1e constructed was a lmost hundred per cent . No~< these hopes have c rashed.

NO:E As we es:abli s1ed experimentally that Mar i nov's formul a and the Lorentz-Ma r i nov

equat ion are wron~ (see OP-?2, p.?Q) and t hat surely a Marinov vector magneti c i nten­

sity does not exi; t, the specul ations and cal culations in the second part of Sect.3,

dedicated t o the action of Bfl<tr on tt>e eccent r ic r. ircula r current. rere i n superfl uous .

We , however, firmly believe that a Mati nov scalar ma gnetic intensity does exist,

so that we !lope. the speculotions and calculat ions ir the first part of SPr:t. 3, dedi­

cated t o the action of Smar en the eccentric circular cur~ent, remain valid, but one

111U:>t toke into account al so :he ac t ion of Smar on the radial te;t curren t elements·

AC KNOO. EDGEMENT

I had the pl easure to duscuss i n de t a il the di f fe-rent a;pect s of tbe scalar

magnet i c fiEl d and of the S IBERIAN COLIU machines with Prof. P.T. Pappas (Athens) du­

ring t he \is it of t he latter J f the Institute for Fundamental Phys ics in Fe~ruary

1996 . ThE· idea to const"Uct eccentric SieERIAN COLIU mach ines with permanent magnets

and co1ls wc.s a result of these discussi cns.

REFERENCES

l. s. "larinov,

' -. S. Mari nov,

3. s. Mari nov,

Divine El ectro-nagnetism, (Ea!;t - \olcst, Graz, l993).

SPEC. Sc . Techn . , 18, 122 ( 1995 )·. •

Nature, 380, p. xi v (28 Marc h 1996). Dele~ Lhe "-"in the first fonnUia (4).

4. s. Marinov, Deutsche Physik, 4(13), 31 (1995); 4(15), 49 (1995) ; 5(17), 43 (1996 );

5(18) , 18 (1Y9b) . 5 . s. Mar i nov , Deutsche Physik , 3{9) , 17 ( 19g4 ) ; 3( 10), 8 ( 1994 ) ; 3 ( 11), 40 ( 1994);

3(12), 13 (1994); 4 (13), 15 (19~!:l) ; 4 (15) . 7 (1995); 4(16), 5 {199E ), !i p ) , 5

(1996); 5(18), 5 (1996); 5(19), 5 (1996).

- 37 -

WHO IS RIGHT; WESLEY OR ~1ARINOV7

Stefan 1·1ari nov lnsti t ute for Fundarrenta l Physics

Morellenf el dgasse 16 A-80 10 Graz, Austria

Veu.:to c.he. Phy.~>.{.k 6 ( 21

{199'7

Wes l ey and t<'ari no-v give two differen t explanations for the Ma ronov-llohfll effect. The cau se i s pleaded that Marinov' s explanation is the right one a nd Wesl ey's wrong. No ttnalysis of the official treatTrent is given, as the offi cia l treatrrent based on "Quantum concepts" is a pure mys tifica tion.

In physics too many different theories ci rculate. The mathemati cal and conceptual

apparatus whi ch are used as backgrounds of these tneories have becorre so complicated

that t he discussi on bet ween the proponents of the different theor ies turn out to be senseless . Thus the followi ng criterion, l~h i ch I call the l otto-cri t erion , can hel p

us to es t abl i sh most quickly which theory is t he r-ight one: For a r ight t heory , at

the present state of knowledge, is to bE< acce?ted this theory which gives right pre­

dictions for the highest number of expedmenta l obser-vations. Al~ other theor ies are to be consi dered as wrong.

In the last months there was e discussion betv;eer. my friertd , Prof. Wes ley, and me

on the topic: Which is the physical explanat ion of the Aharonov-IJ.ohm (A.-B.) effect.

My treatment of the A.-B. effect was given in P-e f. l. Wesl ey's treatment was pre­

sen~d in~ seri e s of pa pers, the last version of which 1va:. s.ent to me on thE.> 28 June

1996 .and now appeared in his book CLASS!Ci!.L QUANTUM THEORY (6 . Wesley. Blumberg) p. 308.

Here is a short recap'itul ation of Mari nov' s treatment (see fig. 1 in Ref. 1) .

Let us consider an infini t ely long cylindrical solenoid with radius R and n t urns Qn a unit of verti cal length in wni cr. the curre nt can be changed from zero t~ I, A beam of coherent e l ectrons separates at point A in t~1o beams whi ch enci rcle the sole·

noid and meet again at point B where one observes their interference~. l f changing

the current from zero to I, a shift in the i nterference picture is observed whid: ~3r1

be calculated by fo rmulas {1) - (5) of Ref. 1. •

Accor ding to my t heory, and according to t he Lorentz equatio~ . megnet\c forces a~t

on the fl ying elect rons on1y during the time of changing of the current, as durtn9

that time there i s ;JAfat # 0. When th~ increasing curren t reaches the value I , no roor~

forces ac t on t he flying electrons. However when the current stops to increase, the

interference pi cture does not return to t he in itial one but reJTain s ~ot1th a shift

(A)

where \= h/mP.ve is e·l ectron's wavel ength, and "'<e• "<?' viii are mass, el ect ric charge

and velocity of thE' electro ns.

-:-he ~ itua tion seems t o b~ strange: There are HO acting for cl!s, but there IS a

shift. One would say: I f t hi nki ng "logica ll y", when t he current stops to increase,

- 38 -

the shift which has been reached has to disappear. - Well!, but WHrCH wn 1 be the

forces 1 eading to sucn a "di sappea ranee"? Whet\ the ctJrrent reaches the constant va­

lue I, no more forces act on the flying electrons. To obtain the initial interference . picture, we nave to diminish tne current from r to zero. Only at I : 0 the initial

situation can be restored.

Tne experiment can be done also in the following way, as Tonomura has done it in­deed(2•3l; First the interference picture is registered when the curl"ent in the sole­

noid is zero. Then the electrons' beam is switched off and then current I is sent to the solenoid, After switching again the electrons beam on, exactly the same shift (A)

has been observed. Now the "logically thinking man" will say: Now there must be no shift, as on these

electrons ne\fer forces have act. - Well, but if there will be no shift, and we decrease the current I to zero, an ''opposite" shift, with respect to the in1tia1 interference

picture, will appear, what, obviously, is a nonsensical result. I agree that these conclusions of "my theory" seem strange. But everybody who has

taken Kirl ian photographs where the aura around a 1 eaf remains the same when one cuts a part of this leaf, and everybody who has experience' in holography will recognize

tnat "my strangeness'' is not at all strange, as physics is so. To show that my theory is right, I carried out the experiment with the long sole­

noid and the two glow discharge tlilbes (see fig. 2 in Ref. 1). Here I observed not the wave-chara~ter of the electrons but their particle-character. And I observed an effect

(change in the length of the dark cathode space) only during the time when the current in the so 1 eno id was char!iled. When the current reached its constant va 1 ue I, the 1 engths

of the dal'k cathode spaces in the t\ibes were the same as in the case when the current was zero. This was a clear indication that when current I flowed in the solenoid, the

electrons in the tubes on both its sides had the· same velocities as in the case when

the current was zero. But if in fig. 1 of Ref. 1 two coherent electrons have separoted at point A at the

same moment, will they. at constant current I, meet at the same moment at point B? -NO! They will meet with a time difference 6t ~ 6/c (see formula (A)). as physics is so.

The interference shift in the Ahsronov-Bohm experiment isaculll.llative effect, while the change in the length of the dark cathode spaces in the glow discharge tubes experi­

ment is an individual effect. The first effect results from the wa'le characterof the

electrons, the second effect results from their particle character. That's all!

Now let me present shortly Wesley's treatment. According to Wesley, besides the Lorentz force, which Wesley calls "conservative

force", on the electrons flying with a velocity Ye acts another force

(B)

which according to Wesley 15 not a conservative force. According to Wesley, the non-

- 39 - No . 21

l.'linservat ~ve force Fwesley • which call act al so when A is constant in time, is respon­

sibl e for the acceleration a nd des~ccel eration of t he elect rons along the one or ano­

ther half-circl es in f ig . 1 of Ref. 1, leading to the o·bserved inteference shift al so

at I ~ Const. Thus Wesl ey does not make a difference 1n the effects when one observes

the wave character. on one s ide, and the particle character, on the other side, of the

flying electrons . So according to Wesl ey t he wave1 ength shift at I ~ Const is not

a result of "Marinov' s 'holographic' and ' Ki rlia-n photographic' equilibri stics" but a

result due t o phys ically existi ng forces. The words taken · in quot ation marks are not

wesl ey ' s, as here I introduce for t he first ti me the parallel between the A.-B. effect

and the holo-Ki rlian -graphy. I think, however. that Wesley, surely, wi11 sign the words

taken in quotation marks .

But 1 et us leave the discussion about the concepts - c:UJ.:pu.:t.o.U.o .eonga., .v.{.ta. bJ:.~v.U.

Wesley writes (p. 314 ): ,;Thi s nonconse rvative force of trotiona1 i nducti on must be

handled separat ely i n s itua tions where it arises, such as t he experi rent t c. register

the Aharonov-Bohm effect, or in the Hooper-Monstein experiment, discussed below" .

The Hooper-Monstein experiment is reported in Ref . 4 and fig . A is Wesley ' s fig .ll.l

in the Hooper-Monstein experiment there are two identi cal magnets, tne one with

south pole up and the other with north pole up. In the symmetry pi ane between the mag­

nets there is a lengthy horizontal wi re which makes a closed circuit via wires that

are fa r enough f r om the magnet s. It is obvious that, because of the anti -syrrmetrv c, f

the magnets , the magnetic intens ity at all points of the symmetry 1 ine will be equa1

to zero. Thus, according to officia l physics , NO electric c urrent can be induced ir­

the wi re . Ho~tever, as Hoope r and Monstein have demonstrated , if moving ~he ma gnet>

vire

s

,.

B lines N

s

" Fig . A. The Hooper-Monstein experiment.

wire

-liae

- 40 -

with the same velocity v towards the wire, current is in~dted,

The effect can be inmediately explained and calculated by my formula for the mo­

tionil-transformer induct i on (see the Editor 's Comments to Monstein's paper{5}}

Emot-tr = {v.grad)A/c. (C)

It is obvious that Wesley's formula (B) and my formula (C) are compl etely different ,

as in (B) " e is the velocity of the test charge, while in (C) v is the velocity of

the magnet generating the magneti c potential A at the location point of the te$t charge.

NOTE . Let me note that i f cal cul ati ng the A.-B. effect for the e~periment shown in fig. 1 of Ref. 1 accordi ng to Wes l ey's fonnula {B), tht! e ffect will be null, and not

different from null, as expected by Wesley . '

ln~ed, cons idering the electrons flyin g along the right semi-circle, we shall have

A ~ 2nr.IR2./cr, Ve = ve+. (D)

Putti ng these values in Wesley's formula (B) and taking the operator (ve.gradj in

cyl i ndri cal coordinates, we obtain, denoting by p the distance from the magnet 's axis

to t he cons i dered wire' s point,

f.wesley = (E)

as A is not a function of .p. -REFERENCES

1. S. Mari nov, Deutsche Physi k, 4 (13) , 45 (1995) .

2 . A. Tonomura, Proc . Int . Symp. Found. Qua. Mech., Tokyo, 1983, p. 20.

3. A. Ton.Jmura , Proc. l '1t . Symp. found. Qua . Mech., Tokyo, 1987, p. 97.

4. C. M'On :;tei n, Deutsche Physik, l ( 4), 10 ( 1992). 5. S. Marinov, Deutsche Physik, l{A), 18 (1992).

AFTERW-\ TH. Wi th a 1 ett er of t he 2 August I sent the a bove paper to Wes 1 ey, sugges­t i ng the p resentat ion of corrments. In his answer of t he 6 August lolesl ey wrote: "I see little merit in your paper that you enclose " and presented the fol lowi ng objecti on :

Your NOTE to your paper should be deleted ; as the electron moving by the solenoid does not move around the solenoid solely in the 1 direction.. The force is given by

where

so

F(Wesley) = - e ( .., • 'iJ)A/ c ,

Y = v e ~'

A = Ke1!r;

and F-- ev (cos rP e_ - si n.f.!....L )re /r ;

. ?1" r?f f

F = ev cos<f Ketlr', which is not zero!

- 41 - No. 21

MY COMr~ENT: Hith the above fonnu la Wes l ey HAS TO CALCULATE t h€ €ffect when the y ight and left beams form a CLOS ED loop . I ASSURE HIM that he wil l NOT obtai n the re­sul t gi ven by my formul a (5} in Ref. 1 {the effect does HOT depend on the FORM of t he cl osed loop formed by t he beams) . As I showed with formula (E) . f or t he PARTICULAR CASE when t he el ect rons f ly along a ci rcula r pat h, Wesley 's formu l a l eads t o a NULL resul t . I shal l be glad to s ee HIS calcul at ion for a square or romboi dal path.

POST SCRIPTU!~. I wish to note that t he di fference between the A. - B. effect and the i-nduction of current in a coil encircl ing the primary coil in wh1ch during time-· T the current is increased from 0 to I i s not as big as it sefl!ls. Indeed, i f ~Je shall look more attentively at the effects appearing in the secondary coil, we shal l see that a lso there all runs exactly as at the Aharonov-Bohm effect: When the current flowi ng in t he pri mary coi l reaches its max imum cons tant value I, the current induced i n the secondary coi l disapears only because t he secondary coil has some resis t ance and its current i s transfo~ into heat . lf the seconda1·y coil i s superconduct ing, t he indu­ced current wi 11 al so reach a rna xi mum va 1 ue l ' and wi 11 conti nue t o f1 ow eternally. Only by reduci ng the cu rrent I i n the pr imary coi l t o zero can we reduce also the i n­duced current I' to zero too. The currents I and [ ' obvi ously wi l l f l ow i n opposite directions and we shall have I • I ', for the case that the coils are very l ong and their radi i almost equal.

AVTHOR' S COMMENTS ~ly experiments with the glow di scharge tubes reported in Ref. 1 and shown in fig.

2 of Ref. 1 can be carried out i n a more impressive way if the cathode-anode l ine of the right tube will remain parall el to t he y-axis (see fig. 1 in Ref . 1) but the c~­thode -anode l i ne of the left t ube wi l l be invert ed at 180° so that i t shou ld poi nt in a di rect i on paral l e l t o the -y-a xi s . Then both t ubes are to be feeded by t he same bat tery and an ~pe~ter i s t o be introduced in the circu i t .

Now, at t he rest-transformer induction, t he dar k cathode spaces in both t ubes wi ll decrease thei r lengths when i ncreasi ng t he current in the solenoi d (duri ng t he t i me of the current change!), as in both t ubes the negative charges f l owi ng f rom the ca­thodes will be accelerated. The amper emet er in the circuit will indi cate an increase> of the current

At the motional-transfonmer inducti on, when moving to right the solenoi d wi t h cur­rent I flowing in the positive direct ion (see fig. 1 in Ref. l}, the dark space in the r ight tube will decrease its l ength, while the dark space in the lef t t ube will increase 1ts length (dur ing the t ime of motio n! ) , as the charges in t he r ight beam will be accele rat ed and in t he left beam desaccelerated. The amperemeter i n t he c ir­cui t will indicate no change.

Final ly, at the motional induct i on. when moving both t ubes to l eft no changes i n t he dark soaces wi l l be observed.

- 42 ~

The case with the mot i onal~ transformer i nducti on shows t«at if a cyl indr ical mag­

net i s enc i n:: l ed by a ci rcu lar wi re and tie move the magnet into a di rection paral lel to t he wi re's pl ane, t ensions are induced i n both wire' s halves . However, as these t wo tensions are equal but with opposi te orientations, no current will flow in the ci rcular wire. The t ensions can be observed only by attaching golden leaves at the ends of the wire's diamet er which is perpendicu lar to the di recti on of motion.

If, however, mov ing the circu lar wire, t he goiden leaves wi ll not indicate the ava i --labi l i ty of induced tens ion.

It i s intere~ting in paral l el to these experiments t o consider Nicol aev' s experi ­ment shown in fig. 17 of OP-2, p. 40 (see al sop. 26 there) . In DIVINE ELECTROMAGNE­TISM I called this experiment the sixth Ni col aev's experiment . Let me note that the explanation with divA gi ven in DP-2 was wrong, as divA generated by a closed circuit (t he circuit of the toroidal magnet) is null . The right explanati on with S = Smar is gi ven on p. 242 of DE.

In my exper iment in fi g. 2 of Ref. 1, t he effect of the cha nge of the length of the cathode space is propor tional t o dl/dt, wh i l ~~hange of th~ l ength of the dark cat hode space i n the sixt h Ni cola ev ' s experiment is proporti onal to I. Thi s substan­tial difference is d.ue t o the fact that in my experiment I observed the action of the rest-transformer electric intensity

E = - aA;cat, rest- t r (F)

wh i le Nicolaev has obse rved in his experiment the action of the Marinov sca lar-magne­tic electric int ensi ty

Esc-mar = (v/ c)Sma r · (G)

I havr. already cal cul ated Smar generated by a very long cylindrical solenoid and found that it is null (see DP-13, p. 38). I sti ll have not calcul ated Srnar generated by a circular or rectangular cross-secti on toroid, as the calcul ation is very diffi­cult. Let me note that to the best of my knowl edge there is neither exact calculat ion of Blor generated by such toroi ds. There is only exact calculation of Blor generated by a circular wi re which l eads to el l ipt ical integral s (seep. 54 in DE) .

An experiment simi lar to t he si xth Ni col aev's experiment was carried out by Solunin and Kos t i n (A .~l. CoJTYIU1li H A.B. KoC'mu , 06 ::l(jljleKTe BeKTOPHOro no-reu!Jiola,a ,!l;!>l 'I'OPOH,!l,a.'lb ­

noro COJJelioJma. non. BI1HJ1'IM, per. 1\" 7!100-84, t hus the year of the publication is 1984) . An electronic beam tube w~encircled by a toroidal coil (fig. B) . The electrons were accelerated by an el ect ric tension of 400 V. To the vertical plates of the tube some el ectric tens ion ~tas applied to obtain a basic d1splacement of the beam on the screen of some 5 - 20 mm . The current i n the sol enoid wa s cha n~ed in the range f rom 0 to 5 A.

The observations are pr esented in Fig. C. On the absci ssa there i s the current JA i n t he toroidal coil in one (positi ve) or another (negative ) direct ion. On the ordi nate

there is the ratio of the vertical · displacement of the beam on the screen, a, to the

- 43 - •

3 1 2

, '

Fig. B. The experiment of Solunin and Kosti n.

>as ic di splacemen t. when the current in t'he toroidal solenoid is zero (on the negr.·

ci ve y-axis one has to put the scores 0.9, 0.8, 0.7). This graph corresponds to tne ;ase whe n t he positive coil's current generate s a positive Ma rinov scala r magnetic

in t en s i t y Smar which desaccelerates t he neg~ tive electrons in the beam and this leads to a. greater vertical displacement of the spot on t he sc reen, as the veloc i ~y

)f the electrons i n the beam decreases. There must be nf6 ~ 0 for JA ~ -~.

Nicol aev and Sol uni n and Kostin thi nk that t he effect i n t hei r experimer.ts 1 ~ ~a~

to t he action of the magnet ic potential A and t hat t he effect s observed are of the

kind of "Ahar onov- Bohm effect s" . ,__ s a matt er of f act the effect i n the i r experiments

is due t o the action of the Mari nov scalar magnetic intensity Smar· Let mr;, shovr ~~.) s.

·4 -3

aJA 1.3+-----~

1.2 1.1..,

1 2 3 4

f ig. C. The effect obs erved by Solunin and Kost in.

s

- 44 -

One can easily calculate the force ~lith which a circular (i.e., not elliptical) • toroid with a rect<~.ngul<tr cross-section or a .circular cross - section acts on a current

element along · its axis ~lithout the necessity to calculate this. force for 1~hole space.

As the force acting on such a current element is of the kind f : I(dr/c)S, th1s calcu­

lation leads, as a matter of fact, to calculation ·of Smar along the axis of the toroid.

a) Smar ALONG THE AXIS OF A TOROID WITH RECTANGULAR CROSS-SECTION.

let us consider first the fourth Nicolaev's experiment (see fig. 14 on p. 39 of DP-2 which I redraw again in fig. D) where there are t\'fO rectangular current 111ires

and a current wire along their "a·xis". I shall do the calculations proceeding from

Marinov's formula (see formula (7) on p. 19 of DP-11) 1~hich I shall write here in its

reduced form

df~ = {(r.dr ')dr + (r .dr )dr ' - 2(dr.dr ')r}/Zr3. (H)

One sees immediately that the wires NK and LM, respectively, N'k' and l'M' , which

are parallel to the wire AB, act on its current elements with forces perpendicular to the latter and with opposite signs. Thus the action of the horizontal wires

of the rectangles on the current elements of the wire AB is null.

The net force with which the wir$KL and K'L ' act on an arbitrary element dr of - - . the wire AB which is at a distance l from they-axis will

zontal and vertical sizes of the rectangles by M and L,

by 2d, and the angle bet'lteen dr' and r by lj!',

y

L 1'

dr' lj!' I

r

K

~,.4 A d ; dr d 1

K'

M

be, if denoting the hori­

the distance between them

M

lj!' dr'

r

N B

I X

N'

L

I' L 0 M'

Fig. D. Two rectangular ~tires acting on a current element along their "axis".

- 45 -• llo. 21

LJ _. __ cos.;,' dr' x , .. / dY' c -

o (d+y)2 + (M/2 +1)2

A ~

X X -

(d2 + (M/2 +1)2 }1/2 (I)

where the last resul t is written for L suffic iently large.

If we shall take into account also the action of the wires r~ll and M' N' , we s hall

have, at the accepted approximati on,

'For 1 = 0, we shall have Smar = 0 and Smar wi l l reach its positive maximum at = M/2 and its negative maximum at 1 = - M/2. if d << M.

(J)

If there is a toroid with N rectangular turns, the obt ai ned results are to be JP.U1-

t ipl ied by N/2.

b) Smar ALONG THE AXIS OF A TOROID ~liTH CIRCULAR CROSS-SECTION.

·Here again we consider first two circular wires along whose "axis" ;~

there- a t;!.lrrent • t ·flowing in the positive direction of the x-axis . In the upper circle the ~ur~·P.nt l'

is flowing in the negative direction and in the lower circle t he curr~r.t l' ;~ ~·;.0wiP.:':

in the positive direction (fig. E). Fonnula (H) gives for the force with which an arbitrary current e1 !!!rent or' ~,; t~

1:1pper circl e acts on an arbitrary element dr of the horizontal w~re at a distar·<~e ·.

from they-ax i s which is to be taken posi t i ve if dr is at r ight from. the y -~ ;.-~s <;.'tiC

negat ive if dr is at l eft . If i nt roducing t he pola r angle e of th€ ~urrer.-:: ~1 <:m~~.~

dr' and t he angle ~h which the horizo.ntal component of dr ' make5 with t he, vect~r ·di ;;-.

tance r, we shall have from equation (H)

r2.d~pper/drdr' = cos (~+¢h) x + ( -cos~h) { -cos~~ + si n~y ) -

2( - cosq,)(cos;Vh(-x) + sin-:i;h(-y)} : - sin4>sinlj.hx -

Analogically we obtain for the force with which a symmetric current e1emen~

the lower circular wire acts on dT

· 2r2df~ower/drdr' = - sin<j>simjlhx + {s i"*cosi/Jh + 2cos¢sin!!Jh)y,

sa .that proceeding from the sum of {K) and (L) , v1e s hall have for the ~larir.ov

magnetic intensity generated by both symmetri c current e lements

dS~ar = (df:pper + df~owe~/dr = - s injo s 1n~'hdr' ; r2

•

p .. ·, •· I

dr- ' cl'

To make more simple the calculation of Smar generated by the cu r rents I ' in ·o<> tt:

ci r cular wi res v;hose radii are R, let us assume that t he distance 2d between the c: i:'-.::­l es is zero. rn such a case the distance between dr ' and dr will be

~ = (R - Rcos~}2 + {1 + Rsin~) 2 . {N}

I'

I '

- 46 -

y

d

14---------to'"{ d 1

• R

] X

Fig. E. Two circular wires acting on a curnmt element along their "axis". Taking

dr ' = Rd¢>, sinojlh = (R - Rcos~)/r,

and putting (N) and (0) i nto (M), we obtain

s• = !}1Tsin4>(cos<!l - 1Jd4l mar R o {( l-coscp)2 + (a+sinq,)2}3/ 2

(0)

(P)

where th~ notation a = l /R was introduced. Th is integral can be t aken by t he general substitution t = tan{~/2) but the calculation seems to be cumbersome and I have not carried it out. We can only easily check that we shall have Smar = 0 for a= o.

Smar wil l obtain it s maximal val ues for 1 =! R, i .e., for a;± 1, at left nega­tive and at r ight pos i tive (ar exact cal culpt ion i s di fficult) .

If there is~ toroid with N circular turns, the obtained results are to be multi ­plied by N/2.

. 47 -Vq.uUche PhyL!i.ll 6 ( Z 1 )

( 1991}

A HISTORY Of' THE THE:OR I ES OF A ETHER AND ELECTRIC ITY

Si~ Edmund Whittaker

Excerpt of Volume l, Chapter I ll

(Fi rst publ i shed 1910, revised ~dition 1951 )

Human ini ti es Press, New Yor~. 1973

. . ... ....

Lightning thus came to be credited with the power of magnetis­ing steel ; and it was doubtless this which led Franklin' in 1751 to attempt to magnetise a sewing-needle by means of the discharge of Leyden jars. The attempt was inde~d ~uccessful ; but, as Van Marum afterwards showed, it was doubtful whether the magnetism was due directly to the current.

Mou experiments followed.1 In 1805 Jean-Nicolas-Pierre Hachette ( 1769-1834) and Charles-Bernard Desormes ( 1777-1862) a.ttemptoed to determine whether an insulated voltaic pile, freely suspended, is oriented by terrestrial magneti"sm ; but without pontive result. In 1807 Hans Christian Oersted (1777-1851), Professor of Natural Philosophy in Copenhagen, ;announ-ced his intention of examining the action of electricity on the magnetic needle ; but it wa.s not for some years that his hopes were reali~cd.

If one of his pupils is to be believed, • he was 'a. man ()f genius, but a very unhappy experimenter ; he could not manipulate instrr.1· ments. He must always have an assistant, or one of his auditors who had ea.sy hands, to arrange the eJ{periment.'

During a course of lectures wh.ich he delivered in the winter of 181~20 on 'Electricity, Galvanism and Magnetism: the id~a occurred to him that the changes observed "'ith the cornp.ass needle during a thunderstorm might give the clue to the effect of which he was in search ; and this led him to think that the experiment should be tried with the galvanic circuit closed instead of open, :L"lrl

to inquire whether any effect is produced on a magnetic needie when an electric current is passed through a neighbouring wire. At first he placed the wire at right angles to the needle, but obsaved no result. After the end of a lecture in which this negative exper;.. ment had been shown, the idea occurred to h im to place the v.>ire parallel to the needle ; on trying it, a p ronounced deflection was

1 Phil. Tram. lOCXix ( 1735}, p. 74 ~ Lelt~r vi (To m Franklin to Col1iMon c In 1774 the Electoral A c,aoemy of :Bavar ia proposed the ques tion, • Is there a real

and physical analogy betw~en electric and nlagnetic forces ) • a' the subject of a pd2e. • cf. a letter from Hanstc~n inserted in Bence Jones.'' Lift of Faradqy, ii, p. 395

81

- 48 -

observed, and the relation between magnetifu: and t.'tJr t:>~ ec.tri~ current was discovered. Mter confirmatorv exoerimems \\.'ith more

• • powerful apparatus~ the public announcement was made in July 182Q.l

Oersted did not determine the quantitative laws of the action., but contented himself with a statement <tf the qualitative effect and some remarks on its cause, which recall the magnetic speculations of Descartes ; indeed, Oersted's conceptions may be regarded as linking those of the Cartesian school to those which were introduced subsequently by Faraday. 'To the effect which takes place in the conductor and in the surrounding space,' he wrote, ' we shall give the name of the ctmjlict of t(t#riciry.' ' The electric conflict acts only on the magnetic particles of matter. All non-magneti.c bodies appear penetrable by the electric conflict, while magnetic bodies, or rather their magnetic particles, resist the passage of this conflict. Hence they can be moved by the impetus of the contending powers.

'It is sufficiently evident from the preceding facts that the electric conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space.

4 From the preceding facts we may likewise collect, that this conflict performs circles; for without this condition, it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it toward the east~ and when placed above it toward the west; for it is the nature of a circle that the motions in oppmite parts should have an opposite direction.'

Oersted's discovery was described at the meeting of the French Academy on 11 September 1820 by an academician (Arago} who had just returned from abroad. Several investigators in France repeated and extended his experiments; and the first precise analysis of the effect was published by two ofthese,Jean-Baptiste Biot (l i74-1862) and Felix Savart (1791-1841), who, at a meeting of the Academy of Sciences on 30 October 1820 announced 1 that the action experienced by a pole of austral or boreal magnetism, when placed at any distance from a straight wire carrying a voltaic current, may be thus expre3scd : 'Draw from the pole a perpa1dicular to the wire ; the force on the pole is at right angles to this line and to the wire, and its intensity is proportional to the reciprocal of the distance.' This result was soon further analysed, the attractive force being divided into constituents, each of which was supposed to b~

1 &ptrimn!ttt cir(a 4fectum ctmfli&tt.~s clcdm in c:tam~ magn8ticam (Copenhagen. 1820) ; German 'Irani. in SchweiggeJ·'• ]OIInll!.l fii,. Clrm!u rmd Physik, JCtix (1820), p. 275 : Engl~h tralll.. in Tho011on'3 .A.7WIIJ of PhilM~y, xvi (1820), p . 273

• Armalt.s dt Clzimit, lCV ( 1820), p. 222 ; ]~nttr11:J Ji Phyt. xci ( 1820) 1 p. 151

8:z

- 49 ~ • No . 21

due to some particular element of the current ; in its new form the law may be stated thus ~ the magnetic force due to 12n llemenJ ds of a circuit) in which a current i is jfowingJ at a point whose ve&tor distance ftom d.s iJ r, ir (in mitable units)

• .!.. [ds. r } l ,. l ids • or cur-. ,

It was now recognised that a magnetic field may be produced as readily by an electric current as by a magnet ; and, as Arago ·soon showed, a this, like any other magnetic field, is capable of inducing ma.gnetisation in iron. The question naturally suggested itself as to whether the similarity of properties between currents and magnets extended still further7 e.g. whether conductors carrying currents. would, like magnets, ~perience ponderomotive forces when placed in a. magnetic field; and whether such conductors would consequently like magnets, exert ponder-omotive forces on each other.

The first step towards answering these inquiries was taken by Oersted' himself. 'As,' he said, ' a body cannot put another in motion without being moved in iu tum, when it possesses th~ req-uisite mobility, it is easy to foresee that the galvanic arc must be moved by the magnet ' ; and this he verified experimentally .15

The next step came from Andre-Marie Ampere (1775-1S36L who at the meeting of the Academy on 18 September, exactly a week after the news of Oersted•s first discovery had arrived, showed that two parallel wires carrying currents attract each other if the eurrentl

are in the same direction, and repel each other if the currents are in opposite directions. During the next three years Ampere continued to prosecute the researches thus inaugurated, and in 1825 published his collected results in one of the most celebrated memoin • in the history of natural philosophy_

Ampere introduces his work by proclaiming himself a follower

1 U a and 11 denote twfl vecton, the vector whose oomponcnb are <c:A - c.J;, a.JJs - aJJ1, o~; - ¥~> is called the ~~«lDr prodJict of a and Jlo, and is denoted by{~. bj. Ib direction ~ at right anglo ~ thor.c of a aod Jlo, r.nd iu ~gnitude is represented tJ,. twice the aru ot lhe trians-le formed by them.

I (( a dmoto any vectOr, the Vector Whose components a!'e

tlar aa~ . d .._, by l ·-· - - zs eno..:u cur a. ax ~ '" ~rt11.2its dl Chimil, zv ( 1820), p. 93

Oat &, Ba:l! aa. a; - az· az- ZJ%'

• Schwc:igger's ]o1t11UJl for CMm. u. Pliys. xx:ix. (I 820), p . 364; Thomson's A11nals ~ P4iJ<Jf~p/ty1 X'l' i (1820) , p, 375

I Davy round in !821 (Phil. TrtliiS. cxi (1821], p. 425) that the electric QfC u deflected bya~n:~p~t.

• Mlm. rJ. l'Ac&f. vi {1825). p. 175 (11:1:) 7

- 50 -

• of that school which explained all physical pnenomena in ic:rmo. o~ equal and oppositely directed forces between pairs of particles ; and he:. renounces the attempt to seek more speculative, though pofis}hly more fundamental, explanations in terms of the motions of ultimate fluids and aethers. Nevertheless, he indicates two conceptionr. of thi~ latter character, on which such explanations might be founded.

In the first :a he suggests that the ponderomotive forces between circuits carrying electric currents may be due to ' the reaction of the elastic fluid which extends throughout all space, whose vibrations produce the phenomena of light:; and which i3 ' put in motion by electric currents.' This fluid ot aether can, he says, 'be no other than that which results from the combination of the two electricities.'

In the second conception, • Ampere suggests that the interspaces between the metallic molecules of a wire which carries a current may be occupied by a fiuid composed of the two electricities, not in the proportions which form the neutral fluid, but with an excess of that one of them which is opposite to the electricity peculiar to the molecules of the metal,. and which consequently masks this latter electricity. In this inter-molecular fluid the opposite electricities. .are continually being dissociated and recombined ; a dissociation of the fluid within ont inter-molecular interval having taken place, the positive electricity thus produced unites with the negative electricity of the interval next to it in the direction of the current, while the negative electridty of the first interval unites with the positive electricity of the next interval in the other direction. Such inter­changes, accorciing to this hypoth~is, constitute the electric current.

Ampere's memoir is1 however, but little occupied with the more speculative side of the subject. His first aim was to investigate thoroughly by experiment the ponderomotive forces on electric currents.

c When,' he remarks, ' M. Oersted discovered the action which a current exercises on a magnet, one might certainly have suspected the existence of a mutUal action between two circuits carrying currents; but this was not a necessary consequence; for a bar of soft iron also acts on a magnetised needle7 although there is no mutual action between two bars of soft iron.'

Ampere, therefore, submitted the matter to the test of the laboratory, and discovered that circuits carrying electric currents exert ponderomotive forces on each other, and that ponderomotive forces are exerted on such currents by magnets. To the science

1 Rmuil tJ>&b-Uf'I1Miei'IJ 1/MtriNipuJmfqrm, p. 215 ; and the memoir jutt cited, pp. 285, 37Cl • Raw;( tl'obsm~~ ~lnH:lyt14111iques, pp. 297, 300, 371

84.

- 51 - • No. 21

which deals with the mutual action of currents he gave the name 1/ectrotf.yTUJml:cs 1 ; and he showed that the action obeys the following laws:

( 1) The effect of a current is reversed when the direction of the current is reversed.

(2) The effect of a current flowing in a circuit twisted into small sinuosities is the same as if the circuit were smoothed out.

(3} The force exerted by a closed circuit on an dement of another drcuit is at right angles to the latter.

(4} The force between two elements of circuits is unaffected when all linear dimensions are increased proportionately, the current-strengths remaining unaltered.

From these data, together with his assumption that the force between two elements of circuits acts along the Hne joining them, Ampere obtained an expression of this force : the deduction may be made in the following way :

Let cia, cis' be the elements, r the line joining them and i, i' the current strengths. From (2) we see that the effect ofds on ds' is the \lector sum of the effects of dx, dJ1 rk on ds', where these are the three components of ds i so the required force must be of the form ;

r x a scalar quantity which is linear and homogeneous in 8; and it must similarly be linear and homogeneous in cis' ; ao using (I), we see that the force must be of the form

F = ii'r {(ds. ds') rf, (r) + (cb. r) (ds'. r) tfo (r)},

where tfo and 1/J denote undetermined functions of r. From (4) it follows that when tis, ds', rare all multiplied by the

same number, F is unaffected : this shows that

~(r) = ~ and 1/J(r} = ~t

where A and B denote constants. Thus we have

F = ii'r{A(ds. ds') + B(ds. r) (ds'. r)} ,.. r' .

Now, by (3), the resolved part ofF along cls'' must vanish when integrated round the circuit s, i.e. it must be a complete differential when clr is taken to be equal to - ds. That is to say,

A(ds. ds') (r. ds') + B ds. r (ds'. r~' ~

a Loc. cit. p. zga 85

- 52 -

must be a complete differential ; or

- _A d(r , ds')a + B(ds • r) l r . ds'\1

2r ~ · \ ·

must be a complete differential ; and therefore

A B d 2? """" - ~(ds • r),

or 3A B - 2fl dr = ~ dr,

or B - - IIA - "'! •

Thus finally we have

F =Constant X ii'r{~(ds. ds') - ~(ds. r) (ds1 .r) }·

This is Ampere's fonnula : the multiplicative constant depends of course on the units chosen and may be taken to be - 1.

The weakness of Ampere~s work evidently lies in the assumption that the force is directed along the line joining the two elements ; for in the analogous case of the action between two magnetic molea cules~ we know that the force is rwt directed along the line j oining the molecules. It is therefore of interest to find the form ofF when this restriction is removed.

For this purpose we observe that we can add to the expression already found ibr F any term of the form

q,(r) . (ds • r) . ds',

where 4>(-r) denotes any arbitrary function of r ; for $ince

) dr (ds. r = - r. ds . di~

this term vanishes when integrated round the circuit s; and it contains ds and ds' linearly and homogeneously, as it should. We can also add any terms of the form

d(r . (ds' • r} . x(r)},

where x(r) denotes any arbitrary function of r, and d denotes differentiation along the arc s, keeping ds' fixed (so that dr = - ds) ; this differential may be written

- ds. (ds'. r). x(r) - rx(r) {ds'. ds) - ~'(r) r (ds. r) (ds'. r ) .

86

- 53 - No. 21

In order that the law of Action and Reaction may not be violated~ we must combine this with the former additional term so as to obtain &n. expression symmetrical in ds and ds' ; and hence we !ee finally tMJ, tb4 general valllt ofF is givm fry the equation

• -= - ii'r { ~(ds. ds') -~ (ds. r) (ds'. t)} + x(r) (ds'. r) ds + x(r) (ds. r) ds' + x(r) (d•. ds') r

+ ~'(r) (d•. r ) (ds', r) r.

'Ibe simplest form of this expression is obtained by taking .. ,

x(r) = ~ •

when we obtain .. ,

F = 7-{(ds. r) da' + (ds'. r)ds - (cis, d11')r),

The comparatively simple expression in brackets is the vect()r part of the quaternion product of the three vectors ds, r , ds'.1

From any of these values of F we can find the ponderomoth.~ force exerted by the whole circuit • on the element ds' ; it :isJ in fact, from the last expression,

ii']1 ~ ((da'. r ) ds - (da. ds') r}.

or ii'jll [ ds'.[ds~ rJ],

or i' [ds' • B],

:B = iJ?,. [ds. 1']. • where

Now this value of B is precisely the value found by Biot and Savart 1 fol' the magnetic intensity at ds' due to the .curre:st i ·~ the circuit s. Thus we see that the ponderomotive force on a currerr! element ds1 in a magnetic field B is i' [ ds '. B].

• The simpler fonn of I' given in the tat is, if" lhe tetm in ds' be omitted, the fmm • riven by Graumann, Ann. J. PJtys: lxiv {1845), po. 1. For further work on hi' mbjeo: ef. T.ait , l"Pw. R. S. Edin. viii (1873), p. Z20 ; Helmholtz, Bnl . ..Uad. Mt:!MlsfHr. (1873}, p. 9j ; ~ Kcrtcwcg, ]hmal for M(Jl}t. xc ( 188 J), p. 49. :Hdmholn llnUmes th ... t the \t.ter..~~u,-. between two current clements i5 dc:rh•l'.ble from :a potential, and this cntaib the: existence of a couple in add~tio!l. to a force along the line joining the elemenb. et: the di.!cuss.imt in chap. vii of the present wor)(.

·• See ante, p. Sa

- 54 -

• Ampere developed to a considerable extent the theory of the

equivalence of magnets with circuits carrying currents ; and showed that .an electric current is equivalent, in its magnetic effects~ to a distribution of magnetism on any surface terminated by the circuit, the axes of the magnetic molecules being everywhere normal to this surface : 1 such a magnetised surface is called a ~ shtJl. He preferred, however, to regard the current rather than the magnetic fluid as the fundamental entity, and considered magnetism to be really an electrical phenomenon ; each magnetic molecule owes its properties, according to this view~ to the presence within it of a small closed circuit in which an electric current is perpetua11y flowing.

The impression produced by Amperc•s memoir was great and lasting. Writing half a century afterwards, Maxwell speaks of it as ' one of the most brilliant achievements in science.~ 1 The whole,' he says, ' theory and experiment seems as if it had leaped,. full~ grown and :full-ann,M, from the brain of the '1 Newton of electricity." It is perfect in form and unassailable in accuracy ; and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of elcctro­dynamks.'

Heaviside, however, in 1888 expressed a different opinion 1 :

' It has been stated, on no less authority than that of the great Maxwell, that Ampere•9 law of force: between a pair of current elements is the cardinal fonnula of dectrodynamics, If so, should we not be always using it ? Do we ever use it ? Did Maxwell in his Treatise ? Surely there is some mistake. I do not in the least mean to rob Ampere of the credit of being the father of electro­dynamics ; I would only transfer the name of cardinal formula to another due to him, expressing the mechanical force on an dement of a conductor supporting current in any magnetic field- the vector product of current and induction. There is something real about it ; it is not like his force between a pair of unclosed elements ; it is fundamental; and, as everybody knows, it is in continual usc, either actually or virtually (through electromotive force), both by theorists and practician~!

•••••••

1 Loc. cit. p. 367 1 &zlri&WII (23 Dec. HJ88), p. 229 ; Heaviside's El«trical P11.pm, U. p. 500

88

- 55 - No. 21

ED!TOR'5 COMMENTS

[o the above excerpt from the classical Whittaker's book two important topics con-

ceming the force of interaction between two current elements are considere d:

,•J. A very e l egant and transparent deduction of Ampere' s formu l a is given.

2: A not elegant and not transparent deduction of Whi ttaker' s formula is given.

Long time ago {in 1990 when I published the historical Grassmann 's article with the demonst ration of Grassmann formula - see TWT-VIII, p. 40) I inte nded to publish

also the hi s t orica l Ampere's art i cle with the demonstra t ion of Ampere ' s formula. How­ever, f i rst , the original publ ication whi ch I f ound i n the Graz libr a r ies was of a

very poor typ ographi c quality and, second, t he demonstrat ion wa s ve ry bad and over ma­

ny pages. On the other hand, the deJDOn$trat i on of 1\mpere ' s form.~la whi ch Max~ll gi ves

in his "Treatise" is also very ba d and over many pages . I coul d not f ind anothe r de­

monstration in the literatun; although, according to Maxwell, Ampere's formula must

be the "cardinal formula in electromagnetism".

Whi ttaker , surprisingly, gives a very good and shor~ demonstr~tion .

. Here· I shall give some hints which may help the reader to foll ow more easily Whitta·

·~l''s demonstration:

: . .. :a) Whitta ker denotes the current element along the acting circuit whi ch "9enerates" :itle force F by ds and the current elerrent along the circuit on which the force is ex-, .. eH:ed, i.e., whi cn "receives" the force F by ds'. Consequently if we s hould integrate

·a·long the pass ive circuit, there is dr ~ ds', where dr i s the i ncr eas e of the radius vec­

tor r pointing from the active current element ds to the pa ssi ve current element ds'

(see thi s case under a } in the figure beneath} .

b) However if we should integrate along the active ci rcuit, it wi ll be dr = - ds

(see thi s case under b) in the f i gure beneath).

c) Let me not e that the notatb ns which I use 1n al l my writi ngs are connected to

Wnittaker's notat ions a s follows :

ds = dr', ds ' = dr, r ~ r , F ~ df .

One sees immediate l y that my notations are more convenient and mo~ economi c.

d) The first expressi on on Whitta~er ' s page 86 can be wri tten in t~e form

r+dr

ds I

d{( -A/2r3)(r.ds'} 2}+ d(A/2r3) (r. ds ' )2 + (B/r3)(dr . r }(r .ds ' )2

r r+ctr

a}

ds

b}

and since t his expression must

be a compl ete differential , we obtai n thus the second equation

on p. 86. From the seco nd equation or.

p. 86 we obt a in the third equa­

tion on p. 86 taking into ac­count tha t

- 56 -

dr = d(~) 1/Z. = 2r .dr : ~, _ ~:!. Z(r2)1}2 r ~

e) The constant which Whitt~~er i ntroduces .in. rn s f1ftll. equat10.r1 on p. 86 is ~~--

1\ar, as we ·can Sjlltstitute not the constant 8 b.~ -3A!2, as Whittaker. lias ~!OnE: in h1 > . . fourth equat iotl o.n p. 66, but A, by -28/3, ana so .w obtain Ampere' s fonnula in the

f orm

F = (!.)ii'rl~du;o)( ds' .r)- ~{ds.ds')l. · . 3 r- . · r·'

'he coefficient (l/3), or the coefficient (-l/2) \<hicn wlll be obtafned at loalittak.ar·~ .•.. . . ca1::ul~tion ~Whittaker hu forgotten the "2" 'In the der:-aninatpr !) is to be canceled.

if one· wishes to obtain a fonnula which will correspond to the observations.(a!> a matter ~ . . . . . .

of fllct: 'to the P.re-Marinov observations j . As far as I can remember, AlnP!!re has obtai-... .. . . ned his for111ula. with th.e c,~e.fftcient (1/2).

let us turn now our attention to Whfttaker' s fo n~~~.~la (as .call ed ~Y .• ), .'i.e . , to the

third formula on p. $7. I repeat that I strongly ~islike the .".deduct1on" loflich .Whitta­

ker gives proceeding from _~pere's .formula. Whlttaker' s fo~la 1s. to· be obtainee oro-. ceeding not f rom .Aa~Pere ' s fo1'111Ul a but from Grassma11n ' s formula (J write it here 1n - . Whittaker' 6 notations) •

simply by synnetr1z1ng it ~nd lnlki ng so that there will be F ., ~ F' . . .

Ai , IIIO!ilevel", J have siiJwn analys in!llllil"t experiments (see DIVIN.E EL£CTR(JIIAGN£TISM), . by symmetrizing Grassmann's fo~la one has to obt~in not Whittaker' s fo~Ta but Ma-

:. . - -ri nov 's fonnul a {I wri te it i n Wh1t'taker's. notations)

F • (ii'/2r3 ~{(ds . r)ds' + ~ ds' .r ) ds - 2( ds .ds' )r }.

1 have no doubt$ that this is the rtght formula 'i'n magnetism.

Mar1nov·•s· formula shows that th' thir<d 141tpere 1s l aw (s~ the top of p. sS) is wro!19,

since the force exerted by a ci·osed cir<:uit on an element of another circuit may be

not at ri!;ht angles to the litter {the S!BERIAH C!i.IU a.chirie demonstrates thts ). - ~rinov's fonaula shows also ·t~t tne '"fifthn k.pere 's ulajj", namely that iiihe force

between two elements of circui.h l'tt s ·along the 1 i ne joi'ning then", is wron9, as by the

help of magnetic. forces I brou!#a soli~ bo4Y in rotation · disposing . of intemal for­ces only (see the Retati ng Ampere Bridge with . .I nterrupte<l Current and the BUL-CUB Ma­ch1ne' w.tth Inte;l'\lpted Current. in my DIVINE ELECTROMAGNETISM). If the "fifth• Ampere's

"law", i.e . , Newton's t~i.rd law applied to the magnetic interactions, _shollld be vel id , . . such an effect (a violation of the angular 10m•ntum conservation law) 1s imP9SSible .

AUTIIlR 'S NOTE. I wrote t~is conwent before having establi shed exoerimentally that Marinov' s fol"lula 1s wrong.

DIE HIN-KRIEGER

• • • 'f .~

.',tf

Georges Bourbaki Ather-Verlag, D-80798 Munchen, Agnesstr. 16, Tel. +49-89-2711491

(Seiten 339,340)

- 58 •

Vor etwa 20 Jahren hatte der Autor diesea Buches ein pemH~ eig<manigcs Erlebnis,

welches irsendwic an clie paradigmatisicrtc Situation der moderncn PhYJik deakcn laJk;

Aua hcutc ni.cht mehr sanz rekoaatruierbaren GrUnden war c:r zu cioer ziemlich

llJU115sJic:ben Zeit • CS lliUB IDOI'8eDS secco 4 oder 5 Uhr friih geweseD Jein - UDlerWep.

Die Stn6c:n wuen leer, die Menachbeit aclaJic( IUld in weiter Ferne kUndip sich der nicbste Morgen an. Bei diescr Fahn durch aeine Hei~Qat~tadt MUnches~. war ihm bcrcits

einc ecwu unaewQmlidte Texaur des Sbdenbel• aufschllcn. I>a abc:r seine Gcdankm woandcn millen., ~ er ~ClaD u~ kcinc wai&crc .Bc&;htwlJ geschenJct. In der Nibc del StacltzenCI"UIU stc.IJtc ca .aic;b daun jodocb hcnu, daf, dcr Verunacber die#$ mc:dtwirdipa SU'dcobclap ci~ ricsiac Scba&triadc war. wclmc von elm Hirtea lllit fahnidcm und drci abpridttaca H~ von SUdaa bcr cotJua dcr lur clunob die Stada ,ICiridiaa -..de. Wcgcu dcr UngewOholidtk.eit dica Vorpnga

hiclt dcr Ea.iblcr an, 11111 sida Gin wenia unto' du Yolk wa blOkmdc:n ViabGiner zu miiChcla. Da du Obc:rqwaa1 eiact bratm Strak mil einer mc:hr all 1000 TieR

umfiUCIIdaa Schaftlordc &owi_ae Sdawiaigkc:itm bcrcjlct • jcda' GrubaJm und jedes

vorhandc:nc 8ba bilclcrl bckmndidl bcrciu cinm Gnmd zum Slcbmbleibm -. wurde &11 Mancbroulc cim Fu8aioacr-11Dd Flb:rrlduntec fiibrung aewibh. um IUf diae Weile

die zur l fiibrc:lldc Z · - ~ m piuietea. Die

Hundc tatm ibrc Albeit UDd dcr'-pnm Vorplt,~ verlief olme weilere ZwilcMDfille, bU aida gmz ao.vauwtct 11.cru•atellte. daB du aardleitiae Ende der l.JDJerfiibnmg durdl

eiucn Brederzaun dJge~~~Qil war. was du:rc:h deG dtmaligea Bail der S-Balm bediDst war. Dieaer Breaen11m kaldete uliirtidlllmlpt dt.D Vonuncb det SdWherde WHI

d•mit sa8 ctieselbe fell Uata' ZurUcldassuq teiae& Flhrrades klelltate dar die Hmie tiihrende Hirte flacbead -aaeb oblm. um mit teinea beideo andcaca Kollepn ibc-z du weitcr'e Vorpbe:n zu ben.tea. Die Hittcnlumde wurdcn clanuftain Uutnaiert, dal sic vom

vorderea. Ellde he:t die Sdaafshc:rdc dun:h Iaiita Belleo zuriicktrcibco soltiCil. T~

intensiver- VenMCbc in die..- · Richtnaa kOMten joclo<:h die Sc:hafe nicht zur UtQkcbr

bewtQt werden, siod doc:h die8C venbmrnten Diester dcnrt ~ daB aic

gewiascn Lcittiereo folaca. Diae Lcitticrc waRD abcr vomc ia del' vcnpc:ntc:D

Untcrfiihnaag cinpkci&t und konntc:a weder voc noch zuriidt. DieM:r ~laOte

die wciter bintcn Slebcaden Schafc, om nldl mchr nach vomc zu ~en. wolltc man

doch aus di~ blten und zv-gigen TUDDOl oh:nc OruhaJme mOglichsl ruda wieder

her•us. lm AndlluB an cine Kunfercnz d.cr Hirtcn obcn auf der SttUSe wurdc nunmehr vmaacht, die Hcrdc von hintm her zur Umkc.br zu bcwegcn, i.ndcm. man einzelne

Schafc an ibrcn Scbwinzcn aus dcm fulk von Ticren berauszog. um lie dann mit

- 59 - No . 21

FWJtritten in die entgegengeretzte Richtung zu jagen. Dies niitzte jedocb herzlich

wenig. denn die derart tnktiertc:n Schafe kehrteft achleunigst wiecler wn, woJlten sic

doc:h von ihlen Angenouen nidlt gc:trennt wc:rden· Auf diese WeiK war cler Sidle al10 lridtt beizukommen. Unter Zuriic:kiUIWlg ibrer Fat.nider kleuertea die drei Hirtm .chliellic:h emeut entlang des Bauzaunes nJcll unteu. um ctic vome fCilgckaltc:n

Leitliere hochmheben und tiber die Rieken dclr cog ancinaudcr ~t ldd1coden

Schafe !:llriiek zum offenen Eingang dtr Unurfiihrung zu j~gCD. Ea•aunlicber•'Cliae

funkUoniertc die~C Methode cinwandfrei, cirete aida doch dicsc:r Wollfetllridl YOD

Sdvtfcn vOiziialidl ala Thurqldptid, IRlf welchcm die Lcitticn dahin•ilmaa komllea.,

of!!M lic:ll dahci ihre dWmen Beincbal Zli bc.-bm. Die vcrWalaido Henle LDCIIk:te m dar Folge recbl bald, daB die ricbtmpweill&'lldeo Gerilche plOamda ~ ww•dln bmen, so dd eine ric:htunpmUigc Umori.,..cicruag crfolgto. Die Oberquenwa dc:r ZwcibriickeDabde fad etwaa tpit« bci voD$1 Taplticht s&aa: Die Hwclc belllea, die Hi.-n ldiOban ibrc Fabrridec unci die iiiOijCilMfficbtz TrtMinlut pben lidl ei11e kleiDe vc:ncM.~~e.

Nit dicac:a innabalb einer Unterfiihnma W. =II • unaae Ho•• clcr Pltysi'k dell 20. Jahrtthundata cinigea &<Pin m baben: bJC'.two 'WOIDC &Bit • LcilftJIIIc:a wic Nobdprooiltripr - denen "''Il ,..,. .. foJaea! Die Mmcbrich"ma iat .,

I~DF ricbti& als gewisse Auldiillstunpn .Ua"PJD. Oefragt unci iD Fl¥ aclldl! weaden duf aicbt, dena wo kimc nn da IO"ti hiD! Uad &lla e1 sich etwa hcxa•lllcDeD _,Jhc, daJl YOI'Ile lceiD Durchkommeo ill, claim mol Ql!lll eben YOD lliJIICII • II l•ll• t iiO"'

'Cbickn, "MnUf lidi vc:oe .moe iJjGidwie do Wt~~ a6flben. wucle..

EDITOR'S COMM ENTS A.Uo l>p!tltc.h ZaJta.t.llLI.otM : How to transfer t he l eading ani ma l s of the he rd of ?~Y ·

sic ists from the bl i nd alley away? - The herd of sheep which my frienri, Georges Bo~r­

baki. met 20 years ago i n Muni ch counted 1000 h-eads, but the herd of ptysi cists 1s

much mor-e numerous and much more stubborn. And an~ther important det.;i?: t !;e l.c;:~;·; ;,~1 animals of the herd of physic ists resist de sperate ly t o any transfer. I t seems, ';ll'J~. that t hi s las t herd wi l l fo r a good many years huddl e into the blind alley , un~i 1 t~

leading animanls will die and begi n to s tink.

- 60 -Veu.U.ch e l'll!J6ik. 6(21 l

{1??7 }

ADDENDUM TO THE PAPER ' THE SEG~ER-MI\RlNOV TUR91NE"

Stefan p.far i nov

Inst itute for Fundarental Physics

Morellenfel dqasse 16 A-8010 Graz, Aus:ria

In th1s addendum ! ·take into accoU1t al so the p~r of weter squirti ng out from t he Segner-Marinov turbine, as its laborato ry velocity i£ different f rom zero and it can thus deliver s011e additional free powe"'.

In Ref. 1 I calculated only the tOTques (driving t orque. Mdr• braking to rque , M0,.,

and net-dri vi ng t orque, Mdr-~t) act i ng on t he Segner-Marinov turbine. The respective

JJO'fters (driving power, Pdr• braking power, Pbr• and net-dri·ting power , Pdr -net} can be

obta ined if we multi ply the to~ues by the a1g~lar vel oci t y n .

For the net- drivirg powP.r we shall have , taking into account equa tiu11 (6),

P ~ l'ld t " : poH{2n - 2) se~-ma"'. r-ne · (A}

Thi s wi ll be the free power which the Segn~ r-Har1nov turb i ne wi l l del i ver. But thi s

wi 11 be not the wh·Jl e free: power •~thi ch t he Segne~-Mari ncv turbi 1e produces, as lhe ve--1 oci ty of the squ i rting out water gi ven by forlliJ 1 a (3) is w' th !"E! soect to thf' tu rbine's

cylindrical surface and s ince the laboratory velocity of. the: la:ter i s QR, the squir­

tin~ out wate r wi l l have a laboratory velocity

vlab = v - M = (gH}l/2(2 - >"2). (B)

The power of th i s w!·;er can be used to rot ate another t urbi ne whose blades will

ser·v~ as eJ<te rr.al border of the cyl in:kical recepien: in fig. 3. This second turbine

wil l be set i n rotat ion opposite to t he ro lation of :he 5egner-l'lari nov turbi ne. Assu­

ming that the second one is a Pelton ~.urbine which transforms the whole power cf the

squirting out ~ter in to kinet ic energy reducing water 's laborator y velO'- i ty t c zero.

we shall have for the power delivered by the Pelton turbine

2 Ppelt = ( l / 2)\n•lab = \JQH(3 - 2/l) . {C)

Thus the whole free power which wi ll be pr,duced will be, from eQus. (A} and (C) .

(D)

where, I repeat, \J is the water mass squirti n~ out f rom t he Segner-Marinov :urbine in

a uni t of t ime when its friction (or load) torque is equal to Mdr-net.

Of the power Pnet 82'.; will b~ delivered t o t he Segne!"-Mar lnov t urbine and 171 to

the Pelton turhioe . The Segner-'tarinov sceptics blame me , I am not well enough acquain·

t ed wi th t he energy conservati o1 law. Equation (D) shows t hal I know what "ener~y c:>n­

servati on law" is.

REFERENCE: 1. S. Marinov , Deutsche Physik, 5 (20) . 17 (19G6).