Mdl f th Elctrn Ph.M. Kanarv * Th intrprtatin f sm f thrtical fundatins f physics will b changd. Planck s cnstant is knwn t b n f such fundatins, which srvs as a basis f quantum mchanics [1], [3], [6], [7], [8], [13]. Lt us cnsidr hw a rfinmnt f intrprtatin f th physical ssnc f this cnstant allws t mak a thrtical pntratin int th dpth f lctrmagntic structur f th lctrn and t cnnct this structur with th rsults f th xprimnt [9], [10]. Difficultis ncuntrd in xplaining th radiatin f th thrtical black bdy wr vrcm in Dcmbr 1900 whn Max Planck suppsd that nrgy, E, in EM frm is nt mittd cntinuusly, but discrt amunts Planck namd quanta; that is [4]: = hν, (1) Ep whr ν - frquncy f EM radiatin; h - a univrsal cnstant latr calld Planck s cnstant. As it is assumd, anthr frmula fr th dtrminatin f nrgy f a singl phtn has bn suggstd by Albrt Einstin. Ep Pag 184 APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 p = mc, () whr m - th mass f a phtn; C - th vlcity f a phtn. Th frquncy f a phtn s scillatins is ν, its vlcity C, and its wavlngth λ ar rlatd by: C = λν (3) Slving (1), () and (3) w find: Kg M h = mλν... S It is difficult t undrstand why Planck has ascribd physical sns f actin t his cnstant, h, which ds nt ncssarily crrspnd t its dimnsinality. If Planck had dtrmind his cnstant as a quantum f angular mmntum mdrn physics wuld hav bn quit diffrnt [11]. Actually Planck s cnstant has dimnsinality f angular mmntum, which has vctr prprtis. But as sm Physicists think, it ds nt man that Planck s cnstant is a vctr valu. W shall nt cntradict thir strtyp mntality, lt us us th suitabl pssibility f hypthtical apprach t this prblm and cnsidr its fruitfulnss. As it is clar, dimnsinality f Planck s cnstant is that f angular mmntum, hw can w crdinat this dimnsinality with th squar f th wavlngth, λ? Th mattr is that in th mathmatical xprssin f Planck s cnstant h = mλν mass m is multiplid by squar valu f wav lngth λ and by frquncy ν. But wav lngth charactrizs wav prcss, and dimnsinality f Planck s cnstant dmnstrats that an lctrmagntic frmatin, which is dscribd by it, rtats rlativ t th wn axis, and w ar facd with th task t crdinat th wav prcss with th rtatin n. Dtaild invstigatins carrid ut by us [4], [9], [10], [0], [] hav shwn that th phtn and th * Kuban Stat Agrarian Univrsity, Dpartmnt f Thrtical Mchanics; E-mail: <kanphil@mail.kuban.su> (4)
lctrn hav such lctrmagntic structurs during rtatin and mvmnt which radii r ar qual t lngths f thir wavs λ, i.. λ = r (5) Nw Planck s cnstant has th fllwing apparanc: h = mr ν. (6) It bcms clar that mr is mmnt f inrtia f th ring, and mr ν is angular mmntum f th rtating ring. It pints ut t th fact that th phtns and th lctrns hav a frm which is similar t th frm f th rtating ring. It is knwn that if angular mmnt is cnstant, th law f cnsrvatin f angular mmntum, n f th main laws f natur, is accmplishd. As Planck s cnstant is cnstant ( h = cnst ) and has dimnsinality f angular mmntum, it charactrizs th law f cnsrvatin f angular mmntum. Thus, th law f cnsrvatin f angular mmntum, n f th main laws f Natur, gvrns cnstancy f Planck s cnstant [10], [14]. It is knwn that th lctrn has its wn nrgy which is usually dtrmind accrding t th frmula E = mc. But th maning f such an assumptin is dciphrd nt always. And th maning is that if th whl nrgy f th lctrn is transfrmd int nrgy f th phtn, its nrgy bcms qual t E = mc. This fact has a strng xprimntal cnfirmatin. It is knwn th masss f lctrn and psitrn ar qual. Whn thy intract thy frm tw γ - phtns. That s why th nrgy bing qual t th nrgy f th phtn which has th crrspnding mass can b attributd t th lctrn. Elctrn rst mass m =9.1 10 31 kg is dtrmind with grat accuracy. Lt us call lctrn nrgy E bing qual t phtn nrgy a phtn nrgy f th lctrn. First f all, lt us invstigat th pssibilitis f th ring mdl f fr lctrn. It is knwn that th lctrn has kintic nrgy and ptntial nrgy which ar qual t ach thr. E = mc = mr = h, (7) whr: r - is th radii f th lctrn; -frquncy f lctrn; h = mr - is Planck s cnstant. Th calculatin accrding t this frmula givs th fllwing valu f phtn nrgy f th lctrn: 31 8 9.109 10 (.998 10 ) 5 E = mc = = 5.110 10 V 19 (8) 1.60 10 If fr lctrn rtats nly rlativly t its axis, angular frquncy f rtatin f ring mdl f fr lctrn dtrmind accrding t th frmula (7) is qual t and radius f th ring is qual t 5 19 E 5.111 10 1.60 10 34 h 6.66 10 5 19 31 0 9.109 10 (1.36 10 ) s 0 1 1.36 10, E 5.111 10 1.60 10 r m Vlcity f V pints f th rtating ring is qual t vlcity f light: 1.46 10 m. V r m s 0 1 8 = = 1.36 10.46 10 =.998 10 /. (11) (9) (10) APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 Pag 185
Lt us try t find such mathmatical mdls which dscrib bhaviur f th ring mdl f th lctrn, which cntain its charg, magntic mmnt M and lctrn lctrmagntic fild strngth B (magntic inductin f lctrn). If w assum that th lctrn charg is distributd unifrmly alng th lngth f its ring mdl, ach lmnt f th ring l will hav mass m and charg (Fig. 1). In this cas th rtating ring mdl f th lctrn will rsmbl ring currnt, and tw frcs which hav qual valus and ppsit dirctins: inrtial frc F i = mv / r and Lrntz frc F = B V (Fig. 1). Fig. 1. Diagram f ring mdl f th lctrn mv B V =. (1) r Lt us pay attntin t th fact that thr ar tw ntins fr th magntic fild charactristic which ar similar as far as physical sns is cncrnd: magntic fild inductin B and magntic fild strngth H which ar cnnctd by th dpndnc: whr µ 0 is magntic cnstant. B H = µ 0 Th analysis xprinc shws that it crats a crtain cnfusin during th frmatin f th idas cncrning magntic fild, that s why sm authrs rfus t us a clumsy trm magntic inductin and prsrv nly n, mr flicitus trm magntic fild strngth using symbl B fr it. Cl. E. Surtz, th authr f th bk Unusual physics f usual phnmna [1], actd in this way, and w fllw his xampl. Magntic fild will b charactrizd by vctr B, it will b calld magntic fild strngth masurd in SI systm in T (tsla). If w writ δ m fr mass dnsity f th ring and δ fr charg dnsity, w shall hav:, m = δ l = δ r ϕ, (13) m m As: = δ l = δ r ϕ. (14) δ m = m, π r (15) δ = π r (16) Pag 186 APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000
and V = C, th quatin (1) assums th frm: B mc dϕ = dϕ πr πr r r mc m r B = = = m, r r (18) whr r= C. Thus, w hav gt th mathmatical rlatin which includs: mass m f fr lctrn, its charg, magntic fild strngth B insid th lctrn ring which is gnratd by rtating ring charg, angular frquncy and radius r f th lctrn ring. Magntic mmnt f lctrn r, as it is calld, Bhr magntn is missing in this rlatin which mathmatical prsntatin is as fllws [19]: M h = = 4π m 4 9.74 10 J / T. Lt us pay attntin t th fact that in th abv-mntind rlatin h is vctr valu; it givs vctr prprtis t Bhr magntn M as wll. It fllws frm th frmula (19) that th dirctins f vctrs h and M cincid. Lt us cnvrt th rlatin (18) in th fllwing way: Th rsult frm it is as fllws: m 4π mh h E B = = = =. 4π h 4π M 4π M 4π B M = E. Nw frm th rlatins (0) w can dtrmin magntic fild strngth B insid th ring md f th lctrn, angular vlcity, rtatins f th ring and its radius r : 5 19 E.5111 10 1.60 10 B 4 4π M 43.14 9.74 10 8 7.017 10 T. Lt us pay attntin t rathr larg magntic fild strngth in th cntr f symmtry f th lctrn and lt us rmind that it diminishs alng th lctrn rtatin axis dirctly prprtinal t th cub f a distanc frm this cntr [1]. W find frm th rlatins (0): 4π M B 43.14 9.74 10 7.05 10 = == = h 6.66 10 (17) (19) (0) (1) 4 8 0 1 1.36 10 s. 34 () As priphral vlcity f th ring pints is qual t vlcity f light, w hav: 8 C.998 10 r 0 1.36 10 1.46 10 m. Th main paramtrs f th ring mdl f fr lctrn: ring radius r (10), (3) and angular frquncy f its rtatin (9), () dtrmind frm th diffrnt rlatins (8) and (1) hav turnd ut t b qual. A drawback f th ring mdl is in th fact that it ds nt pn a caus f psitrn birth, that s why th intuitin prmpts that th ring shuld hav sm intrnal structur. Our nxt task is t find ut this structur. APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 Pag 187 (3)
W d lik t draw th attntin f th radr t th fact that in all cass f ur lctrn bhaviur analysis Planck s cnstant in th intgr frm plays th rl f its spin. In mdrn physics it is accptd t think that th phtn spin is qual t h, and th lctrn spin is qual t 0.5h. But th lctrn spin valu (0.5h ) is usd nly fr th analysis f qualitativ charactristics f lctrn bhaviur. Valu h is usd fr quantitativ calculatins. In ur invstigatins th intgr f angular mmntum h is th spin f th phtn and th lctrn. It is usd fr quantitativ calculatins and qualitativ charactristics f bhaviur f bth phtn and lctrn [], [4], [9], [10], [13], [1]. Trus is th narst rlativ f th ring. Fr th bginning lt us assum that trus is hllw. Lt us writ ρ fr trus sctin circl radius (Fig. ). Th ara f its surfac is dtrmind accrding t th frmula: S = r = r (4) πρ π 4 π ρ. Fig.. Diagram f tridal mdl f th lctrn Lt us writ δ m fr surfac dnsity f lctrmagntic substanc f th lctrn. Thn δ m = m m S = 4π ρ (5). r Lt us dtrmin mmnt f inrtia f hllw trus. W shall hav th fllwing quatin frm Fig. : IZ = m r. (6) m = πρ l δ = πρ δ r ϕ. (7) 1 m m π mr Z = ϕ = π 0 I d m r. (8) As th lctrn dmnstrats th lctrical prprtis and th magntic ns at th sam tim and has angular mmntum, w hav vry rasn t supps that it has tw rtatins. Lt us call th usual rtatin rlativ t th axis f symmtry with angular frquncy kintic rtatin which frms its angular mmntum and kintic nrgy. And scndly, lt us call vrtical rtatin rlativ t th ring axis with angular frquncy (Fig. ) ptntial rtatin which frms its ptntial nrgy and ptntial prprtis. It is natural t assum that th sum f kintic nrgy E and ptntial nrgy E f fr lctrn is qual t its phtn nrgy E. Lt k us cnsidr th pssibility f ralizatin f ur suppsitins. Kintic nrgy f hllw trus rtatin is dtrmind accrding t th frmula (Fig. ): ρ Pag 188 APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000
E 1 1 1 EK = = IZ = m r = h. (9) Frquncy f kintic rtatin f trus is qual t 5 19 E 5.111 10 1.60 10 34 h 6.66 10 W shall dtrmin radius r f trus frm th frmula r = E m 0 1 1.36 10 s. 5 19 5.111 10 1.60 10 = = 31 0 9.109 10 (1.36 10 ) 1.46 10 m. As it is clar, r and (30), (31) cincid with th valus f r and in frmulas (9), (10), () and (3) in this cas as wll. It is intrsting t find ut if thr is an xprimntal cnfirmatin f valu r btaind by us. It turns ut that thr is such cnfirmatin. In 19 A. Cmptn, th Amrican physicist - xprimntr, fund that dissipatd X-rays had largr wav-lngth that incidntal ns. H calculatd th shift f wav λ accrding t th frmula [10], [18], [1]: Th xprimntal valu f magnitud λ turnd ut t b qual t (30) (31) λ = λ (1 cs β). (3) 1.4631058 10 m [17], [19]. Latr n a thrtical valu f this magnitud was btaind by mans f cmplx mathmatical cnvrsins basd 1 n th idas f rlativity λ = h/ m C =.4631060 10 m [18]. Whn w hav studid Cmptn ffct and hav carrid ut its thrtical analysis, w hav shwn that th frmula fr th calculatin f thrtical valu f Cmptn wav-lngth λ is btaind quit simpl if w attach sns f th lctrn radius t th lctrn wav-lngth and cnsidr th diagram f intractin f th ring mdl f lctrn with th ring mdl f rntgn phtn [1]. Th diagram f intractin f th ring mdl f rntgn phtn with th ring mdl f th atmic lctrn is shwn in Fig. 3. Th puls h / C 0 f th phtn falling n th lctrn and th puls ( h )/ C f th phtn rflctd frm th lctrn ar cnnctd by simpl dpndnc: h h = cs β. (33) C C Fig. 3. Diagram f intractin f th phtn with th lctrn in Cmptn ffct Aftr th intractin f th phtn with th lctrn its puls will b changd by th valu: h h h h = cs β (34) C C C C r = (1 cs β). (35) APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 Pag 189
As s r = C / λ è = C / λ, C C C = (1 cs β ) (36) λ λ λ λ λ = λ ( cs β). Th rlatin can b cnvrtd in th fllwing way: As m λ= h and λ = C, th quatin is as fllws: 1 (37) h λ λ = λ = (1 cs β) = λ(1 cs β). (38) mc This is Cmptn frmula f th calculatin f th chang f wav-lngth λ f rflctd rntgn phtn. Valu λ bing a cnstant is calld Cmptn wav-lngth. In th frmula (38) it is a cfficint dtrmind xprimntally and having th valu [17]: 1 λ (xp r) =.4630158 10 m, (39) which cincids cmpltly with th valu f radius r f th lctrn which has bn calculatd by us thrtically accrding t th frmula (10), (3) and (31): r thr 1 ( ).4630157 10 m. = (40) It shuld b ntd that w hav btaind th frmula (38) withut any rlativity ida using nly th classical ntins cncrning th intractin f th ring mdls f th phtn and th lctrn. As th analysis f th rsults f xprimntal spctrscpy has shwn that lctrn wav-lngth is qual t radius f its ring mdl and as th rsults f varius mthds f th calculatin f radius f lctrn cincid cmpltly with Cmptn xprimntal rsult, th tridal mdl f th lctrn is nw th fact that is nugh fr th rslut advancmnt in ur sarch. It is dsirabl t knw th valu f radius ρ f trus crss sctin circumfrnc. Lt us try t find this valu frm th analysis f ptntial rtatin f lctrn with frquncy ρ (Fig. ). W shuld pay attntin t th fact that th puls f bth th phtn and th lctrn is dtrmind accrding t n and th sam rlatin: h h P =. λ = r (41) It mans that bth th phtn and th lctrn display thir puls in th intrval f n wav-lngth. This fact has bn rflctd in th mdls f th phtn as an quality btwn wav-lngth λ f th phtn and its radius r. As th phtn is absrbd and radiatd by th lctrn, th lctrn shuld hav th sam cnnctin btwn th wav-lngth and radius. Bsids, th mdls f th phtn has six lctrmagntic filds; th sam quantity shuld b in th mdl f th lctrn whn it radiats r absrbs th phtn [], [4], [13]. Th dscribd cnditins prv t b fulfilld if n assums that angular frquncy f kintic rtatin is n-sixth f angular frquncy f ptntial rtatin f fr lctrn, i..: ρ ρ = 6. (4) Pag 190 APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000
If w assum that vlcity f th pints f th axis ring f trus in kintic rtatin is qual t vlcity f th pints f th surfac f trus in ptntial rtatin, w shall hav: C = r = ρ = C. (43) Frm ths rlatins w shall find ut: ρ 0 0 1 ρ = 61.36 10 = 7.414 10 s (44) and ρ 8 C.998 10 0 7.416 10 ρ 13 4.043 10. m (45) If w substitut th data bing btaind int th frmula (9), w shall find ut th valu f ptntial nrgy E f th lctrn 31 13 0 1 E = m ρ 9.091 10 (4.043 10 ) (7.416 10 ) 5 ρ = =.555 10 V. 19 1.60 10 If w dubl this rsult, w shall btain cmplt phtn nrgy f fr lctrn (8). Cmplt cincidnc f phtn nrgy f th lctrn btaind in diffrnt ways givs us th rasn t supps that th lctrn is a clsd ring vrtx which frms a tridal structur which rtats rlativly its axis f symmtry gnrating ptntial and kintic nrgy. It rsults frm sixfld diffrnc btwn angular vlcitis ρ that radius r is gratr by sixfld than radius and (46) ρ. W pstulat this fact suppsing that, as w hav shwn, th mst cnmical mdl f th phtn mvmnt is pssibl nly at six lctrmagntic filds [], [4], [9], [13]. This principl is ralizd whn th vrtx mvs in a clsd hlix f th trus. It rsults frm th diffrnc f radii and angular vlcity that th vrtx which mvs alng th surfac f trus maks six rtatins rlativ t th ring axis in a hlix during n rtatin f trus rlativly its axis f rtatin. A lad f a hlix is qual t radius r f th axis ring and wav-lngth λ f th lctrn (Fig. 4) [], [4], [9], [10], [0], []. Fig. 4. Elctrn mdl diagram Bsids rtary mtin, in this cas th lctrn has ptntial (vrtical) rtatin. W hav ntd that a sharp chang f th rlatins btwn kintic and ptntial rtatins f th lctrn lads ithr t absrptin r radiatin f th phtn dpnding n th dirctin f th chang f this rlatin. If this chang slws dwn kintic rtatin, th phtn radiatin prcss taks plac; if this chang acclrats it, th absrptin prcss taks plac. Whn w hav substantiatd th mdl f th lctrn, w hav usd th xisting Culmb s law and Nwtn s law, spctrum frmatin law frmulatd by us, Lrntz lctrmagntic frc and th fllwing APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 Pag 191
cnstants: vlcity f light C, Planck s cnstant h, lctrn rst mass m, its charg, lctrn rst nrgy, Bhr magntn M, lctrical cnstant ε, Cmptn wav-lngth f th lctrn which shuld b calld Cmptn radius f th lctrn. Thus, th lctrn has th frm f th rtating hllw trus (Fig. 5). Its structur prvs t b stabl du t availability f tw rtatins. Th first rtatin taks plac abut an axis which gs thrugh th gmtrical cntr f trus prpndicular t th plan f rtatin. Th scnd rtatin is a vrtical abut th ring axis which gs thrugh th trus crss sctin circumfrnc cntr. Only a part f magntic lins f frc and th lins which charactriz lctric fild f th lctrn is shwn in Fig. 5. If th whl st f ths lins is shwn, th mdl f th lctrn will assum th frm which rsmbls f th frm f an appl. As th lins f frc f th lctric fild ar prpndicular t th lins f frc f th magntic fild, th lctric fild in this mdl will bcm almst sphrical, and th frm f th magntic fild will rsmbl th magntic fild f a bar magnt. Svral mthds f trus radius calculatin which includ its varius nrgy and lctrmagntic prprtis giv th sam rsult which cmpltly cincids with th xprimntal valu f Cmptn wav-lngth f 1 th lctrn, i.. λ = r =.4630157 10 m [17], [19]. Fig. 5. Diagram f lctrmagntic mdl f th lctrn (nly a part f lctric and magntic lins f frc is givn in th figur) Cnclusin Max Planck livd in th tim whn many physics dnid th pssibility f th implmntatin f th classical laws fr its furthr dvlpmnt. Th ppl wh trid t d it wr calld mchanists. Prbably, h fard ths accusatins and usd an uncrtain ntin quantum f th last activity r quanta, r actin fr th dtrminatin f his cnstant. W rturn a tru physical sns t his cnstant. Th Natur has put th law f cnsrvatin f angular mmntum int it. Th rcgnitin f this fact pns wid prspcts fr physics and chmistry f th 1st cntury. Th way fr th xpsur f th lctrmagntic structurs f th lmntary particls, atms, ins and mlculs is pnd. Th bginning fr this way has alrady bn markd [], [4], [9]. [10], [13]. Rfrncs [1] Hward C. Haydn, Cynhia K. Whitny, Ph.D., Schafr W.J. If Sagnac and Michlsn-Gal. Why nt Michlsn-Mrly? Galilan Elctrdynamics. Vl. 1. N. 6, pp. 71-75 (Nv./Dc. 1990) [] Ph.M. Kanarv. Nw Analysis f Fundamntal Prblms f Quantum Mchanics. Krasndar. 1990. 173 p. [3] Ph. M. Kanarv. Th Rl f Spac and Tim in Scintific Prcptin f th Wrld. Galilan Elctrdynamics. Vl. 3, N. 6, pp. 106-109 (Nv./Dc., 199) Pag 19 APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000
[4] Ph.M. Kanarv. On th Way t th Physics f th 1 st Cntury. Krasndar. 1995. 69 pags (In English). [5] Richard H. Wachsman. Th Quirks and Quarks f Physics and Physicists. Infinit Enrgy. Vlum 4, Issu. Pags -5, 6. [6] Spanil G. And Suttn J.F. Classical Elctrn Mass and Filds. Physics Essays. Vl. 5, N. 1, pp. 60-61, 199. [7] David L. Brgman, Ph. D. and J. Paul Wsly, Ph.D. Spinning Chargd Ring Mdl f Elctrn Yilding Anmalus Magntic Mmnt. Galilan Elctrdynamics. Vl. 1, N. 5, pp. 63067. (Spt./Oct., 1990) [8] G.K. Grbnshchikv. Hlicity and Spin f th Elctrn. Hydrgn Atm Mdl. Enrgatmisdat. St.-Ptrsburg. 1994. 60 pags. [9] Ph.M. Kanarv. Crisis f Thrtical Physics. Th third ditin. Krasndar, 1998. 00 pags. [10] Ph.M. Kanarv. Watr as a Nw Enrgy Surc. Krasndar. Th scnd ditin, 146 pags (In English). [11] Danil H. Dutsch, Ph.D. Rintrprting Plank s Cnstant. Galilan Elctrdynamics. Vl. 1, N. 6, pp. 76-79 (Nv/Dc., 1990). [1] Cl. E. Surts. Unusual Physics f Usual Phnmna. Vlum. M.: Nauka, 1987. [13] Ph.M. Kanarv. Analysis f Fundamntal Prblms f Mdrn Physics. Krasndar. 1993. 55 pags. [14] D.A. Bzglasny. Law f Cnsrvatin f Angular Mmntum during Frmatin f th Slar Systm. Prcdings f th intrnatinal cnfrnc Prblm f spac, tim, gravitatin. St.-Ptrsburg. Publishing hus Plytchnic, 1997, pags 118-1. [15] Ph.M. Kanarv. Law f Frmatin f th Spctra f th Atms and Ins. Prcdings f th intrnatinal cnfrnc Prblms f spac, tim, gravitatin. St.-Ptrsburg. Publishing hus Plytchnic, 1997, pp. 30-37. [16] Ph. M. Kanarv. Th Analytical Thry f Spctrscpy. Krasndar, 1993. 88 pags. [17] Quantum mtrlgy and fundamntal cnstants. Cllctin f articls. M.: Mir. 1981. [18] E.V. Shplsky. Atmic Physics. Vlum 1. M.: 1963. 575 pags. [19] Physical ncyclpadic dictinary. M., Svtskaya ntsiklpdia. 1984. 944 pags. [0] Ph.M. Kanarv. Intrductin in Hydrgn Pwr. Krasndar, 1999. pags (In English). [1] Ph. M. Kanarv. A Nw Analysis f Cmptn Effct. Krasndar, 1994. 5 pags. (In English). [] Ph.M. Kanarv. Th Surc f Excss Enrgy frm Watr, Infinit Enrgy. V. 5, Issu 5. pags 5-58. APEIRON Vl. 7 Nr. 3-4, July-Octbr, 000 Pag 193