,transcrib]'s notes3 7#a7 ,numb]s foll[+ lett]s 7)\t space7 l ,c#b 7 orig9ally pr9t$ 9 subscript4 ,:5 lett]s are subscript$1 !y are prec$$ by an und]score1 l ,cn4 7#b7 ,*>act]s foll[+ a c>at 77 7 orig9ally pr9t$ 9 sup]script4 7#c7 ,lett]s topp$ by ,macron are repres5t$ z x4 7#d7 oo /&s = inf9ity2 int = integral2 alpha1 beta1 etc4 = greek lett]s4 7#e7 ,! foll[+ typographical errors h be5 correct$3 ,page #hga3 an equation :i* is v useful1 because x enables u1 if we "k ! di/ribution4 'because' am5d$ f 'becaus'4 ,page #hij3 ,! col\r ( ! lum9osity due to positive rays is n 9 g5]al ! same z t due to anode rays4 'positive' am5d$ f 'po/ive'4 ,page #hij3 ,anode ,rays4--,gehrcke & ,rei*5he9 7,ann4 d] ,phys4 #be1 p4 #hfa7 h f\nd t :5 ! anode consi/s ( a mixture ( sodium & li?ium *loride4 'mixture' am5d$ f 'mixure'4 ,,encyclopa$ia ,,britannica ,a ,,diction>y ,,( ,,arts1 ,,sci5ces1 ,,lit]ature ,,& ,,g5]al ,,in=mation ,,elev5? ,,edition ,,volume ,,vi1 ,,slice ,,viii ,conduction1 ,electric ,article 9 ,?is ,slice3 ,,conduction1 ,,electric ,,conduction1 ,,electric4 ,! electric conductivity ( a sub/ance is t prop]ty 9 virtue ( :i* all its p>ts come spontane\sly to ! same electric pot5tial if ! sub/ance is kept free f ! op]ation ( electric =ce4 ,accord+ly1 ! reciprocal quality1 electric resi/ivity1 may be def9$ z a quality ( a sub/ance 9 virtue ( :i* a diff]5ce ( pot5tial c exi/ betwe5 diff]5t portions ( ! body :5 ^! are 9 contact ) "s con/ant s\rce ( electromotive =ce1 9 su* a mann] z to =m "p ( an electric circuit4 ,all mat]ial sub/ances possess 9 "s degree1 l>ge or small1 electric conductivity1 & may = ! sake ( conv5i5ce be broadly divid$ into five classes 9 ?is respect4 ,betwe5 ^!1 h[ev]1 !re is no %>ply-m>k$ divid+ l9e1 & ! classification mu/ !re=e be accept$ z a m or less arbitr>y "o4 ,^! divisions are3 7#a7 metallic conductors1 7#b7 non-metallic conductors1 7#c7 dielectric conductors1 7#d7 electrolytic conductors1 7#e7 gase\s conductors4 ,! fir/ class comprises all metallic sub/ances1 & ^? mixtures or comb9ations ( metallic sub/ances kn[n z alloys4 ,! second includes su* non-metallic bodies z c>bon1 silicon1 _m ( ! oxides & p]oxides ( ! metals1 & probably also "s oxides ( ! non-metals1 sulphides & sel5ides4 ,_m ( ^! sub/ances1 = in/ance c>bon & silicon1 are well-kn[n to h ! prop]ty ( exi/+ 9 sev]al allotropic =ms1 & 9 "s ( ^! conditions1 s f> f be+ fairly good conductors1 !y may be almo/ p]fect non-conductors4 ,an example ( ?is is se5 9 ! case ( c>bon 9 its ?ree allotropic conditions--*>coal1 graphite & diamond4 ,z *>coal x possesses a fairly well-m>k$ b n v high conductivity 9 comp>ison ) metals2 z graphite1 a conductivity ab\t "o-f\r-hundr$? ( t ( iron2 b z diamond s little conductivity t ! sub/ance is includ$ among/ insulators or non-conductors4 ,! ?ird class includes ^? sub/ances :i* are g5]ally call$ insulators or non-conductors1 b :i* are bett] d5om9at$ dielectric conductors2 x comprises su* solid sub/ances z mica1 ebonite1 %ellac1 india-rubb]1 gutta-p]*a1 p>aff91 & a l>ge numb] ( liquids1 *iefly hydroc>bons4 ,^! sub/ances diff] greatly 9 insulat+ p[]1 & accord+ z ! conductivity is m or less m>k$1 !y are spok5 ( z bad or good insulators4 ,among/ ! latt] _m ( ! liquid gases hold a high position4 ,?us1 liquid oxyg5 & liquid air h be5 %[n by ,sir ,james ,dew> to be almo/ p]fect non-conductors ( electricity4 ,! behavi\r ( sub/ances :i* fall into ^! ?ree classes is discuss$ bel[ 9 section ,i41 deal+ ) metallic conduction4 ,! f\r? class1 namely ! electrolytic conductors comprises all ^? sub/ances :i* und]go *emical decomposition :5 !y =m "p ( an electric circuit trav]s$ by an electric curr5t4 ,!y are discuss$ 9 section ,,ii41 deal+ ) electrolytic conduction4 ,! fif? & la/ class ( conductors includes ! gases4 ,! conditions "u :i* ?is class ( sub/ance becomes possess$ ( electric conductivity are consid]$ 9 section ,,iii41 on conduction 9 gases4 ,9 connexion ) metallic conductors1 x is a fact ( great int]e/ & consid]able practical importance1 t1 al?\gh ! majority ( metals :5 9 a f9ely divid$ or p[d]$ condition are practically non-conductors1 a mass ( metallic p[d] or fil+s may be made to pass sudd5ly into a conductive condition by be+ expos$ to ! influ5ce ( an electric wave4 ,! same is true ( ! loose contact ( two metallic conductors4 ,?us if a /eel po9t1 su* z a ne$le1 presses v lightly aga9/ a metallic plate1 say ( alum9ium1 x is f\nd t ?is metallic contact1 if c>efully adju/$1 is non-conductive1 b t if an electric wave is creat$ any:]e 9 ! neighb\rhood1 ?is non-conduct+ contact passes into a conductive /ate4 ,?is fact1 inve/igat$ & discov]$ indep5d5tly by ,d4 ,e4 ,hughes1 ,c4 ,one/i1 ,e4 ,branly1 ,o4 ,j4 ,lodge & o!rs1 is appli$ 9 ! con/ruction ( ! coh]]1 or s5sitive tube employ$ z a detector or receiv] 9 t =m ( wireless telegraphy *iefly develop$ by ,m>coni4 ,fur!r ref]5ces to x are made 9 ! articles ,,electric ,,waves & ,,telegraphy3 ,wireless4 ,int]national ,ohm4--,! practical unit ( electrical resi/ance 0 legally def9$ 9 ,great ,brita9 by ! au?ority ( ! que5 9 c\ncil 9 #ahid1 z ! resi/ance (f]$ to an inv>iable electric curr5t by a column ( m]cury at ! temp]ature ( melt+ ice1 #ad4deba grammes 9 mass1 ( a con/ant cross-sectional area1 & a l5g? #ajf4c c5timetres4 ,! same unit has be5 also legaliz$ z a /&>d 9 ,france1 ,g]many & ! ,unit$ ,/ates1 & is d5om9at$ ! ,int]national or ,/&>d ,ohm4 ,x is int5d$ to repres5t z ne>ly z possible a resi/ance equal to #aj absolute ,c4,g4,s4 units ( electric resi/ance4 ,conv5i5t multiples & subdivisions ( ! ohm are ! microhm & ! megohm1 ! =m] be+ a million? "p ( an ohm1 & ! latt] a million ohms4 ,! resi/ivity ( sub/ances is !n num]ically express$ by /at+ ! resi/ance ( "o cubic c5timetre ( ! sub/ance tak5 betwe5 oppos$ faces1 & express$ 9 ohms1 microhms or megohms1 z may be mo/ conv5i5t4 ,! reciprocal ( ! ohm is call$ ! mho1 :i* is ! unit ( conductivity1 & is def9$ z ! conductivity ( a sub/ance ^: resi/ance is "o ohm4 ,! absolute unit ( conductivity is ! conductivity ( a sub/ance ^: resi/ivity is "o absolute ,c4,g4,s4 unit1 or "o-?\s&?-million? "p ( an ohm4 ,resi/ivity is a quality 9 :i* mat]ial sub/ances diff] v widely4 ,! metals & alloys1 broadly speak+1 are good conductors1 & _! resi/ivity is conv5i5tly express$ 9 microhms p] cubic c5timetre1 or 9 absolute ,c4,g4,s4 units4 ,v small diff]5ces 9 d5sity & 9 *emical purity make1 h[ev]1 imm5se diff]5ces 9 electric resi/ivity2 h5ce ! values giv5 by diff]5t exp]im5tali/s = ! resi/ivity ( kn[n metals diff] to a consid]able ext5t4 ,i4 ,,conduction ,,9 ,,solids ,x is f\nd conv5i5t to express ! resi/ivity ( metals 9 two diff]5t ways3 7#a7 ,we may /ate ! resi/ivity ( "o cubic c5timetre ( ! mat]ial 9 microhms or absolute units tak5 betwe5 oppos$ faces4 ,?is is call$ ! volume-resi/ivity2 7#b7 we may express ! resi/ivity by /at+ ! resi/ance 9 ohms (f]$ by a wire ( ! mat]ial 9 "q ( uni=m cross-section "o metre 9 l5g?1 & "o gramme 9 weight4 ,?is num]ical measure ( ! resi/ivity is call$ ! mass-resi/ivity4 ,! mass-resi/ivity ( a body is connect$ ) its volume-resi/ivity & ! d5sity ( ! mat]ial 9 ! foll[+ mann]3--,! mass-resi/ivity1 express$ 9 microhms p] metre-gramme1 divid$ by #aj times ! d5sity is num]ically equal to ! volume-resi/ivity p] c5timetre-cube 9 absolute ,c4,g4,s4 units4 ,! mass-resi/ivity p] metre-gramme c always be obta9$ by measur+ ! resi/ance & ! mass ( any wire ( uni=m cross-section ( :i* ! l5g? is kn[n1 & if ! d5sity ( ! sub/ance is !n measur$1 ! volume-resi/ivity c be imm$iately calculat$4 ,if ,r is ! resi/ance 9 ohms ( a wire ( l5g? l1 uni=m cross-section s1 & d5sity d1 !n tak+ rho = ! volume-resi/ivity we h #aji,r rhol_/s2 b lsd ,m1 :]e ,m is ! mass ( ! wire4 ,h5ce #aji,r rhodl_/,m4 ,if l #ajj & ,m #a1 !n ,r rho' resi/ivity 9 ohms p] metre-gramme1 & #ajirho' #aj1jjj;drho1 or rho #ajerho'_/d1 & rho' #aj1jjj,,mr_/l4 ,! foll[+ rules1 !re=e1 are useful 9 connexion ) ^! measurem5ts4 ,to obta9 ! mass-resi/ivity p] metre-gramme ( a sub/ance 9 ! =m ( a uni=m metallic wire3--,multiply toge!r #aj1jjj times ! mass 9 grammes & ! total resi/ance 9 ohms1 & !n divide by ! squ>e ( ! l5g? 9 c5timetres4 ,aga91 to obta9 ! volume-resi/ivity 9 ,c4,g4,s4 units p] c5timetre-cube1 ! rule is to multiply ! mass-resi/ivity 9 ohms by #ajj1jjj & divide by ! d5sity4 ,^! rules1 ( c\rse1 apply only to wires ( uni=m cross-section4 ,9 ! foll[+ ,tables ,i41 ,,ii4 & ,,iii4 are giv5 ! mass & volume resi/ivity ( ord9>y metals & c]ta9 alloys express$ 9 t]ms ( ! int]national ohm or ! absolute ,c4,g4,s4 unit ( resi/ance1 ! values be+ calculat$ f ! exp]im5ts ( ,a4 ,mat?iess5 7#ahca-ahgj7 betwe5 #ahfj & #ahfe1 & f lat] results obta9$ by ,j4 ,a4 ,flem+ & ,sir ,james ,dew> 9 #ahic4 ,,table ,i4--,electric ,mass-,resi/ivity ( ,v>i\s ,metals at #j ,c41 or ,resi/ance p] ,metre-gramme 9 ,int]national ,ohms at #j ,c4 7,mat?iess547 ---------------------------------------- --------------- ,resi/ance at #j ,c4 9 ,int]national ,approximate ,metal4 ,ohms ( a ,wire ,temp]ature #a ,metre long & ,coeffici5t ,weigh+ ne> #bj ,c4 #a ,gramme4 ---------------------------------------- --------------- ,silv] 7anneal$7 4#aebc #j4jjcgg ,silv] 7h>d-drawn7 4#afeg 44 ,copp] 7anneal$7 4#adba #j4jjchh ,copp] 7h>d-drawn7 4#addi 7,mat?iess5's ,/&>d7 ,gold 7anneal$7 4#djbe #j4jjcfe ,gold 7h>d-drawn7 4#djid 44 ,alum9ium 7anneal$7 4#jgeg 44 ,z9c 7press$7 4#djac 44 ,plat9um 7anneal$7 #a4iccg 44 ,iron 7anneal$7 4#gfe 44 ,nickel 7anneal$7 #a4jeha 44 ,t9 7press$7 4#ifah #j4jjcfe ,lead 7press$7 #b4bbfh #j4jjchg ,antimony 7press$7 #b4cghg #j4jjchi ,bismu? 7press$7 #ab4heeda #j4jjced ,m]cury 7liquid7 #ab4hheb #j4jjjgb ---------------------------------------- --------------- ,! data commonly us$ = calculat+ metallic resi/ivities 7 obta9$ by ,a4 ,mat?iess51 & 8 results are set out 9 ! ,table ,,ii4 :i* is tak5 f ,cantor lectures giv5 by ,fleem+ ,j5k9 9 #ahff at or ab\t ! date :5 ! rese>*es 7 made4 ,! figures giv5 by ,j5k9 h1 h[ev]1 be5 r$uc$ to int]national ohms & ,c4,g4,s4 units by multiply+ by 7pi_/#d7 #j4ihff #aje #gg1dhe4 ,subsequ5tly num]\s det]m9ations ( ! resi/ivity ( v>i\s pure metals 7 made by ,flem+ & ,dew>1 ^: results are set out 9 ,table ,,iii4 ,,table ,,ii4--,electric ,volume-,resi/ivity ( ,v>i\s ,metals at #j ,c41 or ,resi/ance p] ,c5timetre-cube 9 ,c4,g4,s4 ,units at #j ,c4 ---------------------------------------- -- ,volume-,resi/ivity4 ,metal4 at #j ,c4 9 ,c4,g4,s4 ,units ---------------------------------------- -- ,silv] 7anneal$7 #a1ejb ,silv] 7h>d-drawn7 #a1fbi ,copp] 7anneal$7 #a1eid ,copp] 7h>d-drawn7 #a1fcjc ,gold 7anneal$7 #b1jeb ,gold 7h>d-drawn7 #b1jij ,alum9ium 7anneal$7 #c1jjf ,z9c 7press$7 #e1fba ,plat9um 7anneal$7 #i1jce ,iron 7anneal$7 #aj1efh ,nickel 7anneal$7 #ab1dbid ,t9 7press$7 #ac1agh ,lead 7press$7 #ai1ehj ,antimony 7press$7 #ce1dah ,bismu? 7press$7 #acj1hgb ,m]cury 7liquid7 #id1hife ---------------------------------------- -- ,,table ,,iii4--,electric ,volume-,resi/ivity ( ,v>i\s ,metals at #j ,c41 or ,resi/ance p] ,c5timetre-cube at #j ,c4 9 ,c4,g4,s4 ,units4 7,flem+ & ,dew>1 ,phil4 ,mag41 ,septemb] #ahic47 ---------------------------------------- ---------------------- ,resi/ance ,mean ,temp]ature ,metal4 at #j ,c4 p] ,coeffici5t ,c5timetre-cube betwe5 #j ,c4 9 ,c4,g4,s4 ,units4 & #ajj ,c4 ---------------------------------------- ---------------------- ,silv] 7electrolytic & well anneal$7#f #a1dfh #j4jjdjj ,copp] 7electrolytic & well anneal$7#f #a1efa #j4jjdbh ,gold 7anneal$7 #b1aig #j4jjcgg ,alum9ium 7anneal$7 #b1ffe #j4jjdce ,magnesium 7press$7 #d1cee #j4jjcha ,z9c #e1gea #j4jjdjf ,nickel 7electrolytic7#f #f1ice #j4jjfah ,iron 7anneal$7 #i1jfe #j4jjfbe ,cadmium #aj1jbc #j4jjdai ,palladium #aj1bai #j4jjced ,plat9um 7anneal$7 #aj1iag #j4jjcffi ,t9 7press$7 #ac1jdh #j4jjddj ,?allium 7press$7 #ag1fcc #j4jjcih ,lead 7press$7 #bj1chj #j4jjdaa ,bismu? 7electrolytic7#g #aaj1jjj #j4jjdcc ---------------------------------------- ---------------------- ,resi/ivity ( ,m]cury4--,! volume-resi/ivity ( pure m]cury is a v important electric con/ant1 & s9ce #ahhj _m ( ! mo/ compet5t exp]im5tali/s h direct$ _! att5tion to ! det]m9ation ( its value4 ,! exp]im5tal process has usually be5 to fill a glass tube ( kn[n dim5sions1 hav+ l>ge cup-l ext5sions at ! ends1 ) pure m]cury1 & det]m9e ! absolute resi/ance ( ?is column ( metal4 ,= ! practical details ( ?is me?od ! foll[+ ref]5ces may be consult$3--,! ,specific ,resi/ance ( ,m]cury1 ,"l ,rayleigh & ,mrs ,sidgwick1 ,phil4 ,trans41 #ahhc1 "p i4 p4 #agc1 & ,r4 ,t4 ,glazebrook1 ,phil4 ,mag41 #ahhe1 p4 #bj2 ,on ! ,specific ,resi/ance ( ,m]cury1 ,r4 ,t4 ,glazebrook & ,t4 ,c4 ,fitzpatrick1 ,phil4 ,trans41 #ahhh1 p4 #agi1 or ,proc4 ,roy4 ,soc41 #ahhh1 p4 #dd1 or ,electrician1 #ahhh1 #ba1 p4 #ech2 ,rec5t ,det]m9ations ( ! ,absolute ,resi/ance ( ,m]cury1 ,r4 ,t4 ,glazebrook1 ,electrician1 #ahij1 #be1 pp4 #edc & #ehh4 ,also see ,j4 ,v4 ,jones1 ,on ! ,det]m9ation ( ! ,specific ,resi/ance ( ,m]cury 9 ,absolute ,measure1 ,phil4 ,trans41 #ahia1 ,a1 p4 #b4 ,table ,,iv4 gives ! values ( ! volume-resi/ivity ( m]cury z det]m9$ by v>i\s obs]v]s1 ! con/ant be+ express$ 7a7 9 t]ms ( ! resi/ance 9 ohms ( a column ( m]cury "o millimetre 9 cross-section & #ajj c5timetres 9 l5g?1 tak5 at #j ,c42 & 7b7 9 t]ms ( ! l5g? 9 c5timetres ( a column ( m]cury "o squ>e millimetre 9 cross-section tak5 at #j ,c4 ,! result ( all ! mo/ c>eful det]m9ations has be5 to %[ t ! resi/ivity ( pure m]cury at #j ,c4 is ab\t #id1jgj ,c4,g4,s4 electromagnetic units ( resi/ance1 & t a column ( m]cury #ajf4c c5timetres 9 l5g? hav+ a cross-sectional area ( "o squ>e millimetre w\ld h a resi/ance at #j ,c4 ( "o int]national ohm4 ,^! values h accord+ly be5 accept$ z ! (ficial & recogniz$ values = ! specific resi/ance ( m]cury1 & ! def9ition ( ! ohm4 ,! table also /ates ! me?ods :i* h be5 adopt$ by ! diff]5t obs]v]s = obta9+ ! absolute value ( ! resi/ance ( a kn[n column ( m]cury1 or ( a resi/ance coil aft]w>ds comp>$ ) a kn[n column ( m]cury4 ,a column ( figures is add$ %[+ ! value 9 fractions ( an int]national ohm ( ! ,briti% ,association ,unit 7,b4,a4,u471 =m]ly suppos$ to repres5t ! true ohm4 ,! real value ( ! ,b4,a4,u4 is n[ tak5 z 4#ihff ( an int]national ohm4 ,,table ,,iv4--,det]m9ations ( ! ,absolute ,value ( ! ,volume-,resi/ivity ( ,m]cury & ! ,m]cury ,equival5t ( ! ,ohm4 ---------------------------------------- -------------------------------- ,value ( ,value ( ,value (#ajj ,c5ti-,ohm 9 ,obs]v]4 ,date4 ,me?od4 ,b4,a4,u4 metres ( ,c5ti- 9 ,ohms4,m]cury metres ( 9 ,ohms4 ,m]cury4 ---------------------------------------- -------------------------------- ,"l ,rayleigh #ahhb ,rotat+ coil 4#ihfea 4#idacc #ajf4ca ,"l ,rayleigh #ahhc ,lor5z me?od 4#ihfgg 44 #ajf4bg ,g4 ,wi$emann #ahhd ,rotation ?r\gh #ahj 44 44 #ajf4ai ,e4 ,e4 ,n4 ,masc>t #ahhd ,induc$ curr5t 4#ihfaa 4#idjif #ajf4cc ,h4 ,a4 ,r[l& #ahhg ,mean ( sev]al 4#ihfdd 4#idjga #ajf4cb me?ods ,f4 ,kohlraus* #ahhg ,damp+ ( magnets 4#ihffj 4#idjfa #ajf4cb ,r4 ,t4 ,glazebrook #ahhb ,induc$ curr5ts 4#ihffe 4#idjgd #ajf4bi #ahhh ,wuilleumei] #ahij 4#ihfhf 4#idjgg #ajf4ca ,duncan & ,wilkes #ahij ,lor5z 4#ihfcd 4#idjfg #ajf4cd ,j4 ,v4 ,jones #ahia ,lor5z 44 4#idjfg #ajf4ca --------------------------- ,mean value 4#ihfec ,/rek] #ahhe ,an absolute det]m9- 4#idjef #ajf4cb ,hut*9son #ahhh ation ( resi/ance 4#idjgd #ajf4cj ,e4 ,salvioni #ahij 0 n made4 ,! 4#idjed #ajf4cc ,e4 ,salvioni 44 value 4#ihfef has 4#idjgf #ajf4cj be5 us$ ------------------- ,mean value 4#idjgf #ajf4ca ,h4 ,f4 ,web] #ahhd ,induc$ curr5t ,absolute measure- #aje4cg ,h4 ,f4 ,web] 44 ,rotat+ coil m5ts comp>$ #ajf4af ,a4 ,roiti #ahhd ,mean effect ( ) ,g]man silv] #aje4hi induc$ curr5t wire coils issu$ ,f4 ,him/$t #ahhe by ,siem5s & #aje4ih ,/rek] ,f4 ,e4 ,dorn #ahhi ,damp+ ( a magnet #ajf4bd ,wild #ahhc ,damp+ ( a magnet #ajf4jc ,l4 ,v4 ,lor5z #ahhe ,lor5z me?od #aje4ic ---------------------------------------- --------------------------------- ,= a critical discussion ( ! me?ods :i* h be5 adopt$ 9 ! absolute det]m9ation ( ! resi/ivity ( m]cury1 & ! value ( ! ,briti% ,association unit ( resi/ance1 ! read] may be ref]r$ to ! ,briti% ,association ,reports = #ahij & #ahib 7,report ( ,electrical ,/&>ds ,committee71 & to ! ,electrician1 #be1 p4 #def1 & #bi1 p4 #dfb4 ,a discussion ( ! relative value ( ! results obta9$ betwe5 #ahhb & #ahij 0 giv5 by ,r4 ,t4 ,glazebrook 9 a pap] pres5t$ to ! ,briti% ,association at ,le$s1 #ahij4 ,resi/ivity ( ,copp]4--,9 connexion ) electro-te*nical "w ! det]m9ation ( ! conductivity or resi/ivity values ( anneal$ & h>d-drawn copp] wire at /&>d temp]atures is a v important matt]4 ,mat?iess5 devot$ consid]able att5tion to ?is subject betwe5 ! ye>s #ahfj & #ahfd 7see ,phil4 ,trans41 #ahfj1 p4 #aej71 & s9ce t "t mu* additional "w has be5 c>ri$ out4 ,mat?iess5's value1 kn[n z ,mat?iess5's ,/&>d1 = ! mass-resi/ivity ( pure h>d-drawn copp] wire1 is ! resi/ance ( a wire ( pure h>d-drawn copp] "o metre long & weigh+ "o gramme1 & ?is is equal to #j4addic int]national ohms at #j ,c4 ,= _m purposes x is m conv5i5t to express temp]ature 9 ,fahr5heit degrees1 & ! recomm5dation ( ! #ahii committee on copp] conductors#h is z foll[s3--,mat?iess5's /&>d = h>d-drawn conductivity comm]cial copp] %all be consid]$ to be ! resi/ance ( a wire ( pure h>d-drawn copp] "o metre long1 weigh+ "o gramme :i* at #fj ,f4 is #j4aecheh int]national ohms4 ,mat?iess5 also measur$ ! mass-resi/ivity ( anneal$ copp]1 & f\nd t its conductivity is great] ?an t ( h>d-drawn copp] by ab\t #b4be to #b4e ,z anneal$ copp] may v>y consid]ably 9 its /ate ( anneal+1 & is always some:at h>d5$ by b5d+ & w9d+1 x is f\nd 9 practice t ! resi/ivity ( comm]cial anneal$ copp] is ab\t #a less ?an t ( h>d-drawn copp]4 ,! /&>d n[ accept$ = su* copp]1 on ! recomm5dation ( ! #ahii ,committee1 is a wire ( pure anneal$ copp] "o metre long1 weigh+ "o gramme1 ^: resi/ance at #j ,c4 is #j4adba int]national ohms1 or at #fj ,f41 #j4aejhbb int]national ohms4 ,! specific gravity ( copp] v>ies f ab\t #h4hi to #h4ie1 & ! /&>d value accept$ = high conductivity comm]cial copp] is #h4iab1 correspond+ to a weight ( #eee lb p] cubic foot at #fj ,f4 ,h5ce ! volume-resi/ivity ( pure anneal$ copp] at #j ,c4 is #a4eid microhms p] c4c41 or #aeid ,c4,g4,s4 units1 & t ( pure h>d-drawn copp] at #j ,c4 is #a4fbf microhms p] c4c41 or #afbf ,c4,g4,s4 units4 ,s9ce ,mat?iess5's rese>*es1 ! mo/ c>eful sci5tific inve/igation on ! conductivity ( copp] is t ( ,t4 ,c4 ,fitzpatrick1 c>ri$ out 9 #ahij4 7,brit4 ,assoc4 ,report1 #ahij1 ,app5dix #c1 p4 #abj47 ,fitzpatrick confirm$ ,mat?iess5's *ief result1 & obta9$ values = ! resi/ivity ( h>d-drawn copp] :i*1 :5 correct$ = temp]ature v>iation1 are 9 entire agreem5t ) ^? ( ,mat?iess5 at ! same temp]ature4 ,! volume resi/ivity ( alloys is1 g5]ally speak+1 mu* high] ?an t ( pure metals4 ,table ,v4 %[s ! volume resi/ivity at #j ,c4 ( a numb] ( well-kn[n alloys1 ) _! *emical composition4 ,,table ,v4--,volume-,resi/ivity ( ,alloys ( kn[n ,composition at #j ,c4 9 ,c4,g4,s4 ,units p] ,c5timetre-cube4 ,mean ,temp]ature ,coeffici5ts tak5 at #ae ,c4 7,flem+ & ,dew>47 ---------------------------------------- ------------------------ ,resi/ivity,temp]ature,composition 9 p] ,alloys4 at #j ,c4 ,coeffici5t c5ts4 at #ae ,c4 ---------------------------------------- ------------------------ ,plat9um-silv] #ca1ehb 4#jjjbdc ,pt #cc1 ,ag #ff ,plat9um-iridium #cj1hif 4#jjjhbb ,pt #hj1 ,ir #bj ,plat9um-rhodium #ba1adb 4#jjadc ,pt #ij1 ,rd #aj ,gold-silv] #f1bhj 4#jjabd ,au #ij1 ,ag #aj ,manganese-/eel #fg1adh 4#jjabg ,mn #ab1 ,fe #gh ,nickel-/eel #bi1deb 4#jjbja ,ni #d4ce1 rema9+ p]c5tage *iefly iron1 b unc]ta9 ,g]man silv] #bi1ihb 4#jjjbgc ,cu#e,zn#c,ni#b ,plat9oid#i #da1gca 4#jjjca ,mangan9 #df1fgh 4#jjjj ,cu #hd1 ,mn #ab1 ,ni #d ,alum9ium-silv] #d1fda 4#jjbch ,al #id1 ,ag #f ,alum9ium-copp] #b1ijd 4#jjcha ,al #id1 ,cu #f ,copp]-alum9ium #h1hdg 4#jjjhig ,cu #ig1 ,al #c ,copp]-nickel-alum9ium #ad1iab 4#jjjfdc ,cu #hg1 ,ni #f4e1 ,al #f4e ,titanium-alum9ium #c1hhg 4#jjbij ---------------------------------------- ------------------------ ,g5]ally speak+1 an alloy hav+ high resi/ivity has poor me*anical qualities1 t is to say1 its t5sile /r5g? & ductility are small4 ,x is possible to =m alloys hav+ a resi/ivity z high z #ajj microhms p] cubic c5timetre2 b1 on ! o!r h&1 ! value ( an alloy = electro-te*nical purposes is judg$ n m]ely by its resi/ivity1 b also by ! degree to :i* its resi/ivity v>ies ) temp]ature1 & by its capability ( be+ easily drawn into f9e wire ( n v small t5sile /r5g?4 ,"s pure metals :5 alloy$ ) a small proportion ( ano!r metal d n suff] mu* *ange 9 resi/ivity1 b 9 o!r cases ! resultant alloy has a mu* high] resi/ivity4 ,?us an alloy ( pure copp] ) #c ( alum9ium has a resi/ivity ab\t #e times t ( copp]2 b if pure alum9ium is alloy$ ) #f ( copp]1 ! resi/ivity ( ! product is n m ?an #bj great] ?an t ( pure alum9ium4 ,! pres5ce ( a v small proportion ( a non-metallic elem5t 9 a metallic mass1 su* z oxyg51 sulphur or phosphorus1 has a v great effect 9 increas+ ! resi/ivity4 ,c]ta9 metallic elem5ts also h ! same p[]2 ?us plat9oid has a resi/ivity #cj great] ?an ,g]man silv]1 ?\gh x diff]s f x m]ely 9 conta9+ a trace ( tung/54 ,! resi/ivity ( non-metallic conductors is 9 all cases high] ?an t ( any pure metal4 ,! resi/ivity ( c>bon1 = in/ance1 9 ! =ms ( *>coal or c>boniz$ organic mat]ial & graphite1 v>ies f #fjj to #fjjj microhms p] cubic c5timetre1 z %[n 9 ,table ,,vi43-- ,,table ,,vi4--,electric ,volume-,resi/ivity 9 ,microhms p] ,c5timetre-cube ( ,v>i\s ,=ms ( ,c>bon at #ae ,c4 ---------------------------------------- ---------------- ,sub/ance4 ,resi/ivity4 ---------------------------------------- ---------------- ,arc lamp c>bon rod #hjjj ,jablo*k(f c&le c>bon #djjj ,c>r c>bon #cdjj ,c>boniz$ bamboo #fjjj ,c>boniz$ p>*m5tiz$ ?read #djjj to #ejjj ,ord9>y c>bon filam5t f gl[-lamp treat$ or fla%$ #bdjj to #bejj ,deposit$ or second>y c>bon #fjj to #ijj ,graphite #djj to #ejj ---------------------------------------- ---------------- ,! resi/ivity ( liquids is1 g5]ally speak+1 mu* high] ?an t ( any metals1 metallic alloys or non-metallic conductors4 ,?us fus$ lead *loride1 "o ( ! be/ conduct+ liquids1 has a resi/ivity 9 its fus$ condition ( #j4cgf ohm p] c5timetre-cube1 or #cgf1jjj microhms p] c5timetre-cube1 :]eas t ( metallic alloys only 9 few cases exce$s #ajj microhms p] c5timetre-cube4 ,! resi/ivity ( solutions ( metallic salts also v>ies v l>gely ) ! proportion ( ! dilu5t or solv5t1 & 9 "s in/ances1 z 9 ! aque\s solutions ( m9]al acids2 !re is a maximum conductivity correspond+ to a c]ta9 dilution4 ,! resi/ivity ( _m liquids1 su* z alcohol1 e!r1 b5z5e & pure wat]1 is s high1 9 o!r words1 _! conductivity is s small1 t !y are practically insulators1 & ! resi/ivity c only be appropriately express$ 9 megohms p] c5timetre-cube4 ,9 ,table ,,vii4 are giv5 ! names ( a few ( ^! badly-conduct+ liquids1 ) ! values ( _! volume-resi/ivity 9 megohms p] c5timetre-cube3-- ,,table ,,vii4--,electric ,volume-,resi/ivity ( ,v>i\s ,badly-,conduct+ ,liquids 9 ,megohms p] ,c5timetre-cube4 ---------------------------------------- ------------------------ ,resi/ivity ,sub/ance4 9 ,megohms ,obs]v]4 p] c4c4 ---------------------------------------- ------------------------ ,e?yl alcohol #j4e ,pfeiff]4 ,e?yl e!r #a4age to #c4gfj ,w4 ,kohlraus*4 ,b5z5e #d4gjj ,absolutely pure wat] #be4j at #ah ,c4 ,value e/imat$ approximates probably to by ,f4 ,kohlraus* & ,a4 ,heydweil]4 ,all v dilute aque\s #a4jj at #ah ,c4 ,f results by salt solutions hav+ a ,f4 ,kohlraus* conc5tration ( ab\t & o!rs4 #j4jjjja ( an equival5t gramme molecule#aj p] litre approximate to ---------------------------------------- ------------------------ ,! resi/ivity ( all ^? sub/ances :i* are g5]ally call$ dielectrics or insulators is also s high t x c only be appropriately express$ 9 millions ( megohms p] c5timetre-cube1 or 9 megohms p] quadrant-cube1 ! quadrant be+ a cube ! side ( :i* is #aji cms4 7see ,table ,,viii474 ,effects ( ,heat4--,temp]ature affects ! resi/ivity ( ^! diff]5t classes ( conductors 9 diff]5t ways4 ,9 all cases1 s f> z is yet kn[n1 ! resi/ivity ( a pure metal is increas$ if its temp]ature is rais$1 & decreas$ if ! temp]ature is l[]$1 s t if x c\ld be br\ght to ! absolute z]o ( temp]ature 7-#bgc ,c47 its resi/ivity w\ld be r$uc$ to a v small fraction ( its resi/ance at ord9>y temp]atures4 ,) metallic alloys1 h[ev]1 rise ( temp]ature does n always increase resi/ivity3 x sometimes dim9i%es x1 s t _m alloys are kn[n :i* h a maximum resi/ivity correspond+ to a c]ta9 temp]ature1 & at or ne> ?is po9t !y v>y v little 9 resi/ance ) temp]ature4 ,su* alloys h1 !re=e1 a negative temp]ature-v>iation ( resi/ance at & above fix$ temp]atures4 ,prom95t among/ ^! metallic comp\nds are alloys ( iron1 manganese1 nickel & copp]1 "s ( :i* 7 discov]$ by ,edw>d ,we/on1 9 ! ,unit$ ,/ates4 ,"o well-kn[n alloy ( copp]1 manganese & nickel1 n[ call$ mangan91 :i* 0 br\ght to ! notice ( electricians by ! c>eful inve/igations made at ! ,b]l9 ,physikalis*-,te*nis*e ,rei*san/alt1 is *>act]iz$ by hav+ a z]o temp]ature coeffici5t at or ab\t a c]ta9 temp]ature 9 ! neighb\rhood ( #ae ,c4 ,h5ce )9 a c]ta9 range ( temp]ature on ei!r side ( ?is critical value ! resi/ivity ( mangan9 is h>dly affect$ at all by temp]ature4 ,simil> alloys c be produc$ f copp] & f]ro-manganese4 ,an alloy =m$ ( #hj copp] & #bj manganese 9 an anneal$ condition has a ne>ly z]o temp]ature-v>iation ( resi/ance betwe5 #bj ,c4 & #ajj ,c4 ,9 ! case ( non-metals ! action ( temp]ature is g5]ally to dim9i% ! resi/ivity z temp]ature rises1 ?\gh ?is is n univ]sally s4 ,! int]e/+ obs]vation has be5 record$ by ,j4 ,w4 ,h[ell1 t treat$ c>bon filam5ts & graphite are sub/ances :i* h a m9imum resi/ance correspond+ to a c]ta9 temp]ature approa*+ r$ heat 7,electrician1 vol4 xxxviii4 p4 #hce74 ,at & beyond ?is temp]ature increas$ heat+ appe>s to increase _! resi/ivity2 ?is ph5om5on may1 h[ev]1 be accompani$ by a molecul> *ange & n be a true temp]ature v>iation4 ,9 ! case ( dielectric conductors & ( electrolytes1 ! action ( ris+ temp]ature is to r$uce resi/ivity4 ,_m ( ! s-call$ insulators1 su* z mica1 ebonite1 indi>ubb]1 & ! insulat+ oils1 p>aff91 c41 decrease 9 resi/ivity ) great rapidity z ! temp]ature rises4 ,) guttap]*a a rise 9 temp]ature f #j ,c4 to #bd ,c4 is suffici5t to r$uce ! resi/ivity ( "o-tw5tie? "p ( its value at #j ,c41 & ! resi/ivity ( fl9t glass at #adj ,c4 is only "o-hundr$? ( :at x is at #fj ,c4 ,,table ,,viii4--,electric ,volume-,resi/ivity ( ,dielectrics reckon$ 9 ,millions ( ,megohms 7,mega-megohms7 p] ,c5timetre-cube1 & 9 ,megohms p] ,quadrant-cube1 i4e4 a ,cube ^: ,side is #aji cms4 ---------------------------------------- --------------------- ,resi/ivity4 -------------------------- ,temp]a- ,sub/ance4 ,mega-megohms ,megohms p] tura p] c4c4 ,quadrant-cube4 ,c5t4 ---------------------------------------- -------------------- ,bohemian glass #fa 4#jfa #fj ,mica #hd 4#jhd #bj ,gutta-p]*a #dej 4#de #bd ,fl9t glass #a1jbj #a4jb #fj ,glov]'s vulcaniz$ indi>ubb] #a1fcj #a4fc #ae ,siem5s' ord9>y pure vulcaniz$ indi>ubb] #b1bhj #b4bh #ae ,%ellac #i1jjj #i4j #bh ,indi>ubb] #aj1ijj #aj4i #bd ,siem5s' high-insulat+ fibr\s mat]ial #aa1ijj #aa4i #ae ,siem5s' special high-insulat+ indi>ubb]4 #af1agj #af4ag #ae ,fl9t glass #bj1jjj #bj4j #bj ,ebonite #bh1jjj #bh4 #df ,p>aff9 #cd1jjj #cd4 #df ---------------------------------------- -------------------- ,a def9ition may "h be giv5 ( ! mean+ ( ! t]m ,temp]ature ,coeffici5t4 ,if1 9 ! fir/ place1 we suppose t ! resi/ivity 7rhot7 at any temp]ature 7t7 is a simple l9e> function ( ! resi/ivity 7rho#j7 at #j ,c41 !n we c write rhot rho#j7a alphat71 or alpha 7rhot - rho#j7_/rho#jt4 ,! quantity alpha is !n call$ ! temp]ature-coeffici5t1 & its reciprocal is ! temp]ature at :i* ! resi/ivity w\ld become z]o4 ,by an ext5sion ( ?is notion we c call ! quantity drho_/rhodt ! temp]ature coeffici5t correspond+ to any temp]ature t at :i* ! resi/ivity is rho4 ,9 all cases ! relation betwe5 ! resi/ivity ( a sub/ance & ! temp]ature is be/ set out 9 ! =m ( a curve call$ a temp]ature-resi/ance curve4 ,if a s]ies ( su* curves are drawn = v>i\s pure metals1 temp]ature be+ tak5 z abscissa & resi/ance z ord9ate1 & if ! temp]ature range ext5ds f ! absolute z]o ( temp]ature upw>ds1 !n x is f\nd t ^! temp]ature-resi/ance l9es are curv$ l9es hav+ _! convexity ei!r upw>ds or d[nw>ds4 ,9 o!r words1 ! second diff]5tial coeffici5t ( resi/ance ) respect to temp]ature is ei!r a positive or negative quantity4 ,an ext5sive s]ies ( obs]vations conc]n+ ! =m ( ! resi/ivity curves = v>i\s pure metals ov] a range ( temp]ature ext5d+ f -#bjj ,c4 to #bjj ,c4 0 c>ri$ out 9 #ahib & #ahic by ,flem+ & ,dew> 7,phil4 ,mag4 ,oct4 #ahib & ,sept4 #ahic74 ,! resi/ance obs]vations 7 tak5 ) resi/ance coils con/ruct$ ) wires ( v>i\s metals obta9$ 9 a /ate ( great *emical purity4 ,! l5g?s & mean diamet]s ( ! wires 7 c>efully measur$1 & _! resi/ance 0 !n tak5 at c]ta9 kn[n temp]atures obta9$ by imm]s+ ! coils 9 boil+ anil9e1 boil+ wat]1 melt+ ice1 melt+ c>bonic acid 9 e!r1 & boil+ liquid oxyg51 ! temp]atures ?us giv5 be+ #ahd4e ,c41 #ajj ,c41 #j ,c41 -#gh4b ,c4 & -#ahb4e ,c4 ,! resi/ivities ( ! v>i\s metals 7 !n calculat$ & set out 9 t]ms ( ! temp]ature4 ,f ^! data a *>t 0 prep>$ %[+ ! temp]ature-resi/ance curves ( ^! metals ?r\gh\t a range ( #djj degrees4 ,! exact =m ( ^! curves ?r\gh ! region ( temp]ature ly+ betwe5 -#bjj ,c4 & -#bgc ,c4 is n yet kn[n4 ,z %[n on ! *>t1 ! curves evid5tly d n conv]ge to precisely ! same po9t4 ,x is1 h[ev]1 mu* less probable t ! resi/ance ( any metal %\ld vani% at a temp]ature above ! absolute z]o ?an at ! absolute z]o itself1 & ! precise pa? ( ^! curves at _! l[] ends _c be del9eat$ until means are f\nd = fix+ indep5d5tly ! temp]ature ( "s regions 9 :i* ! resi/ance ( metallic wires c be measur$4 ,sir ,j4 ,dew> subsequ5tly %[$ t = c]ta9 pure metals x is cle> t ! resi/ance w\ld n vani% at ! absolute z]o b w\ld be r$uc$ to a f9ite b small value 7see ,electric ,resi/ance ,!rmometry at ! ,temp]ature ( ,boil+ ,hydrog51 ,proc4 ,roy4 ,soc4 #aijd1 #gc1 p4 #bdd74 ,! resi/ivity curves ( ! magnetic metals are also rem>kable = ! *ange ( curvature !y exhibit at ! magnetic critical temp]ature4 ,?us ,j4 ,hopk9son & ,d4 ,k4 ,morris 7,phil4 ,mag4 ,septemb] #ahig1 p4 #bac7 obs]v$ ! rem>kable alt]ation t takes place 9 ! iron resi/ance temp]ature curve 9 ! neighb\rhood ( #ghj ,c4 ,at t temp]ature ! direction ( ! curvature ( ! curve *anges s t x becomes convex upw>ds in/ead ( convex d[nw>ds1 & 9 addition ! value ( ! temp]ature coeffici5t und]goes a great r$uction4 ,! mean temp]ature coeffici5t ( iron 9 ! neighb\rhood ( #j ,c4 is #j4jjeg2 at #gfe ,c4 x rises to a maximum value #j4jbjd2 b at #ajjj ,c4 x falls aga9 to a l[] value1 #j4jjbdd4 ,a simil> rise to a maximum value & subsequ5t fall are also not$ 9 ! case ( ! specific heat ( iron4 ,! *anges 9 ! curvature ( ! resi/ivity curves are und\bt$ly connect$ ) ! molecul> *anges t occur 9 ! magnetic metals at _! critical temp]atures4 ,a fact ( consid]able int]e/ 9 connexion ) resi/ivity is ! influ5ce ex]t$ by a /rong magnetic field 9 ! case ( "s metals1 notably bismu?4 ,x 0 discov]$ by ,a4 ,righi & confirm$ by ,s4 ,a4 ,l$uc 7,j\rn4 de ,phys4 #ahhf1 #e1 p4 #aaf1 & #ahhg1 #f1 p4 #ahi7 t if a pure bismu? wire is plac$ 9 a magnetic field transv]sely to ! direction ( ! magnetic field1 its resi/ance is consid]ably increas$4 ,?is increase is greatly affect$ by ! temp]ature ( ! metal 7,dew> & ,flem+1 ,proc4 ,roy4 ,soc4 #ahig1 #fj1 p4 #dbg74 ,! temp]ature coeffici5t ( pure copp] is an important con/ant1 & its value z det]m9$ by ,messrs ,cl>k1 ,=de & ,taylor 9 t]ms ( ,fahr5heit temp]ature is rhot rho#cb #a #j4jjbcgjh7t - #cb7 #j4jjjjjcdedh7t - #cb74 ,"t ,effects4--,9 ! case ( dielectric conductors1 commonly call$ insulators1 su* z indi>ubb]1 guttap]*a1 glass & mica1 ! electric resi/ivity is n only a function ( ! temp]ature b also ( ! "t dur+ :i* ! electromotive =ce employ$ to measure x is impos$4 ,?us if an indi>ubb]-cov]$ cable is imm]s$ 9 wat] & ! resi/ance ( ! dielectric betwe5 ! copp] conductor & ! wat] measur$ by asc]ta9+ ! curr5t :i* c be caus$ to fl[ ?r\gh x by an electromotive =ce1 ?is curr5t is f\nd to v>y v rapidly ) ! "t dur+ :i* ! electromotive =ce is appli$4 ,ap>t f ! small initial effect due to ! electro/atic capacity ( ! cable1 ! application ( an electromotive =ce to ! dielectric produces a curr5t ?r\gh x :i* rapidly falls 9 value1 z if ! electric resi/ance ( ! dielectric 7 increas+4 ,! curr5t1 h[ev]1 does n fall cont9u\sly b t5ds to a limit+ value1 & x appe>s t if ! electromotive =ce is kept appli$ to ! cable = a prolong$ "t1 a small & ne>ly con/ant curr5t w ultimately be f\nd fl[+ ?r\gh x4 ,x is cu/om>y 9 electro-te*nical "w to consid] ! resi/ivity ( ! dielectric z ! value x has aft] ! electromotive =ce has be5 appli$ = "o m9ute1 ! /&>d temp]ature be+ #ge ,f4 ,?is1 h[ev]1 is a purely conv5tional proce$+1 & ! numb] s obta9$ does n necess>ily repres5t ! true or ohmic resi/ance ( ! dielectric4 ,if ! electromotive =ce is increas$1 9 ! case ( a l>ge numb] ( ord9>y dielectrics ! app>5t resi/ance at ! end ( "o m9ute's electrification decreases z ! electromotive =ce increases4 ,practical ,/&>ds4--,! practical measurem5t ( resi/ivity involves _m processes & in/rum5ts 7see ,,:eat/one',s ,,bridge & ,,ohmmet]74 ,broadly speak+1 ! processes are divid$ into ,comp>ison ,me?ods & ,absolute ,me?ods4 ,9 ! =m] a comp>ison is effect$ betwe5 ! resi/ance ( a mat]ial 9 a kn[n =m & "s /&>d resi/ance4 ,9 ! ,absolute ,me?ods ! resi/ivity is det]m9$ )\t ref]5ce to any o!r sub/ance1 b ) ref]5ce only to ! fundam5tal /&>ds ( l5g?1 mass & "t4 ,imm5se lab\r has be5 exp5d$ 9 inve/igations conc]n$ ) ! production ( a /&>d ( resi/ance & its evaluation 9 absolute measure4 ,9 "s cases ! absolute /&>d is con/ruct$ by fill+ a c>efully-calibrat$ tube ( glass ) m]cury1 9 ord] to realize 9 a mat]ial =m ! (ficial def9ition ( ! ohm2 9 ?is mann] mo/ ( ! pr9cipal national physical laboratories h be5 provid$ ) /&>d m]cury ohms4 7,= a full description ( ! /&>d m]cury ohm ( ! ,b]l9 ,physikalis*-,te*nis*e ,rei*san/alt1 see ! ,electrician1 xxxvii4 #efi47 ,= practical purposes x is m conv5i5t to employ a /&>d ( resi/ance made ( wire4 ,op9ion is n yet p]fectly settl$ on ! "q :e!r a wire made ( any alloy c be consid]$ to be a p]fectly unalt]able /&>d ( resi/ance1 b exp]i5ce has %[n t a plat9um silv] alloy 7#ff silv]1 #cc plat9um71 & also ! alloy call$ mangan91 seem to possess ! qualities ( p]man5ce ess5tial = a wire-resi/ance /&>d4 ,a comp>ison made 9 #ahib & #ahid ( all ! mangan9 wire copies ( ! ohm made at ! ,rei*san/alt 9 ,b]l91 %[$ t ^! /&>ds _h rema9$ con/ant = two ye>s to )9 "o or two p>ts 9 #ajj1jjj4 ,x appe>s1 h[ev]1 t 9 ord] t mangan9 may rema9 con/ant 9 resi/ivity :5 us$ 9 ! manufacture ( a resi/ance coil1 x is necess>y t ! alloy %\ld be ag$ by heat+ x to a temp]ature ( #adj ,c4 = t5 h\rs2 & to prev5t subsequ5t *anges 9 resi/ivity1 sold]s conta9+ z9c mu/ be avoid$1 & a silv] sold] conta9+ #ge ( silv] employ$ 9 sold]+ ! mangan9 wire to its connexions4 ,! au?orities ( ! ,b]l9 ,rei*san/alt h devot$ consid]able att5tion to ! "q ( ! be/ =m = a wire /&>d ( electric resi/ance4 ,9 t n[ adopt$ ! resi/ance wire is c>efully insulat$ & w\nd on a brass cyl9d]1 be+ d\bl$ on itself to annul inductance z mu* z possible4 ,9 ! coil two wires are w\nd on 9 p>allel1 "o be+ mu* f9] ?an ! o!r1 & ! f9al adju/m5t ( ! coil to an exact value is made by %ort5+ ! f9] ( ! two4 ,a /&>d ( resi/ance = use 9 a laboratory n[ g5]ally consi/s ( a wire ( mangan9 or plat9um-silv] c>efully insulat$ & enclos$ 9 a brass case4 ,?ick copp] rods are connect$ to ! t]m9als ( ! wire 9 ! int]ior ( ! case1 & br\ght to ! outside1 be+ c>efully insulat$ at ! same "t f "o ano!r & f ! case4 ,! coil s con/ruct$ c be plac$ "u wat] or p>aff9 oil1 ! temp]ature ( :i* c be exactly obs]v$ dur+ ! process ( tak+ a resi/ance measurem5t4 ,equalization ( ! temp]ature ( ! surr\nd+ m$ium is effect$ by ! employm5t ( a /irr]1 work$ by h& or by a small electric motor4 ,! con/ruction ( a /&>d ( electrical resi/ance consi/+ ( m]cury 9 a glass tube is an op]ation requir+ consid]able precautions1 & only to be und]tak5 by ^? exp]i5c$ 9 ! matt]4 ,op9ions are divid$ on ! "q :e!r great] p]man5ce 9 resi/ance c be secur$ by m]cury-9-glass /&>ds ( resi/ance or by wire /&>ds1 b ! latt] are at lea/ m portable & less fragile4 ,a full description ( ! con/ruction ( a /&>d wire-resi/ance coil on ! plan adopt$ by ! ,b]l9 ,physikalis*-,te*nis*e ,rei*san/alt is giv5 9 ! ,report ( ! ,briti% ,association ,committee on ,electrical ,/&>ds1 pres5t$ at ! ,ed9burgh ,meet+ 9 #ahib4 ,= ! design & con/ruction ( /&>ds ( electric resi/ances adapt$ = employm5t 9 ! comp>ison & measurem5t ( v l[ or v high resi/ances1 ! read] may be ref]r$ to /&>d treatises on electric measurem5ts4 ,,bibliography4--,see also ,j4 ,a4 ,flem+1 ,a ,h&book = ! ,electrical ,laboratory & ,te/+ ,room1 vol4 i4 7,london1 #aija72 ,reports ( ! ,briti% ,association ,committee on ,electrical ,/&>ds1 edit$ by ,fleem+ ,j5k9 7,london1 #ahgc72 ,a4 ,mat?iess5 & ,c4 ,vogt1 ,on ! ,influ5ce ( ,temp]ature on ! ,conduct+ ,p[] ( ,alloys1 ,phil4 ,trans41 #ahfd1 #aed1 p4 #afg1 & ,phil4 ,mag41 #ahfe1 #bi1 p4 #cfc2 ,a4 ,mat?iess5 & ,m4 ,holtzmann1 ,on ! ,effect ( ! ,pres5ce ( ,metals & ,metalloids ^u ! ,electric ,conduct+ ,p[] ( ,pure ,copp]1 ,phil4 ,trans41 #ahfj1 #aej1 p4 #he2 ,t4 ,c4 ,fitzpatrick1 ,on ! ,specific ,resi/ance ( ,copp]1 ,brit4 ,assoc4 ,report1 #ahij1 p4 #abj1 or ,electrician1 #ahij1 #be1 p4 #fjh2 ,r4 ,appley>d1 ,! ,conductomet] & ,electrical ,conductivity2 ,cl>k1 ,=de & ,taylor1 ,temp]ature ,coeffici5ts ( ,copp] 7,london1 #aija74 7,j4 ,a4 ,f47 ,,ii4 ,,conduction ,,9 ,,liquids ,?r\gh liquid metals1 su* z m]cury at ord9>y temp]atures & o!r metals at temp]atures above _! melt+ po9ts1 ! electric curr5t fl[s z 9 solid metals )\t *ang+ ! /ate ( ! conductor1 except 9 s f> z heat is develop$ by ! electric resi/ance4 ,b ano!r class ( liquid conductors exi/s1 & 9 !m ! ph5om5a are q diff]5t4 ,! conductivity ( fus$ salts1 & ( solutions ( salts & acids1 al?\gh less ?an t ( metals1 is v great comp>$ ) ! traces ( conductivity f\nd 9 s-call$ non-conductors4 ,9 fus$ salts & conduct+ solutions ! passage ( ! curr5t is always accompani$ by def9ite *emical *anges2 ! sub/ance ( ! conductor or electrolyte is decompos$1 & ! products ( ! decomposition appe> at ! electrodes1 i4e4 ! metallic plates by means ( :i* ! curr5t is l$ into & out ( ! solution4 ,! *emical ph5om5a are consid]$ 9 ! article ,,electrolysis2 we are "h conc]n$ solely ) ! me*anism ( ?is electrolytic conduction ( ! curr5t4 ,to expla9 ! appe>ance ( ! products ( decomposition at ! electrodes only1 :ile ! int]v5+ solution is unalt]$1 we suppose t1 "u ! action ( ! electric =ces1 ! opposite p>ts ( ! electrolyte move 9 opposite directions ?r\gh ! liquid4 ,^! opposite p>ts1 nam$ ions by ,f>aday1 mu/ !re=e be associat$ ) electric *>ges1 & x is ! convective movem5t ( ! opposite /reams ( ions c>ry+ _! *>ges ) !m t1 on ?is view1 con/itutes ! electric curr5t4 ,9 metallic conduction x is f\nd t ! curr5t is proportional to ! appli$ electromotive =ce--a relation kn[n by ! "n ( ,ohm's law4 ,if we place 9 a circuit ) a small electromotive =ce an electrolytic cell consi/+ ( two plat9um electrodes & a solution1 ! initial curr5t soon dies away1 & we %all f9d t a c]ta9 m9imum electromotive =ce mu/ be appli$ to ! circuit be=e any consid]able p]man5t curr5t passes4 ,! *emical *anges :i* are initiat$ on ! surfaces ( ! electrodes set up a rev]se electromotive =ce ( pol>ization1 &1 until ?is is ov]come1 only a m9ute curr5t1 probably due to ! sl[ b /eady removal ( ! products ( decomposition f ! electrodes by a process ( diffusion1 w pass ?r\gh ! cell4 ,?us x is evid5t t1 consid]+ ! electrolytic cell z a :ole1 ! passage ( ! curr5t ?r\gh x _c con=m to ,ohm's law4 ,b ! pol>ization is due to *emical *anges1 :i* are conf9$ to ! surfaces ( ! electrodes2 & x is necess>y to inquire :e!r1 if ! pol>ization at ! electrodes be elim9at$1 ! passage ( ! curr5t ?r\gh ! bulk ( ! solution itself is proportional to ! electromotive =ce actually appli$ to t solution4 ,r\gh exp]im5t %[s t ! curr5t is proportional to ! excess ( ! electromotive =ce ov] a con/ant value1 & ?us v]ifies ! law approximately1 ! con/ant electromotive =ce to be ov]come be+ a measure ( ! pol>ization4 ,a m satisfactory exam9ation ( ! "q 0 made by ,f4 ,kohlraus* 9 ! ye>s #ahgc to #ahgf4 ,ohm's law /ates t ! curr5t ,c is proportional to ! electromotive =ce ,e1 or ,c k,r1 :]e k is a con/ant call$ ! conductivity ( ! circuit4 ,! equation may also be writt5 z ,c ,e_/,r1 :]e ,r is a con/ant1 ! reciprocal ( k1 kn[n z ! resi/ance ( ! circuit4 ,! ess5ce ( ! law is ! proportionality betwe5 ,c & ,e1 :i* means t ! ratio ,e_/,c is a con/ant4 ,b ,e_/,c ,r1 & ?us ! law may be te/$ by exam9+ ! con/ancy ( ! measur$ resi/ance ( a conductor :5 diff]5t curr5ts are pass+ ?r\gh x4 ,9 ?is way ,ohm's law has be5 confirm$ 9 ! case ( metallic conduction to a v high degree ( accuracy4 ,a simil> pr9ciple 0 appli$ by ,kohlraus* to ! case ( electrolytes1 & he 0 ! fir/ to %[ t an electrolyte possesses a def9ite resi/ance :i* has a con/ant value :5 measur$ ) diff]5t curr5ts & by diff]5t exp]im5tal me?ods4 ,measurem5t ( ! ,resi/ance ( ,electrolytes4--,!re are two effects ( ! passage ( an electric curr5t :i* prev5t ! possibility ( measur+ electrolytic resi/ance by ! ord9>y me?ods ) ! direct curr5ts :i* are us$ 9 ! case ( metals4 ,! products ( ! *emical decomposition ( ! electrolyte appe> at ! electrodes & set up ! oppos+ electromotive =ce ( pol>ization1 & unequal dilution ( ! solution may occur 9 ! neighb\rhood ( ! two electrodes4 ,! *emical & electrolytic aspects ( ^! ph5om5a are treat$ 9 ! article ,,electrolysis1 b f our pres5t po9t ( view also x is evid5t t !y are aga9 ( fundam5tal importance4 ,! pol>ization at ! surface ( ! electrodes w set up an oppos+ electromotive =ce1 & ! unequal dilution ( ! solution w turn ! electrolyte into a conc5tration cell & produce a subsidi>y electromotive =ce ei!r 9 ! same direction z t appli$ or 9 ! rev]se accord+ z ! anode or ! ca?ode solution becomes ! m dilute4 ,bo? effects ?us involve int]nal electromotive =ces1 & prev5t ! application ( ,ohm's law to ! electrolytic cell z a :ole4 ,b ! exi/5ce ( a def9ite measurable resi/ance z a *>act]i/ic prop]ty ( ! sy/em dep5ds on ! con=mity ( ! sy/em to ,ohm's law1 & x is !re=e necess>y to elim9ate bo? ^! effects be=e attempt+ to measure ! resi/ance4 ,! usual & mo/ satisfactory me?od ( measur+ ! resi/ance ( electrolytes consi/s 9 elim9at+ ! effects ( pol>ization by ! use ( alt]nat+ curr5ts1 t is1 curr5ts t are rev]s$ 9 direction _m times a second4#aa ,! *emical action produc$ by ! fir/ curr5t is ?us rev]s$ by ! second curr5t 9 ! opposite direction1 & ! pol>ization caus$ by ! fir/ curr5t on ! surface ( ! electrodes is de/roy$ be=e x rises to an appreciable value4 ,! pol>ization is also dim9i%$ 9 ano!r way4 ,! electromotive =ce ( pol>ization is due to ! deposition ( films ( ! products ( *emical decomposition on ! surface ( ! electrodes1 & only rea*es its full value :5 a cont9u\s film is =m$4 ,if ! curr5t be /opp$ be=e su* a film is complet$1 ! rev]se electromotive =ce is less ?an its full value4 ,a giv5 curr5t fl[+ = a giv5 "t deposits a def9ite am\nt ( sub/ance on ! electrodes1 & !re=e ! am\nt p] unit area is inv]sely proportional to ! area ( ! electrodes--to ! area ( contact1 t is1 betwe5 ! electrode & ! liquid4 ,?us1 by increas+ ! area ( ! electrodes1 ! pol>ization due to a giv5 curr5t is decreas$4 ,n[ ! area ( free surface ( a plat9um plate c be increas$ enorm\sly by coat+ ! plate ) plat9um black1 :i* is metallic plat9um 9 a spongy /ate1 & ) su* a plate z electrode ! effects ( pol>ization are dim9i%$ to a v m>k$ ext5t4 ,! coat+ is effect$ by pass+ an electric curr5t fir/ "o way & !n ! o!r betwe5 two plat9um plates imm]s$ 9 a #c solution ( plat9um *loride to :i* a trace ( lead acetate is sometimes add$4 ,! plat9iz$ plates ?us obta9$ are q satisfactory = ! inve/igation ( /rong solutions4 ,!y h ! p[]1 h[ev]1 ( absorb+ a c]ta9 am\nt ( salt f ! solutions & ( giv+ x up aga9 :5 wat] or m dilute solution is plac$ 9 contact ) !m4 ,! measurem5t ( v dilute solutions is ?us made difficult1 b1 if ! plates be heat$ to r$ness aft] be+ plat9iz$1 a grey surface is obta9$ :i* possesses suffici5t area = use ) dilute solutions & yet does n absorb an appreciable quantity ( salt4 ,any conv5i5t s\rce ( alt]nat+ curr5t may be us$4 ,! curr5ts f ! second>y circuit ( a small induction coil are satisfactory1 or ! curr5ts ( an alt]nat+ electric light supply may be trans=m$ d[n to an electromotive =ce ( "o or two volts4 ,) su* curr5ts x is necess>y to consid] ! effects ( self-induction 9 ! circuit & ( electro/atic capacity4 ,9 balanc+ ! resi/ance ( ! electrolyte1 resi/ance coils may be us$ 9 :i* self-induction & ! capacity are r$uc$ to a m9imum by w9d+ ! wire ( ! coil backw>ds & =w>ds 9 alt]nate lay]s4 ,illu/ration3 ,,fig4 #a4 ,) ^! arrangem5ts ! usual me?od ( measur+ resi/ance by means ( ,:eat/one's bridge may be adapt$ to ! case ( electrolytes4 ,) alt]nat+ curr5ts1 h[ev]1 x is impossible to use a galvanomet] 9 ! usual way4 ,! galvanomet] 0 !re=e replac$ by ,kohlraus* by a telephone1 :i* gives a s\nd :5 an alt]nat+ curr5t passes ?r\gh x4 ,! mo/ common plan ( ! app>atus is %[n diagrammatically 9 fig4 #a4 ,! electrolytic cell & a resi/ance box =m two arms ( ! bridge1 & ! slid+ contact is mov$ along ! metre wire :i* =ms ! o!r two arms till no s\nd is he>d 9 ! telephone4 ,! resi/ance ( ! electrolyte is to t ( ! box z t ( ! "r-h& end ( ! wire is to t ( ! left-h& end4 ,a m accurate me?od ( us+ alt]nat+ curr5ts1 & "o m pleasant to use1 gets rid ( ! telephone 7,phil4 ,trans41 #aijj1 #aid1 p4 #cba74 ,! curr5t f "o or two voltaic cells is l$ to an ebonite drum turn$ by a motor or a h&-:eel & cord4 ,on ! drum are fix$ brass /rips ) wire bru%es t\*+ !m 9 su* a mann] t ! curr5t f ! bru%es is rev]s$ sev]al times 9 ea* revolution ( ! drum4 ,! wires f ! bru%es are connect$ ) ! ,:eat/one's bridge4 ,a mov+ coil galvanomet] is us$ z indicator1 its connexions be+ rev]s$ 9 "t ) ^? ( ! batt]y by a slightly n>r[] set ( brass /rips fix$ on ! o!r end ( ! ebonite commutator4 ,?us any residual curr5t ?r\gh ! galvanomet] is direct & n alt]nat+4 ,! high mom5t ( in]tia ( ! coil makes ! p]iod ( sw+ sl[ comp>$ ) ! p]iod ( alt]nation ( ! curr5t1 & ! slight p]iodic di/urbances are ?us prev5t$ f affect+ ! galvanomet]4 ,:5 ! measur$ resi/ance is n alt]$ by increas+ ! spe$ ( ! commutator or *ang+ ! ratio ( ! arms ( ! bridge1 ! di/urb+ effects may be consid]$ to be elim9at$4 ,illu/ration3 ,,fig4 #b4 ,illu/ration3 ,,fig4 #c4 ,! =m ( vessel *os5 to conta9 ! electrolyte dep5ds on ! ord] ( resi/ance to be measur$4 ,= dilute solutions ! %ape ( cell %[n 9 fig4 #b w be f\nd conv5i5t1 :ile = m conc5trat$ solutions1 t indicat$ 9 fig4 #c is suitable4 ,! absolute resi/ances ( c]ta9 solutions h be5 det]m9$ by ,kohlraus* by comp>ison ) m]cury1 &1 by us+ "o ( ^! solutions 9 any cell1 ! con/ant ( t cell may be f\nd once = all4 ,f ! obs]v$ resi/ance ( any giv5 solution 9 ! cell ! resi/ance ( a c5timetre cube--! s-call$ specific resi/ance--may be calculat$4 ,! reciprocal ( ?is1 or ! conductivity1 is a m g5]ally useful con/ant2 x is conv5i5tly express$ 9 t]ms ( a unit equal to ! reciprocal ( an ohm4 ,?us ,kohlraus* f\nd t a solution ( potassium *loride1 conta9+ "o-t5? ( a gram equival5t 7#g4df grams7 p] litre1 has at #ah ,c4 a specific resi/ance ( #hi4cg ohms p] c5timetre cube1 or a conductivity ( #a4aai #aj-b mhos or #a4aai #aj-aa ,c4,g4,s4 units4 ,z ! temp]ature v>iation ( conductivity is l>ge1 usually ab\t #b p] degree1 x is necess>y to place ! resi/ance cell 9 a p>aff9 or wat] ba?1 & to obs]ve its temp]ature ) "s accuracy4 ,ano!r way ( elim9at+ ! effects ( pol>ization & ( dilution has be5 us$ by ,w4 ,/r\d & ,j4 ,b4 ,h5d]son 7,phil4 ,mag41 #ahig #e1 #dc1 p4 #ai74 ,two ( ! arms ( a ,:eat/one's bridge are compos$ ( n>r[ tubes fill$ ) ! solution1 ! tubes be+ ( equal diamet] b ( diff]5t l5g?4 ,! o!r two arms are made ( coils ( wire ( equal resi/ance1 & metallic resi/ance is add$ to ! %ort] tube till ! bridge is balanc$4 ,direct curr5ts ( some:at high electromotive =ce are us$ to "w ! bridge4 ,equal curr5ts !n fl[ ?r\gh ! two tubes2 ! effects ( pol>ization & dilution mu/ be ! same 9 ea*1 & ! resi/ance add$ to ! %ort] tube mu/ be equal to ! resi/ance ( a column ( liquid ! l5g? ( :i* is equal to ! diff]5ce 9 l5g? ( ! two tubes4 ,a some:at diff]5t pr9ciple 0 adopt$ by ,e4 ,b\ty 9 #ahhd4 ,if a curr5t be pass$ ?r\gh two resi/ances 9 s]ies by means ( an appli$ electromotive =ce1 ! electric pot5tial falls f "o end ( ! resi/ances to ! o!r1 &1 if we apply ,ohm's law to ea* resi/ance 9 succession1 we see t1 s9ce = ea* ( !m ,e ,,cr1 & ,c ! curr5t is ! same ?r\gh bo?1 ,e ! electromotive =ce or fall ( pot5tial betwe5 ! ends ( ea* resi/ance mu/ be proportional to ! resi/ance betwe5 !m4 ,?us by measur+ ! pot5tial diff]5ce betwe5 ! ends ( ! two resi/ances successively1 we may comp>e _! resi/ances4 ,if1 on ! o!r h&1 we c measure ! pot5tial diff]5ce 9 "s kn[n units1 & simil>ly measure ! curr5t fl[+1 we c det]m9e ! resi/ance ( a s+le electrolyte4 ,! details ( ! app>atus may v>y1 b its pr9ciple is illu/rat$ 9 ! foll[+ description4 ,a n>r[ glass tube is fix$ horizontally into side op5+s 9 two glass vessels1 & an electric curr5t pass$ ?r\gh x by means ( plat9um electrodes & a batt]y ( consid]able electromotive =ce4 ,9 ?is way a /eady fall ( electric pot5tial is set up along ! l5g? ( ! tube4 ,to measure ! pot5tial diff]5ce betwe5 ! ends ( ! tube1 tapp+ electrodes are con/ruct$1 e4g4 by plac+ z9c rods 9 vessels ) z9c sulphate solution & connect+ ^! vessels 7by means ( ?9 siphon tubes also fill$ ) solution7 ) ! vessels at ! ends ( ! long tube :i* conta9s ! electrolyte to be exam9$4 ,:atev] be ! contact pot5tial diff]5ce betwe5 z9c & its solution1 x is ! same at bo? ends1 & ?us ! pot5tial diff]5ce betwe5 ! z9c rods is equal to t betwe5 ! liquid at ! two ends ( ! tube4 ,?is pot5tial diff]5ce may be measur$ )\t pass+ any appreciable curr5t ?r\gh ! tapp+ electrodes1 & ?us ! resi/ance ( ! liquid d$uc$4 ,equival5t ,conductivity ( ,solutions4--,z is ! case 9 ! o!r prop]ties ( solutions1 ! ph5om5a are mu* m simple :5 ! conc5tration is small ?an :5 x is great1 & a /udy ( dilute solutions is !re=e ! be/ way ( gett+ an insight into ! ess5tial pr9ciples ( ! subject4 ,! f\ndation ( our k 0 laid by ,kohlraus* :5 he _h develop$ ! me?od ( measur+ electrolyte resi/ance describ$ above4 ,he express$ 8 results 9 t]ms ( equival5t conductivity1 t is1 ! conductivity 7k7 ( ! solution divid$ by ! numb] 7m7 ( gram-equival5ts ( electrolyte p] litre4 ,he f9ds t1 z ! conc5tration dim9i%es1 ! value ( k_/m approa*es a limit1 & ev5tually becomes con/ant1 t is to say1 at great dilution ! conductivity is proportional to ! conc5tration4 ,kohlraus* fir/ prep>$ v pure wat] by repeat$ di/illation & f\nd t its resi/ance cont9ually increas$ z ! process ( purification proce$$4 ,! conductivity ( ! wat]1 & ( ! slight impurities :i* mu/ always rema91 0 subtract$ f t ( ! solution made ) x1 & ! result1 divid$ by m1 gave ! equival5t conductivity ( ! sub/ance dissolv$4 ,?is proc$ure appe>s ju/ifiable1 = z long z conductivity is proportional to conc5tration x is evid5t t ea* "p ( ! dissolv$ matt] produces its own indep5d5t effect1 s t ! total conductivity is ! sum ( ! conductivities ( ! p>ts2 :5 ?is ceases to hold1 ! conc5tration ( ! solution has 9 g5]al become s great t ! conductivity ( ! solv5t may be neglect$4 ,! g5]al result ( ^! exp]im5ts c be repres5t$ graphically by plott+ k_/m z ord9ates & root #cm z abscissae1 root #cm be+ a numb] proportional to ! reciprocal ( ! av]age di/ance betwe5 ! molecules1 to :i* x seems likely t ! molecul> conductivity may be relat$4 ,! g5]al types ( curve = a simple neutral salt l potassium or sodium *loride & = a cau/ic alkali or acid are %[n 9 fig4 #d4 ,! curve = ! neutral salt comes to a limit+ value2 t = ! acid atta9s a maximum at a c]ta9 v small conc5tration1 & falls aga9 :5 ! dilution is c>ri$ f>!r4 ,x has usually be5 consid]$ t ?is de/ruction ( conductivity is due to *emical action betwe5 ! acid & ! residual impurities 9 ! wat]4 ,at su* great dilution ^! impurities are pres5t 9 quantities comp>able ) ! am\nt ( acid :i* !y conv]t into a less highly conduct+ neutral salt4 ,9 ! case ( acids1 !n1 ! maximum mu/ be tak5 z ! limit+ value4 ,! decrease 9 equival5t conductivity at great dilution is1 h[ev]1 s con/ant t ?is explanation seems insuffici5t4 ,! true cause ( ! ph5om5on may p]haps be connect$ ) ! fact t ! bodies 9 :i* x occurs1 acids & alkalis1 conta9 ! ions1 hydrog5 9 ! "o case1 hydroxyl 9 ! o!r1 :i* are pres5t 9 ! solv5t1 wat]1 & h1 p]haps because ( ?is relation1 velocities high] ?an ^? ( any o!r ions4 ,! values ( ! molecul> conductivities ( all neutral salts are1 at great dilution1 ( ! same ord] ( magnitude1 :ile ^? ( acids at _! maxima are ab\t ?ree times z l>ge4 ,! influ5ce ( increas+ conc5tration is great] 9 ! case ( salts conta9+ dival5t ions1 & greate/ ( all 9 su* cases z solutions ( ammonia & acetic acid1 :i* are sub/ances ( v l[ conductivity4 ,illu/ration3 ,,fig4 #d4 ,!ory ( ,mov+ ,ions4--,kohlraus* f\nd t1 :5 ! pol>ization at ! electrodes 0 elim9at$1 ! resi/ance ( a solution 0 con/ant h[ev] det]m9$1 & ?us e/abli%$ ,ohm's ,law = electrolytes4 ,! law 0 confirm$ 9 ! case ( /rong curr5ts by ,g4 ,f4 ,fitzg]ald & ,f4 ,t4 ,tr\ton 7,b4,a4 ,report1 #ahhf1 p4 #cab74 ,n[1 ,ohm's ,law implies t no "w is done by ! curr5t 9 ov]com+ rev]sible electromotive =ces su* z ^? ( pol>ization4 ,?us ! molecul> int]*ange ( ions1 :i* mu/ occur 9 ord] t ! products may be able to "w _! way ?r\gh ! liquid & appe> at ! electrodes1 cont9ues ?r\gh\t ! solution :e!r a curr5t is fl[+ or n4 ,! influ5ce ( ! curr5t on ! ions is m]ely directive1 &1 :5 x fl[s1 /reams ( electrifi$ ions travel 9 opposite directions1 &1 if ! appli$ electromotive =ce is en\gh to ov]come ! local pol>ization1 give up _! *>ges to ! electrodes4 ,we may !re=e repres5t ! facts by consid]+ ! process ( electrolysis to be a k9d ( convection4 ,f>aday's classical exp]im5ts prov$ t :5 a curr5t fl[s ?r\gh an electrolyte ! quantity ( sub/ance lib]at$ at ea* electrode is proportional to its *emical equival5t weight1 & to ! total am\nt ( electricity pass$4 ,accurate det]m9ations h s9ce %[n t ! mass ( an ion deposit$ by "o electromagnetic unit ( electricity1 i4e4 its electro-*emical equival5t1 is #a4jcf #aj-d its *emical equival5t weight4 ,?us ! am\nt ( electricity associat$ ) "o gram-equival5t ( any ion is #ajd_/a4jcf #ifec units4 ,ea* monoval5t ion mu/ !re=e be associat$ ) a c]ta9 def9ite *>ge1 :i* we may take to be a natural unit ( electricity2 a dival5t ion c>ries two su* units1 & s on4 ,a cation1 i4e4 an ion giv+ up its *>ge at ! ca?ode1 z ! electrode at :i* ! curr5t leaves ! solution is call$1 c>ries a positive *>ge ( electricity2 an anion1 travell+ 9 ! opposite direction1 c>ries a negative *>ge4 ,x w n[ be se5 t ! quantity ( electricity fl[+ p] second1 i4e4 ! curr5t ?r\gh ! solution1 dep5ds on 7#a7 ! numb] ( ! ions conc]n$1 7#b7 ! *>ge on ea* ion1 & 7#c7 ! velocity ) :i* ! ions travel pa/ ea* o!r4 ,n[1 ! numb] ( ions is giv5 by ! conc5tration ( ! solution1 = ev5 if all ! ions are n actively engag$ 9 c>ry+ ! curr5t at ! same in/ant1 !y mu/1 on any dynamical idea ( *emical equilibrium1 be all active 9 turn4 ,! *>ge on ea*1 z we h se51 c be express$ 9 absolute units1 & !re=e ! velocity ) :i* !y move pa/ ea* o!r c be calculat$4 ,?is 0 fir/ done by ,kohlraus* 7,gtt+5 ,na*ri*t51 #ahgf1 p4 #bac1 & ,das ,leitv]mg5 d] ,elektrolyte1 ,leipzig1 #ahih7 ab\t #ahgi4 ,9 ord] to develop ,kohlraus*'s !ory1 let u take1 z an example1 ! case ( an aque\s solution ( potassium *loride1 ( conc5tration n gram-equival5ts p] cubic c5timetre4 ,!re w !n be n gram-equival5ts ( potassium ions & ! same numb] ( *lor9e ions 9 ?is volume4 ,let u suppose t on ea* gram-equival5t ( potassium !re reside e units ( electricity1 & on ea* gram-equival5t ( *lor9e ions -e units4 ,if u d5otes ! av]age velocity ( ! potassium ion1 ! positive *>ge c>ri$ p] second across unit area normal to ! fl[ is n e u4 ,simil>ly1 if v be ! av]age velocity ( ! *lor9e ions1 ! negative *>ge c>ri$ 9 ! opposite direction is n e v4 ,b positive electricity mov+ 9 "o direction is equival5t to negative electricity mov+ 9 ! o!r1 s t1 be=e *anges 9 conc5tration s5sibly sup]v5e1 ! total curr5t1 ,c1 is ne7u v74 ,n[ let u consid] ! am\nts ( potassium & *lor9e lib]at$ at ! electrodes by ?is curr5t4 ,at ! ca?ode1 if ! *lor9e ions 7 at re/1 ! excess ( potassium ions w\ld be simply ^? arriv+ 9 "o second1 namely1 nu4 ,b s9ce ! *lor9e ions move also1 a fur!r sep>ation occurs1 & nv potassium ions are left )\t p>tn]s4 ,! total numb] ( gram-equival5ts lib]at$ is !re=e n7u v74 ,by ,f>aday's law1 ! numb] ( grams lib]at$ is equal to ! product ( ! curr5t & ! electro-*emical equival5t ( ! ion2 ! numb] ( gram-equival5ts !re=e mu/ be equal to eta,c1 :]e eta d5otes ! electro-*emical equival5t ( hydrog5 9 ,c4,g4,s4 units4 ,?us we get n7u v7 eta,c etane7u v71 & x foll[s t ! *>ge1 e1 on #a gram-equival5t ( ea* k9d ( ion is equal to #a_/;eta4 ,we "k t ,ohm's ,law holds good = electrolytes1 s t ! curr5t ,c is also giv5 by kd,p_/dx1 :]e k d5otes ! conductivity ( ! solution1 & d,p_/dx ! pot5tial gradi5t1 i4e4 ! *ange 9 pot5tial p] unit l5g? along ! l9es ( curr5t fl[4 ,?us n -----7u v7 kd,p_/dx2 eta !re=e k d,p u v eta - --4 n dx ,n[ eta is #a4jcf #aj-d1 & ! conc5tration ( a solution is usually express$ 9 t]ms ( ! numb]1 m1 ( gram-equival5ts p] litre in/ead ( p] cubic c5timetre4 ,!re=e k d,p u v #a4jcf #aj-a - -- --4 m dx ,:5 ! pot5tial gradi5t is "o volt 7#ajh ,c4,g4,s4 units7 p] c5timetre ?is becomes u v #a4jcf #aj-g k_/m4 ,?us by measur+ ! value ( k_/m1 :i* is kn[n z ! equival5t conductivity ( ! solution1 we c f9d u v1 ! velocity ( ! ions relative to ea* o!r4 ,= in/ance1 ! equival5t conductivity ( a solution ( potassium *loride conta9+ "o-t5? ( a gram-equival5t p] litre is #aaai #aj-ac ,c4,g4,s4 units at #ah ,c4 ,!re=e u v #a4jcf #ajg #aaai #aj-ac #a4aei #aj-c #j4jjaaei cm4 p] sec4 ,9 ord] to obta9 ! absolute velocities u & v1 we mu/ f9d "s o!r relation betwe5 !m4 ,let u resolve u into 7u v7 9 "o direction1 say to ! "r1 & 7u - v7 to ! left4 ,simil>ly v c be resolv$ into 7vu7 to ! left & 7v-u7 to ! "r4 ,on pair+ ^! velocities we h a comb9$ movem5t ( ! ions to ! "r1 ) a spe$ ( 7u - v7 & a drift "r & left1 pa/ ea* o!r1 ea* ion travell+ ) a spe$ ( 7u v71 con/itut+ ! electrolytic sep>ation4 ,if u is great] ?an v1 ! comb9$ movem5t involves a conc5tration ( salt at ! ca?ode1 & a correspond+ dilution at ! anode1 & vice v]sa4 ,! rate at :i* salt is electrolys$1 & ?us remov$ f ! solution at ea* electrode1 is 7u v74 ,?us ! total loss ( salt at ! ca?ode is 7u v7 - 7u - v7 or v1 & at ! anode1 7v u7 - 7v - u71 or u4 ,!re=e1 z is expla9$ 9 ! article ,,electrolysis1 by measur+ ! dilution ( ! liquid r\nd ! electrodes :5 a curr5t pass$1 ,w4 ,hittorf 7,pogg4 ,ann41 #ahec-ahei1 #hi1 p4 #agg2 #ih1 p4 #a2 #ajc1 p4 #a2 #ajf1 pp4 #ccg & #eac7 0 able to d$uce ! ratio ( ! two velocities1 = simple salts :5 no complex ions are pres5t1 & _m fur!r exp]im5ts h be5 made on ! subject 7see ,das ,leitv]mg5 d] ,elektrolyte74 ,by comb9+ ! results ?us obta9$ ) ! sum ( ! velocities1 z det]m9$ f ! conductivities1 ,kohlraus* calculat$ ! absolute velocities ( diff]5t ions "u /at$ conditions4 ,?us1 9 ! case ( ! solution ( potassium *loride consid]$ above1 ,hittorf's exp]im5ts %[ u t ! ratio ( ! velocity ( ! anion to t ( ! cation 9 ?is solution is 4#ea 3 4#di4 ,! absolute velocity ( ! potassium ion "u unit pot5tial gradi5t is !re=e #j4jjjefg cm4 p] sec41 & t ( ! *lor9e ion #j4jjjeib cm4 p] sec4 ,simil> calculations c be made = solutions ( o!r conc5trations1 & ( diff]5t sub/ances4 ,table ,,ix4 %[s ,kohlraus*'s values = ! ionic velocities ( ?ree *lorides ( alkali metals at #ah ,c1 calculat$ = a pot5tial gradi5t ( #a volt p] cm42 ! numb]s are 9 t]ms ( a unit equal to #aj-f cm4 p] sec43-- ,,table ,,ix4 ---------------------------------------- -------------------- ,k,cl ,na,cl ,li,cl ---------------------------------------- ------------------ m u v u v u v u v u v u v ---------------------------------------- ------------------ #j #acej #ffj #fij #aadj #dej #fij #ajej #cfj #fij #j4jjja #acce #fed #fha #aabi #ddh #fha #ajcg #cef #fha 4#jja #acac #fdc #fgj #aaaj #ddj #fgj #ajac #cdc #fgj 4#ja #abfc #fai #fdd #ajei #dae #fdd #ifb #cah #fdd 4#jc #abah #eig #fba #ajac #cij #fbc #iag #bih #fai 4#a #aaec #efd #ehi #ieb #cfj #eib #hec #bei #eid 4#c #ajhh #eca #eeg #hgf #cbd #eeb #ggd #bag #eeg #a4j #ajaa #dia #ebj #gfe #bgh #dhg #fea #afi #dhb #c4j #iaa #ddb #dfi #ehb #bjf #cgf #dfc #aae #cdh #e4j #dch #aec #bhe #ccd #hj #bed #aj4j #aag #be #ib ---------------------------------------- ------------------ ,^! numb]s %[ cle>ly t !re is an increase 9 ionic velocity z ! dilution proce$s4 ,moreov]1 if we comp>e ! values = ! *lor9e ion obta9$ f obs]vations on ^! ?ree diff]5t salts1 we see t z ! conc5trations dim9i% ! velocity ( ! *lor9e ion becomes ! same 9 all ( !m4 ,a simil> relation appe>s 9 o!r cases1 &1 9 g5]al1 we may say t at great dilution ! velocity ( an ion is indep5d5t ( ! nature ( ! o!r ion pres5t4 ,?is introduces ! conception ( specific ionic velocities1 = :i* "s values at #ah ,c4 are giv5 by ,kohlraus* 9 ,table ,x43-- ,table ,x4 ------------------------------------ ,k #ff #aj-e cms4 p] sec4 ,na #de ,li #cf ,,nh#d #ff ,h #cbj ,ag #eg ,cl #fi ,i #fi ,,no#c #fd ,,oh #afb ,c#b;,h#c,o#b #cf ,c#c;,h#e,o#b #cc ------------------------------------ ,hav+ obta9$ ^! numb]s we c d$uce ! conductivity ( ! dilute solution ( any salt1 & ! comp>ison ( ! calculat$ ) ! obs]v$ values furni%$ ! fir/ confirmation ( ,kohlraus*'s !ory4 ,"s exceptions1 h[ev]1 are kn[n4 ,?us acetic acid & ammonia give solutions ( mu* l[] conductivity ?an is indicat$ by ! sum ( ! specific ionic velocities ( _! ions z det]m9$ f o!r comp\nds4 ,an attempt to f9d 9 ,kohlraus*'s !ory "s explanation ( ?is discrepancy %[s t x c\ld be due to "o ( two causes4 ,ei!r ! velocities ( ! ions mu/ be mu* less 9 ^! solutions ?an 9 o!rs1 or else only a fractional "p ( ! numb] ( molecules pres5t c be actively conc]n$ 9 convey+ ! curr5t4 ,we %all return to ?is po9t lat]4 ,friction on ! ,ions4--,x is int]e/+ to calculate ! magnitude ( ! =ces requir$ to drive ! ions ) a c]ta9 velocity4 ,if we h a pot5tial gradi5t ( #a volt p] c5timetre ! electric =ce is #ajh 9 ,c4,g4,s4 units4 ,! *>ge ( electricity on #a gram-equival5t ( any ion is #a_/4jjjajcf #ifec units1 h5ce ! me*anical =ce act+ on ?is mass is #ifec #ajh dynes4 ,?is1 let u say1 produces a velocity u2 !n ! =ce requir$ to produce unit velocity is ,,pa #i4fec #ajaa_/u dynes #i4hd #aje_/u kilograms-weight4 ,if ! ion h an equival5t weight ,a1 ! =ce produc+ unit velocity :5 act+ on #a gram is ,p#a #i4hd #aje_/;,au kilograms-weight4 ,?us ! aggregate =ce requir$ to drive #a gram ( potassium ions ) a velocity ( #a c5timetre p] second ?r\gh a v dilute solution mu/ be equal to ! weight ( #ch million kilograms4 ,table ,,xi4 ------------------------------- ,kilograms-weight4 ------------------------------- ,,pa ,p#a ,k #ae #ajh #ch #ajf ,na #bb #ie ,li #bg #cij ,,nh#d #ae #hc ,h #c4a #caj ,ag #ag #af ,cl #ad #dj ,i #ad #aa ,,no#c #ae #be ,,oh #e4d #cb ,c#b;,h#h,o#b #bg #df ,c#c;,h#e,o#b #cj #da ------------- ----------------- ,s9ce ! ions move ) uni=m velocity1 ! frictional resi/ances br\ght into play mu/ be equal & opposite to ! driv+ =ces1 & !re=e ^! numb]s also repres5t ! ionic friction coeffici5ts 9 v dilute solutions at #ah ,c4 ,direct ,measurem5t ( ,ionic ,velocities4--,sir ,oliv] ,lodge 0 ! fir/ to directly measure ! velocity ( an ion 7,b4,a4 ,report1 #ahhf1 p4 #chi74 ,9 a horizontal glass tube connect+ two vessels fill$ ) dilute sulphuric acid he plac$ a solution ( sodium *loride 9 solid ag>-ag> jelly4 ,?is solid solution 0 made alkal9e ) a trace ( cau/ic soda 9 ord] to br+ out ! r$ col\r ( a little ph5ol-ph?ale9 add$ z indicator4 ,an electric curr5t 0 !n pass$ f "o vessel to ! o!r4 ,! hydrog5 ions f ! anode vessel ( acid 7 ?us c>ri$ along ! tube1 &1 z !y travell$1 decol\riz$ ! ph5ol-ph?ale94 ,by ?is me?od ! velocity ( ! hydrog5 ion ?r\gh a jelly solution "u a kn[n pot5tial gradi5t 0 obs]v$ to ab\t #j4jjbf cm4 p] sec1 a numb] ( ! same ord] z t requir$ by ,kohlraus*'s !ory4 ,direct det]m9ations ( ! velocities ( a few o!r ions h be5 made by ,w4 ,c4 ,d4 ,:e?am 7,phil4 ,trans4 vol4 #ahd1 ,a1 p4 #ccg2 vol4 #ahf1 ,a1 p4 #ejg2 ,phil4 ,mag41 ,octob] #ahid74 ,two solutions hav+ "o ion 9 common1 ( equival5t conc5trations1 diff]5t d5sities1 diff]5t col\rs1 & ne>ly equal specific resi/ances1 7 plac$ "o ov] ! o!r 9 a v]tical glass tube4 ,9 "o case1 = example1 dec9ormal solutions ( potassium c>bonate & potassium bi*romate 7 us$4 ,! col\r ( ! latt] is due to ! pres5ce ( ! bi*romate gr\p1 ,cr#b,o#g4 ,:5 a curr5t 0 pass$ across ! junction1 ! anions ,,co#c & ,cr#b,o#g travell$ 9 ! direction opposite to t ( ! curr5t1 & _! velocity c\ld be det]m9$ by measur+ ! rate at :i* ! col\r b\nd>y mov$4 ,simil> exp]im5ts 7 made ) alcoholic solutions ( cobalt salts1 9 :i* ! velocities ( ! ions 7 f\nd to be mu* less ?an 9 wat]4 ,! behavi\r ( ag> jelly 0 !n inve/igat$1 & ! velocity ( an ion ?r\gh a solid jelly 0 %[n to be v little less ?an 9 an ord9>y liquid solution4 ,! velocities c\ld !re=e be measur$ by trac+ ! *ange 9 col\r ( an indicator or ! =mation ( a precipitate4 ,?us dec9ormal jelly solutions ( b>ium *loride & sodium *loride1 ! latt] conta9+ a trace ( sodium sulphate1 7 plac$ 9 contact4 ,"u ! influ5ce ( an electromotive =ce ! b>ium ions mov$ up ! tube1 disclos+ _! pres5ce by ! trace ( insoluble b>ium sulphate =m$4 ,aga91 a measurem5t ( ! velocity ( ! hydrog5 ion1 :5 travell+ ?r\gh ! solution ( an acetate1 %[$ t its velocity 0 !n only ab\t ! "o-=tie? "p ( t f\nd dur+ its passage ?r\gh *lorides4 ,f ?is1 z f ! measurem5ts on alcohol solutions1 x is cle> t :]e ! equival5t conductivities are v l[ ! effective velocities ( ! ions are r$uc$ 9 ! same proportion4 ,ano!r s]ies ( direct measurem5ts has be5 made by ,orme ,masson 7,phil4 ,trans4 vol4 #aib1 ,a1 p4 #cca74 ,he plac$ ! gelat9e solution ( a salt1 potassium *loride1 = example1 9 a horizontal glass tube1 & f\nd ! rate ( migration ( ! potassium & *lor9e ions by obs]v+ ! spe$ at :i* !y 7 replac$ :5 a col\r$ anion1 say1 ! ,cr#b,o#g f a solution ( potassium bi*romate1 ent]$ ! tube at "o end1 & a col\r$ cation1 say1 ! ,cu f copp] sulphate1 at ! o!r4 ,! col\r$ ions are specifically sl[] ?an ! col\rless ions :i* !y foll[1 & 9 ?is case x foll[s t ! col\r$ solution has a high] resi/ance ?an ! col\rless4 ,= ! same curr5t1 !re=e1 ! pot5tial gradi5t is high] 9 ! col\r$ solution & l[] 9 ! col\rless "o4 ,?us a col\r$ ion :i* gets 9 front ( ! advanc+ b\nd>y f9ds itself act$ on by a small] =ce & falls back into l9e1 :ile a /raggl+ col\rless ion is pu%$ =w>d aga94 ,h5ce a %>p b\nd>y is pres]v$4 ,b4 ,d4 ,/eele has %[n t ) ^! %>p b\nd>ies ! use ( col\r$ ions is unnecess>y1 ! junction l9e be+ visible ow+ to ! diff]5ce 9 ! optical refractive indices ( two col\rless solutions4 ,once ! b\nd>y is =m$1 too1 no gelat9e is necess>y1 & ! motion c be wat*$ ?r\gh liquid aque\s solutions 7see ,r4 ,b4 ,d5ison & ,b4 ,d4 ,/eele1 ,phil4 ,trans41 #aijf74 ,all ! direct measurem5ts :i* h be5 made on simple b9>y electrolytes agree ) ,kohlraus*'s results )9 ! limits ( exp]im5tal error4 ,8 !ory1 !re=e1 probably holds good 9 su* cases1 :atev] be ! solv5t1 if ! prop] values are giv5 to ! ionic velocities1 i4e4 ! values express+ ! velocities ) :i* ! ions actually move 9 ! solution ( ! /r5g? tak51 & "u ! conditions ( ! exp]im5t4 ,if we "k ! specific velocity ( any "o ion1 we c d$uce1 f ! conductivity ( v dilute solutions1 ! velocity ( any o!r ion ) :i* x may be associat$1 a proce$+ :i* does n involve ! difficult task ( det]m9+ ! migration con/ant ( ! comp\nd4 ,?us1 tak+ ! specific ionic velocity ( hydrog5 z #j4jjjcb cm4 p] second1 we c f9d1 by det]m9+ ! conductivity ( dilute solutions ( any acid1 ! specific velocity ( ! acid radicle involv$4 ,or aga91 s9ce we "k ! specific velocity ( silv]1 we c f9d ! velocities ( a s]ies ( acid radicles at great dilution by measur+ ! conductivity ( _! silv] salts4 ,by su* me?ods ,w4 ,o/wald1 ,g4 ,br$ig & o!r obs]v]s h f\nd ! specific velocities ( _m ions bo? ( inorganic & organic comp\nds1 & exam9$ ! relation betwe5 con/itution & ionic velocity4 ,! velocity ( elem5t>y ions is f\nd to be a p]iodic function ( ! atomic weight1 simil> elem5ts ly+ on correspond+ portions ( a curve drawn to express ! relation betwe5 ^! two prop]ties4 ,su* a curve mu* resembles t giv+ ! relation betwe5 atomic weight & viscosity 9 solution4 ,= complex ions ! velocity is l>gely an additive prop]ty2 to a cont9u\s additive *ange 9 ! composition ( ! ion corresponds a cont9u\s b decreas+ *ange 9 ! velocity4 ,! foll[+ table gives ,o/wald's results = ! =mic acid s]ies3-- ,table ,,xii4 ---------------------------------------- ------------- ,velocity4 ,diff]5ce = ,,*#b4 ---------------------------------------- ------------- ,=mic acid ,,hco#b #ea4b 44 ,acetic ,h#c;,c#b,o#b #ch4c -#ab4i ,propionic ,h#e;,c#c,o#b #cd4c - #d4j ,butyric ,h#g;,c#d,o#b #cj4h - #c4e ,val]ic ,h#i;,c#e,o#b #bh4h - #b4j ,caprionic ,h#aa;,c#f,o#b #bg4d - #a4d ---------------------------------------- ------------- ,nature ( ,electrolytes4--,we h z yet said no?+ ab\t ! fundam5tal cause ( electrolytic activity1 nor consid]$ :y1 = example1 a solution ( potassium *loride is a good conductor1 :ile a solution ( sug> all[s practically no curr5t to pass4 ,all ! prec$+ acc\nt ( ! subject is1 !n1 indep5d5t ( any view we may take ( ! nature ( electrolytes1 & /&s on ! basis ( direct exp]im5t4 ,nev]!less1 ! facts consid]$ po9t to a v def9ite conclusion4 ,! specific velocity ( an ion is indep5d5t ( ! nature ( ! opposite ion pres5t1 & ?is sugge/s t ! ions !mselves1 :ile travell+ ?r\gh ! liquid1 are dissociat$ f ea* o!r4 ,fur!r evid5ce1 po9t+ 9 ! same direction1 is furni%$ by ! fact t s9ce ! conductivity is proportional to ! conc5tration at great dilution1 ! equival5t-conductivity1 & !re=e ! ionic velocity1 is indep5d5t ( x4 ,! importance ( ?is relation w be se5 by consid]+ ! alt]native to ! dissociation hypo!sis4 ,if ! ions are n p]man5tly free f ea* o!r _! mobility z p>ts ( ! dissolv$ molecules mu/ be secur$ by cont9ual int]*anges4 ,! velocity ) :i* !y "w _! way ?r\gh ! liquid mu/ !n increase z su* molecul> re>rangem5ts become m frequ5t1 & w !re=e dep5d on ! numb] ( solute molecules1 i4e4 on ! conc5tration4 ,on ?is supposition ! obs]v$ con/ancy ( velocity w\ld be impossible4 ,we %all !re=e adopt z a word+ hypo!sis ! !ory1 confirm$ by o!r ph5om5a 7see ,,electrolysis71 t an electrolyte consi/s ( dissociat$ ions4 ,x w be notic$ t nei!r ! evid5ce 9 fav\r ( ! dissociation !ory :i* is "h consid]$1 nor t describ$ 9 ! article ,,electrolysis1 requires m ?an ! effective dissociation ( ! ions f ea* o!r4 ,!y may well be connect$ 9 "s way ) solv5t molecules1 & !re are sev]al indications t an ion consi/s ( an electrifi$ "p ( ! molecule ( ! dissolv$ salt ) an att5dant atmosph]e ( solv5t r\nd x4 ,! conductivity ( a salt solution dep5ds on two factors--7#a7 ! fraction ( ! salt ioniz$2 7#b7 ! velocity ) :i* ! ions1 :5 free f ea* o!r1 move "u ! electric =ces4#ab ,:5 a solution is heat$1 bo? ^! factors may *ange4 ,! coeffici5t ( ionization usually1 ?\gh n always1 decreases2 ! specific ionic velocities increase4 ,n[ ! rate ( increase ) temp]ature ( ^! ionic velocities is v ne>ly id5tical ) ! rate ( decrease ( ! viscosity ( ! liquid4 ,if ! curves obta9$ by obs]vations at ord9>y temp]atures be c>ri$ on !y indicate a z]o ( fluidity & a z]o ( ionic velocity ab\t ! same po9t1 #ch4e ,c4 bel[ ! freez+ po9t ( wat] 7,kohlraus*1 ,sitz4 preuss4 ,akad4 ,wiss41 #aija1 #db1 p4 #ajbf74 ,su* relations sugge/ t ! frictional resi/ance to ! motion ( an ion is due to ! ord9>y viscosity ( ! liquid1 & t ! ion is analog\s to a body ( "s size urg$ ?r\gh a visc\s m$ium r ?an to a p>ticle ( molecul> dim5sions f9d+ its way ?r\gh a cr[d ( molecules ( simil> magnitude4 ,f ?is po9t ( view ,w4 ,k4 ,b\sfield has calculat$ ! sizes ( ions on ! assumption t ,/okes's !ory ( ! motion ( a small sph]e ?r\gh a visc\s m$ium might be appli$ 7,zeits4 phys4 ,*em41 #aije1 #ec1 p4 #beg2 ,phil4 ,trans4 ,a1 #aijf1 #bjf1 p4 #aja74 ,! radius ( ! potassium or *lor9e ion ) its envelope ( wat] appe>s to be ab\t #a4b #aj-h c5timetres4 ,= ! bibliography ( electrolytic conduction see ,,electrolysis4 ,! books :i* deal m especially ) ! p>ticul> subject ( ! pres5t article are ,das ,leitv]mg5 d] ,elektrolyte1 by ,f4 ,kohlraus* & ,l4 ,holborn 7,leipzig1 #ahih71 & ,! ,!ory ( ,solution & ,electrolysis1 by ,w4 ,c4 ,d4 ,:e?am 7,cambridge1 #aijb74 7,w4 ,c4 ,d4 ,w47 ,,iii4 ,,electric ,,conduction ,,?r\gh ,,gases ,a gas su* z air :5 x is "u normal conditions conducts electricity to a small b only to a v small ext5t1 h[ev] small ! electric =ce act+ on ! gas may be4 ,! electrical conductivity ( gases n expos$ to special conditions is s small t x 0 only def9itely e/abli%$ 9 ! e>ly ye>s ( ! #bj? c5tury1 al?\gh x _h engag$ ! att5tion ( physici/s = m ?an a hundr$ ye>s4 ,x _h be5 kn[n = a long "t t a body *>g$ ) electricity sl[ly lo/ its *>ge ev5 :5 insulat$ ) ! greate/ c>e1 & ?\gh long ago "s physici/s believ$ t "p ( ! leak ( electricity took place ?r\gh ! air1 ! g5]al view seems to h be5 t x 0 due to almo/ unavoidable defects 9 ! insulation or to du/ 9 ! air1 :i* aft] /rik+ ! *>g$ body 0 repell$ f x & w5t (f ) "s ( ! *>ge4 ,c4 ,a4 ,c\lomb1 :o made "s v c>eful exp]im5ts :i* 7 publi%$ 9 #aghe 7,mm4 de l',acad4 des ,sci5ces1 #aghe1 p4 #fab71 came to ! conclusion t aft] all[+ = ! leakage along ! ?reads :i* support$ ! *>g$ body !re 0 a balance ov]1 :i* he attribut$ to leakage ?r\gh ! air4 ,8 view 0 t :5 ! molecules ( air come into contact ) a *>g$ body "s ( ! electricity goes on to ! molecules1 :i* are !n repell$ f ! body c>ry+ _! *>ge ) !m4 ,we %all see lat] t ?is explanation is n t5able4 ,c4 ,matteucci 7,ann4 *im4 phys41 #ahej1 #bh1 p4 #cij7 9 #ahej also came to ! conclusion t ! electricity f a *>g$ body passes ?r\gh ! air2 he 0 ! fir/ to prove t ! rate at :i* electricity escapes is less :5 ! pressure ( ! gas is l[ ?an :5 x is high4 ,he f\nd t ! rate 0 ! same :e!r ! *>g$ body 0 surr\nd$ by air1 c>bonic acid or hydrog54 ,subsequ5t inve/igations h %[n t ! rate 9 hydrog5 is 9 g5]al mu* less ?an 9 air4 ,?us 9 #ahgb ,e4 ,g4 ,w>burg 7,pogg4 ,ann41 #ahgb1 #ade1 p4 #egh7 f\nd t ! leak ?r\gh hydrog5 0 only ab\t "o-half ( t ?r\gh air3 he confirm$ ,matteucci's obs]vations on ! effect ( pressure on ! rate ( leak1 & also f\nd t x 0 ! same :e!r ! gas 0 dry or damp4 ,he 0 incl9$ to attribute ! leak to du/ 9 ! air1 a view :i* 0 /r5g!n$ by an exp]im5t ( ,j4 ,w4 ,hittorf's 7,wi$4 ,ann41 #ahgi1 #g1 p4 #eie71 9 :i* a small c>efully insulat$ electroscope1 plac$ 9 a small vessel fill$ ) c>efully filt]$ gas1 reta9$ its *>ge = sev]al days2 we "k n[ t ?is 0 due to ! smallness ( ! vessel & n to ! abs5ce ( du/1 z x has be5 prov$ t ! rate ( leak 9 small vessels is less ?an 9 l>ge ones4 ,great light 0 ?r[n on ?is subject by "s exp]im5ts on ! rates ( leak f *>g$ bodies 9 clos$ vessels made almo/ simultane\sly by ,h4 ,geitel 7,phys4 ,zeit41 #aijj1 #b1 p4 #aaf7 & ,c4 ,t4 ,r4 ,wilson 7,proc4 ,camb4 ,phil4 ,soc41 #aijj1 #aa1 p4 #cb74 ,^! obs]v]s e/abli%$ t 7#a7 ! rate ( escape ( electricity 9 a clos$ vessel is mu* small] ?an 9 ! op51 & ! l>g] ! vessel ! great] is ! rate ( leak2 & 7#b7 ! rate ( leak does n increase 9 proportion to ! diff]5ces ( pot5tial betwe5 ! *>g$ body & ! walls ( ! vessel3 ! rate soon rea*es a limit beyond :i* x does n increase1 h[ev] mu* ! pot5tial diff]5ce may be increas$1 provid$1 ( c\rse1 t ?is is n great en\gh to cause sp>ks to pass f ! *>g$ body4 ,on ! assumption t ! maximum leak is proportional to ! volume1 ,wilson's exp]im5ts1 :i* 7 made 9 vessels less ?an #a litre 9 volume1 %[$ t 9 du/-free air at atmosph]ic pressure ! maximum quantity ( electricity :i* c escape 9 "o second f a *>g$ body 9 a clos$ volume ( ,v cubic c5timetres is ab\t #aj-h,v electro/atic units4 ,e4 ,ru!r=d & ,s4 ,t4 ,allan 7,phys4 ,zeit41 #aijb1 #c1 p4 #bbe71 work+ 9 ,montreal1 obta9$ results 9 close agreem5t ) ?is4 ,work+ betwe5 pressures ( f #dc to #gdc millimetres ( m]cury1 ,wilson %[$ t ! maximum rate ( leak is v approximately proportional to ! pressure2 x is ?us exce$+ly small :5 ! pressure is l[--a result illu/rat$ 9 a /rik+ way by an exp]im5t ( ,sir ,w4 ,crookes 7,proc4 ,roy4 ,soc41 #ahgi1 #bh1 p4 #cdg7 9 :i* a pair ( gold leaves reta9$ an electric *>ge = sev]al mon?s 9 a v high vacuum4 ,subsequ5t exp]im5ts h %[n t x is only 9 v small vessels t ! rate ( leak is proportional to ! volume & to ! pressure2 9 l>ge vessels ! rate ( leak p] unit volume is consid]ably small] ?an 9 small ones4 ,9 small vessels ! maximum rate ( leak 9 diff]5t gases1 is1 ) ! exception ( hydrog51 approximately proportional to ! d5sity ( ! gas4 ,wilson's results on ?is po9t are %[n 9 ! foll[+ table 7,proc4 ,roy4 ,soc41 #aija1 #fj1 p4 #bgg73-- ---------------------------------------- ---------- ,gas4 ,relative ,rate ( ,leak4 ,rate ( ,leak4 ,sp4 ,gr4 ---------------------------------------- ---------- ,air #a4jj #a ,h#b 4#ahd #b4g ,,co#b #a4fi #a4aj ,,s#b #b4fd #a4ba ,,*#c;,cl #d4g #a4ji ,ni7,,co7#d #e4a 4#hfg ---------------------------------------- ---------- ,! rate ( leak ( electricity ?r\gh gas conta9$ 9 a clos$ vessel dep5ds to "s ext5t on ! mat]ial ( :i* ! walls ( ! vessel are made2 ?us x is great]1 o!r circum/ances be+ ! same1 :5 ! vessel is made ( lead ?an :5 x is made ( alum9ium4 ,x also v>ies1 z ,campbell & ,wood 7,phil4 ,mag4 #f1 #ac1 p4 #bfe7 h %[n1 ) ! "t ( ! day1 hav+ a well-m>k$ m9imum at ab\t #c o'clock 9 ! morn+3 x also v>ies f mon? to mon?4 ,ru!r=d 7,phys4 ,rev41 #aijc1 #af1 p4 #ahc71 ,cooke 7,phil4 ,mag41 #aijc #f1 #f1 p4 #djc7 & ,m',cl5nan & ,burton 7,phys4 ,rev41 #aijc1 #af1 p4 #ahd7 h %[n t ! leak 9 a clos$ vessel c be r$uc$ by ab\t #cj by surr\nd+ ! vessel ) %eets ( ?ick lead1 b t ! r$uction is n increas$ beyond ?is am\nt1 h[ev] ?ick ! lead %eets may be4 ,?is result indicates t "p ( ! leak is due to a v p5etrat+ k9d ( radiation1 :i* c get ?r\gh ! ?9 walls ( ! vessel b is /opp$ by ! ?ick lead4 ,a l>ge "p ( ! leak we are describ+ is due to ! pres5ce ( radioactive sub/ances su* z radium & ?orium 9 ! e>?'s cru/ & 9 ! walls ( ! vessel1 & to ! gase\s radioactive emanations :i* diffuse f !m into ! atmosph]e4 ,?is expla9s ! v int]e/+ effect discov]$ by ,j4 ,el/] & ,h4 ,geitel 7,phys4 ,zeit41 #aija1 #b1 p4 #efj71 t ! rate ( leak 9 caves & cell>s :5 ! air is /agnant & only r5ew$ sl[ly is mu* great] ?an 9 ! op5 air4 ,9 "s cases ! diff]5ce is v m>k$2 ?us !y f\nd t 9 ! cave call$ ! ,baumann%hle 9 ! ,h>z m\nta9s ! electricity escap$ at sev5 times ! rate x did 9 ! air outside4 ,9 caves & cell>s ! radioactive emanations f ! walls c accumulate & are n bl[n away z 9 ! op5 air4 ,! electrical conductivity ( gases 9 ! normal /ate is1 z we h se51 exce$+ly small1 s small t ! inve/igation ( its prop]ties is a matt] ( consid]able difficulty2 !re are1 h[ev]1 _m ways by :i* ! electrical conductivity ( a gas c be increas$ s greatly t ! inve/igation becomes comp>atively easy4 ,among su* me?ods are rais+ ! temp]ature ( ! gas above a c]ta9 po9t4 ,gases drawn f ! neighb\rhood ( flames1 electric arcs & sp>ks1 or gl[+ pieces ( metal or c>bon are conductors1 z are also gases ?r\gh :i* ,rntg5 or ca?ode rays or rays ( positive electricity are pass+2 ! rays f ! radioactive metals1 radium1 ?orium1 polonium & act9ium1 produce ! same effect1 z does also ultra-violet light ( exce$+ly %ort wave-l5g?4 ,! gas1 aft] be+ made a conductor ( electricity by any ( ^! means1 is f\nd to possess c]ta9 prop]ties2 ?us x reta9s its conductivity = "s little "t aft] ! ag5t :i* made x a conductor has ceas$ to act1 ?\gh ! conductivity dim9i%es v rapidly & f9ally gets too small to be appreciable4 ,illu/ration3 ,,fig4 #e4 ,?is & sev]al o!r prop]ties ( conduct+ gas may readily be prov$ by ! aid ( ! app>atus repres5t$ 9 fig4 #e4 ,v is a te/+ vessel 9 :i* an electroscope is plac$4 ,two tubes ,a & ,c are fitt$ into ! vessel1 ,a be+ connect$ ) a wat] pump1 :ile ! f> end ( ,c is 9 ! region :]e ! gas is expos$ to ! ag5t :i* makes x a conductor ( electricity4 ,let u suppose t ! gas is made conduct+ by ,rntg5 rays produc$ by a vacuum tube :i* is plac$ 9 a box1 cov]$ except = a w9d[ at ,b ) lead s z to protect ! electroscope f ! direct action ( ! rays4 ,if a sl[ curr5t ( air is drawn by ! wat] pump ?r\gh ! te/+ vessel1 ! *>ge on ! electroscope w gradually leak away4 ,! leak1 h[ev]1 ceases :5 ! curr5t ( air is /opp$4 ,?is result %[s t ! gas reta9s its conductivity dur+ ! "t tak5 by x to pass f "o end to ! o!r ( ! tube ,c4 ,! gas loses its conductivity :5 filt]$ ?r\gh a plug ( glass-wool1 or :5 x is made to bubble ?r\gh wat]4 ,?is c readily be prov$ by ins]t+ 9 ! tube ,c a plug ( glass-wool or a wat] trap2 !n if by work+ ! pump a little h>d] ! same curr5t ( air is produc$ z be=e1 x w be f\nd t ! electroscope w n[ reta9 its *>ge1 %[+ t ! conductivity c1 z x 71 be filt]$ out ( ! gas4 ,! conductivity c also be remov$ f ! gas by mak+ ! gas trav]se a /rong electric field4 ,we c %[ ?is by replac+ ! tube ,c by a metal tube ) an insulat$ wire pass+ d[n ! axis ( ! tube4 ,if !re is no pot5tial diff]5ce betwe5 ! wire & ! tube !n ! electroscope w leak :5 a curr5t ( air is drawn ?r\gh ! vessel1 b ! leak w /op if a consid]able diff]5ce ( pot5tial is ma9ta9$ betwe5 ! wire & ! tube3 ?is %[s t a /rong electric field removes ! conductivity f ! gas4 ,! fact t ! conductivity ( ! gas is remov$ by filt]+ %[s t x is due to some?+ mix$ ) ! gas :i* is remov$ f x by filtration1 & s9ce ! conductivity is also remov$ by an electric field1 ! cause ( ! conductivity mu/ be *>g$ ) electricity s z to be driv5 to ! sides ( ! tube by ! electric =ce4 ,s9ce ! gas z a :ole is n electrifi$ ei!r positively or negatively1 !re mu/ be bo? negative & positive *>ges 9 ! gas1 ! am\nt ( electricity ( "o sign be+ equal to t ( ! o!r4 ,we are ?us l$ to ! conclusion t ! conductivity ( ! gas is due to electrifi$ p>ticles be+ mix$ up ) ! gas1 "s ( ^! p>ticles hav+ *>ges ( positive electricity1 o!rs ( negative4 ,^! electrifi$ p>ticles are call$ ions1 & ! process by :i* ! gas is made a conductor is call$ ! ionization ( ! gas4 ,we %all %[ lat] t ! *>ges & masses ( ! ions c be det]m9$1 & t ! gase\s ions are n id5tical ) ^? met ) 9 ! electrolysis ( solutions4 ,illu/ration3 ,,fig4 #f4 ,"o v *>act]i/ic prop]ty ( conduction ( electricity ?r\gh a gas is ! relation betwe5 ! curr5t ?r\gh ! gas & ! electric =ce :i* gave rise to x4 ,?is relation is n 9 g5]al t express$ by ,ohm's law1 :i* always1 z f> z our pres5t k ext5ds1 expresses ! relation = conduction ?r\gh metals & electrolytes4 ,) gases1 on ! o!r h&1 x is only :5 ! curr5t is v small t ,ohm's law is true4 ,if we repres5t graphically by means ( a curve ! relation betwe5 ! curr5t pass+ betwe5 two p>allel metal plates sep>at$ by ioniz$ gas & ! diff]5ce ( pot5tial betwe5 ! plates1 ! curve is ( ! "* %[n 9 fig4 #f :5 ! ord9ates repres5t ! curr5t & ! abscissae ! diff]5ce ( pot5tial betwe5 ! plates4 ,we see t :5 ! pot5tial diff]5ce is v small1 i4e4 close to ! orig91 ! curve is approximately /raight1 b t soon ! curr5t increases mu* less rapidly ?an ! pot5tial diff]5ce1 & t a /age is rea*$ :5 no appreciable increase ( curr5t is produc$ :5 ! pot5tial diff]5ce is increas$2 :5 ?is /age is rea*$ ! curr5t is con/ant1 & ?is value ( ! curr5t is call$ ! saturation value4 ,:5 ! pot5tial diff]5ce approa*es ! value at :i* sp>ks w\ld pass ?r\gh ! gas1 ! curr5t aga9 increases ) ! pot5tial diff]5ce2 ?us ! curve repres5t+ ! relation betwe5 ! curr5t & pot5tial diff]5ce ov] v wide ranges ( pot5tial diff]5ce has ! %ape %[n 9 fig4 #g2 curves ( ?is k9d h be5 obta9$ by von ,s*weidl] 7,wi54 ,b]41 #ahii1 #ajh1 p4 #bgc71 & ,j4 ,e4 ,s4 ,t[ns5d 7,phil4 ,mag41 #aija #f1 #a1 p4 #aih74 ,we %all discuss lat] ! causes ( ! rise 9 ! curr5t ) l>ge pot5tial diff]5ces1 :5 we consid] ionization by collision4 ,! g5]al features ( ! e>li] "p ( ! curve are readily expla9$ on ! ionization hypo!sis4 ,on ?is view ! ,rntg5 rays or o!r ioniz+ ag5t act+ on ! gas betwe5 ! plates1 produces positive & negative ions at a def9ite rate4 ,let u suppose t q positive & q negative ions are by ?is means produc$ p] second betwe5 ! plates2 ^! "u ! electric =ce w t5d to move1 ! positive ones to ! negative plate1 ! negative ones to ! positive4 ,"s ( ^! ions w rea* ! plate1 o!rs be=e rea*+ ! plate w get s ne> "o ( ! opposite sign t ! attraction betwe5 !m w cause !m to unite & =m an electrically neutral sy/em2 :5 !y d ?is !y end _! exi/5ce z ions4 ,! curr5t betwe5 ! plates is proportional to ! numb] ( ions :i* rea* ! plates p] second4 ,n[ x is evid5t t we _c g on tak+ m ions out ( ! gas ?an are produc$2 ?us we _c1 :5 ! curr5t is /eady1 h m ?an q positive ions driv5 to ! negative plate p] second1 & ! same numb] ( negative ions to ! positive4 ,if ea* ( ! positive ions c>ries a *>ge ( e units ( positive electricity1 & if !re is an equal & opposite *>ge on ea* negative ion1 !n ! maximum am\nt ( electricity :i* c be giv5 to ! plates p] second is qe1 & ?is is equal to ! saturation curr5t4 ,?us if we measure ! saturation curr5t1 we get a direct measure ( ! ionization1 & ?is does n require u to "k ! value ( any quantity except ! con/ant *>ge on ! ion4 ,if we attempt$ to d$uce ! am\nt ( ionization by measurem5ts ( ! curr5t be=e x 0 saturat$1 we %\ld require to "k 9 addition ! velocity ) :i* ! ions move "u a giv5 electric =ce1 ! "t t elapses betwe5 ! lib]ation ( an ion & its comb9ation ) "o ( ! opposite sign1 & ! pot5tial diff]5ce betwe5 ! plates4 ,?us if we wi% to measure ! am\nt ( ionization 9 a gas we %\ld be c>eful to see t ! curr5t is saturat$4 ,illu/ration3 ,,fig4 #g4 ,! diff]5ce betwe5 conduction ?r\gh gases & ?r\gh metals is %[n 9 a /rik+ way :5 we use pot5tial diff]5ces l>ge en\gh to produce ! saturation curr5t4 ,suppose we h got a pot5tial diff]5ce betwe5 ! plates m ?an suffici5t to produce ! saturation curr5t1 & let u increase ! di/ance betwe5 ! plates4 ,if ! gas 7 to act l a metallic conductor ?is w\ld dim9i% ! curr5t1 because ! great] l5g? w\ld involve a great] resi/ance 9 ! circuit4 ,9 ! case we are consid]+ ! sep>ation ( ! plates w increase ! curr5t1 because n[ !re is a l>g] volume ( gas expos$ to ! rays2 !re are !re=e m ions produc$1 & z ! saturation curr5t is proportional to ! numb] ( ions ! saturation curr5t is increas$4 ,if ! pot5tial diff]5ce betwe5 ! plates 7 mu* less ?an t requir$ to saturate ! curr5t1 !n increas+ ! di/ance w\ld dim9i% ! curr5t2 ! gas = su* pot5tial diff]5ces obeys ,ohm's law & ! behavi\r ( ! gase\s resi/ance is !re=e simil> to t ( a metallic "o4 ,9 ord] to produce ! saturation curr5t ! electric field mu/ be /rong en\gh to drive ea* ion to ! electrode be=e x has "t to ent] into comb9ation ) "o ( ! opposite sign4 ,?us :5 ! plates 9 ! prec$+ example are f> ap>t1 x w take a l>g] pot5tial diff]5ce to produce ?is curr5t ?an :5 ! plates are close toge!r4 ,! pot5tial diff]5ce requir$ to saturate ! curr5t w increase z ! squ>e ( ! di/ance betwe5 ! plates1 = if ! ions are to be deliv]$ 9 a giv5 "t to ! plates _! spe$ mu/ be proportional to ! di/ance betwe5 ! plates4 ,b ! spe$ is proportional to ! electric =ce act+ on ! ion2 h5ce ! electric =ce mu/ be proportional to ! di/ance betwe5 ! plates1 & z 9 a uni=m field ! pot5tial diff]5ce is equal to ! electric =ce multipli$ by ! di/ance betwe5 ! plates1 ! pot5tial diff]5ce w v>y z ! squ>e ( ?is di/ance4 ,! pot5tial diff]5ce requir$ to produce saturation w1 o!r circum/ances be+ ! same1 increase ) ! am\nt ( ionization1 = :5 ! numb] ( ions is l>ge & !y are cr[d$ toge!r1 ! "t :i* w elapse be=e a positive "o comb9es ) a negative w be small] ?an :5 ! numb] ( ions is small4 ,! ions h !re=e to be remov$ m quickly f ! gas :5 ! ionization is great ?an :5 x is small2 ?us !y mu/ move at a high] spe$ & mu/ !re=e be act$ ^u by a l>g] =ce4 ,:5 ! ions are n remov$ f ! gas1 !y w increase until ! numb] ( ions ( "o sign :i* comb9e ) ions ( ! opposite sign 9 any "t is equal to ! numb] produc$ by ! ioniz+ ag5t 9 t "t4 ,we c easily calculate ! numb] ( free ions at any "t aft] ! ioniz+ ag5t has comm5c$ to act4 ,let q be ! numb] ( ions 7positive or negative7 produc$ 9 "o cubic c5timetre ( ! gas p] second by ! ioniz+ ag5t1 n#a1 n#b1 ! numb] ( free positive & negative ions respectively p] cubic c5timetre ( ! gas4 ,! numb] ( collisions betwe5 positive & negative ions p] second 9 "o cubic c5timetre ( ! gas is proportional to n#an#b4 ,if a c]ta9 fraction ( ! collisions betwe5 ! positive & negative ions result 9 ! =mation ( an electrically neutral sy/em1 ! numb] ( ions :i* disappe> p] second on a cubic c5timetre w be equal to alphan#a n#b1 :]e alpha is a quantity :i* is indep5d5t ( n#a1 n#b2 h5ce if t is ! "t s9ce ! ioniz+ ag5t 0 appli$ to ! gas1 we h dn#a_/;dt q - alphan#a n#b1 dn#b_/;dt q - alphan#a n#b4 ,?us n#a - n#b is con/ant1 s if ! gas is un*>g$ to beg9 )1 n#a w always equal n#b4 ,putt+ n#a n#b n we h dn_/dt q - alphan 7#a71 ! solution ( :i* is1 s9ce n #j :5 t #j1 k7epsilon#bkalphat - #a7 n ---------------------------- 7#b7 epsilon#bkalphat #a if k q_/alpha4 ,n[ ! numb] ( ions :5 ! gas has rea*$ a /eady /ate is got by putt+ t equal to inf9ity 9 ! prec$+ equation1 & is !re=e giv5 by ! equation n#j k root7q_/alpha74 ,we see f equation 7#a7 t ! gas w n approximate to its /eady /ate until #bkalphat is l>ge1 t is until t is l>ge comp>$ ) #a_/bkalpha or ) #a_/broot7qalpha74 ,we may ?us take #a_/broot7qalpha7 z a measure ( ! "t tak5 by ! gas to rea* a /eady /ate :5 expos$ to an ioniz+ ag5t2 z ?is "t v>ies inv]sely z rootq we see t :5 ! ionization is feeble x may take a v consid]able "t = ! gas to rea* a /eady /ate4 ,?us 9 ! case ( our atmosph]e :]e ! production ( ions is only at ! rate ( ab\t #cj p] cubic c5timetre p] second1 & :]e1 z we %all see1 alpha is ab\t #aj-f1 x w\ld take "s m9utes = ! ionization 9 ! air to get into a /eady /ate if ! ioniz+ ag5t 7 sudd5ly appli$4 ,we may use equation 7#a7 to det]m9e ! rate at :i* ! ions disappe> :5 ! ioniz+ ag5t is remov$4 ,putt+ q#j 9 t equation we get dn_/alphat -alphan4 ,h5ce n n#j_/7a n#j;alphat7 7#c71 :]e n#j is ! numb] ( ions :5 t #j4 ,?us ! numb] ( ions falls to "o-half its initial value 9 ! "t #a_/n#j;alpha4 ,! quantity alpha is call$ ! coeffici5t ( recomb9ation1 & its value = diff]5t gases has be5 det]m9$ by ,ru!r=d 7,phil4 ,mag4 #ahig #e1 #dd1 p4 #dbb71 ,t[ns5d 7,phil4 ,trans41 #aijj1 #aic1 p4 #abi71 ,mc,clung 7,phil4 ,mag41 #aijb #f1 #c1 p4 #bhc71 ,langev9 7,ann4 *im4 phys4 #g1 #bh1 p4 #bhi71 ,rets*9sky 7,ann4 d4 ,phys41 #aije1 #ag1 p4 #eah71 ,h5dr$ 7,phys4 ,rev41 #aije1 #ba1 p4 #cad74 ,! values ( alpha_/e1 e be+ ! *>ge on an ion 9 electro/atic measure z det]m9$ by ^! obs]v]s = diff]5t gases1 is giv5 9 ! foll[+ table3-- ---------------------------------------- ----------------- ,t[ns5d4 ,mc,clung4 ,langev94,rets*9sky4 ,h5dr$4 ---------------------------------------- ----------------- ,air #cdbj #cchj #cbjj #dadj #cejj ,o#b #cchj ,,co#b #cejj #cdij #cdjj ,h#b #cjbj #bidj ---------------------------------------- ----------------- ,! gases 9 ^! exp]im5ts 7 c>efully dri$ & free f du/2 ! app>5t value ( alpha is mu* increas$ :5 du/ or small drops ( wat] are pres5t 9 ! gas1 = !n ! ions get caught by ! du/ p>ticles1 ! mass ( a p>ticle is s great comp>$ ) t ( an ion t !y are practically immovable "u ! action ( ! electric field1 & s ! ions cl++ to !m escape detection :5 electrical me?ods are us$4 ,tak+ e z #c4e #aj-aj1 we see t alpha is ab\t #a4b #aj-f1 s t ! numb] ( recomb9ations 9 unit "t betwe5 n positive & n negative ions 9 unit volume is #a4b #aj-fn4 ,! k9etic !ory ( gases %[s t if we h n molecules ( air p] cubic c5timetre1 ! numb] ( collisions p] second is #a4b #aj-ajn at a temp]ature ( #j ,c4 ,?us we see t ! numb] ( recomb9ations betwe5 oppositely *>g$ ions is enorm\sly great] ?an ! numb] ( collisions betwe5 ! same numb] ( neutral molecules4 ,we %all see t ! diff]5ce 9 size betwe5 ! ion & ! molecule is n ne>ly suffici5t to acc\nt = ! diff]5ce betwe5 ! collisions 9 ! two cases2 ! diff]5ce is due to ! =ce betwe5 ! oppositely *>g$ ions1 :i* drags ions into collisions :i* b = ?is =ce w\ld h miss$ ea* o!r4 ,sev]al me?ods h be5 us$ to measure alpha4 ,9 "o me?od air1 expos$ to "s ioniz+ ag5t at "o end ( a long tube1 is sl[ly suck$ ?r\gh ! tube & ! saturation curr5t measur$ at diff]5t po9ts along ! tube4 ,^! curr5ts are proportional to ! values ( n at ! place ( obs]vation3 if we "k ! di/ance ( ?is place f ! end ( ! tube :5 ! gas 0 ioniz$ & ! velocity ( ! /ream ( gas1 we c f9d t 9 equation 7#c71 & kn[+ ! value ( n we c d$uce ! value ( alpha f ! equation #a_/n#a - #a_/n#b alpha7t#a - t#b71 :]e n#a1 n#b are ! values ( n at ! times t#a1 t#b respectively4 ,9 ?is me?od ! tubes ought to be s wide t ! loss ( ions by diffusion to ! sides ( ! tube is negligible4 ,!re are o!r me?ods :i* involve ! k ( ! spe$ ) :i* ! ions move "u ! action ( kn[n electric =ces2 we %all def] ! consid]ation ( ^! me?ods until we h discuss$ ! "q ( ^! spe$s4 ,9 measur+ ! value ( alpha x %\ld be rememb]$ t ! !ory ( ! me?ods supposes t ! ionization is uni=m ?r\gh\t ! gas4 ,if ! total ionization ?r\gh\t a gas rema9s con/ant1 b in/ead ( be+ uni=mly di/ribut$ is conc5trat$ 9 pat*es1 x is evid5t t ! ions w recomb9e m quickly 9 ! second case ?an 9 ! fir/1 & t ! value ( alpha w be diff]5t 9 ! two cases4 ,?is probably expla9s ! l>ge values ( alpha obta9$ by ,rets*9sky1 :o ioniz$ ! gas by ! alpha rays f radium1 a me?od :i* produces v pat*y ionization4 ,v>iation ( alpha ) ! ,pressure ( ! ,gas4--,all obs]v]s agree t !re is little v>iation 9 alpha ) ! pressures = pressures ( betwe5 #e & #a atmosph]es2 at l[] pressures1 h[ev]1 ! value ( alpha seems to dim9i% ) ! pressure3 ?us ,langev9 7,ann4 *im4 phys41 #aijc1 #bh1 p4 #bhg7 f\nd t at a pressure ( #a_/e ( an atmosph]e ! value ( alpha 0 ab\t #a_/e ( its value at atmosph]ic pressure4 ,v>iation ( alpha ) ! ,temp]ature4--,erikson 7,phil4 ,mag41 ,aug4 #aiji7 has %[n t ! value ( alpha = air increases z ! temp]ature dim9i%es1 & t at ! temp]ature ( liquid air -#ahj ,c41 x is m ?an twice z great z at #ab ,c4 ,s9ce1 z we h se51 ! recomb9ation is due to ! com+ toge!r ( ! positive & negative ions "u ! influ5ce ( ! electrical attraction betwe5 !m1 x foll[s t a l>ge electric =ce suffici5t to ov]come ?is attraction w\ld keep ! ions ap>t & h5ce dim9i% ! coeffici5t ( recomb9ation4 ,simple consid]ations1 h[ev]1 w %[ t x w\ld require exce$+ly /rong electric fields to produce an appreciable effect4 ,! value ( alpha indicates t = two oppositely *>g$ ions to unite !y mu/ come )9 a di/ance ( ab\t #a4e #aj-f c5timetres2 at ?is di/ance ! attraction betwe5 !m is e #ajab_/b4be1 & if ,x is ! ext]nal electric =ce1 ! =ce t5d+ to pull !m ap>t _c be great] ?an ,xe2 if ?is is to be comp>able ) ! attraction1 ,x mu/ be comp>able ) e #ajab_/b4be1 or putt+ e #d #aj-aj1 ) #a4h #aj2 ?is is #ed1jjj volts p] c5timetre1 a =ce :i* c\ld n be appli$ to gas at atmosph]ic pressure )\t produc+ a sp>k4 ,diffusion ( ! ,ions4--,! ioniz$ gas acts l a mixture ( gases1 ! ions correspond+ to two diff]5t gases1 ! non-ioniz$ gas to a ?ird4 ,if ! conc5tration ( ! ions is n uni=m1 !y w diffuse ?r\gh ! non-ioniz$ gas 9 su* a way z to produce a m uni=m di/ribution4 ,a v valuable s]ies ( det]m9ations ( ! coeffici5t ( diffusion ( ions ?r\gh v>i\s gases has be5 made by ,t[ns5d 7,phil4 ,trans41 #aijj1 ,a1 #aic1 p4 #abi74 ,! me?od us$ 0 to suck ! ioniz$ gas ?r\gh n>r[ tubes2 by measur+ ! loss ( bo? ! positive & negative ions aft] ! gases _h pass$ ?r\gh a kn[n l5g? ( tube1 & all[+ = ! loss by recomb9ation1 ! loss by diffusion & h5ce ! coeffici5t ( diffusion c\ld be det]m9$4 ,! foll[+ tables give ! values ( ! coeffici5ts ( diffusion ,d on ! ,c4,g4,s4 sy/em ( units z det]m9$ by ,t[ns5d3-- ,table ,i4--,coeffici5ts ( ,diffusion 7,d7 9 ,dry ,gases4 ---------------------------------------- ----------------- ,gas4 ,d = ions4,d = -ions4,mean ,value ,ratio ( ,d = ( ,d4 - to ,d = ions4 ---------------------------------------- ----------------- ,air 4#jbh 4#jdc 4#jcdg #a4ed ,o#b 4#jbe 4#jcif 4#jcbc #a4eh ,,co#b 4#jbc 4#jbf 4#jbde #a4ac ,h#b 4#abc 4#aij 4#aef #a4ed ---------------------------------------- ----------------- ,table ,,ii4--,coeffici5ts ( ,diffusion 9 ,moi/ ,gases4 ---------------------------------------- ----------------- ,gas4 ,d = ions4,d = -ions4,mean ,value ,ratio ( ,d = ( ,d4 - to ,d = ions4 ---------------------------------------- ----------------- ,air 4#jcb 4#jcg 4#jcce #a4ji ,o#b 4#jbhh 4#jceh 4#jcbc #a4bd ,,co#b 4#jbde 4#jbee 4#jbe #a4jd ,h#b 4#abh 4#adb 4#ace #a4aa ---------------------------------------- ----------------- ,x is int]e/+ to comp>e ) ^! coeffici5ts ! values ( ,d :5 v>i\s gases diffuse ?r\gh ea* o!r4 ,d = hydrog5 ?r\gh air is 4#fcd1 = oxyg5 ?r\gh air 4#agg1 = ! vap\r ( isobutyl amide ?r\gh air 4#jdb4 ,we ?us see t ! velocity ( diffusion ( ions ?r\gh air is mu* less ?an t ( ! simple gas1 b t x is q comp>able ) t ( ! vap\rs ( "s complex organic comp\nds4 ,! prec$+ tables %[ t ! negative ions diffuse m rapidly ?an ! positive1 especially 9 dry gases4 ,! sup]ior mobility ( ! negative ions 0 obs]v$ fir/ by ,zel5y 7,phil4 ,mag41 #ahih #e1 #df1 p4 #abj71 :o %[$ t ! velocity ( ! negative ions "u an electric =ce is great] ?an t ( ! positive4 ,x w be notic$ t ! diff]5ce betwe5 ! mobility ( ! negative & ! positive ions is mu* m pron\nc$ 9 dry gases ?an 9 moi/4 ,! diff]5ce 9 ! rates ( diffusion ( ! positive & negative ions is ! reason :y ioniz$ gas1 9 :i*1 to beg9 )1 ! positive & negative *>ges 7 ( equal am\nts1 sometimes becomes electrifi$ ev5 al?\gh ! gas is n act$ ^u by electric =ces4 ,?us1 = example1 if su* gas be bl[n ?r\gh n>r[ tubes1 x w be positively electrifi$ :5 x comes out1 = s9ce ! negative ions diffuse m rapidly ?an ! positive1 ! gas 9 its passage ?r\gh ! tubes w lose by diffusion m negative ?an positive ions & h5ce w em]ge positively electrifi$4 ,zel5y sn[$ t ?is effect does n occur :51 z 9 c>bonic acid gas1 ! positive & negative ions diffuse at ! same rates4 ,t[ns5d 7loc4 cit47 %[$ t ! coeffici5t ( diffusion ( ! ions is ! same :e!r ! ionization is produc$ by ,rntg5 rays1 radioactive sub/ances1 ultra-violet light1 or electric sp>ks4 ,! ions produc$ by *emical reactions & 9 flames are mu* less mobile2 ?us1 = example1 ,blo* 7,ann4 *im4 phys41 #aije #h1 #d1 p4 #be7 f\nd t = ! ions produc$ by draw+ air ov] phosphorus ! value ( alpha_/e 0 betwe5 #a & #f in/ead ( ov] #cjjj1 ! value :5 ! air 0 ioniz$ by ,rntg5 rays4 ,velocity ( ,ions 9 an ,electric ,field4--,! velocity ( ions 9 an electric field1 :i* is ( fundam5tal importance 9 conduction1 is v closely relat$ to ! coeffici5t ( diffusion4 ,measurem5ts ( ?is velocity = ions produc$ by ,rntg5 rays h be5 made by ,ru!r=d 7,phil4 ,mag4 #e1 #dd1 p4 #dbb71 ,zel5y 7,phil4 ,mag4 #e1 #df1 p4 #abj71 ,langev9 7,ann4 ,*im4 ,phys41 #aijc1 #bh1 p4 #bhi71 ,phillips 7,proc4 ,roy4 ,soc4 #gh1 ,a1 p4 #afg71 & ,wellis* 7,phil4 ,trans41 #aiji1 #bji1 p4 #bdi74 ,! ions produc$ by radioactive sub/ance h be5 inve/igat$ by ,ru!r=d 7,phil4 ,mag4 #e1 #dg1 p4 #aji7 & by ,franck & ,pohl 7,v]h4 deuts*4 phys4 ,gesell41 #aijg1 #i1 p4 #fi71 & ! negative ions produc$ :5 ultra-violet light falls on a metal plate by ,ru!r=d 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #dja74 ,h4 ,a4 ,wilson 7,phil4 ,trans4 #aib1 p4 #d,o#i71 ,m>x 7,ann4 de ,phys4 #aa1 p4 #gfe71 ,moreau 7,j\rn4 de ,phys4 #d1 #aa1 p4 #eeh2 ,ann4 ,*im4 ,phys4 #g1 #cj1 p4 #e7 & ,gold 7,proc4 ,roy4 ,soc4 #gi1 p4 #dc7 h inve/igat$ ! velocities ( ions produc$ by putt+ v>i\s salts into flames2 ,mc,clelland 7,phil4 ,mag4 #df1 p4 #bi7 ! velocity ( ! ions 9 gases suck$ f ! neighb\rhood ( flames & arcs2 ,t[ns5d 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #cde7 & ,blo* 7loc4 cit47 ! velocity ( ions produc$ by *emical reaction2 & ,*attock 7,phil4 ,mag4 #e1 #dh1 p4 #dja7 ! velocity ( ! ions produc$ :5 electricity escapes f a %>p ne$le po9t into a gas4 ,sev]al me?ods h be5 employ$ to det]m9e ^! velocities4 ,! "o mo/ frequ5tly employ$ is to f9d ! electromotive int5sity requir$ to =ce an ion aga9/ ! /ream ( gas mov+ ) a kn[n velocity p>allel to ! l9es ( electric =ce4 ,?us1 ( two p]=at$ plane electrodes v]tically ov] ea* o!r1 suppose ! l[] to be positively1 ! upp] negatively electrifi$1 & suppose t ! gas is /ream+ v]tically d[nw>ds ) ! velocity ,v2 !n unless ! upw>d velocity ( ! positive ion is great] ?an ,v1 no positive electricity w rea* ! upp] plate4 ,if we increase ! /r5g? ( ! field betwe5 ! plates1 & h5ce ! upw>d velocity ( ! positive ion1 until ! positive ions j beg9 to rea* ! upp] plate1 we "k t ) ?is /r5g? ( field ! velocity ( ! positive ion is equal to ,v4 ,by ?is me?od1 :i* has be5 us$ by ,ru!r=d1 ,zel5y & ,h4 ,a4 ,wilson1 ! velocity ( ions 9 fields ( v>i\s /r5g?s has be5 det]m9$4 ,! arrangem5t us$ by ,zel5y is repres5t$ 9 fig4 #h4 ,p & ,q are squ>e brass plates4 ,!y are bor$ ?r\gh _! c5tres1 & to ! op5+s ! tubes ,r & ,s are atta*$1 ! space betwe5 ! plates be+ cov]$ 9 s z to =m a clos$ box4 ,k is a piece ( wire gauze completely cov]+ ! op5+ 9 ,q2 ,t is an insulat$ piece ( wire gauze ne>ly b n q fill+ ! op5+ 9 ! plate ,p1 & connect$ ) "o pair ( quadrants ( an electromet] ,e4 ,a plug ( glass wool ,g filt]s out ! du/ f a /ream ( gas :i* ent]s ! vessel by ! tube ,d & leaves x by ,f2 ?is plug also makes ! velocity ( ! fl[ ( ! gas uni=m across ! section ( ! tube4 ,! ,rntg5 rays to ionize ! gas 7 produc$ by a bulb at ,o1 ! bulb & coil be+ 9 a lead-cov]$ box1 ) an alum9ium w9d[ ?r\gh :i* ! rays pass$4 ,q is connect$ ) "o pole ( a batt]y ( cells1 ,p & ! o!r pole ( ! batt]y are put to e>?4 ,! *anges 9 ! pot5tial ( ,t are due to ions giv+ up _! *>ges to x4 ,) a giv5 velocity ( air-bla/ ! pot5tial ( ,t 0 f\nd n to *ange unless ! diff]5ce ( pot5tial betwe5 ,p & ,q exce$$ a critical value4 ,! field correspond+ to ?is critical value ?us made ! ions move ) ! kn[n velocity ( ! bla/4 ,illu/ration3 ,,fig4 #h4 ,illu/ration3 ,,fig4 #i4 ,ano!r me?od :i* has be5 employ$ by ,ru!r=d & ,mc,clelland is bas$ on ! action ( an electric field 9 de/roy+ ! conductivity ( gas /ream+ ?r\gh x4 ,suppose t ,,bab1 ,,dcd 7fig4 #i7 are a sy/em ( p>allel plates box$ 9 s t a /ream ( gas1 aft] fl[+ betwe5 ,,bb1 passes betwe5 ,,dd )\t any loss ( gas 9 ! int]val4 ,suppose ! plates ,,dd are insulat$1 & connect$ ) "o pair ( quadrants ( an electromet]1 by *>g+ up ,c to a suffici5tly high pot5tial we c drive all ! positive ions :i* ent] ! sy/em ,,dcd aga9/ ! plates ,d2 ?is w cause a deflexion ( ! electromet]1 :i* 9 "o second w be proportional to ! numb] ( positive ions :i* h ent]$ ! sy/em 9 t "t4 ,if we *>ge ,a up to a high pot5tial1 ,b be+ put to e>?1 we %all f9d t ! deflexion ( ! electromet] connect$ ) ,,dd is less ?an x 0 :5 ,a & ,b 7 at ! same pot5tial1 because "s ( ! positive ions 9 _! passage ?r\gh ,,bab are driv5 aga9/ ! plates ,b4 ,if u is ! velocity along ! l9es ( =ce 9 ! uni=m electric field betwe5 ,a & ,b1 & t ! "t x takes = ! gas to pass ?r\gh ,,bab1 !n all ! positive ions )9 a di/ance ut ( ! plates ,b w be driv5 up aga9/ ^! plates1 & ?us if ! positive ions are equally di/ribut$ ?r\gh ! gas1 ! numb] ( positive ions :i* em]ge f ! sy/em :5 ! electric field is on w be> to ! numb] :i* em]ge :5 ! field is (f ! ratio ( #a - ut_/l to unity1 :]e l is ! di/ance betwe5 ,a & ,b4 ,?is ratio is equal to ! ratio ( ! deflexions 9 "o second ( ! electromet] atta*$ to ,d1 h5ce ! obs]vations ( ?is in/rum5t give #a - ut_/l4 ,if we "k ! velocity ( ! gas & ! l5g? ( ! plates ,a & ,b1 we c det]m9e t1 & s9ce l c be easily measur$1 we c f9d u1 ! velocity ( ! positive ion 9 a field ( giv5 /r5g?4 ,by *>g+ ,a & ,c negatively in/ead ( positively we c arrive at ! velocity ( ! negative ion4 ,9 practice x is m conv5i5t to use cyl9drical tubes ) coaxial wires in/ead ( ! sy/ems ( p>allel plates1 ?\gh 9 ?is case ! calculation ( ! velocity ( ! ions f ! obs]vations is a little m complicat$1 inasmu* z ! electric field is n uni=m betwe5 ! tubes4 ,illu/ration3 ,,fig4 #aj4 ,a me?od :i* gives v accurate results1 ?\gh x is only applicable 9 c]ta9 cases1 is ! "o us$ by ,ru!r=d to measure ! velocity ( ! negative ions produc$ close to a metal plate by ! incid5ce on ! plate ( ultra-violet light4 ,! pr9ciple ( ! me?od is z foll[s3--,,ab 7fig4 #aj7 is an insulat$ horizontal plate ( well-poli%$ z9c1 :i* c be mov$ v]tically up & d[n by means ( a screw2 x is connect$ ) "o pair ( quadrants ( an electromet]1 ! o!r pair ( quadrants be+ put to e>?4 ,,cd is a base-plate ) a hole ,,ef 9 x2 ?is hole is cov]$ ) f9e wire gauze1 ?r\gh :i* ultra-violet light passes & falls on ! plate ,,ab4 ,! plate ,,cd is connect$ ) an alt]nat+ curr5t dynamo1 :i* produces a simply-p]iodic pot5tial diff]5ce betwe5 ,,ab & ,,cd1 ! o!r pole be+ put to e>?4 ,suppose t at any in/ant ! plate ,,cd is at a high] pot5tial ?an ,,ab1 !n ! negative ions f ,,ab w move t[>ds ,,cd1 & w cont9ue to d s z long z ! pot5tial ( ,,cd is high] ?an t ( ,,ab4 ,if1 h[ev]1 ! pot5tial diff]5ce *anges sign be=e ! negative ions rea* ,,cd1 ^! ions w g back to ,,ab4 ,?us ,,ab w n lose any negative *>ge unless ! di/ance betwe5 ! plates ,,ab & ,,cd is less ?an ! di/ance trav]s$ by ! negative ion dur+ ! "t ! pot5tial ( ,,cd is high] ?an t ( ,,ab4 ,by alt]+ ! di/ance betwe5 ! plates until ,,cd j beg9s to lose a negative *>ge1 we f9d ! velocity ( ! negative ion "u unit electromotive int5sity4 ,= suppose ! diff]5ce ( pot5tial betwe5 ,,ab & ,,cd is equal to a s9 pt1 !n if d is ! di/ance betwe5 ! plates1 ! electric int5sity is equal to a s9 pt_/d2 if we suppose ! velocity ( ! ion is proportional to ! electric int5sity1 & if u is ! velocity = unit electric int5sity1 ! velocity ( ! negative ion w be ua s9 pt_/d4 ,h5ce if x repres5t ! di/ance ( ! ion f ,,ab dx ua --- --- s9 pt d,t d ua x ----7#a - cos pt71 if x #j :5 t #j4 pd ,?us ! greate/ di/ance ! ion c get f ! plate is equal to #b;au_/pd1 & if ! di/ance betwe5 ! plates is gradually r$uc$ to ?is value1 ! plate ,,ab w beg9 to lose a negative *>ge2 h5ce :5 ?is happ5s d #b;au_/pd1 or u pd_/#b;a1 an equation by means ( :i* we c f9d u4 ,9 ?is =m ! me?od is n applicable :5 ions ( bo? signs are pres5t4 ,franck & ,pohl 7,v]h4 deuts*4 physik4 ,gesell4 #aijg1 #i1 p4 #fi7 h by a slight modification remov$ ?is re/riction4 ,! modification consi/s 9 conf9+ ! ionization to a lay] ( gas bel[ ! gauze ,,ef4 ,if ! velocity ( ! positive ions is to be det]m9$1 ^! ions are =c$ ?r\gh ! gauze by apply+ to ! ioniz$ gas a small con/ant electric =ce act+ upw>ds2 if negative ions are requir$1 ! con/ant =ce is rev]s$4 ,aft] pass+ ?r\gh ! gauze ! ions are act$ ^u by alt]nat+ =ces z 9 ,ru!r=d's me?od4 ,langev9 7,ann4 *im4 phys41 #aijc1 #bh1 p4 #bhi7 devis$ a me?od ( measur+ ! velocity ( ! ions :i* has be5 ext5sively us$2 x has ! advantage ( n requir+ ! rate ( ionization to rema9 uni=m4 ,! g5]al idea is z foll[s4 ,suppose t we expose ! gas betwe5 two p>allel plates ,a1 ,b to ,rntg5 rays or "s o!r ioniz+ ag5t1 !n /op ! rays & apply a uni=m electric field to ! region betwe5 ! plates4 ,if ! =ce on ! positive ion is f ,a to ,b1 ! plate ,b w receive a positive *>ge ( electricity4 ,aft] ! electric =ce has act$ = a "t ,t rev]se x4 ,b w n[ beg9 to receive negative electricity & w g on do+ s until ! supply ( negative ions is exhau/$4 ,let u consid] h[ ! quantity ( positive electricity receiv$ by ,b w v>y ) ,t4 ,to fix our ideas1 suppose ! positive ions move m sl[ly ?an ! negative2 let ,t#b & ,t#a be respectively ! times tak5 by ! positive & negative ions to move "u ! electric field ?r\gh a di/ance equal to ,,ab1 ! di/ance betwe5 ! planes4 ,!n if ,t is great] ?an ,t#b all ! ions w h be5 driv5 f betwe5 ! plates be=e ! field is rev]s$1 & !re=e ! positive *>ge receiv$ by ,b w n dep5d ^u ,t4 ,next let ,t be less ?an ,t#b b great] ?an ,t#a2 !n at ! "t :5 ! field is rev]s$ all ! negative ions w h be5 driv5 f betwe5 ! plates1 s t ! positive *>ge receiv$ by ,b w n be neutraliz$ by ! arrival ( fre% ions com+ to x aft] ! rev]sal ( ! field4 ,! numb] ( positive ions driv5 aga9/ ! plate ,b w be proportional to ,t4 ,?us if we measure ! value ( ! positive *>ge on ,b = a s]ies ( values ( ,t1 ea* value be+ less ?an ! prec$+1 we %all f9d t until ,t rea*es a c]ta9 value ! *>ge rema9s con/ant1 b z soon z we r$uce ! "t bel[ ?is value ! *>ge dim9i%es4 ,! value ( ,t :5 ! dim9ution 9 ! field beg9s is ,t#b1 ! "t tak5 = a positive ion to cross f ,a to ,b "u ! electric field2 ?us f ,t#b we c calculate ! velocity ( ! positive ion 9 ?is field4 ,if we /ill fur!r dim9i% ,t1 we %all f9d t we rea* a value :5 ! dim9ution ( ! positive *>ge on ,b ) ! "t sudd5ly becomes mu* m rapid2 ?is *ange occurs :5 ,t falls bel[ ,t#a ! "t tak5 = ! negative ions to g f "o plate to ! o!r1 = n[ :5 ! field is rev]s$ !re are /ill "s negative ions left betwe5 ! plates1 & ^! w be driv5 aga9/ ,b & rob x ( "s ( ! positive *>ge x _h acquir$ be=e ! field 0 rev]s$4 ,by obs]v+ ! "t :5 ! increase 9 ! rate ( dim9ution ( ! positive *>ge ) ! "t sudd5ly sets 9 we c det]m9e ,t#a1 & h5ce ! velocity ( ! negative ions4 ,! velocity ( ! ions produc$ by ! dis*>ge ( electricity f a f9e po9t 0 det]m9$ by ,*attock by an entirely diff]5t me?od4 ,9 ?is case ! electric field is s /rong & ! velocity ( ! ion s great t ! prec$+ me?ods are n applicable4 ,suppose ,p repres5ts a v]tical ne$le dis*>g+ electricity into air1 consid] ! =ce act+ on ! ions includ$ betwe5 two horizontal planes ,a1 ,b4 ,if ,p is ! d5sity ( ! electrification1 & ,z ! v]tical compon5t ( ! electric int5sity1 ,f ! resultant =ce on ! ions betwe5 ,a & ,b is v]tical & equal to _/ _/ _/ ,zrhodxdydz4 _/_/_/ ,let u suppose t ! velocity ( ! ion is proportional to ! electric int5sity1 s t if w is ! v]tical velocity ( ! ions1 :i* are suppos$ all to be ( "o sign1 w ,,rz4 ,sub/itut+ ?is value ( ,z1 ! v]tical =ce on ! ions betwe5 ,a & ,b is equal to #a _/ _/ _/ - wrhodxdydz4 ,r _/_/_/ ,b integralintegralwrhodxdy iota1 :]e iota is ! curr5t /ream+ f ! po9t4 ,?is curr5t1 :i* c be easily measur$ by putt+ a galvanomet] 9 s]ies ) ! dis*>g+ po9t1 is indep5d5t ( z1 ! v]tical di/ance ( a plane betwe5 ,a & ,b bel[ ! *>g+ po9t4 ,h5ce we h iota _/ iota ,f ------ dz ------z4 ,r _/ ,r ,?is =ce mu/ be c\nt]balanc$ by ! diff]5ce ( gase\s pressures ov] ! planes ,a & ,b2 h5ce if p,b & p,a d5ote respectively ! pressures ov] ,b & ,a1 we h iota p,b - p,a ------ z4 ,r ,h5ce by ! measurem5t ( ^! pressures we c det]m9e ,r1 & h5ce ! velocity ) :i* an ion moves "u a giv5 electric int5sity4 ,!re are o!r me?ods ( det]m9+ ! velocities ( ! ions1 b z ^! dep5d on ! !ory ( ! conduction ( electricity ?r\gh a gas conta9+ *>g$ ions1 we %all consid] !m 9 our discussion ( t !ory4 ,by ! use ( ^! me?ods x has be5 %[n t ! velocities ( ! ions 9 a giv5 gas are ! same :e!r ! ionization is produc$ by ,rntg5 rays1 radioactive sub/ances1 ultra-violet light1 or by ! dis*>ge ( electricity f po9ts4 ,:5 ! ionization is produc$ by *emical action ! ions are v mu* less mobile1 mov+ 9 ! same electric field ) a velocity less ?an "o-?\s&? "p ( ! velocity ( ! fir/ k9d ( ions4 ,on ! o!r h&1 z we %all see lat]1 ! velocity ( ! negative ions 9 flames is enorm\sly great] ?an t ( ev5 ! fir/ k9d ( ion "u simil> electric fields & at ! same pressure4 ,b :5 ^! negative ions get into ! cold "p ( ! flame1 !y move sluggi%ly ) velocities ( ! ord] ( ^? possess$ by ! second k9d4 ,! results ( ! v>i\s det]m9ations ( ! velocities ( ! ions are giv5 9 ! foll[+ table4 ,! velocities are 9 c5timetres p] second "u an electric =ce ( "o volt p] c5timetre1 ! pressure ( ! gas be+ #a atmosph]e4 ,v d5otes ! velocity ( ! positive ion1 ,v- t ( ! negative4 ,v is ! mean velocity ( ! positive & negative ions4 ,velocities ( ,ions4--,ions produc$ by ,rntg5 ,rays4 ---------------------------------------- ----------------- ,gas4 ,v4 ,v-4 ,v4 ,obs]v]4 ---------------------------------------- ----------------- ,air 44 44 #a4f ,ru!r=d ,air 7dry7 #a4cf #a4hg 44 ,zel5y #a4fj #a4gj 44 ,langev9 #a4ci #a4gh 44 ,phillips #a4ed #a4gh 44 ,wellis* ,air 7moi/7 #a4cg #a4ha 44 ,zel5y ,oxyg5 7dry7 #a4cf #a4hj 44 ,oxyg5 7moi/7 #a4bi #a4eb 44 ,c>bonic acid 7dry7 #j4gf #j4ha 44 #j4hf #j4ij 44 ,langev9 #j4ha #j4he 44 ,wellis* ,c>bonic acid 7moi/7 #j4hb #j4ge 44 ,zel5y ,hydrog5 7dry7 #f4gj #g4ie 44 ,nitrog5 44 44 #a4f ,ru!r=d ,sulphur dioxide #j4dd #j4da 44 ,wellis* ,hydro*loric acid 44 44 #a4bg ,ru!r=d ,*lor9e 44 44 #a4j ,helium 7dry7 #e4ji #f4ca 44 ,franck & ,pohl ,c>bon monoxide #a4aj #a4ad 44 ,wellis* ,nitr\s oxide #j4hb #j4ij 44 ,ammonia #j4gd #j4hj 44 ,aldehyde #j4ca #j4cj 44 ,e?yl alcohol #j4cd #j4bg 44 ,acetone #j4ca #j4bi 44 ,e?yl *loride #j4cc #j4ca 44 ,p5tane #j4cf #j4ce 44 ,me?yl acetate #j4cc #j4cf 44 ,e?yl =mate #j4cj #j4ca 44 ,e?yl e!r #j4bi #j4ca 44 ,e?yl acetate #j4ca #j4bh 44 ,me?yl bromide #j4bi #j4bh 44 ,me?yl iodide #j4ba #j4bb 44 ,c>bon tetra*loride #j4cj #j4ca 44 ,e?yl iodide #j4ag #j4af 44 ---------------------------------------- ----------------- ,ions produc$ by ,ultra-,violet ,light4 ,air #a4d ,ru!r=d ,hydrog5 #c4i ,ru!r=d ,c>bonic acid #j4gh ,ru!r=d ,ions 9 ,gases suck$ f ,flames4 ,velocities v>y+ f 4#jd to 4#bc ,mc,clelland ,ions 9 ,flames conta9+ ,salts4 ,negative ions #ab4i cm4_/sec4 ,gold ions = salts ( ,li1 ,na1 ,k1 ,rb1 ,cs #fb ,h4 ,a4 ,wilson #bjj ,m>x #hj ,moreau ,ions lib]at$ by ,*emical ,action4 ,velocities ( ! ord] ( #j4jjje cm4_/sec4 ,blo* ,ions f ,po9t ,dis*>ge4 ---------------------------------------- ---- ,hydrog5 #e4d #g4dc #f4da ,*attock ,c>bonic acid #j4hc #j4ibe #j4hh ,*attock ,air #a4cb #a4hj #a4ee ,*attock ,oxyg5 #a4cj #a4he #a4eg ,*attock ---------------------------------------- ---- ,x w be se5 f ?is table t ! great] mobility ( ! negative ions is v mu* m m>k$ 9 ! case ( ! light] & simpl] gases ?an 9 t ( ! heavi] & m complicat$ ones2 ) ! vap\rs ( organic sub/ances !re seems b little diff]5ce betwe5 ! mobilities ( ! positive & negative ions1 inde$ 9 "o or two cases ! positive "o seems slightly b v slightly ! m mobile ( ! two4 ,9 ! case ( ! simple gases ! diff]5ce is mu* great] :5 ! gases are dry ?an :5 !y are moi/4 ,x has be5 %[n by direct exp]im5t t ! velocities are directly proportional to ! electric =ce4 ,v>iation ( ,velocities ) ,pressure4--,until ! pressure gets l[ ! velocities ( ! ions1 negative z well z positive1 v>y inv]sely z ! pressure4 ,langev9 7loc4 cit47 0 ! fir/ to %[ t at v l[ pressures ! velocity ( ! negative ions increases m rapidly z ! pressure is dim9i%$ ?an ?is law indicates4 ,if ! nature ( ! ion did n *ange ) ! pressure1 ! k9etic !ory ( gases indicates t ! velocity w\ld v>y inv]sely z ! pressure1 s t ,langev9's results indicate a *ange 9 ! nature ( ! negative ion :5 ! pressure is dim9i%$ bel[ a c]ta9 value4 ,langev9's results are giv5 9 ! foll[+ table1 :]e p repres5ts ! pressure measur$ 9 c5timetres ( m]cury1 ,v & ,v- ! velocities ( ! positive & negative ions 9 air "u unit electro/atic =ce1 i4e4 #cjj volts p] c5timetre3-- ---------------------------------------- ---- ,negative ,ions4 ,positive ,ions4 ---------------------------------------- p4 ,v-4 p,v-_/#gf4 p4 ,v4 p,v_/#gf4 ---------------------------------------- #g4e #fefj #fdg #g4e #ddcj #dcg #bj4j #bbjd #ehj #bj4j #afcd #dcj #da4e #iid #ecj #da4e #ghb #dbg #gf4j #eaj #eaj #gf4j #dhj #dbj #adb4j #bgj #eje #adb4j #bbe #dbe ---------------------------------------- ,! increase 9 ! case ( p,v- indicates t ! /ructure ( ! negative ion gets simpl] z ! pressure is r$uc$4 ,wallis* 9 "s exp]im5ts made at ! ,cav5di% ,laboratory f\nd t ! dim9ution 9 ! value ( p,v- at l[ pressures is mu* m m>k$ 9 "s gases ?an 9 o!rs1 & 9 "s gases he fail$ to detect x2 b x mu/ be rememb]$ t x is difficult to get measurem5ts at pressures ( only a few millimetres1 z ! am\nt ( ionization is s exce$+ly small at su* pressures t ! quantities to be obs]v$ are h>dly l>ge en\gh to admit ( accurate measurem5ts by ! me?ods available at high] pressures4 ,effect ( ,temp]ature on ! ,velocity ( ! ,ions4--,phillips 7,proc4 ,roy4 ,soc41 #aijf1 #gh1 p4 #afg7 inve/igat$1 us+ ,langev9's me?od1 ! velocities ( ! & - ions ?r\gh air at atmosph]ic pressure at temp]atures rang+ f t ( boil+ liquid air to #daa ,c42 ,r#a & ,r#b are ! velocities ( ! & - ions respectively :5 ! =ce is a volt p] c5timetre4 ----------------------------------- ,r#a4 ,r#b4 ,temp]ature ,absolute4 ----------------------------------- #b4jj #b4die #daa #a4ie #b4dj #cii #a4he #b4cj #chc #a4ha #b4ba #cgc #a4fg #b4abe #cdh #a4fj #b4jj #ccc #a4ci #a4ghe #bhe #j4ide #a4bc #bji #j4bce #j4bce #id ----------------------------------- ,we see t except 9 ! case ( ! l[e/ temp]ature1 t ( liquid air1 :]e !re is a great drop 9 ! velocity1 ! velocities ( ! ions are proportional to ! absolute temp]ature4 ,on ! hypo!sis ( an ion ( con/ant size we %\ld1 f ! k9etic !ory ( gases1 expect ! velocity to be proportional to ! squ>e root ( ! absolute temp]ature1 if ! *>ge on ! ion did n affect ! numb] ( collisions betwe5 ! ion & ! molecules ( ! gas ?r\gh :i* x is mov+4 ,if ! collisions 7 br\ght ab\t by ! electrical attraction betwe5 ! ions & ! molecules1 ! velocity w\ld be proportional to ! absolute temp]ature4 ,h4 ,a4 ,wilson 7,phil4 ,trans4 #aib1 p4 #dii71 9 8 exp]im5ts on ! conduction ( flames & hot gases into :i* salts _h be5 put1 f\nd t ! velocity ( ! positive ions 9 flames at a temp]ature ( #bjjj ,c4 conta9+ ! salts ( ! alkali metals 0 #fb cm4_/sec4 "u an electric =ce ( "o volt p] c5timetre1 :ile ! velocity ( ! positive ions 9 a /ream ( hot air at #ajjj ,c4 conta9+ ! same salts 0 only #g cm4_/sec4 "u ! same =ce4 ,! great effect ( temp]ature is also %[n 9 "s exp]im5ts ( ,mc,clelland 7,phil4 ,mag4 #e1 #df1 p4 #bi7 on ! velocities ( ! ions 9 gases drawn f ,buns5 flames & arcs2 he f\nd t ^! dep5d$ ^u ! di/ance ! gas _h travell$ f ! flame4 ,?us1 ! velocity ( ! ions at a di/ance ( #e4e cm4 f ! ,buns5 flame :5 ! temp]ature 0 #bcj ,c4 0 4#bc cm4_/sec4 = a volt p] c5timetre2 at a di/ance ( #aj cm4 f ! flame :5 ! temp]ature 0 #afj ,c4 ! velocity 0 4#ba cm4_/sec2 :ile at a di/ance ( #ad4e cm4 f ! flame :5 ! temp]ature 0 #aje ,c4 ! velocity 0 only 4#jd cm4_/sec4 ,if ! temp]ature ( ! gas at ?is di/ance f ! flame 0 rais$ by ext]nal means1 ! velocity ( ! ions increas$4 ,we c d]ive "s in=mation z to ! con/itution ( ! ions by calculat+ ! velocity ) :i* a molecule ( ! gas w\ld move 9 ! electric field if x c>ri$ ! same *>ge z ! ion4 ,f ! !ory ( ! diffusion ( gases1 z develop$ by ,maxwell1 we "k t if ! p>ticles ( a gas ,a are surr\nd$ by a gas ,b1 !n1 if ! p>tial pressure ( ,a is small1 ! velocity u ) :i* its p>ticles w move :5 act$ ^u by a =ce ,xe is giv5 by ! equation ,xe u ------- ,d1 7p#a_/,n#a7 :]e ,d repres5ts ! coeffici5t ( int]-diffusion ( ,a into ,b1 & ,n#a ! numb] ( p>ticles ( ,a p] cubic c5timetre :5 ! pressure due to ,a is p#a4 ,let u calculate by ?is equation ! velocity ) :i* a molecule ( hydrog5 w\ld move ?r\gh hydrog5 if x c>ri$ ! *>ge c>ri$ by an ion1 :i* we %all prove %ortly to be equal to ! *>ge c>ri$ by an atom ( hydrog5 9 ! electrolysis ( solutions4 ,s9ce p#a_/,n#a is indep5d5t ( ! pressure1 x is equal to ,pi_/,n1 :]e ,pi is ! atmosph]ic pressure & ,n ! numb] ( molecules 9 a cubic c5timetre ( gas at atmosph]ic pressure4 ,n[ ,ne #a4bb #ajaj1 if e is measur$ 9 electro/atic units2 ,pi #ajf & ,d 9 ?is case is ! coeffici5t ( diffusion ( hydrog5 into itself1 & is equal to #a4g4 ,sub/itut+ ^! values we f9d u #a4ig #ajd,x4 ,if ! pot5tial gradi5t is #a volt p] c5timetre1 ,x #a_/cjj4 ,sub/itut+ ?is value = ,x1 we f9d u #ff cm4_/sec1 = ! velocity ( a hydrog5 molecule4 ,we h se5 t ! velocity ( ! ion 9 hydrog5 is only ab\t #e cm4_/sec1 s t ! ion moves m sl[ly ?an x w\ld if x 7 a s+le molecule4 ,"o way ( expla9+ ?is is to suppose t ! ion is bigg] ?an ! molecule1 & is 9 fact an aggregation ( molecules1 ! *>g$ ion act+ z a nucleus ar\nd :i* molecules collect l du/ r\nd a *>g$ body4 ,?is view is support$ by ! effect produc$ by moi/ure 9 dim9i%+ ! velocity ( ! negative ion1 =1 z ,c4 ,t4 ,r4 ,wilson 7,phil4 ,trans4 #aic1 p4 #bhi7 has %[n1 moi/ure t5ds to collect r\nd ! ions1 & cond5ses m easily on ! negative ?an on ! positive ion4 ,9 connexion ) ! velocities ( ions 9 ! gases drawn f flames1 we f9d o!r in/ances :i* sugge/ t cond5sation takes place r\nd ! ions4 ,an increase 9 ! size ( ! sy/em is n1 h[ev]1 ! only way by :i* ! velocity might fall bel[ t calculat$ = ! hydrog5 molecule1 = we mu/ rememb] t ! hydrog5 molecule1 ^: coeffici5t ( diffusion is #a4g1 is n *>g$1 :ile ! ion is4 ,! =ces ex]t$ by ! ion on ! o!r molecules ( hydrog5 are n ! same z ^? :i* w\ld be ex]t$ by a molecule ( hydrog51 & z ! coeffici5t ( diffusion dep5ds on ! =ces betwe5 ! molecules1 ! coeffici5t ( diffusion ( a *>g$ molecule into hydrog5 might be v diff]5t f t ( an un*>g$ "o4 ,wellis* 7loc4 cit47 has %[n t ! effect ( ! *>ge on ! ion is suffici5t 9 _m cases to expla9 ! small velocity ( ! ions1 ev5 if !re 7 no aggregation4 ,mixture ( ,gases4--,! ionization ( a mixture ( gases raises "s v int]e/+ que/ions4 ,if we ionize a mixture ( two v diff]5t gases1 say hydrog5 & c>bonic acid1 & inve/igate ! nature ( ! ions by measur+ _! velocities1 ! "q arises1 %all we f9d two k9ds ( positive & two k9ds ( negative ions mov+ ) diff]5t velocities1 z we %\ld d if "s ( ! positive ions 7 positively *>g$ hydrog5 molecules1 :ile o!rs 7 positively *>g$ molecules ( c>bonic acid2 or %all we f9d only "o velocity = ! positive ions & "o = ! negative8 ,_m exp]im5ts h be5 made on ! velocity ( ions 9 mixtures ( two gases1 b z yet no evid5ce has be5 f\nd ( ! exi/5ce ( two diff]5t k9ds ( ei!r positive or negative ions 9 su* mixtures1 al?\gh "s ( ! me?ods = det]m9+ ! velocities ( ! ions1 especially ,langev9's1 ought to give evid5ce ( ?is effect1 if x exi/$4 ,! exp]im5ts seem to %[ t ! positive 7& ! same is true = ! negative7 ions 9 a mixture ( gases are all ( ! same k9d4 ,?is conclusion is "o ( consid]able importance1 z x w\ld n be true if ! ions consi/$ ( s+le molecules ( ! gas f :i* !y are produc$4 ,recomb9ation4--,sev]al me?ods enable u to d$uce ! coeffici5t ( recomb9ation ( ! ions :5 we "k _! velocities4 ,p]haps ! simple/ ( ^! consi/s 9 det]m9+ ! relation betwe5 ! curr5t pass+ betwe5 two p>allel plates imm]s$ 9 ioniz$ gas & ! pot5tial diff]5ce betwe5 ! plates4 ,= let q be ! am\nt ( ionization1 i4e4 ! numb] ( ions produc$ p] second p] unit volume ( ! gas1 ,a ! area ( "o ( ! plates1 & d ! di/ance betwe5 !m2 !n if ! ionization is con/ant ?r\gh ! volume1 ! numb] ( ions ( "o sign produc$ p] second 9 ! gas is q,ad4 ,n[ if i is ! curr5t p] unit area ( ! plate1 e ! *>ge on an ion1 i,a_/e ions ( ea* sign are driv5 out ( ! gas by ! curr5t p] second4 ,9 addition to ?is s\rce ( loss ( ions !re is ! loss due to ! recomb9ation2 if n is ! numb] ( positive or negative ions p] unit volume1 !n ! numb] :i* recomb9e p] second is alphan p] cubic c5timetre1 & if n is con/ant ?r\gh ! volume ( ! gas1 z w approximately be ! case if ! curr5t ?r\gh ! gas is only a small fraction ( ! saturation curr5t1 ! numb] ( ions :i* disappe> p] second ?r\gh recomb9ation is alphan,ad4 ,h5ce1 s9ce :5 ! gas is 9 a /eady /ate ! numb] ( ions produc$ mu/ be equal to ! numb] :i* disappe>1 we h q,ad i,a_/e alphan,ad1 q i_/ed alphan#b4 ,if u#a & u#b are ! velocities ) :i* ! positive & negative ions move1 nu#a;e & nu#b;e are respectively ! quantities ( positive electricity pass+ 9 "o direction ?r\gh unit area ( ! gas p] second1 & ( negative 9 ! opposite direction1 h5ce i nu#a;e nu#b;e4 ,if ,x is ! electric =ce act+ on ! gas1 k#a & k#b ! velocities ( ! positive & negative ions "u unit =ce1 u#a k#a,x1 u#b k#b,x2 h5ce n i_/7k#a k#b7,xe1 & we h i alphai q -- --------------4 ed 7k#a k#b7;e,x ,b q$ is ! saturation curr5t p] unit area ( ! plate2 call+ ?is ,i1 we h dalphai ,i - i ------------- e7k#a k#b7,x or idalpha ,x ------------------4 e7,i - i77k#a k#b7 ,h5ce if we det]m9e correspond+ values ( ,x & i we c d$uce ! value ( alpha_/e if we also "k 7k#a k#b74 ,! value ( ,i is easily det]m9$1 z x is ! curr5t :5 ,x is v l>ge4 ,! prec$+ result only applies :5 i is small comp>$ ) ,i1 z x is only 9 ?is case t ! values ( n & ,x are uni=m ?r\gh\t ! volume ( ! gas4 ,ano!r me?od :i* answ]s ! same purpose is due to ,langev9 7,ann4 ,*im4 ,phys41 #aijc1 #bh1 p4 #bhi72 x is z foll[s4 ,let ,a & ,b be two p>allel planes imm]s$ 9 a gas1 & let a slab ( ! gas b\nd$ by ! planes a1 b p>allel to ,a & ,b be ioniz$ by an in/antane\s fla% ( ,rntg5 rays4 ,if ,a & ,b are at diff]5t electric pot5tials1 !n all ! positive ions produc$ by ! rays w be attract$ by ! negative plate & all ! negative ions by ! positive1 if ! electric field 7 exce$+ly l>ge !y w\ld rea* ^! plates be=e !y _h "t to recomb9e1 s t ea* plate w\ld receive ,n#j ions if ! fla% ( ,rntg5 rays produc$ ,n#j positive & ,n#j negative ions4 ,) weak] fields ! numb] ( ions receiv$ by ! plates w be less z "s ( !m w recomb9e be=e !y c rea* ! plates4 ,we c f9d ! numb] ( ions :i* rea* ! plates 9 ?is case 9 ! foll[+ way3--,9 consequ5ce ( ! movem5t ( ! ions ! slab ( ioniz$ gas w broad5 out & w consi/ ( ?ree portions1 "o 9 :i* !re are no?+ b positive ions1--?is is on ! side ( ! negative plate1--ano!r on ! side ( ! positive plate 9 :i* !re are no?+ b negative ions1 & a portion betwe5 ^! 9 :i* !re are bo? positive & negative ions2 x is 9 ?is lay] t recomb9ation takes place1 & "h if n is ! numb] ( positive or negative ions at ! "t t aft] ! fla% ( ,rntg5 rays1 n n#j_/7a alphan#jt74 ,) ! same notation z be=e1 ! bread? ( ei!r ( ! out] lay]s w 9 "t dt increase by ,x7k#a k#b7;dt1 & ! numb] ( ions 9 x by ,x7k#a k#b7ndt2 ^! ions w rea* ! plate1 ! out] lay]s w receive fre% ions until ! middle "o disappe>s1 :i* x w d aft] a "t l_/,x7k#a k#b71 :]e l is ! ?ickness ( ! slab ab ( ioniz$ gas2 h5ce ,n1 ! numb] ( ions rea*+ ei!r plate1 is giv5 by ! equation _/ l_/,x7k#ak#b7 n#j,x7k#a k#b7 ,x7k#a k#b7 _/ n#j;alphal ,n --------------dt ---------- log7 #a ---------- 74 _/ #j #a n#j;alphat alpha ,x7k#a k#b7 _/ ,if ,q is ! *>ge receiv$ by ! plate1 ,x _/ ,q#j;epsilon ,q ,ne -------------- log 7 #a ----------- 71 #dpiepsilon #dpi,x _/ :]e ,q#j n#jle is ! *>ge receiv$ by ! plate :5 ! electric =ce is l>ge en\gh to prev5t recomb9ation1 & epsilon alpha#dpie7,r#a ,r#b74 ,we c f ?is result d$uce ! value ( epsilon & h5ce ! value ( alpha :5 ,r#a,r#b is kn[n4 ,di/ribution ( ,electric ,=ce :5 a ,curr5t is pass+ ?r\gh an ,ioniz$ ,gas4--,let ! two plates be at "r angles to ! axis ( x2 !n we may suppose t betwe5 ! plates ! electric int5sity ,x is ev]y:]e p>allel to ! axis ( x4 ,! velocities ( bo? ! positive & negative ions are assum$ to be proportional to ,x4 ,let k#a,x1 k#b,x repres5t ^! velocities respectively2 let n#a1 n#b be respectively ! numb] ( positive & negative ions p] unit volume at a po9t fix$ by ! co-ord9ate x2 let q be ! numb] ( positive or negative ions produc$ 9 unit "t p] unit volume at ?is po9t2 & let ! numb] ( ions :i* recomb9e 9 unit volume 9 unit "t be alphan#an#b2 !n if e is ! *>ge on ! ion1 ! volume d5sity ( ! electrification is 7n#a - n#b7;e1 h5ce d,x -- #dpi7n#a - n#b7;e 7#a74 dx ,if ,i is ! curr5t ?r\gh unit area ( ! gas & if we neglect any diffusion except t caus$ by ! electric field1 n#a;ek#a,x n#b;ek#b,x ,i 7#b74 ,f equations 7#a7 & 7#b7 we h #a _/ ,i k#b d,x n#a;e ------- 7 - ----- -- 7 7#c71 k#a k#b ,x #dpi dx _/ #a _/ ,i k#a d,x n#b;e ------- 7 - - ----- -- 7 7#d71 k#a k#b ,x #dpi dx _/ & f ^! equations we c1 if we "k ! di/ribution ( electric int5sity betwe5 ! plates1 calculate ! numb] ( positive & negative ions4 ,9 a /eady /ate ! numb] ( positive & negative ions 9 unit volume at a giv5 place rema9s con/ant1 h5ce neglect+ ! loss by diffusion1 we h d --7k#an#a,x7 q - alphan#an#b 7#e74 dx d - --7k#bn#b,x7 q - alphan#an#b 7#f74 dx ,if k#a & ,k#b are con/ant1 we h f 7#a71 7#e7 & 7#f7 d,x _/ #a #a ---- #hpie7q - alphan#an#b77 --- --- 7 7#g71 dx k#a k#b _/ an equation :i* is v useful1 because x enables u1 if we "k ! di/ribution ( ,x1 to f9d :e!r at any po9t 9 ! gas ! ionization is great] or less ?an ! recomb9ation ( ! ions4 ,we see t q - alphan#an#b1 :i* is ! excess ( ionization ov] recomb9ation1 is proportional to d,x_/dx4 ,?us :5 ! ionization exce$s ! recomb9ation1 i4e4 :5 q - alphan#an#b is positive1 ! curve = ,x is convex to ! axis ( x1 :ile :5 ! recomb9ation exce$s ! ionization ! curve = ,x w be concave to ! axis ( x4 ,?us1 = example1 fig4 #aa repres5ts ! curve = ,x obs]v$ by ,graham 7,wi$4 ,ann4 #fd1 p4 #di7 9 a tube ?r\gh :i* a /eady curr5t is pass+4 ,int]pret+ x by equation 7#g71 we inf] t ionization 0 mu* 9 excess ( recomb9ation at ,a & ,b1 slightly s along ,c1 :ile along ,d ! recomb9ation exce$$ ! ionization4 ,sub/itut+ 9 equation 7#g7 ! values ( n#a1 n#b giv5 9 7#c71 7#d71 we get d,x alpha _/ k d,x _/ k#b d,x _/ #a #a ---- #hpie q - -------------- 7#a ----- --- 7 7#a - ----- --- 7 7 --- --- 7 7#h74 dx e,x7k#a k#b7 #hpi dx _/ #hpi dx _/ k#a k#b _/ ,illu/ration3 ,fig4 #aa4 ,?is equation c be solv$ 7see ,?omson1 ,phil4 ,mag4 xlvii4 ,p4 #bec71 :5 q is con/ant & k#a k#b4 ,f ! solution x appe>s t if ,x#a be ! value ( x close to "o ( ! plates1 & ,x#j ! value midway betwe5 !m1 #a ,x#a_/,x#j ------------------ beta - #b_/;beta :]e beta #hpiek#a_/;alpha4 ,s9ce e #d #aj-aj1 alpha #b #aj-f1 & k#a = air at atmosph]ic pressure #dej1 beta is ab\t #b4c = air at atmosph]ic pressure & x becomes mu* great] at l[] pressures4 ,?us ,x#a_/,x#j is always great] ?an unity1 & ! value ( ! ratio increases f unity to inf9ity z beta increases f z]o to inf9ity4 ,z beta does n involve ei!r q or ,i1 ! ratio ( ,x#a to ,x#j is indep5d5t ( ! /r5g? ( ! curr5t & ( ! int5sity ( ! ionization4 ,no g5]al solution ( equation 7#h7 has be5 f\nd :5 k#a is n equal to k#b1 b we c get an approximation to ! solution :5 q is con/ant4 ,! equations 7#a71 7#b71 7#c71 7#d7 are satisfi$ by ! values-- n#a n#b 7q _/ alpha7 k#a k#an#a,xe ------- ,i1 k#a k#b k#b k#bn#b,xe ------- ,i1 k#a k#b _/alpha ,i ,x 7 ------- 7 ----------4 q _/ e7k#a k#b7 ,^! solutions _c1 h[ev]1 hold "r up to ! surface ( ! plates1 = across ea* unit ( area1 at a po9t ,p1 k#a;,i_/7k#ak#b7;e positive ions pass 9 unit "t1 & ^! mu/ all come f ! region betwe5 ,p & ! positive plate4 ,if lambda is ! di/ance ( ,p f ?is plate1 ?is region _c furni% m ?an qlambda positive ions1 & only ?is numb] if !re are no recomb9ations4 ,h5ce ! solution _c hold :5 qlambda is less ?an k#a;,i_/7k#a k#b7;e1 or :]e lambda is less ?an k#a;,i_/7k#a k#b7qe4 ,simil>ly ! solution _c hold ne>] to ! negative plate ?an ! di/ance k#b;,i_/7k#a k#b7qe4 ,illu/ration3 ,,fig4 #ab4 ,! =ce 9 ^! lay]s w be great] ?an t 9 ! middle ( ! gas1 & s ! loss ( ions by recomb9ation w be small] 9 comp>ison ) ! loss due to ! removal ( ! ions by ! curr5t4 ,if we assume t 9 ^! lay]s ! loss ( ions by recomb9ation c be neglect$1 we c by ! me?od ( ! next article f9d an expression = ! value ( ! electric =ce at any po9t 9 ! lay]4 ,?is1 9 conjunction ) ! value _/alpha ,i ,x#j 7 ------- 7 ---------- q _/ e7k#a k#b7 = ! gas outside ! lay]1 w give ! value ( ,x at any po9t betwe5 ! plates4 ,x foll[s f ?is inve/igation t if ,x#a & ,x#b are ! values ( ,x at ! positive & negative plates respectively1 & ,x#j ! value ( ,x outside ! lay]1 _/ k#a ,i _/ k#b ,i ,x#a ,x#j 7 ,i -- --------- 7 1 ,x#b ,x#j 7 ,i -- --------- 7 1 k#b epsilon_/ k#a epsilon_/ :]e epsilon alpha_/#dpie7k#a k#b74 ,langev9 f\nd t = air at a pressure ( #aeb mm4 epsilon #j4ja1 at #cge mm4 epsilon #j4jf1 & at #gfj mm4 epsilon #j4bg4 ,?us at fairly l[ pressures #a_/;epsilon is l>ge1 & we h approximately _/k#a ,i _/k#b ,i ,x#a ,x#j 7 -- 7 ---------------1 ,x#b ,x#j 7 -- 7 ---------------4 k#b_/ rootepsilon k#a_/ rootepsilon ,!re=e ,x#a_/,x#b k#a_/k#b1 or ! =ce at ! positive plate is to t at ! negative plate z ! velocity ( ! positive ion is to t ( ! negative ion4 ,?us ! =ce at ! negative plate is great] ?an t at ! positive4 ,! falls ( pot5tial ,v#a1 ,v#b at ! two lay]s :5 #a_/;epsilon is l>ge c be %[n to be giv5 by ! equations _/epsilon#c_/b _/k#aa_/b ,v#a #hpi7 --------- 7 k#a 7 -- 7 i1 q alpha_/ k#b_/ _/epsilon#c_/b _/k#ba_/b ,v#b #hpi7 --------- 7 k#b 7 -- 7 i1 q alpha_/ k#a_/ h5ce ,v#a_/,v#b k#a_/k#b1 s t ! pot5tial falls at ! electrodes are proportional to ! squ>es ( ! velocities ( ! ions4 ,! *ange 9 pot5tial across ! lay]s is proportional to ! squ>e ( ! curr5t1 :ile ! pot5tial *ange betwe5 ! lay]s is proportional to ! curr5t1 ! total pot5tial diff]5ce betwe5 ! plates is ! sum ( ^! *anges1 h5ce ! relation betwe5 ,v & i w be ( ! =m ,v ,ai ,bi4 ,mie 7,ann4 d]4 ,phys41 #aijd1 #ac1 ,p4 #heg7 has by ! me?od ( successive approximations obta9$ solutions ( equation 7#h7 7i47 :5 ! curr5t is only a small fraction ( ! saturation curr5t1 7ii47 :5 ! curr5t is ne>ly saturat$4 ,! results ( 8 inve/igations are repres5t$ 9 fig4 #ab1 :i* repres5ts ! di/ribution ( electric =ce along ! pa? ( ! curr5t = v>i\s values ( ! curr5t express$ z fractions ( ! saturation curr5t4 ,x w be se5 t until ! curr5t am\nts to ab\t "o-fif? ( ! maximum curr5t1 ! type ( solution is ! "o j indicat$1 i4e4 ! electric =ce is con/ant except 9 ! neighb\rhood ( ! electrodes :5 x increases rapidly4 ,?\gh we are unable to obta9 a g5]al solution ( ! equation 7#h71 !re are "s v important special cases 9 :i* t equation c be solv$ )\t difficulty4 ,we %all consid] two ( ^!1 ! fir/ be+ t :5 ! curr5t is saturat$4 ,9 ?is case !re is no loss ( ions by recomb9ation1 s t us+ ! same notation z be=e we h d --7n#ak#a,x7 q1 dx d --7n#bk#b,x7 -q4 dx ,! solutions ( :i* if q is con/ant are n#ak#a,x qx1 n#bk#b,x ,i_/e - qx q7l - x71 if l is ! di/ance betwe5 ! plates1 & x #j at ! positive electrode4 ,s9ce d,x_/dx #dpi7n#a - n#b7;e1 we get #a d,x _/ #a #a l ----- --- qx 7 -- -- 7 - q --1 #hpi dx k#a k#b _/ k#b or ,x x _/ #a #a lx ----- q -- 7 -- -- 7 - q -- ,c1 #hpi #b k#a k#b _/ k#b :]e ,c is a quantity to be det]m9$ by ! condition t _/ l ,xdx ,v1 _/#j :]e ,v is ! giv5 pot5tial diff]5ce betwe5 ! plates4 ,:5 ! =ce is a m9imum d,x_/dx #j1 h5ce at ?is po9t lk#a lk#b x -------1 l - x -------4 k#a k#b k#a k#b ,h5ce ! ratio ( ! di/ances ( ?is po9t f ! positive & negative plates respectively is equal to ! ratio ( ! velocities ( ! positive & negative ions4 ,! o!r case we %all consid] is ! v important "o 9 :i* ! velocity ( ! negative ion is exce$+ly l>ge comp>$ ) ! positive2 ?is is ! case 9 flames :]e1 z ,gold 7,proc4 ,roy4 ,soc4 #ig1 p4 #dc7 has %[n1 ! velocity ( ! negative ion is _m ?\s& times ! velocity ( ! positive2 x is also v probably ! case 9 all gases :5 ! pressure is l[4 ,we may get ! solution ( ?is case ei!r by putt+ k#a_/k#b #j 9 equation 7#h71 or indep5d5tly z foll[s3--,us+ ! same notation z be=e1 we h i n#ak#a,xe n#bk#b,xe1 d --7n#bk#b,x7 q - alphan#an#b1 dx d,x -- #dpi7n#a - n#b7;e4 dx ,9 ?is case practically all ! curr5t is c>ri$ by ! negative ions s t i n#bk#b,xe1 & !re=e q alphan#an#b4 ,?us n#b i_/k#b,xe1 n#a qk#b,xe_/alphai4 ,?us d,x #dpiek#bq,x #dpii -- ----------- - ------1 dx alphai k#b,x or d,x #hpiek#bq,x #hpii -- - ------------ - ------4 dx alphai k#b ,! solution ( ?is equation is alpha i ,x ------- ----- ,cepsilon7#hpiek#bqx_/alphai7 q k#b;e ,"h x is measur$ f ! positive electrode2 x is m conv5i5t 9 ?is case1 h[ev]1 to measure x f ! negative electrode4 ,if x be ! di/ance f ! negative electrode at :i* ! electric =ce is ,x1 we h f equation 7#g7 alpha i ,x ------- ----- ,cepsilon7#hpiek#bqx_/alphai7 q k#b;e ,to f9d ! value ( ,c we see by equation 7#g7 t d,x k#ak#b #a --- ------- ------ q - alphan#an#b2 d,x k#a k#b #hpie h5ce d,x k#ak#b #a x#a _/ x#a --- ------- ------ 7q - alphan#an#b7;dx4 d,x k#a k#b #hpie _/#j ,! "r h& side ( ?is equation is ! excess ( ionization ov] recomb9ation 9 ! region ext5d+ f ! ca?ode to x#a2 x mu/ !re=e1 :5 ?+s are 9 a /eady /ate1 equal ! excess ( ! numb] ( negative ions :i* leave ?is region ov] ^? :i* ent] x4 ,! numb] :i* leave is i_/e & ! numb] :i* ent] is i#j_/;e1 if x is ! curr5t ( negative ions com+ f unit area ( ! ca?ode1 z hot metal ca?odes emit l>ge quantities ( negative electricity i#j may 9 "s cases be consid]able1 ?us ! "r h& side ( equation is 7i - i#j7_/;e4 ,:5 x#a is l>ge d,x_/dx #j2 h5ce we h f equation alphai7i - i#j7 k#a k#b ,c ---------------- -------1 qk#ak#b;e k#b & s9ce k#a is small comp>$ ) k#b1 we h alphai _/ k#b i - i#j ,x --------- 7#a -- ------ epsilon-#hpiek#bqx_/alphai 74 qk#b;e k#a i _/ ,f ! values :i* h be5 f\nd = k#b & alpha1 we "k t #hpiek#b_/;alpha is a l>ge quantity1 h5ce ! second t]m inside ! bracket w be v small :5 eqx is equal to or great] ?an i2 ?us ?is t]m w be v small outside a lay] ( gas next ! ca?ode ( su* ?ickness t ! numb] ( ions produc$ on x w\ld be suffici5t1 if !y 7 all utiliz$ = ! purpose1 to c>ry ! curr5t2 9 ! case ( flames ?is lay] is exce$+ly ?9 unless ! curr5t is v l>ge4 ,! value ( ! electric =ce 9 ! uni=m "p ( ! field is equal to i_/k#b;eroot7alpha_/q71 :ile :5 i#j #j1 ! =ce at ! ca?ode itself be>s to ! uni=m =ce ! ratio ( 7k#a k#b7 to k#a4 ,z k#a is _m ?\s& times k#b ! =ce increases ) great rapidity z we approa* ! ca?ode2 ?is is a v *>act]i/ic feature ( ! passage ( electricity ?r\gh flames & hot gases4 ,?us 9 an exp]im5t made by ,h4 ,a4 ,wilson ) a flame #ah cm4 long1 ! drop ( pot5tial )9 #a c5timetre ( ! ca?ode 0 ab\t five times ! drop 9 ! o!r #ag cm4 ( ! tube4 ,! relation betwe5 ! curr5t & ! pot5tial diff]5ce :5 ! velocity ( ! negative ion is mu* great] ?an ! positive is v easily obta9$4 ,s9ce ! =ce is uni=m & equal to i_/k#b;eroot7alpha_/q71 until we get close to ! ca?ode ! fall ( pot5tial 9 ?is "p ( ! dis*>ge w be v approximately equal to i_/k#b;eroot7alphal_/q71 :]e l is ! di/ance betwe5 ! electrodes4 ,close to ! ca?ode1 ! electric =ce :5 i#j is n ne>ly equal to i is approximately giv5 by ! equation i _/alpha ,x --------- 7---------7 epsilon-#dpiek#bqx_/alphai1 e7k#ak#b7 q _/ 1 & ! fall ( pot5tial at ! ca?ode is equal approximately to oo _/ ,x dx1 _/#j t is to i _/alpha alpha i --------- 7---------7 ----------4 e7k#ak#b7 q _/ #dpiek#bq ,! pot5tial diff]5ce betwe5 ! plates is ! sum ( ! fall ( pot5tial 9 ! uni=m "p ( ! dis*>ge plus ! fall at ! ca?ode1 h5ce _/alpha i _/ ialpha #a ,v 7---------7 --- 7 il --------- ------------ 74 q _/ ek#b #dpieq root7k#ak#b7_/ ,! fall ( pot5tial at ! ca?ode is proportional to ! squ>e ( ! curr5t1 :ile ! fall 9 ! re/ ( ! circuit is directly proportional to ! curr5t4 ,9 ! case ( flames or hot gases1 ! fall ( pot5tial at ! ca?ode is mu* great] ?an t 9 ! re/ ( ! circuit1 s t 9 su* cases ! curr5t ?r\gh ! gas v>ies ne>ly z ! squ>e root ( ! pot5tial diff]5ce4 ,! equation we h j obta9$ is ( ! =m ,v ,ai ,bi1 & ,h4 ,a4 ,wilson has %[n t a relation ( ?is =m repres5ts ! results ( 8 exp]im5ts on ! conduction ( electricity ?r\gh flames4 ,! expression = ! fall ( pot5tial at ! ca?ode is inv]sely proportional to q7#c_/b71 q be+ ! numb] ( ions produc$ p] cubic c5timetre p] second close to ! ca?ode2 ?us any increase 9 ! ionization at ! ca?ode w dim9i% ! pot5tial fall at ! ca?ode1 & z practically ! :ole pot5tial diff]5ce betwe5 ! electrodes occurs at ! ca?ode1 a dim9ution 9 ! pot5tial fall !re w be mu* m important ?an a dim9ution 9 ! electric =ce 9 ! uni=m "p ( ! dis*>ge1 :5 ! =ce is comp>atively insignificant4 ,?is consid]ation expla9s a v /rik+ ph5om5on discov]$ _m ye>s ago by ,hittorf1 :o f\nd t if he put a wire c>ry+ a bead ( a volatile salt into ! flame1 x produc$ little effect ^u ! curr5t1 unless x 7 plac$ close to ! ca?ode :]e x gave rise to an enorm\s increase 9 ! curr5t1 sometimes increas+ ! curr5t m ?an a hundr$fold4 ,! introduction ( ! salt increases v l>gely ! numb] ( ions produc$1 s t q is mu* great] = a salt$ flame ?an = a pla9 "o4 ,?us ,hittorf's result co9cides ) ! conclusions we h drawn f ! !ory ( ?is class ( conduction4 ,! fall ( pot5tial at ! ca?ode is proportional to i - i#j1 :]e i#j is ! /ream ( negative electricity :i* comes f ! ca?ode itself1 ?us z i#j increases ! fall ( pot5tial at ! ca?ode dim9i%es & ! curr5t s5t by a giv5 pot5tial diff]5ce ?r\gh ! gas increases4 ,n[ all metals give out negative p>ticles :5 heat$1 at a rate :i* increases v rapidly ) ! temp]ature1 b at ! same temp]ature "s metals give out m ?an o!rs4 ,if ! ca?ode is made ( a metal :i* emits l>ge quantities ( negative p>ticles1 7i - i#j7 w = a giv5 value ( i be small] ?an if ! metal only emitt$ a small numb] ( p>ticles2 ?us ! ca?ode fall w be small] = ! metal ) ! great] emissitivity1 & ! relation betwe5 ! pot5tial diff]5ce & ! curr5t w be diff]5t 9 ! two cases4 ,^! consid]ations are confirm$ by exp]i5ce1 = x has be5 f\nd t ! curr5t betwe5 electrodes imm]s$ 9 a flame dep5ds to a great ext5t ^u ! metal ( :i* ! electrodes are made4 ,?us ,pett9elli 7,acc4 dei ,l9cei #e1 v4 p4 #aah7 f\nd t1 cet]is p>ibus1 ! curr5t betwe5 two c>bon electrodes 0 ab\t #ejj times t betwe5 two iron ones4 ,if "o electrode 0 c>bon & ! o!r iron1 ! curr5t :5 ! c>bon 0 ca?ode & ! iron anode 0 m ?an #ajj times ! curr5t :5 ! electrodes 7 rev]s$4 ,! emission ( negative p>ticles by "s metallic oxides1 notably ^? ( calcium & b>ium1 has be5 %[n by ,wehnelt 7,ann4 d] ,phys4 #aa1 p4 #dbe7 to be f> great] ?an t ( any kn[n metal1 & ! increase ( curr5t produc$ by coat+ ! ca?odes ) ^! oxides is exce$+ly l>ge2 9 "s cases inve/igat$ by ,tufts & ,/>k 7,physik4 ,zeits41 #aijh1 #e1 p4 #bdh7 ! curr5t 0 increas$ _m ?\s& times by coat+ ! ca?ode ) lime4 ,no appreciable effect is produc$ by putt+ lime on ! anode4 ,conduction :5 all ! ,ions are ( "o ,sign4--,!re are _m important cases 9 :i* ! ions produc+ ! curr5t come f "o electrode or f a ?9 lay] ( gas close to ! electrode1 no ionization occurr+ 9 ! body ( ! gas or at ! o!r electrode4 ,among su* cases may be m5tion$ ^? :]e "o ( ! electrodes is rais$ to inc&esc5ce :ile ! o!r is cold1 or :5 ! negative electrode is expos$ to ultra-violet light4 ,9 su* cases if ! electrode at :i* ! ionization occurs is ! positive electrode1 all ! ions w be positively *>g$1 :ile if x is ! negative electrode ! ions w all be *>g$ negatively4 ,! !ory ( ?is case is exce$+ly simple4 ,suppose ! electrodes are p>allel planes at "r angles to ! axis ( x2 let ,x be ! electric =ce at a di/ance x f ! electrode :]e ! ionization occurs1 n ! numb] ( ions 7all ( :i* are ( "o sign7 at ?is place p] cubic c5timetre1 k ! velocity ( ! ion "u unit electric =ce1 e ! *>ge on an ion1 & i ! curr5t p] unit area ( ! electrode4 ,!n we h d,x_/dx #dpine1 & if u is ! velocity ( ! ion neu i4 ,b u k,x1 h5ce we h k,x_/#dpi d,x_/dx i1 & s9ce ! "r h& side ( ?is equation does n dep5d ^u x1 we get k,x_/#hpi ix ,c1 :]e ,c is a con/ant to be det]m9$4 ,if l is ! di/ance betwe5 ! plates1 & ,v ! pot5tial diff]5ce betwe5 !m1 _/ l #a _/#hpi ,v ,xdx --- _/ ----- 7 il ,c 7#c_/b - ,c#c_/b 4 _/#j i _/ k ,we %all %[ t :5 ! curr5t is f> bel[ ! saturation value1 ,c is v small comp>$ ) il1 s t ! prec$+ equation becomes ,v #hpili_/k 7#a74 ,to %[ t = small curr5ts ,c is small comp>$ ) il1 consid] ! case :5 ! ionization is conf9$ to a ?9 lay]1 ?ickness d close to ! electrode1 9 t lay] let n#j be ! value ( n1 !n we h q alphan#j i_/ed4 ,if ,x#j be ! value ( ,x :5 x #j1 k,x#jn#j;e i1 &1 k,x#j i alpha i ,c ----- ----------- -------- -------- 7#b74 #hpi n#jke#hpi #hpike q i_/ed ,s9ce alpha_/#hpike is1 z we h se51 less ?an unity1 ,c w be small comp>$ ) il1 if i_/7eq i_/d7 is small comp>$ ) l4 ,if ,i#j is ! saturation curr5t1 q ,i#j_/;ed1 s t ! =m] expression id_/7,i#j i71 if i is small comp>$ ) ,i#j1 ?is expression is small comp>$ ) d1 & !re=e a =tiori comp>$ ) l1 s t we are ju/ifi$ 9 ?is case 9 us+ equation 7#a74 ,f equation 7#b7 we see t ! curr5t increases z ! squ>e ( ! pot5tial diff]5ce4 ,"h an increase 9 ! pot5tial diff]5ce produces a mu* great] p]c5tage increase ?an 9 conduction ?r\gh metals1 :]e ! curr5t is proportional to ! pot5tial diff]5ce4 ,:5 ! ionization is di/ribut$ ?r\gh ! gas1 we h se5 t ! curr5t is approximately proportional to ! squ>e root ( ! pot5tial1 & s increases m sl[ly ) ! pot5tial diff]5ce ?an curr5ts ?r\gh metals4 ,f equation 7#a7 ! curr5t is inv]sely proportional to ! cube ( ! di/ance betwe5 ! electrodes1 s t x falls (f ) great rapidity z ?is di/ance is increas$4 ,we may note t = a giv5 pot5tial diff]5ce ! expression = ! curr5t does n involve q1 ! rate ( production ( ! ions at ! electrode1 9 o!r words1 if we v>y ! ionization ! curr5t w n beg9 to be affect$ by ! /r5g? ( ! ionization until ?is falls s l[ t ! curr5t is a consid]able fraction ( ! saturation curr5t4 ,= ! same pot5tial diff]5ce ! curr5t is proportional to k1 ! velocity "u unit electric =ce ( ! ion :i* c>ries ! curr5t4 ,z ! velocity ( ! negative ion is great] ?an t ( ! positive1 ! curr5t :5 ! ionization is conf9$ to ! neighb\rhood ( "o ( ! electrodes w be great] :5 t electrode is made ca?ode ?an :5 x is anode4 ,?us ! curr5t w appe> to pass m easily 9 "o direction ?an 9 ! opposite4 ,s9ce ! ions :i* c>ry ! curr5t h to travel all ! way f "o electrode to ! o!r1 any ob/acle :i* is imp]vi\s to ^! ions w1 if plac$ betwe5 ! electrodes1 /op ! curr5t to ! electrode :]e !re is no ionization4 ,a plate ( metal w be z effectual z "o made ( a non-conductor1 & ?us we get ! rem>kable result t by int]pos+ a plate ( an excell5t conductor l copp] or silv] betwe5 ! electrode1 we c entirely /op ! curr5t4 ,?is exp]im5t c easily be tri$ by us+ a hot plate z ! electrode at :i* ! ionization takes place3 !n if ! o!r electrode is cold ! curr5t :i* passes :5 ! hot plate is ca?ode c be entirely /opp$ by int]pos+ a cold metal plate betwe5 ! electrodes4 ,me?ods ( c\nt+ ! ,numb] ( ,ions4--,! detection ( ! ions & ! e/imation ( _! numb] 9 a giv5 volume is mu* facilitat$ by ! prop]ty !y possess ( promot+ ! cond5sation ( wat]-drops 9 du/-free air sup]saturat$ ) wat] vap\r4 ,if su* air conta9s no ions1 !n x requires ab\t an eightfold sup]saturation be=e any wat]-drops are =m$2 if1 h[ev]1 ions are pres5t ,c4 ,t4 ,r4 ,wilson 7,phil4 ,trans4 #ahi1 p4 #bfe7 has %[n t a sixfold sup]saturation is suffici5t to cause ! wat] vap\r to cond5se r\nd ! ions & to fall d[n z ra9drops4 ,! abs5ce ( ! drops :5 no ions are pres5t is due to ! curvature ( ! drop comb9$ ) ! surface t5sion caus+1 z ,"l ,kelv9 %[$1 ! evaporation f a small drop to be exce$+ rapid1 s t ev5 if a drop ( wat] 7 =m$ ! evaporation w\ld be s great 9 its e>ly /ages t x w\ld rapidly evaporate & disappe>4 ,x has be5 %[n1 h[ev] 7,j4 ,j4 ,?omson1 ,application ( ,dynamics to ,physics & ,*emi/ry1 p4 #afd2 ,conduction ( ,electricity ?r\gh ,gases1 #bnd ed4 p4 #agi71 t if a drop ( wat] is *>g$ ) electricity ! effect ( ! *>ge is to dim9i% ! evaporation2 if ! drop is bel[ a c]ta9 size ! effect ! *>ge has 9 promot+ cond5sation m ?an c\nt]balances ! effect ( ! surface t5sion 9 promot+ evaporation4 ,?us ! electric *>ge protects ! drop 9 ! mo/ critical p]iod ( its gr[?4 ,! effect is easily %[n exp]im5tally by tak+ a bulb connect$ ) a pi/on arrang$ s z to move ) great rapidity4 ,:5 ! pi/on moves s z to increase ! volume ( ! air conta9$ 9 ! bulb ! air is cool$ by expansion1 & if x 0 saturat$ ) wat] vap\r be=e x is sup]saturat$ aft] ! expansion4 ,by alt]+ ! ?r[ ( ! pi/on ! am\nt ( sup]saturation c be adju/$ )9 v wide limits4 ,let x be adju/$ s t ! expansion produces ab\t a sixfold sup]saturation2 !n if ! gas is n expos$ to any ioniz+ ag5ts v few drops 7& ^! probably due to ! small am\nt ( ionization :i* we h se5 is always pres5t 9 gases7 are =m$4 ,if1 h[ev]1 ! bulb is expos$ to /rong ,rntg5 rays expansion produces a d5se cl\d :i* gradually falls d[n & disappe>s4 ,if ! gas 9 ! bulb at ! "t ( its exposure to ! ,rntg5 rays is subject to a /rong electric field h>dly any cl\d is =m$ :5 ! gas is sudd5ly exp&$4 ,! electric field removes ! *>g$ ions f ! gas z soon z !y are =m$ s t ! numb] ( ions pres5t is greatly r$uc$4 ,?is exp]im5t furni%es a v direct pro( t ! drops ( wat] :i* =m ! cl\d are only =m$ r\nd ! ions4 ,?is me?od gives u an exce$+ly delicate te/ = ! pres5ce ( ions1 = !re is no difficulty 9 detect+ t5 or s ra9drops p] cubic c5timetre2 we are ?us able to detect ! pres5ce ( ?is numb] ( ions4 ,?is result illu/rates ! enorm\s diff]5ce betwe5 ! delicacy ( ! me?ods ( detect+ ions & ^? = detect+ un*>g$ molecules2 we h se5 t we c easily detect t5 ions p] cubic c5timetre1 b !re is no kn[n me?od1 spectroscopic or *emical1 :i* w\ld enable u to detect a billion 7#ajab7 times ?is numb] ( un*>g$ molecules4 ,! =mation ( ! wat]-drops r\nd ! *>g$ ions gives u a means ( c\nt+ ! numb] ( ions pres5t 9 a cubic c5timetre ( gas2 we cool ! gas by sudd5 expansion until ! sup]saturation produc$ by ! cool+ is suffici5t to cause a cl\d to be =m$ r\nd ! ions1 & ! problem ( f9d+ ! numb] ( ions p] cubic c5timetre ( gas is ?us r$uc$ to t ( f9d+ ! numb] ( drops p] cubic c5timetre 9 ! cl\d4 ,unless ! drops are v few & f> betwe5 we _c d ?is by direct c\nt+2 we c1 h[ev]1 arrive at ! result 9 ! foll[+ way4 ,f ! am\nt ( expansion ( ! gas we c calculate ! l[]+ produc$ 9 its temp]ature & h5ce ! total quantity ( wat] precipitat$4 ,! wat] is precipitat$ z drops1 & if all ! drops are ! same size ! numb] p] cubic c5timetre w be equal to ! volume ( wat] deposit$ p] cubic c5timetre1 divid$ by ! volume ( "o ( ! drops4 ,h5ce we c calculate ! numb] ( drops if we "k _! size1 & ?is c be det]m9$ by measur+ ! velocity ) :i* !y fall "u gravity ?r\gh ! air4 ,! !ory ( ! fall ( a heavy drop ( wat] ?r\gh a visc\s fluid %[s t v 7#b_/i7;ga_/mu1 :]e a is ! radius ( ! drop1 g ! accel]ation due to gravity1 & mu ! coeffici5t ( viscosity ( ! gas ?r\gh :i* ! drop falls4 ,h5ce if we "k v we c d$uce ! value ( a & h5ce ! volume ( ea* drop & ! numb] ( drops4 ,*>ge on ,ion4--,by ?is me?od we c det]m9e ! numb] ( ions p] unit volume ( an ioniz$ gas4 ,kn[+ ?is numb] we c proce$ to det]m9e ! *>ge on an ion4 ,to d ?is let u apply an electric =ce s z to s5d a curr5t ( electricity ?r\gh ! gas1 tak+ c>e t ! curr5t is only a small fraction ( ! saturat+ curr5t4 ,!n if u is ! sum ( ! velocities ( ! positive & negative ions produc$ 9 ! electric field appli$ to ! gas1 ! curr5t ?r\gh unit area ( ! gas is neu1 :]e n is ! numb] ( positive or negative ions p] cubic c5timetre1 & e ! *>ge on an ion4 ,we c easily measure ! curr5t ?r\gh ! gas & ?us det]m9e neu2 we c det]m9e n by ! me?od j describ$1 & u1 ! velocity ( ! ions "u ! giv5 electric field1 is kn[n f ! exp]im5ts ( ,zel5y & o!rs4 ,?us s9ce ! product neu1 & two ( ! factors n1 u are kn[n1 we c det]m9e ! o!r factor e1 ! *>ge on ! ion4 ,?is me?od 0 us$ by ,j4 ,j4 ,?omson1 & details ( ! me?od w be f\nd 9 ,phil4 ,mag4 #e1 #df1 p4 #ebh2 #e1 #dh1 p4 #edg2 #f1 #e1 p4 #cdf4 ,! result ( ^! measurem5ts %[s t ! *>ge on ! ion is ! same :e!r ! ionization is by ,rntg5 rays or by ! influ5ce ( ultra-violet light on a metal plate4 ,x is ! same :e!r ! gas ioniz$ is hydrog51 air or c>bonic acid1 & ?us is presumably indep5d5t ( ! nature ( ! gas4 ,! value ( e =m$ by ?is me?od 0 #c4d #aj-aj electro/atic units4 ,h4 ,a4 ,wilson 7,phil4 ,mag4 #f1 #e1 p4 #dbi7 us$ ano!r me?od4 ,drops ( wat]1 z we h se51 cond5se m easily on negative ?an on positive ions4 ,x is possible1 !re=e1 to adju/ ! expansion s t a cl\d is =m$ on ! negative b n on ! positive ions4 ,wilson arrang$ ! exp]im5ts s t su* a cl\d 0 =m$ betwe5 two horizontal plates :i* c\ld be ma9ta9$ at diff]5t pot5tials4 ,! *>g$ drops betwe5 ! plates 7 act$ ^u by a uni=m v]tical =ce :i* affect$ _! rate ( fall4 ,let ,x be ! v]tical electric =ce1 e ! *>ge on ! drop1 v#a ! rate ( fall ( ! drop :5 ?is =ce acts1 & v ! rate ( fall due to gravity alone4 ,!n s9ce ! rate ( fall is proportionate to ! =ce on ! drop1 if a is ! radius ( ! drop1 & rho its d5sity1 !n ,xe 7#d_/c7pirhoga v#a ---------------------- ---1 #d_/cpirhoga v or ,xe 7#d_/c7pirhoga7v#a - v7_/v4 ,b v #b_/i;garho_/mu1 s t _/ _/ mu v7#c_/b77v#a - v7 ,xe _/ #b4ipi - _/ ------ ---------------4 _/ grho v ,?us if ,x1 v1 v#a are kn[n e c be det]m9$4 ,wilson by ?is me?od f\nd t e 0 #c4a #aj-aj electro/atic units4 ,a few ( ! ions c>ri$ *>ges #b;e or #c;e4 ,t[ns5d has us$ ! foll[+ me?od to comp>e ! *>ge c>ri$ by a gase\s ion ) t c>ri$ by an atom ( hydrog5 9 ! electrolysis ( solution4 ,we h u_/,d ,ne_/,pi1 :]e ,d is ! coeffici5t ( diffusion ( ! ions ?r\gh ! gas1 u ! velocity ( ! ion 9 ! same gas :5 act$ on by unit electric =ce1 ,n ! numb] ( molecules 9 a cubic c5timetre ( ! gas :5 ! pressure is ,pi dynes p] squ>e c5timetre1 & e ! *>ge 9 electro/atic units4 ,?is relation is obta9$ on ! hypo!sis t ,n ions 9 a cubic c5timetre produce ! same pressure z ,n un*>g$ molecules4 ,we "k ! value ( ,d f ,t[ns5d's exp]im5ts & ! values ( u f ^? ( ,zel5y4 ,we get ! foll[+ values = ,ne #aj-aj3-- ---------------------------------------- ----------------- ,moi/ ,gas4 ,moi/ ,gas4 ---------------------------------------- --------------- ,gas4 ,positive ,negative ,positive ,negative ,ions4 ,ions4 ,ions4 ,ions4 ---------------------------------------- --------------- ,air #a4bh #a4bi #a4df #a4ca ,oxyg5 #a4cd #a4bg #a4fc #a4cf ,c>bonic acid #a4ja 4#hg 4#ii 4#ic ,hydrog5 #a4bd #a4ah #a4fc #a4be ---------------------------------------- --------------- ,mean #a4bb #a4ae #a4dc #a4ba ---------------------------------------- --------------- ,s9ce #a4bb cubic c5timetres ( hydrog5 at ! temp]ature #ae ,c4 & pressure #gfj mm4 ( m]cury are lib]at$ by ! passage ?r\gh acidulat$ wat] ( "o electromagnetic unit ( electricity or #c #ajaj electro/atic units1 & s9ce 9 "o cubic c5timetre ( ! gas !re are #b4df ,n atoms ( hydrog51 we h1 if ,e is ! *>ge 9 electro/atic units1 on ! atom ( hydrog5 9 ! electrolysis ( solutions #b4df,,ne #c #ajaj1 or ,,ne #a4bb #ajaj4 ,! mean ( ! values ( ,ne 9 ! prec$+ table is #a4bd #ajaj4 ,h5ce we may conclude t ! *>ge ( electricity c>ri$ by a gase\s ion is equal to ! *>ge c>ri$ by ! hydrog5 atom 9 ! electrolysis ( solutions4 ,! values ( ,ne = ! diff]5t gases diff] m ?an we %\ld h expect$ f ! probable accuracy ( ! det]m9ation ( ,d & ! velocity ( ! ions3 ,t[ns5d 7,proc4 ,roy4 ,soc4 #hj1 p4 #bjg7 has %[n t :5 ! ionization is produc$ by ,rntg5 rays "s ( ! positive ions c>ry a d\ble *>ge & t ?is acc\nts = ! values ( ,ne be+ great] = ! positive ?an = ! negative ions4 ,s9ce we "k ! value ( e1 viz4 #c4e #aj-aj1 &1 also ,ne1 #a4bd #ajaj1 we f9d ,n ! numb] ( molecules 9 a cubic c5timetre ( gas at /&>d temp]ature & pressure to be equal to #c4e #ajai4 ,?is me?od ( obta9+ ,n is ! only "o :i* does n involve any assumption z to ! %ape ( ! molecules & ! =ces act+ betwe5 !m4 ,ano!r me?od ( det]m9+ ! *>ge c>ri$ by an ion has be5 employ$ by ,ru!r=d 7,proc4 ,roy4 ,soc4 #ha1 pp4 #ada1 #afb71 9 :i* ! positively electrifi$ p>ticles emitt$ by radium are made use (4 ,! me?od consi/s (3 7#a7 ,c\nt+ ! numb] ( alpha p>ticles emitt$ by a giv5 quantity ( radium 9 a kn[n "t4 7#b7 ,measur+ ! electric *>ge emitt$ by ?is quantity 9 ! same "t4 ,to c\nt ! numb] ( ! alpha p>ticles ! radium 0 s arrang$ t x %ot into an ionization *amb] a small numb] ( alpha p>ticles p] m9ute2 ! int]val betwe5 ! emission ( individual p>ticles 0 sev]al seconds4 ,:5 an alpha p>ticle pass$ into ! vessel x ioniz$ ! gas inside & s greatly increas$ its conductivity2 ?us1 if ! gas 7 kept expos$ to an electric field1 ! curr5t ?r\gh ! gas w\ld sudd5ly increase :5 an alpha p>ticle pass$ into ! vessel4 ,al?\gh ea* alpha p>ticle produces ab\t ?irty ?\s& ions1 ?is is h>dly l>ge en\gh to produce ! conductivity appreciable )\t ! use ( v delicate app>atus2 to increase ! conductivity ,ru!r=d took advantage ( ! fact t ions1 especially negative ones1 :5 expos$ to a /rong electric field1 produce o!r ions by collision aga9/ ! molecules ( ! gas ?r\gh :i* !y are mov+4 ,by suitably *oos+ ! electric field & ! pressure 9 ! ionization *amb]1 ! #cj1jjj ions produc$ by ea* alpha p>ticle c be multipli$ to su* an ext5t t an appreciable curr5t passes ?r\gh ! ionization *amb] on ! arrival ( ea* alpha p>ticle4 ,an electromet] plac$ 9 s]ies ) ?is vessel w %[ by its deflection :5 an alpha p>ticle ent]s ! *amb]1 & by c\nt+ ! numb] ( deflections p] m9ute we c det]m9e ! numb] ( alpha p>ticles giv5 out by ! radium 9 t "t4 ,ano!r me?od ( c\nt+ ?is numb] is to let ! p>ticles fall on a phosphoresc5t scre51 & c\nt ! numb] ( sc9tillations on ! scre5 9 a c]ta9 "t4 ,ru!r=d has %[n t ^! two me?ods give concordant results4 ,! *>ge ( positive electricity giv5 out by ! radium 0 measur$ by cat*+ ! alpha p>ticles 9 a ,f>aday cyl9d] plac$ 9 a v highly exhau/$ vessel1 & measur+ ! *>ge p] m9ute receiv$ by ?is cyl9d]4 ,9 ?is way ,ru!r=d %[$ t ! *>ge on ! alpha p>ticle 0 #i4d #aj-aj electro/atic units4 ,n[ e_/m = ! alpha p>ticle #e #aj1 & !re is evid5ce t ! alpha p>ticle is a *>g$ atom ( helium2 s9ce ! atomic weight ( helium is #d & e_/m = hydrog5 is #ajd1 x foll[s t ! *>ge on ! helium atom is twice t on ! hydrog51 s t ! *>ge on ! hydrog5 atom is #d4g #aj-aj electro/atic units4 ,calculation ( ! ,mass ( ! ,ions at ,l[ ,pressures4--,al?\gh at ord9>y pressures ! ion seems to h a v complex /ructure & to be ! aggregate ( _m molecules1 yet we h evid5ce t at v l[ pressures ! /ructure ( ! ion1 & especially ( ! negative "o1 becomes v mu* simpl]4 ,?is evid5ce is af=d$ by det]m9ation ( ! mass ( ! atom4 ,we c measure ! ratio ( ! mass ( an ion to ! *>ge on ! ion by obs]v+ ! deflections produc$ by magnetic & electric =ces on a mov+ ion4 ,if an ion c>ry+ a *>ge e is mov+ ) a velocity v1 at a po9t :]e ! magnetic =ce is ,h1 a me*anical =ce acts on ! ion1 ^: direction is at "r angles bo? to ! direction ( motion ( ! ion & to ! magnetic =ce1 & ^: magnitude is ev,h s9 !ta1 :]e !ta is ! angle betwe5 v & ,h4 ,suppose !n t we h an ion mov+ ?r\gh a gas ^: pressure is s l[ t ! free pa? ( ! ion is long comp>$ ) ! di/ance ?r\gh :i* x moves :il/ we are exp]im5t+ ^u x2 9 ?is case ! motion ( ! ion w be free1 & w n be affect$ by ! pres5ce ( ! gas4 ,s9ce ! =ce is always at "r angles to ! direction ( motion ( ! ion1 ! spe$ ( ! ion w n be alt]$ by ! action ( ?is =ce2 & if ! ion is project$ ) a velocity v 9 a direction at "r angles to ! magnetic =ce1 & if ! magnetic =ce is con/ant 9 magnitude & direction1 ! ion w describe a curve 9 a plane at "r angles to ! magnetic =ce4 ,if rho is ! radius ( curvature ( ?is curve1 m ! mass ( ! ion1 mv_/rho mu/ equal ! normal =ce act+ on ! ion1 i4e4 x mu/ be equal to ,hev1 or rho mv_/,he4 ,?us ! radius ( curvature is con/ant2 ! pa? is !re=e a circle1 & if we c measure ! radius ( ?is circle we "k ! value ( mv_/,he4 ,9 ! case ( ! rapidly mov+ negative ions project$ f ! ca?ode 9 a highly exhau/$ tube1 :i* are kn[n z ca?ode rays1 ! pa? ( ! ions c be readily det]m9$ s9ce !y make _m sub/ances lum9\s :5 !y imp+e aga9/ !m4 ,?us by putt+ a scre5 ( su* a sub/ance 9 ! pa? ( ! rays ! %ape ( ! pa? w be det]m9$4 ,let u n[ suppose t ! ion is act$ ^u by a v]tical electric =ce ,x & is free f magnetic =ce1 if x be project$ ) a horizontal velocity v1 ! v]tical deflection y aft] a "t t is et_/m1 or if l is ! horizontal di/ance travell$ ov] by ! ion 9 ?is "t we h s9ce l vt1 ,xe l y -- --4 m v ,?us if we measure y & l we c d$uce e_/mv4 ,f ! effect ( ! magnetic =ce we "k e_/mv4 ,comb9+ ^! results we c f9d bo? e_/m & v4 ,illu/ration3 ,,fig4 #ac4 ,! me?od by :i* ?is det]m9ation is c>ri$ out 9 practice is illu/rat$ 9 fig4 #ac4 ,! ca?ode rays />t f ! electrode ,c 9 a highly exhau/$ tube1 pass ?r\gh two small holes 9 ! plugs ,a & ,b1 ! holes be+ 9 ! same horizontal l9e4 ,?us a p5cil ( rays em]g+ f ,b is horizontal & produces a bright spot at ! f> end ( ! tube4 ,9 ! c\rse ( _! j\rney to ! end ( ! tube !y pass betwe5 ! horizontal plates ,e & ,d1 by connect+ ^! plates ) an electric batt]y a v]tical electric field is produc$ betwe5 ,e & ,d & ! phosphoresc5t spot is deflect$4 ,by measur+ ?is deflection we det]m9e e_/mv4 ,! tube is n[ plac$ 9 a uni=m magnetic field1 ! l9es ( magnetic =ce be+ horizontal & at "r angles to ! plane ( ! pap]4 ,! magnetic =ce makes ! rays describe a circle 9 ! plane ( ! pap]1 & by measur+ ! v]tical deflection ( ! phosphoresc5t pat* at ! end ( ! tube we c det]m9e ! radius ( ?is circle1 & h5ce ! value ( e_/mv4 ,f ! two obs]vations ! value ( e_/m & v c be calculat$4 ,ano!r me?od ( f9d+ e_/m = ! negative ion :i* is applicable 9 _m cases to :i* ! prec$+ "o is n suitable1 is z foll[s3 ,let u suppose t ! ion />ts f re/ & moves 9 a field :]e ! electric & magnetic =ces are bo? uni=m1 ! electric =ce ,x be+ p>allel to ! axis ( x1 & ! magnetic =ce ,z p>allel to ! axis ( z2 !n if x1 y1 are ! co-ord9ates ( ! ion at ! "t t1 ! equations ( motion ( ! ion are-- dx dy m --- ,xe - ,he -- 1 dt dt dy dx m --- ,he --4 dt dt ,! solution ( ^! equations1 if x1 y1 dx_/dt1 dy_/dt all vani% :5 t #j1 is ,xm _/ _/ e x --- #a - cos7 -- ,ht 7 e,h m _/ _/ ,xm _/e _/ e y --- -- ,ht - s97 -- ,ht 7 4 e,h m m _/ _/ ,^! equations %[ t ! pa? ( ! ion is a cycloid1 ! g5]at+ circle ( :i* has a diamet] equal to #b,xm_/e,h1 & rolls on ! l9e x #j4 ,suppose n[ t we h a numb] ( ions />t+ f ! plane x #j1 & mov+ t[>ds ! plane x a4 ,! p>ticles />t+ f x #j describe cycloids1 & ! greate/ di/ance !y c get f ! plane is equal to ! diamet] ( ! g5]at+ circle ( ! cycloid1 i4e4 to #b,xm_/e,h4 7,aft] rea*+ ?is di/ance !y beg9 to approa* ! plane47 ,h5ce if a is less ?an ! diamet] ( ! g5]at+ circle1 all ! p>ticles />t+ f x #j w rea* ! plane x a1 if ?is is unlimit$ 9 ext5t2 :ile if a is great] ?an ! diamet] ( ! g5]at+ circle none ( ! p>ticles :i* />t f x #j w rea* ! plane x a4 ,?us1 if x #j is a plane illum9at$ by ultra-violet light1 & consequ5tly ! seat ( a supply ( negative ions1 & x a a plane connect$ ) an electromet]1 !n if a def9ite electric int5sity is e/abli%$ betwe5 ! planes1 i4e4 if ,x be fix$1 s t ! rate ( emission ( negative ions f ! illum9at$ plate is giv51 & if a is less ?an #b,xm_/e,h1 all ! ions :i* />t f x #j w rea* x a4 ,t is1 ! rate at :i* ?is plane receives an electric *>ge w be ! same :e!r !re is a magnetic field betwe5 ! plate or n1 b if a is great] ?an #b,xm_/e,h1 !n no p>ticle :i* />ts f ! plate x #j w rea* ! plate x a1 & ?is plate w receive no *>ge4 ,?us ! supply ( electricity to ! plate has be5 entirely /opp$ by ! magnetic field4 ,?us1 on ?is !ory1 if ! di/ance betwe5 ! plates is less ?an a c]ta9 value1 ! magnetic =ce %\ld produce no effect on ! rate at :i* ! electromet] plate receives a *>ge1 :ile if ! di/ance is great] ?an ?is value ! magnetic =ce w\ld completely /op ! supply ( electricity to ! plate4 ,! actual ph5om5a are n s abrupt z ?is !ory indicates4 ,we f9d t :5 ! plates are v ne> toge!r ! magnetic =ce produces a v slight effect1 & ?is an increase 9 ! rate ( *>g+ ( ! plate4 ,on increas+ ! di/ance we come to a /age :]e ! magnetic =ce produces a great dim9ution 9 ! rate ( *>g+4 ,x does n1 h[ev]1 /op x abruptly1 !re be+ a consid]able range ( di/ance1 9 :i* ! magnetic =ce dim9i%es b does n de/roy ! curr5t4 ,at /ill great] di/ances ! curr5t to ! plate "u ! magnetic =ce is q inappreciable comp>$ ) t :5 !re is no magnetic =ce4 ,we %\ld get ?is gradual in/ead ( abrupt decay ( ! curr5t if "s ( ! p>ticles1 in/ead ( all />t+ f re/1 />t$ ) a f9ite velocity2 9 t case ! fir/ p>ticles /opp$ w\ld be ^? :i* />t$ f re/4 ,?is w\ld be :5 a #b,xm_/e,h4 ,?us if we measure ! value ( a :5 ! magnetic =ce fir/ beg9s to affect ! leak to ! electromet] we det]m9e #b,xm_/e,h1 & z we c easily measure ,x & ,h1 we c d$uce ! value ( m_/e4 ,by ^! me?ods ,?omson det]m9$ ! value ( e_/m = ! negative ions produc$ :5 ultra-violet light falls on a metal plate1 z well z = ! negative ions produc$ by an inc&esc5t c>bon filam5t 9 an atmosph]e ( hydrog5 7,phil4 ,mag4 #e1 #dh1 p4 #edg7 z well z = ! ca?ode rays4 ,x 0 f\nd t ! value ( e_/m = ! negative ions 0 ! same 9 all ^! cases1 & t x 0 a con/ant quantity indep5d5t ( ! nature ( ! gas f :i* ! ions are produc$ & ! means us$ to produce !m4 ,x 0 f\nd1 too1 t ?is value 0 m ?an a ?\s& times ! value ( e_/,m1 :]e e is ! *>ge c>ri$ by an atom ( hydrog5 9 ! electrolysis ( solutions1 & ,m ! mass ( an atom ( hydrog54 ,we h se5 t ?is *>ge is ! same z t c>ri$ by ! negative ion 9 gases2 ?us s9ce e_/m is m ?an a ?\s& times e_/,m1 x foll[s t ,m mu/ be m ?an a ?\s& times m4 ,?us ! mass ( ! negative ion is exce$+ly small comp>$ ) ! mass ( ! atom ( hydrog51 ! smalle/ mass recogniz$ 9 *emi/ry4 ,! production ( negative ions ?us involves ! splitt+ up ( ! atom1 z f a collection ( atoms some?+ is deta*$ ^: mass is less ?an t ( a s+le atom4 ,x is important to notice 9 connexion ) ?is subject t an entirely diff]5t l9e ( argum5t1 bas$ on ! ,zeeman effect 7see ,,magneto-,,optics71 leads to ! recognition ( negatively electrifi$ p>ticles = :i* e_/m is ( ! same ord] z t d$uc$ f ! consid]ation ( purely electrical ph5om5a4 ,^! small negatively electrifi$ p>ticles are call$ corpuscles4 ,! late/ det]m9ations ( e_/m = corpuscles available are ! foll[+3-- ,obs]v]4 e_/m4 ,class5 7,b]4 deut4 phys4 ,ges4 #f1 p4 #gjj7 #a4ggbh #ajg ,bu*]] 7,ann4 d] ,phys41 #bh1 p4 #eac7 #a4gfc #ajg ,x foll[s f electrical !ory t :5 ! corpuscles are mov+ ) a velocity comp>able ) t ( light _! masses increase rapidly ) _! velocity4 ,?is effect has be5 detect$ by ,kauffmann 7,gtt4 ,na*41 ,nov4 #h1 #aija71 :o us$ ! corpuscles %ot out f radium1 "s ( :i* move ) velocities only a few p] c5t less ?an t ( light4 ,o!r exp]im5ts on ?is po9t h be5 made by ,bu*]] 7,ann4 d] ,phys4 #bh1 p4 #eac74 ,conductivity ,produc$ by ,ultra-,violet ,light4--,s mu* use has be5 made 9 rec5t times ( ultra-violet light = produc+ ions t x is desirable to give "s acc\nt ( ! electrical effects produc$ by light4 ,! discov]y by ,h]tz 7,wi$4 ,ann4 #ca1 p4 #ihc7 9 #ahhg1 t ! incid5ce ( ultra-violet light on a sp>k gap facilitates ! passage ( a sp>k1 l$ to a s]ies ( inve/igations by ,hallwa*s1 ,hoor1 ,righi & ,/olet[1 on ! effect ( ultra-violet light on electrifi$ bodies4 ,^! rese>*es h %[n t a fre%ly clean$ metal surface1 *>g$ ) negative electricity1 rapidly loses its *>ge1 h[ev] small1 :5 expos$ to ultra-violet light1 & t if ! surface is insulat$ & )\t *>ge initially1 x acquires a positive *>ge "u ! influ5ce ( ! light4 ,! magnitude ( ?is positive *>ge may be v mu* increas$ by direct+ a bla/ ( air on ! plate4 ,?is1 z ,zel5y 7,phil4 ,mag4 #e1 #de1 p4 #bgb7 %[$1 has ! effect ( bl[+ f ! neighb\rhood ( ! plate negatively electrifi$ gas1 :i* has simil> prop]ties to ! *>g$ gas obta9$ by ! sep>ation ( ions f a gas expos$ to ,rntg5 rays or uranium radiation4 ,if ! metal plate is positively electrifi$1 !re is no loss ( electrification caus$ by ultra-violet light4 ,?is has be5 que/ion$1 b a v c>eful exam9ation ( ! "q by ,el/] & ,geitel 7,wi$4 ,ann4 #eg1 p4 #bd7 has %[n t ! app>5t exceptions are due to ! accid5tal exposure to reflect$ ultra-violet light ( metal surfaces 9 ! neighb\rhood ( ! plate negatively electrifi$ by induction1 s t ! app>5t loss ( *>ge is due to negative electricity com+ up to ! plate1 & n to positive electricity go+ away f x4 ,! ultra-violet light may be obta9$ f an arc-lamp1 ! effectiv5ess ( :i* is increas$ if "o ( ! t]m9als is made ( z9c or alum9ium1 ! light f ^! sub/ances be+ v ri* 9 ultra-violet rays2 x may also be got v conv5i5tly by sp>k+ ) an induction coil betwe5 z9c or cadmium t]m9als4 ,sunlight is n ri* 9 ultra-violet light1 & does n produce any?+ l s great an effect z ! arc light4 ,el/] & ,geitel1 :o h inve/igat$ ) great success ! effects ( light on electrifi$ bodies1 h %[n t ! m electro-positive metals lose negative *>ges :5 expos$ to ord9>y light1 & d n ne$ ! pres5ce ( ! ultra-violet rays4 ,?us !y f\nd t amalgams ( sodium or potassium enclos$ 9 a glass vessel lose a negative *>ge :5 expos$ to daylight1 ?\gh ! glass /ops ! small am\nt ( ultra-violet light left 9 sunlight aft] its passage ?r\gh ! atmosph]e4 ,if sodium or potassium be employ$1 or1 :at is m conv5i5t1 ! m]cury-l liquid obta9$ by mix+ sodium & potassium 9 ! proportion ( _! comb9+ weights1 !y f\nd t negative electricity 0 dis*>g$ by an ord9>y petroleum lamp4 ,if ! /ill m electro-positive metal rubidium is us$1 ! dis*>ge c be produc$ by ! light f a glass rod j heat$ to r$ness2 b !re is no dis*>ge till ! glass is lum9\s4 ,el/] & ,geitel arrange ! metals 9 ! foll[+ ord] = ! facility ) :i* negative electrification is dis*>g$ by light3 rubidium1 potassium1 alloy ( sodium & potassium1 sodium1 li?ium1 magnesium1 ?allium1 z9c4 ,) copp]1 plat9um1 lead1 iron1 cadmium1 c>bon & m]cury ! effects ) ord9>y light are too small to be appreciable4 ,! ord] is ! same z t 9 ,volta's electro-*emical s]ies4 ,) ultra-violet light ! diff]5t metals %[ mu* small] diff]5ces 9 _! p[] ( dis*>g+ negative electricity ?an !y d ) ord9>y light4 ,el/] & ,geitel f\nd t ! ratio ( ! photo-electric effects ( two metals expos$ to approximately mono*romatic light dep5d$ ^u ! wave-l5g? ( ! light1 diff]5t metals %[+ a maximum s5sitiv5ess 9 diff]5t p>ts ( ! spectrum4 ,?is is %[n by ! foll[+ table = ! alkal9e metals4 ,! numb]s 9 ! table are ! rates ( emission ( negative electricity "u simil> circum/ances4 ,! rate ( emission "u ! light f a petroleum lamp 0 tak5 z unity3-- ,blue4 ,yell[4 ,orange4 ,r$4 ,rb 4#af 4#fd 4#cc 4#jci ,na 4#cg 4#cf 4#ad 4#jji ,k 4#eg 4#jg 4#jd 4#jjb ,! table %[s t ! absorption ( light by ! metal has great influ5ce on ! photo-electric effect1 = :ile potassium is m s5sitive 9 blue light ?an sodium1 ! /rong absorption ( yell[ light by sodium makes x m ?an five times m s5sitive to ?is light ?an potassium4 ,/olet[1 at an e>ly p]iod1 call$ att5tion to ! connexion betwe5 /rong absorption & photo-electric effects4 ,he %[$ t wat]1 :i* does n absorb to any great ext5t ei!r ! ultra-violet or visible rays1 does n %[ any photo-electric effect1 :ile /rongly col\r$ solutions1 & especially solutions ( fluoresc5t sub/ances su* z me?yl gre5 or me?yl violet1 d s to a v consid]able ext5t2 inde$1 a solution ( me?yl gre5 is m s5sitive ?an z9c4 ,hallwa*s 7,wi$4 ,ann4 #cg1 p4 #fff7 prov$ t 9 liquids %[+ photo-electric effects !re is always /rong absorption2 we may1 h[ev]1 h absorption )\t ^! effects4 ,phosphoresc5t sub/ances1 su* z calcium sulphide %[ ?is effect1 z also d v>i\s specim5s ( fluor-sp>4 ,z phosphoresc5ce & fluoresc5ce are probably accompani$ by a v int5se absorption by ! surface lay]s1 ! evid5ce is /rong t to get ! photo-electric effects we mu/ h /rong absorption ( "s k9d ( light1 ei!r visible or ultra-violet4 ,illu/ration3 ,,fig4 #ad4 ,if a conductor ,a is plac$ ne> a conductor ,b expos$ to ultra-violet light1 & if ,b is made ! negative electrode & a diff]5ce ( pot5tial e/abli%$ betwe5 ,a & ,b1 a curr5t ( electricity w fl[ betwe5 ! conductors4 ,! relation betwe5 ! magnitude ( ! curr5t & ! diff]5ce ( pot5tial :5 ,a & ,b are p>allel plates has be5 inve/igat$ by ,/olet[ 7,j\rnal de physique1 #ahij1 #aa1 p4 #dfi71 von ,s*weidl] 7,wi54 ,b]41 #ahii1 #ajh1 p4 #bgc7 & ,v>ley 7,phil4 ,trans4 ,a41 #aijd1 #bjb1 p4 #dci74 ,! results ( "s ( ,v>ley's exp]im5ts are repres5t$ 9 ! curves %[n 9 fig4 #ad1 9 :i* ! ord9ates are ! curr5ts & ! abscissae ! pot5tials4 ,x w be se5 t :5 ! pressure is exce$+ly l[ ! curr5t is indep5d5t ( ! pot5tial diff]5ce & is equal to ! negative *>ge c>ri$ (f 9 unit "t by ! corpuscles emitt$ f ! surface expos$ to ! light4 ,at high] pressures ! curr5t rises f> above ^! values & increases rapidly ) ! pot5tial diff]5ce4 ,?is is due to ! corpuscles emitt$ by ! illum9at$ surface acquir+ "u ! electric field su* high velocities t :5 !y /rike aga9/ ! molecules ( ! gas ?r\gh :i* !y are pass+ !y ionize !m1 produc+ fre% ions :i* c c>ry on additional curr5t4 ,! relation betwe5 ! curr5t & ! pot5tial diff]5ce 9 ?is case is 9 accordance ) ! results ( ! !ory ( ionization by collision4 ,! corpuscles emitt$ f a body "u ! action ( ultra-violet light />t f ! surface ) a f9ite velocity4 ,! velocity is n ! same = all ! corpuscles1 nor inde$ c\ld we expect t x %\ld be3 = z ,lad5burg has %[n 7,ann4 d] ,phys41 #aijc1 #ab1 p4 #eeh7 ! seat ( _! emission is n conf9$ to ! surface lay] ( ! illum9at$ metal b ext5ds to a lay] ( f9ite1 ?\gh small1 ?ickness4 ,?us ! p>ticles :i* />t deep d[n w h to =ce _! way ?r\gh a lay] ( metal be=e !y rea* ! surface1 & 9 do+ s w h _! velocities ret>d$ by an am\nt dep5d+ on ! ?ickness ( ?is lay]4 ,! v>iation 9 ! velocity ( ! corpuscles is %[n 9 ! foll[+ table1 due to ,l5>d 7,ann4 d] ,phys41 #aijb1 #h1 p4 #adi74 ---------------------------------------- ------------------------- ,c>bon4 ,plat9um4 ,alum9ium4 ---------------------------------------- ------------------------- ,corpuscles emitt$ ) velocities betwe5 #ab & #h #ajg cm sec4 #j4jjj #j4jjj #j4jjd betwe5 #h & #d #ajg cm sec4 #j4jdi #j4aee #j4aea betwe5 #d & #j #ajg cm sec4 #j4fg #j4fe #j4di ,corpuscles only emitt$ ) ! help ( an ext]nal electric #j4bh #j4ba #j4ce field4 ----------------------------- #a4jj #a4jj #a4jj ---------------------------------------- ------------------------- ,if ! illum9at$ surface is completely surr\nd$ by an envelope ( ! same metal insulat$ f & completely %ield$ f ! light1 ! emission ( ! negative corpuscles f ! illum9at$ surface w\ld g on until ! pot5tial diff]5ce ,v betwe5 ?is surface & ! envelope became s great t ! corpuscles ) ! greate/ velocity lo/ _! en]gy be=e rea*+ ! envelope1 i4e4 if m is ! mass1 e ! *>ge on a corpuscle1 v ! greate/ velocity ( projection1 until ,ve mv4 ,! values f\nd = ,v by diff]5t obs]v]s are n v consi/5t4 ,l5>d f\nd t ,v = alum9ium 0 ab\t #c volts & = plat9um #b4 ,millikan & ,w9*e/] 7,phil4 ,mag41 ,july #aijg7 f\nd = alum9ium ,v 4#gch4 ,! app>atus us$ by !m 0 s complex t ! int]pretation ( _! results is difficult4 ,an extremely int]e/+ fact discov]$ by ,l5>d is t ! velocity ) :i* ! corpuscles are emitt$ f ! metal is indep5d5t ( ! int5sity ( ! incid5t light4 ,! quantity ( corpuscles increases ) ! int5sity1 b ! velocity ( ! individual corpuscles does n4 ,x is wor?y ( notice t 9 o!r cases :5 negative corpuscles are emitt$ f metals1 z = example :5 ! metals are expos$ to ca?ode rays1 ,canal-/rahl51 or ,rntg5 rays1 ! velocity ( ! emitt$ corpuscles is indep5d5t ( ! int5sity ( ! prim>y radiation :i* excites !m4 ,! velocity is n1 h[ev]1 indep5d5t ( ! nature ( ! prim>y rays4 ,?us :5 light is us$ to produce ! emission ( corpuscles ! velocity1 z ,lad5burg has %[n1 dep5ds on ! wave l5g? ( ! light1 increas+ z ! wave l5g? dim9i%es4 ,! velocity ( corpuscles emitt$ "u ! action ( ca?ode rays is great] ?an t ( ^? eject$ by light1 :ile ! incid5ce ( ,rntg5 rays produces ! emission ( corpuscles mov+ mu* m rapidly ?an ^? 9 ! cases already m5tion$1 & ! h>d] ! prim>y rays ! great] is ! velocity ( ! corpuscles4 ,! importance ( ! fact t ! velocity & !re=e ! en]gy ( ! corpuscles emitt$ f ! metal is indep5d5t ( ! int5sity ( ! incid5t light c h>dly be ov]e/imat$4 ,x raises ! mo/ fundam5tal que/ions z to ! nature ( light & ! con/itution ( ! molecules4 ,:at is ! s\rce ( ! en]gy possess$ by ^! corpuscles8 ,is x ! light1 or 9 ! /ores ( int]nal en]gy possess$ by ! molecule8 ,let u foll[ ! consequ5ces ( suppos+ t ! en]gy comes f ! light4 ,!n1 s9ce ! en]gy is indep5d5t ( ! int5sity ( ! light1 ! electric =ces :i* lib]ate ! corpuscles mu/ also be indep5d5t ( t int5sity4 ,b ?is _c be ! case if1 z is usually assum$ 9 ! electromagnetic !ory1 ! wave front consi/s ( a uni=m di/ribution ( electric =ce )\t /ructure1 = 9 ?is case ! magnitude ( ! electric =ce is proportional to ! squ>e root ( ! int5sity4 ,on ! emission !ory ( light a difficulty ( ?is k9d w\ld n arise1 = on t !ory ! en]gy 9 a lum9if]\s p>ticle rema9s con/ant z ! p>ticle pursues its flight ?r\gh space4 ,?us any process :i* a s+le p>ticle is able to effect by virtue ( its en]gy w be done j z well a ?\s& miles away f ! s\rce ( light z at ! s\rce itself1 ?\gh ( c\rse 9 a giv5 space !re w n be ne>ly s _m p>ticles to d ?is process f> f ! s\rce z !re are close 94 ,?us1 if "o ( ! p>ticles :5 x /ruck aga9/ a piece ( metal caus$ ! ejection ( a corpuscle ) a giv5 velocity1 ! velocity ( emission w\ld n dep5d on ! int5sity ( ! light4 ,!re does n seem any reason = believ+ t ! electromagnetic !ory is inconsi/5t ) ! idea t on ?is !ory1 z on ! emission !ory1 ! en]gy 9 ! light wave may in/ead ( be+ uni=mly di/ribut$ ?r\gh space be conc5trat$ 9 bundles :i* occupy only a small fraction ( ! volume trav]s$ by ! light1 & t z ! wave travels out ! bundles get f>!r ap>t1 ! en]gy 9 ea* rema9+ undim9i%$4 ,"s su* view ( ! /ructure ( light seems to be requir$ to acc\nt = ! fact t :5 a plate ( metal is /ruck by a wave ( ultra-violet light1 x w\ld take ye>s be=e ! corpuscles emitt$ f ! metal w\ld equal 9 numb] ! molecules on ! surface ( ! metal plate1 & yet on ! ord9>y !ory ( light ea* "o ( ^! is )\t int]ruption expos$ to ! action ( ! light4 ,! fact discov]$ by ,e4 ,lad5burg 7,v]h4 d4 deuts*4 physik4 ,ges4 #i1 p4 #ejd7 t ! velocity ) :i* ! corpuscles are emitt$ dep5ds on ! wave l5g? ( ! light sugge/s t ! en]gy 9 ea* bundle dep5ds ^u ! wave l5g? & increases z ! wave l5g? dim9i%es4 ,^! consid]ations illu/rate ! evid5ce af=d$ by photo-electric effects on ! nature ( light2 ^! effects may also h a deep significance ) reg>d to ! /ructure ( matt]4 ,! fact t ! en]gy ( ! individual corpuscles is indep5d5t ( ! int5sity ( ! light might be expla9$ by ! hypo!sis t ! en]gy ( ! corpuscles does n come f ! light b f ! en]gy /or$ up 9 ! molecules ( ! metal expos$ to ! light4 ,we may suppose t "u ! action ( ! light "s ( ! molecules are ?r[n into an un/able /ate & explode1 eject+ corpuscles2 ! light 9 ?is case acts only z a trigg] to lib]ate ! en]gy 9 ! atom1 & x is ?is en]gy & n t ( ! light :i* goes into ! corpuscles4 ,9 ?is way ! velocity ( ! corpuscles w\ld be indep5d5t ( ! int5sity ( ! light4 ,b x may be ask$1 is ?is view consi/5t ) ! result obta9$ by ,lad5burg t ! velocity ( ! corpuscles dep5ds ^u ! nature ( ! light8 ,if light ( a def9ite wave l5g? expell$ corpuscles ) a def9ite & uni=m velocity1 x w\ld be v improbable t ! emission ( ! corpuscles is due to an explosion ( ! atoms4 ,! exp]im5tal facts z f> z !y are kn[n at pres5t d n all[ u to say t ! connexion betwe5 ! velocity ( ! corpuscles & ! wave l5g? ( ! light is ( ?is def9ite "*1 & a connexion su* z a gradual increase ( av]age velocity z ! wave l5g? ( ! light dim9i%es1 w\ld be q consi/5t ) ! view t ! corpuscles are eject$ by ! explosion ( ! atom4 ,= 9 a complex ?+ l an atom !re may be m ?an "o sy/em :i* becomes un/able :5 expos$ to light4 ,let u suppose t !re are two su* sy/ems1 ,a & ,b1 ( :i* ,b ejects ! corpuscles ) ! great] velocity4 ,if ,b is m s5sitive to ! %ort waves1 & ,a to ! long ones1 !n z ! wave l5g? ( ! light dim9i%es ! proportion ( ! corpuscles :i* come f ,b w increase1 & z ^! are ! fa/]1 ! av]age velocity ( ! corpuscles emitt$ w also increase4 ,& al?\gh ! pot5tial acquir$ by a p]fectly insulat$ piece ( metal :5 expos$ to ultra-violet light w\ld dep5d only on ! velocity ( ! fa/e/ corpuscles & n ^u _! numb]1 9 practice p]fect insulation is unatta9able1 & ! pot5tial actually acquir$ is det]m9$ by ! condition t ! ga9 ( negative electricity by ! metal ?r\gh lack ( insulation1 is equal to ! loss by ! emission ( negatively electrifi$ corpuscles4 ,! pot5tial acquir$ w fall bel[ t correspond+ to p]fect insulation by an am\nt dep5d+ on ! numb] ( ! fa/] corpuscles emitt$1 & ! pot5tial w rise if ! proportion ( ! rapidly mov+ corpuscles is increas$1 ev5 ?\gh !re is no increase 9 _! velocity4 ,x is int]e/+ to comp>e o!r cases 9 :i* corpuscles are emitt$ ) ! case ( ultra-violet light4 ,:5 a metal or gas is bomb>d$ by ca?ode rays x emits corpuscles & ! velocity ( ^! is f\nd to be indep5d5t ( ! velocity ( ! ca?ode rays :i* excite !m2 ! velocity is great] ?an = corpuscles emitt$ "u ultra-violet light4 ,aga91 :5 bodies are expos$ to ,rntg5 rays !y emit corpuscles mov+ ) a mu* great] velocity ?an ^? excit$ by ca?ode rays1 b aga9 ! velocity does n dep5d ^u ! int5sity ( ! rays al?\gh x does to "s ext5t on _! h>dness4 ,9 ! case ( ca?ode & ,rntg5 rays1 ! velocity ) :i* ! corpuscles are emitt$ seems1 z f> z we "k at pres5t1 to v>y slightly1 b only slightly1 ) ! nature ( ! sub/ance on :i* ! rays fall4 ,may n ?is indicate t ! fir/ effect ( ! prim>y rays is to deta* a neutral d\blet1 consi/+ ( a positive & negative *>ge1 ?is d\blet be+ ! same f :atev] sy/em x is deta*$8 ,& t ! d\blet is un/able & explodes1 expell+ ! negative *>ge ) a high velocity1 & ! positive "o1 hav+ a mu* l>g] *>ge1 ) a mu* small] velocity1 ! mom5tum ( ! negative *>ge be+ equal to t ( ! positive4 ,up to n[ we h be5 consid]+ ! effects produc$ :5 light is incid5t on metals4 ,l5>d f\nd 7& ! result has be5 confirm$ by ! exp]im5ts ( ,j4 ,j4 ,?omson & ,lyman7 t c]ta9 k9ds ( ultra-violet light ionize a gas :5 !y pass ?r\gh4 ,! type ( ultra-violet light :i* produces ?is effect is s easily absorb$ t x is /opp$ by a lay] a few millimetres ?ick ( air at atmosph]ic pressure4 ,ionization by ,collision4--,:5 ! ionization ( ! gas is produc$ by ext]nal ag5ts su* z ,rntg5 rays or ultra-violet light1 ! electric field produces a curr5t by sett+ ! positive ions mov+ 9 "o direction1 & ! negative ones 9 ! opposite2 x makes use ( ions already made & does n itself give rise to ionization4 ,9 _m cases1 h[ev]1 su* z 9 electric sp>ks1 !re are no ext]nal ag5ts to produce ionization & ! electric field has to produce ! ions z well z set !m 9 motion4 ,:5 ! ionization is produc$ by ext]nal means ! smalle/ electric field is able to produce a curr5t ?r\gh ! gas2 :51 h[ev]1 ^! ext]nal means are abs5t no curr5t is produc$ unless ! /r5g? ( ! electric field exce$s a c]ta9 critical value1 :i* dep5ds n m]ely ^u ! nature ( ! gas b also ^u ! pressure & ! dim5sions ( ! vessel 9 :i* x is conta9$4 ,! v>iation ( ! electric field requir$ to produce dis*>ge c be completely expla9$ if we suppose t ! ionization ( ! gas is produc$ by ! impact ) its molecules ( corpuscles1 & 9 c]ta9 cases ( positive ions1 :i* "u ! influ5ce ( ! electric field h acquir$ consid]able k9etic en]gy4 ,we h direct evid5ce t rapidly mov+ corpuscles are able to ionize molecules aga9/ :i* !y /rike1 = ! ca?ode rays consi/ ( su* corpuscles1 & ^! :5 !y pass ?r\gh a gas produce l>ge am\nts ( ionization4 ,suppose !n t we h 9 a gas expos$ to an electric field a few corpuscles4 ,^! w be set 9 motion by ! field & w acquire an am\nt ( en]gy 9 proportion to ! product ( ! electric =ce1 _! *>ge1 & ! di/ance travell$ 9 ! direction ( ! electric field betwe5 two collisions ) ! molecules ( ! gas4 ,if ?is en]gy is suffici5t to give !m ! ioniz+ prop]ty possess$ by ca?ode rays1 !n :5 a corpuscle /rikes aga9/ a molecule x w deta* ano!r corpuscle2 ?is "u ! action ( ! electric field w acquire en\gh en]gy to produce corpuscles on its own acc\nt1 & s z ! corpuscles move ?r\gh ! gas _! numb] w increase 9 geometrical progression4 ,?us1 ?\gh !re 7 b few corpuscles to beg9 )1 !re may be great ionization aft] ^! h be5 driv5 "s di/ance ?r\gh ! gas by ! electric field4 ,! numb] ( ions produc$ by collisions c be calculat$ by ! foll[+ me?od4 ,let ! electric =ce be p>allel to ! axis ( x1 & let n be ! numb] ( corpuscles p] unit volume at a place fix$ by ! co-ord9ate x2 !n 9 unit "t ^! corpuscles w make nu_/lambda collisions ) ! molecules1 if u is ! velocity ( a corpuscle & lambda ! mean free pa? ( a corpuscle4 ,:5 ! corpuscles are mov+ fa/ en\gh to produce ions by collision _! velocities are v mu* great] ?an ^? !y w\ld possess at ! same temp]ature if !y 7 n act$ on by electrical =ce1 & s we may reg>d ! velocities z be+ p>allel to ! axis ( x & det]m9$ by ! electric =ce & ! mean free pa? ( ! corpuscles4 ,we h to consid] h[ _m ( ! nu_/lambda collisions :i* take place p] second w produce ions4 ,we %\ld expect t ! ionization ( a molecule w\ld require a c]ta9 am\nt ( en]gy1 s t if ! en]gy ( ! corpuscle fell bel[ ?is am\nt no ionization w\ld take place1 :ile if ! en]gy ( ! corpuscle 7 exce$+ly l>ge1 e collision w\ld result 9 ionization4 ,we %all suppose t a c]ta9 fraction ( ! numb] ( collisions result 9 ionization & t ?is fraction is a function ( ! en]gy possess$ by ! corpuscle :5 x collides aga9/ ! molecules4 ,?is en]gy is proportional to ,xelambda :5 ,x is ! electric =ce1 e ! *>ge on ! corpuscle1 & lambda ! mean free pa?4 ,if ! fraction ( collisions :i* produce ionization is int7,xelambda71 !n ! numb] ( ions produc$ p] cubic c5timetre p] second is int7,xelambda7nu_/lambda4 ,if ! collisions foll[ ea* o!r ) great rapidity s t a molecule has n _h "t to recov] f "o collision be=e x is /ruck aga91 ! effect ( collisions might be cumulative1 s t a succession ( collisions might give rise to ionization1 ?\gh none ( ! collisions w\ld produce an ion by itself4 ,9 ?is case int w\ld involve ! frequ5cy ( ! collisions z well z ! en]gy ( ! corpuscle2 9 o!r words1 x might dep5d on ! curr5t ?r\gh ! gas z well z ^u ! int5sity ( ! electric field4 ,we %all1 h[ev]1 to beg9 )1 assume t ! curr5t is s small t ?is cumulative effect may be neglect$4 ,let u n[ consid] ! rate ( increase1 dn_/dt1 9 ! numb] ( corpuscles p] unit volume4 ,9 consequ5ce ( ! collisions1 int7,xelambda7nu_/lambda corpuscles are produc$ p] second2 9 consequ5ce ( ! motion ( ! corpuscles1 ! numb] :i* leave unit volume p] second is great] ?an ^? :i* ent] x by 7d_/dx77nu72 :ile 9 a c]ta9 numb] ( collisions a corpuscle w /ick to ! molecule & w ?us cease to be a free corpuscle4 ,let ! fraction ( ! numb] ( collisions 9 :i* ?is occurs be beta4 ,?us ! ga9 9 ! numb] ( corpuscles is int7,xelambda7nu_/lambda1 :ile ! loss is 7d_/dx77nu7 beta7nu7_/lambda2 h5ce dn nu d betanu -- int7,xelambda7 -------- - --7nu7 - --------4 dt lambda dx lambda ,:5 ?+s are 9 a /eady /ate dn_/dt #j1 & we h d #a _/ --7nu7 --------7 int7,xelambda7 - beta 7nu4 dx lambda _/ ,if ! curr5t is s small t ! electrical *>ges 9 ! gas are n able to produce any appreciable v>iations 9 ! field1 ,x w be con/ant & we get nu ,cepsilonalphax1 :]e alpha int7,xelambda7 - beta_/lambda4 ,if we take ! orig9 f :i* we measure x at ! ca?ode1 ,c is ! value ( nu at ! ca?ode1 i4e4 x is ! numb] ( corpuscles emitt$ p] unit area ( ! ca?ode p] unit "t2 ?is is equal to i#j_/;e if i#j is ! quantity ( negative electricity com+ f unit area ( ! ca?ode p] second1 & e ! electric *>ge c>ri$ by a corpuscle4 ,h5ce we h nue i#j;epsilonalphax4 ,if l is ! di/ance betwe5 ! anode & ! ca?ode1 ! value ( nue1 :5 x l1 is ! curr5t pass+ ?r\gh unit area ( ! gas1 if we neglect ! electricity c>ri$ by negatively electrifi$ c>ri]s o!r ?an corpuscles4 ,h5ce i i#j;epsilonalphal4 ,?us ! curr5t betwe5 ! plates increases 9 geometrical progression ) ! di/ance betwe5 ! plates4 ,by measur+ ! v>iation ( ! curr5t z ! di/ance betwe5 ! plates is increas$1 ,t[ns5d1 to :om we owe mu* ( our k on ?is subject1 det]m9$ ! values ( alpha = diff]5t values ( ,x & = diff]5t pressures = air1 hydrog5 & c>bonic acid gas 7,phil4 ,mag4 #f1 #a1 p4 #aih74 ,s9ce lambda v>ies inv]sely z ! pressure1 we see t alpha may be writt5 9 ! =m pphi7,x_/p7 or alpha_/,x ,f7,x_/p74 ,! foll[+ are "s ( ! values ( alpha f\nd by ,t[ns5d = air4 ---------------------------------------- ------------------- ,x ,volts ,pressure ,pressure ,pressure ,pressure ,pressure p] cm4 4#ag mm4 4#ch mm4 #a4aj mm4 #b4a mm4 #d4a mm4 ---------------------------------------- ------------------- #bj 4#bd #dj 4#fe 4#cd #hj #a4ce #a4c 4#de 4#ac #abj #a4h #b4j #a4a 4#db 4#ac #afj #b4a #b4h #b4j 4#i 4#bh #bjj #c4d #b4h #a4f 4#e #bdj #b4de #c4h #d4j #b4ce 4#ii #cbj #b4g #d4e #e4e #d4j #b4a #djj #e4j #f4h #f4j #c4f #dhj #c4ae #e4d #h4j #g4h #e4c #efj #e4h #i4c #i4d #g4a #fdj #c4be #f4b #aj4f #aj4h #h4i ---------------------------------------- ------------------- ,we see f ?is table t = a giv5 value ( ,x1 alpha = small pressures increases z ! pressure increases2 x atta9s a maximum at a p>ticul> pressure1 & !n dim9i%es z ! pressure increases4 ,! increase 9 ! pressure increases ! numb] ( collisions1 b dim9i%es ! en]gy acquir$ by ! corpuscle 9 ! electric field1 & ?us dim9i%es ! *ange ( any "o collision result+ 9 ionization4 ,if we suppose ! field is s /rong t at "s p>ticul> pressure ! en]gy acquir$ by ! corpuscle is well above ! value requir$ to ionize at ea* collision1 !n x is evid5t t increas+ ! numb] ( collisions w increase ! am\nt ( ionization1 & !re=e alpha1 & alpha _c beg9 to dim9i% until ! pressure has increas$ to su* an ext5t t ! mean free pa? ( a corpuscle is s small t ! en]gy acquir$ by ! corpuscle f ! electric field falls bel[ ! value :5 ea* collision results 9 ionization4 ,! value ( p1 :5 ,x is giv51 = :i* alpha is a maximum1 is proportional to ,x2 ?is foll[s at once f ! fact t alpha is ( ! =m ,x,f7,x_/p74 ,! value ( ,x_/p = :i* ,f7,x_/p7 is a maximum is se5 f ! prec$+ table to be ab\t #dbj1 :5 ,x is express$ 9 volts p] c5timetre & p 9 millimetres ( m]cury4 ,! maximum value ( ,f7,x_/p7 is ab\t #a_/fj4 ,s9ce ! curr5t pass+ betwe5 two planes at a di/ance l ap>t is i#j;epsilonalphal or i#j;epsilon,xl,f7,x_/p71 & s9ce ! =ce betwe5 ! plates is suppos$ to be uni=m1 ,xl is equal to ,v1 ! pot5tial betwe5 ! plates2 h5ce ! curr5t betwe5 ! plates is i#j;epsilon,vl,f7,x_/p71 & ! greate/ value x c h is i#j;epsilon,v_/#fj4 ,?us ! ratio betwe5 ! curr5t betwe5 ! plates :5 !re is ionization & :5 !re is none _c be great] ?an epsilon,v_/#fj1 :5 ,v is measur$ 9 volts4 ,?is result is bas$ on ,t[ns5d's exp]im5ts ) v weak curr5ts2 we mu/ rememb]1 h[ev]1 t :5 ! collisions are s frequ5t t ! effects ( collisions c accumulate1 alpha may h mu* l>g] values ?an :5 ! curr5t is small4 ,9 "s exp]im5ts made by ,j4 ,j4 ,?omson ) int5se curr5ts f ca?odes cov]$ ) hot lime1 ! increase 9 ! curr5t :5 ! pot5tial diff]5ce 0 #fj volts1 in/ead ( be+ e times ! curr5t :5 !re 0 no ionization1 z ! prec$+ !ory indicates1 0 sev]al hundr$ times t value1 ?us indicat+ a great increase 9 alpha ) ! /r5g? ( ! curr5t4 ,t[ns5d has %[n t we c d$uce f ! values ( alpha ! mean free pa? ( a corpuscle4 ,= if ! ionization is due to ! collisions ) ! corpuscles1 !n unless "o collision deta*es m ?an "o corpuscle ! maximum numb] ( corpuscles produc$ w be equal to ! numb] ( collisions4 ,:5 ea* collision results 9 ! production ( a corpuscle1 alpha #a_/lambda & is indep5d5t ( ! /r5g? ( ! electric field4 ,h5ce we see t ! value ( alpha1 :5 x is indep5d5t ( ! electric field1 is equal to ! reciprocal ( ! free pa?4 ,?us f ! table we inf] t at a pressure ( #ag mm4 ! mean free pa? is #a_/cbe cm42 h5ce at #a mm4 ! mean free pa? ( a corpuscle is #a_/ai cm4 ,t[ns5d has %[n t ?is value ( ! mean free pa? agrees well ) ! value #a_/ba cm4 d$uc$ f ! k9etic !ory ( gases = a corpuscle mov+ ?r\gh air4 ,by measur+ ! values ( alpha = hydrog5 & c>bonic acid gas ,t[ns5d & ,kirby 7,phil4 ,mag4 #f1 #a1 p4 #fcj7 %[$ t ! mean free pa?s = corpuscles 9 ^! gases are respectively #a_/aa4e & #a_/bi cm4 at a pressure ( #a mm4 ,^! results aga9 agree well ) ! values giv5 by ! k9etic !ory ( gases4 ,if ! numb] ( positive ions p] unit volume is m & v is ! velocity1 we h nuemve i1 :]e i is ! curr5t ?r\gh unit area ( ! gas4 ,s9ce nue i#j;epsilonnx & i i#j;epsilonnl1 :5 l is ! di/ance betwe5 ! plates1 we see t nu _/ mv epsilon7nx7 _/ 7epsilon7nl7 - epsilon7nx771 n v epsilon7nx7 -- -- -------------------------------4 m u epsilon7ne7 - epsilon7nx7 ,s9ce v_/u is a v small quantity we see t n w be less ?an m except :5 epsilonnl - epsilonnx is small1 i4e4 except close to ! anode4 ,?us !re w be an excess ( positive electricity f ! ca?ode almo/ up to ! anode1 :ile close to ! anode !re w be an excess ( negative4 ,?is di/ribution ( electricity w make ! electric =ce dim9i% f ! ca?ode to ! place :]e !re is z mu* positive z negative electricity1 :]e x w h its m9imum value1 & !n increase up to ! anode4 ,! expression i i#j;epsilonalphal applies to ! case :5 !re is no s\rce ( ionization 9 ! gas o!r ?an ! collisions2 if 9 addition to ?is !re is a s\rce ( uni=m ionization produc+ q ions p] cubic c5timetre1 we c easily %[ t qe i i#j;epsilonalphal -------7ealphal - #a74 alpha ,) reg>d to ! m9imum en]gy :i* mu/ be possess$ by a corpuscle to enable x to produce ions by collision1 ,t[ns5d 7loc4 cit47 came to ! conclusion t to ionize air ! corpuscle mu/ possess an am\nt ( en]gy equal to t acquir$ by ! fall ( its *>ge ?r\gh a pot5tial diff]5ce ( ab\t #b volts4 ,?is is also ! value arriv$ at by ,h4 ,a4 ,wilson by entirely diff]5t consid]ations4 ,/>k1 h[ev]1 gives #ag volts z ! m9imum = ionization4 ,! en]gy dep5ds ^u ! nature ( ! gas2 rec5t exp]im5ts by ,dawes & ,gill & ,p$duck 7,phil4 ,mag41 ,aug4 #aijh7 h %[n t x is small] = helium ?an = air1 hydrog51 or c>bonic acid gas4 ,if !re is no ext]nal s\rce ( ionization & no emission ( corpuscles f ! ca?ode1 !n x is evid5t t ev5 if "s corpuscles happ5$ to be pres5t 9 ! gas :5 ! electric field 7 appli$1 we c\ld n get a p]man5t curr5t by ! aid ( collisions made by ^! corpuscles4 ,= "u ! electric field1 ! corpuscles w\ld be driv5 f ! ca?ode to ! anode1 & 9 a %ort "t all ! corpuscles orig9ally pres5t 9 ! gas & ^? produc$ by !m w\ld be driv5 f ! gas aga9/ ! anode1 & if !re 0 no s\rce f :i* fre% corpuscles c\ld be introduc$ into ! gas ! curr5t w\ld cease4 ,! curr5t1 h[ev]1 c\ld be ma9ta9$ indef9itely if ! positive ions 9 _! j\rney back to ! ca?ode also produc$ ions by collisions1 = !n we %\ld h a k9d ( reg5]ative process by :i* ! supply ( corpuscles c\ld be cont9ually r5ew$4 ,to ma9ta9 ! curr5t x is n necess>y t ! ionization result+ f ! positive ions %\ld be any?+ l z great z t f ! negative1 z ! inve/igation giv5 bel[ %[s a v small am\nt ( ionization by ! positive ions w suffice to ma9ta9 ! curr5t4 ,! exi/5ce ( ionization by collision ) positive ions has be5 prov$ by ,t[ns5d4 ,ano!r me?od by :i* ! curr5t c\ld be & is ma9ta9$ is by ! anode emitt+ corpuscles "u ! impact ( ! positive ions driv5 aga9/ x by ! electric field4 ,j4 ,j4 ,?omson has %[n by direct exp]im5t t positively electrifi$ p>ticles :5 !y /rike aga9/ a metal plate cause ! metal to emit corpuscles 7,j4 ,j4 ,?omson1 ,proc4 ,camb4 ,phil4 ,soc4 #ac1 p4 #bab2 ,au/91 ,phys4 ,rev4 #bb1 p4 #cab74 ,if we assume t ! numb] ( corpuscles emitt$ by ! plate 9 "o second is proportional to ! en]gy 9 ! positive ions :i* /rike ! plate 9 t second1 we c readily f9d an expression = ! diff]5ce ( pot5tial :i* w ma9ta9 )\t any ext]nal ionization a curr5t ( electricity ?r\gh ! gas4 ,z ?is inve/igation br+s into prom95ce _m ( ! mo/ important features ( ! electric dis*>ge1 we %all consid] x 9 "s detail4 ,let u suppose t ! electrodes are p>allel plates ( metal at "r angles to ! axis ( x1 & t at ! ca?ode x #j & at ! anode x d1 d be+ ?us ! di/ance betwe5 ! plates4 ,let u also suppose t ! curr5t ( electricity fl[+ betwe5 ! plates is s small t ! electrification betwe5 ! plates due to ! accumulation ( ions is n suffici5t to di/urb appreciably ! electric field1 :i* we reg>d z uni=m betwe5 ! plates1 ! electric =ce be+ equal to ,v_/d1 :]e ,v is ! pot5tial diff]5ce betwe5 ! plates4 ,! numb] ( positive ions produc$ p] second 9 a lay] ( gas betwe5 ! planes x & xdx is alphanudx4 ,"h n is ! numb] ( corpuscles p] unit volume1 alpha ! coeffici5t ( ionization 7= /rong electric field alpha #a_/lambda'1 :]e lambda' is ! mean free pa? ( a corpuscle71 & u ! velocity ( a corpuscle p>allel to x4 ,we h se5 t nu i#j;epsilonalphax1 :]e i#j is ! numb] ( corpuscles emitt$ p] second by unit area ( ! ca?ode4 ,?us ! numb] ( positive ions produc$ 9 ! lay] is alphai#j;epsilonalphax dx4 ,if ^! w5t /raight to ! ca?ode )\t a collision1 ea* ( !m w\ld h receiv$ an am\nt ( k9etic en]gy ,vex_/d :5 !y /ruck ! ca?ode1 & ! en]gy ( ! gr\p ( ions w\ld be ,vex_/dalphai#j;epsilondx dx4 ,! positive ions w1 h[ev]1 collide ) ! molecules ( ! gas ?r\gh :i* !y are pass+1 & ?is w dim9i% ! en]gy !y possess :5 !y rea* ! ca?ode4 ,! dim9ution 9 ! en]gy w increase 9 geometrical proportion ) ! l5g? ( pa? travell$ by ! ion & w ?us be proportional to epsilon-betax1 beta w be proportional to ! numb] ( collisions & w ?us be proportional to ! pressure ( ! gas4 ,?us ! k9etic en]gy possess$ by ! ions :5 !y rea* ! ca?ode w be epsilon-betax ,v7ex_/d7 alphai#j;epsilonalphax dx1 & ,e1 ! total am\nt ( en]gy 9 ! positive ions :i* rea* ! ca?ode 9 unit "t1 w be giv5 by ! equation _/d ,e epsilon-betax ,v7ex_/d7 alphai#j;epsilonalphax dx _/#j ,vealphai#j _/d ----------- epsilon-7beta-alpha7xxdx d _/#j ,vealphai#j _/ #a _/ #a d ----------- ---------------- - epsilon-7beta-alpha7d ----------------- ---------------- 7#a74 d 7beta-alpha7 7beta-alpha7 7beta-alpha7_/ _/ ,if ! numb] ( corpuscles emitt$ by ! ca?ode 9 unit "t is proportional to ?is en]gy we h i#j k,e1 :]e k is a con/ant2 h5ce by equation 7#a7 we h 7beta-alpha7 d ,v ----------------- --1 kealpha ,i :]e ,i #a - epsilon-7beta-alpha7d 7#a d7beta - alpha774 ,s9ce bo? beta & alpha are proportional to ! pressure1 ,i & 7beta - alpha7d_/alpha are bo? functions ( pd1 ! product ( ! pressure & ! sp>k l5g?1 h5ce we see t ,v is express$ by an equation ( ! =m #a ,v -- int7pd7 7#b71 ke :]e int7pd7 d5otes a function ( pd1 & nei!r p nor d ent] into ! expression = ,v except 9 ?is product4 ,?us ! pot5tial diff]5ce requir$ to produce dis*>ge is con/ant z long z ! product ( ! pressure & sp>k l5g? rema9s con/ant2 9 o!r words1 ! sp>k pot5tial is con/ant z long z ! mass ( ! gas betwe5 ! electrodes is con/ant4 ,?us1 = example1 if we halve ! pressure ! same pot5tial diff]5ce w produce a sp>k ( twice ! l5g?4 ,?is law1 :i* 0 discov]$ by ,pas*5 = fairly long sp>ks 7,annal51 #cg1 p4 #gi71 & has be5 %[n by ,c>r 7,phil4 ,trans41 #aijc7 to hold = %ort ones1 is "o ( ! mo/ important prop]ties ( ! electric dis*>ge4 ,we see f ! expression = ,v t :5 7beta - alpha7d is v l>ge ,v 7beta - alpha7d_/kealpha4 ,?us ,v becomes inf9ite :5 d is inf9ite4 ,aga9 :5 7beta - alpha7d is v small we f9d ,v #a_/kealphad2 ?us ,v is aga9 inf9ite :5 d is no?+4 ,!re mu/ !re=e be "s value ( d int]m$iate betwe5 z]o & inf9ity = :i* ,v is a m9imum4 ,?is value is got by f9d+ 9 ! usual way ! value ( d1 :i* makes ! expression = ,v giv5 9 equation 7#a7 a m9imum4 ,we f9d t d mu/ satisfy ! equation _/ #a epsilon-7beta-alpha7d #a 7beta - alpha7d 7beta - alphad74 _/ ,we f9d by a process ( trial & error t 7beta-alpha7d #a4h is approximately a solution ( ?is equation2 h5ce ! di/ance = m9imum pot5tial is #a4h_/7;beta - alpha74 ,s9ce beta & alpha are bo? proportional to ! pressure1 we see t ! critical sp>k l5g? v>ies inv]sely z ! pressure4 ,if we sub/itute ?is value 9 ! expression = ,v we f9d t ,v1 ! m9imum sp>k pot5tial1 is giv5 by beta - alpha #b4b ,v ---------------- ---4 alpha ke ,s9ce beta & alpha are ea* proportional to ! pressure1 ! m9imum pot5tial is indep5d5t ( ! pressure ( ! gas4 ,on ?is view ! m9imum pot5tial dep5ds ^u ! metal ( :i* ! ca?ode is made1 s9ce k measures ! numb] ( corpuscles emitt$ p] unit "t by ! ca?ode :5 /ruck by positive ions c>ry+ unit en]gy1 & unless beta be>s ! same ratio to alpha = all gases ! m9imum pot5tial w also v>y ) ! gas4 ,! measurem5ts :i* h be5 made ( ! ca?ode fall ( pot5tial1 :i* z we %all see is equal to ! m9imum pot5tial requir$ to produce a sp>k1 %[ t ?is quantity v>ies ) ! mat]ial ( :i* ! ca?ode is made & also ) ! nature ( ! gas4 ,s9ce a metal plate1 :5 bomb>d$ by positive ions1 emits corpuscles1 ! effect we h be5 consid]+ mu/ play a "p 9 ! dis*>ge2 x is n1 h[ev]1 ! only effect :i* has to be consid]$1 = z ,t[ns5d has %[n1 positive ions :5 mov+ above a c]ta9 spe$ ionize ! gas1 & cause x to emit corpuscles4 ,x is ?us necess>y to take into acc\nt ! ionization ( ! positive ions4 ,let m be ! numb] ( positive ions p] unit volume1 & w _! velocity1 ! numb] ( collisions :i* occur 9 "o second 9 "o cubic c5timetre ( ! gas w be proportional to mwp1 :]e p is ! pressure ( ! gas4 ,let ! numb] ( ions :i* result f ^! collisions be gammamw2 gamma w be a function ( p & ( ! /r5g? ( ! electric field4 ,let z be=e n be ! numb] ( corpuscles p] cubic c5timetre1 u _! velocity1 & alphanu ! numb] ( ions :i* result 9 "o second f ! collisions betwe5 ! corpuscles & ! gas4 ,! numb] ( ions produc$ p] second p] cubic c5timetre is equal to alphanu gammamw2 h5ce :5 ?+s are 9 a /eady /ate d --7nu7 alphanu gammamw 1 dx & e7nu mw7 i1 :]e e is ! *>ge on ! ion & i ! curr5t ?r\gh ! gas4 ,! solution ( ^! equations :5 ! field is uni=m betwe5 ! plates1 is enu ,cepsilon7alpha-gamma7x - gammai_/7alpha - gamma71 emw -,cepsilon7alpha-gamma7x alphai_/7alpha - gamma71 :]e ,c is a con/ant ( integration4 ,if !re is no emission ( positive ions f ! anode enu i1 :5 x d4 ,det]m9+ ,c f ?is condition we f9d i _/ enu ----------------- alphaepsilon7alpha-gamma77x-d7 - gamma 1 alpha - gamma _/ alphai _/ emw ----------------- #a - epsilon7alpha-gamma77x-d7 4 alpha - gamma _/ ,if ! ca?ode did n emit any corpuscles ow+ to ! bomb>dm5t by positive ions1 ! condition t ! *>ge %\ld be ma9ta9$ is t !re %\ld be en\gh positive ions at ! ca?ode to c>ry ! curr5t i4e4 t emw i2 :5 x #j1 ! condition gives i _/ ----------------- alphaepsilon-7alpha-gamma7d - gamma #j1 alpha - gamma _/ or epsilonalphad_/alpha epsilongammad_/gamma4 ,s9ce alpha & gamma are bo? ( ! =m pf7,x_/p7 & ,x ,v_/d1 we see t ,v w be a function ( pd1 9 agreem5t ) ,pas*5's law4 ,if we take into acc\nt bo? ! ionization ( ! gas & ! emission ( corpuscles by ! metal we c easily %[ t alpha-gammaepsilon7alpha-gamma7d kalpha,ve #a ---------------------------------------- ----- ---------- ------------------------- - alpha - gamma d 7betagamma-alpha7 _/ #a d epsilon-7betagamma-alpha7d ------------------------ ---------------------- 1 7betagamma-alpha7 betagamma-alpha_/ :]e k & beta h ! same mean+ z 9 ! previ\s inve/igation4 ,:5 d is l>ge1 epsilon7alpha-gamma7d is also l>ge2 h5ce 9 ord] t ! left-h& side ( ?is equation %\ld n be negative gamma mu/ be less ?an alpha_/epsilon 7alpha-gamma7d2 z ?is dim9i%es z d increases we see t :5 ! sp>ks are v long dis*>ge w take place1 practically z soon z gamma has a f9ite value1 i4e4 z soon z ! positive ions beg9 to produce fre% ions by _! collisions4 ,9 ! prec$+ inve/igation we h suppos$ t ! electric field betwe5 ! plates 0 uni=m2 if x 7 n uni=m we c\ld get dis*>ges produc$ by v mu* small] diff]5ces ( pot5tial ?an are necess>y 9 a uni=m field4 ,= to ma9ta9 ! dis*>ge x is n necess>y t ! positive ions %\ld act z ioniz]s all along _! pa?2 x is suffici5t t !y %\ld d s 9 ! neighb\rhood ( ca?ode4 ,?us if we h a /rong field close to ! ca?ode we might /ill get ! dis*>ge ?\gh ! re/ ( ! field 7 comp>atively weak4 ,su* a di/ribution ( electric =ce requires1 h[ev]1 a great accumulation ( *>g$ ions ne> ! ca?ode2 until ^! ions accumulate ! field w be uni=m4 ,if ! uni=m field exi/+ 9 ! gas be=e ! dis*>ge beg9s 7 /rong en\gh to make ! corpuscles produce ions by collision1 b n /rong en\gh to make ! positive ions act z ioniz]s1 !re w\ld be "s accumulation ( ions1 & ! am\nt ( ?is accumulation w\ld dep5d ^u ! numb] ( free corpuscles orig9ally pres5t 9 ! gas1 & ^u ! /r5g? ( ! electric field4 ,if ! accumulation 7 suffici5t to make ! field ne> ! ca?ode s /rong t ! positive ions c\ld produce fre% ions ei!r by collision ) ! ca?ode or ) ! gas1 ! dis*>ge w\ld pass ?\gh ! gas2 if n1 !re w be no cont9u\s dis*>ge4 ,z ! am\nt ( ! accumulation dep5ds on ! numb] ( corpuscles pres5t 9 ! gas1 we c und]/& h[ x is t aft] a sp>k has pass$1 leav+ = a "t a supply ( corpuscles beh9d x1 x is easi] to get a dis*>ge to pass ?r\gh ! gas ?an x 0 be=e4 ,illu/ration3 ,fig4 #ae4 ,! inequality ( ! electric field 9 ! gas :5 a cont9u\s dis*>ge is pass+ ?r\gh x is v obvi\s :5 ! pressure ( ! gas is l[4 ,9 ?is case ! dis*>ge pres5ts a highly diff]5tiat$ appe>ance ( :i* a type is repres5t$ 9 fig4 #ae4 ,/>t+ f ! ca?ode we h a ?9 velvety lum9\s gl[ 9 contact ) ! surface2 ?is gl[ is (t5 call$ ! fir/ ca?ode lay]4 ,next ?is we h a comp>atively d>k space ^: ?ickness increases z ! pressure dim9i%es2 ?is is call$ ! ,crookes's d>k space1 or ! second ca?ode lay]4 ,next ?is we h a lum9\s position call$ ! negative gl[ or ! ?ird ca?ode lay]4 ,! b\nd>y betwe5 ! second & ?ird lay]s is (t5 v %>ply def9$4 ,next to ! ?ird lay] we h ano!r d>k space call$ ! ,f>aday d>k space4 ,next to ?is & rea*+ up to ! anode is ano!r region ( lum9osity1 call$ ! positive column1 sometimes 7z 9 fig4 #ae1 a7 cont9u\s1 sometimes 7z 9 fig4 #ae1 b7 brok5 up into light or d>k pat*es call$ /riations4 ,! dim5sions ( ! ,f>aday d>k space & ! positive column v>y greatly ) ! curr5t pass+ ?r\gh ! gas & ) its pressure2 sometimes "o or o!r ( !m is abs5t4 ,^! diff]5ces 9 appe>ances are accompani$ by great diff]5ce 9 ! /r5g? ( ! electric field4 ,! magnitude ( ! electric =ce at diff]5t p>ts ( ! dis*>ge is repres5t$ 9 fig4 #af1 :]e ! ord9ates repres5t ! electric =ce at diff]5t p>ts ( ! tube1 ! ca?ode be+ on ! "r4 ,we see t ! electric =ce is v l>ge inde$ betwe5 ! negative gl[ & ! ca?ode1 mu* l>g] ?an 9 any o!r "p ( ! tube4 ,x is n con/ant 9 ?is region1 b increases z we approa* ! ca?ode4 ,! =ce rea*es a m9imum ei!r 9 ! negative gl[ itself or 9 ! "p ( ! ,f>aday d>k space j outside1 aft] :i* x increases t[>ds ! positive column4 ,9 ! case ( a uni=m positive column ! electric =ce along x is con/ant until we get q close to ! anode1 :5 a sudd5 *ange1 call$ ! anode fall1 takes place 9 ! pot5tial4 ,illu/ration3 ,dis*>ge 9 ,hydrog5 ,pressure #b4be m4m4 ,curr5t #j4efhaj-c amp]e ,,fig4 #af4 ,! diff]5ce ( pot5tial betwe5 ! ca?ode & ! negative gl[ is call$ ! ca?ode pot5tial fall & is f\nd to be con/ant = wide v>iations 9 ! pressure ( ! gas & ! curr5t pass+ ?r\gh4 ,x increases1 h[ev]1 consid]ably :5 ! curr5t ?r\gh ! gas exce$s a c]ta9 critical value1 dep5d+ among o!r ?+s on ! size ( ! ca?ode4 ,?is ca?ode fall ( pot5tial is %[n by exp]im5t to be v approximately equal to ! m9imum pot5tial diff]5ce4 ,! foll[+ table conta9s a comp>ison ( ! measurem5ts ( ! ca?ode fall ( pot5tials 9 v>i\s gases made by ,w>burg 7,wi$4 ,ann41 #ahhg1 #ca1 p4 #ede1 & #ahij1 #dj1 p4 #a71 ,cap/ick 7,proc4 ,roy4 ,society1 #ahih1 #fc1 p4 #cef71 & ,/rutt 7,phil4 ,trans41 #aijj1 #aic1 p4 #cgg71 & ! measurem5ts by ,/rutt ( ! smalle/ diff]5ce ( pot5tial :i* w ma9ta9 a sp>k ?r\gh ^! gases4 ---------------------------------------- --------------------------- ,ca?ode fall 9 ,volts4 ,lea/ pot5tial ,gas4 ---------------------------------------- diff]5ce ,plat9um ,electrodes4 ,alum9ium requir$ to ,electrodes4ma9ta9 a ,sp>k4 ---------------------------------------- ------------------------ ,w>burg4 ,cap/ick4,/rutt4 ,w>burg4 ,/rutt4 ---------------------------------------- ------------------------ ,air #cdj-cej 44 44 44 #cda ,h#b ab\t #cjj #bih 44 #afh #cjb-cjh ,o#b 44 #cfi 44 44 44 ,n#b #bcj if free #bcb 44 #bjg #bea f oxyg5 ,hg vap\r #cdj 44 44 44 44 ,helium 44 44 #bbf 44 #bfa-cbf ,h#b,o 44 #dfi 44 44 44 ,,nh#c 44 #ehb 44 44 44 ---------------------------------------- ------------------------ ,?us 9 ! cases 9 :i* ! measurem5ts c\ld be made ) ! greate/ accuracy ! agreem5t betwe5 ! ca?ode fall & ! m9imum pot5tial diff]5ce is v close4 ,! ca?ode fall dep5ds on ! mat]ial ( :i* ! t]m9als are made1 z is %[n by ! foll[+ table due to ,mey 7,v]h4 deuts*4 physik4 ,gesell41 #aijc1 #e1 p4 #gb74 ---------------------------------------- ----------- ,gas4 ,electrode4 ---------------------------------------- - ,pt ,hg ,ag ,cu ,fe ,zn ,al ,mg ,na ,na-,k ,k ---------------------------------------- - ,o#b #cfi 44 44 44 44 44 44 44 44 44 44 ,h#b #cjj 44#biebhjbcjbacaijafhaheafi #agb ,n#b #bcbbbf 44 44 44 44 44#bjgaghabe #agj ,he #bbf 44 44 44 44 44 44 44 #hj #gh4e #fi ,argon #afg 44 44 44 44 44#ajj 44 44 44 44 ---------------------------------------- - ,! dep5d5ce ( ! m9imum pot5tial requir$ to produce a sp>k ^u ! metal ( :i* ! ca?ode is made has n be5 cle>ly e/abli%$1 "s obs]v]s be+ unable to detect any diff]5ce betwe5 ! pot5tial requir$ to sp>k betwe5 electrodes ( alum9ium & ^? ( brass1 :ile o!rs ?\ght !y _h detect$ su* a diff]5ce4 ,x is only ) sp>ks n mu* long] ?an ! critical sp>k l5g? t we c\ld hope to detect ?is diff]5ce4 ,:5 ! curr5t ?r\gh ! gas exce$s a c]ta9 critical value dep5d+ among o!r ?+s on ! size ( ! ca?ode1 ! ca?ode fall ( pot5tial increases rapidly & at ! same "t ! ?ickness ( ! d>k spaces dim9i%es4 ,we may reg>d ! "p ( ! dis*>ge betwe5 ! ca?ode & ! negative gl[ z a dis*>ge tak+ place "u m9imum pot5tial diff]5ce ?r\gh a di/ance equal to ! critical sp>k l5g?4 ,an inspection ( fig4 #af w %[ t we _c reg>d ! electric field z con/ant ev5 = ?is small di/ance2 x ?us becomes a matt] ( int]e/ to "k :at w\ld be ! effect on ! m9imum pot5tial diff]5ce requir$ to produce a sp>k if !re 7 suffici5t ions pres5t to produce v>iations 9 ! electric field analog\s to ^? repres5t$ 9 fig4 #af4 ,if ! electric =ce at a di/ance x f ! ca?ode 7 proportional to epsilon-px we %\ld h a /ate ( ?+s mu* resembl+ ! di/ribution ( electric =ce ne> ! ca?ode4 ,if we apply to ?is di/ribution ! me?ods us$ above = ! case :5 ! =ce 0 uni=m1 we %all f9d t ! m9imum pot5tial is less & ! critical sp>k l5g? great] ?an :5 ! electric =ce is uni=m4 ,pot5tial ,diff]5ce requir$ to produce a ,sp>k ( giv5 ,l5g?4--,we may reg>d ! region betwe5 ! ca?ode & ! negative gl[ z a place = ! production ( corpuscles1 ^! corpuscles f9d+ _! way f ?is region ?r\gh ! negative gl[4 ,! p>ts ( ?is gl[ t[>ds ! anode we may reg>d z a ca?ode1 f :i*1 z f a hot lime ca?ode1 corpuscles are emitt$4 ,let u n[ consid] :at w happ5 to ^! corpuscles %ot out f ! negative gl[ ) a velocity dep5d+ on ! ca?ode fall ( pot5tial & indep5d5t ( ! pressure4 ,^! corpuscles w collide ) ! molecules ( ! gas1 & unless !re is an ext]nal electric field to ma9ta9 _! velocity !y w soon come to re/ & accumulate 9 front ( ! negative gl[4 ,! electric =ce ex]t$ by ?is cl\d ( corpuscles w dim9i% ! /r5g? ( ! electric field 9 ! region betwe5 ! ca?ode & ! negative gl[1 & ?us t5d to /op ! dis*>ge4 ,to keep up ! dis*>ge we mu/ h a suffici5tly /rong electric field betwe5 ! negative gl[ & ! anode to remove ! corpuscles f ?is region z fa/ z !y are s5t into x f ! ca?ode4 ,if1 h[ev]1 !re is no production ( ions 9 ! region betwe5 ! negative gl[ & ! anode1 all ! ions 9 ?is region w h come f ne> ! ca?ode & w be negatively *>g$2 ?is negative electrification w dim9i% ! electric =ce on ! ca?ode side ( x & ?us t5d to /op ! dis*>ge4 ,?is back electric field c\ld1 h[ev]1 be prev5t$ by a little ionization 9 ! region betwe5 ! anode & gl[1 = ?is w\ld af=d a supply ( positive ions1 & ?us af=d an opportunity = ! gas 9 ?is region to h 9 x z _m positive z negative ions2 9 ?is case x w\ld n give rise to any back electromotive =ce4 ,! ionization :i* produces ^! positive ions may1 if ! field is int5se1 be due to ! collisions ( corpuscles1 or x may be due to radiation analog\s to ultra-violet1 or s(t ,rntg5 rays1 :i* h be5 %[n by exp]im5t to accompany ! dis*>ge4 ,?us 9 ! mo/ simple conditions = dis*>ge we %\ld h suffici5t ionization to keep up ! supply ( positive ions1 & an electric field /rong en\gh to keep ! velocity ( ! negative corpuscle equal to ! value x has :5 x em]ges f ! negative gl[4 ,?us ! =ce mu/ be su* z to give a con/ant velocity to ! corpuscle1 & s9ce ! =ce requir$ to move an ion ) a giv5 velocity is proportional to ! pressure1 ?is =ce w be proportional to ! pressure ( ! gas4 ,let u call ?is =ce ap2 !n if l is ! di/ance ( ! anode f ! negative gl[ ! pot5tial diff]5ce betwe5 ^! po9ts w be alp4 ,! pot5tial diff]5ce betwe5 ! negative gl[ & ! ca?ode is con/ant & equals c2 h5ce if ,v is ! pot5tial diff]5ce betwe5 ! anode & ca?ode1 !n ,v c alp1 a relation :i* expresses ! connexion betwe5 ! pot5tial diff]5ce & sp>k l5g? = sp>k l5g?s great] ?an ! critical di/ance4 ,x is to be rememb]$ t ! result we h obta9$ applies only to su* a case z t indicat$ above1 :]e ! electric =ce is con/ant along ! positive column4 ,exp]im5ts ) ! dis*>ge ?r\gh gases at l[ pressure %[ ! dis*>ge may take o!r =ms4 ,?us ! positive column may be /riat$ :5 ! =ce along x is no long] uni=m1 or ! positive column may be abs5t2 ! dis*>ge may be *ang$ f "o ( ^! =ms to ano!r by alt]+ ! curr5t4 ,! relation betwe5 ! pot5tial & ! di/ance betwe5 ! electrodes v>ies greatly1 z we might expect1 ) ! curr5t pass+ ?r\gh ! gas4 ,! connexion betwe5 ! pot5tial diff]5ce & ! sp>k l5g? has be5 made ! subject ( a l>ge numb] ( exp]im5ts4 ,! fir/ measurem5ts 7 made by ,"l ,kelv9 9 #ahfj 7,collect$ ,pap]s on ,electro/atics & ,magnetism1 p4 #bdg72 subsequ5t exp]im5ts h be5 made by ,baille 7,ann4 de *imie et de physique1 #e1 #be1 p4 #dhf71 ,liebig 7,phil4 ,mag4 #e1 #bd1 p4 #ajf71 ,pas*5 7,wi$4 ,ann4 #cg1 p4 #gi71 ,peace 7,proc4 ,roy4 ,soc41 #ahib1 #eb1 p4 #ii71 ,orgl] 7,ann4 d] ,phys4 #a1 p4 #aei71 ,/rutt 7,phil4 ,trans4 #aic1 p4 #cgg71 ,b\ty 7,comptes r5dus1 #aca1 pp4 #dfi1 #ejc71 ,e>h>t 7,phil4 ,mag4 #f1 #a1 p4 #adg71 ,c>r 7,phil4 ,trans41 #aijc71 ,russell 7,phil4 ,mag4 #e1 #fd1 p4 #bcg71 ,hobbs 7,phil4 ,mag4 #f1 #aj1 p4 #fag71 ,k9sley 7,phil4 ,mag4 #f1 #i1 #fib71 ,ritt] 7,ann4 d] ,phys4 #ad1 p4 #aah74 ,! results ( _! exp]im5ts %[ t = sp>ks consid]ably long] ?an ! critical sp>k l5g?1 ! relation betwe5 ! pot5tial diff]5ce ,v & ! sp>k l5g? l may be express$ :5 ! electrodes are l>ge ) great accuracy by ! l9e> relation ,v c blp1 :]e p is ! pressure & c & b are con/ants dep5d+ on ! nature ( ! gas4 ,:5 ! sp>ks are long ! t]m blp is ! mo/ important & ! sp>k+ pot5tial is proportional to ! sp>k l5g?4 ,?\gh !re are consid]able discrepancies betwe5 ! results obta9$ by diff]5t obs]v]s1 ^! indicate t ! production ( a long sp>k betwe5 l>ge electrodes 9 air at atmosph]ic pressure requires a pot5tial diff]5ce ( #cj1jjj volts = ea* c5timetre ( sp>k l5g?4 ,9 hydrog5 only ab\t half ?is pot5tial diff]5ce is requir$1 9 c>bonic acid gas ! pot5tial diff]5ce is ab\t ! same z 9 air1 :ile ,ritt]'s exp]im5ts %[ t 9 helium only ab\t "o-t5? ( ?is pot5tial diff]5ce is requir$4 ,9 ! case :5 ! electric field is n uni=m1 z = example :5 ! dis*>ge takes place betwe5 sph]ical electrodes1 ,russell's exp]im5ts %[ t ! dis*>ge takes place z soon z ! maximum electric =ce 9 ! field betwe5 ! electrodes rea*es a def9ite value1 :i* he f\nd 0 = air at atmosph]ic pressure ab\t #ch1jjj volts p] c5timetre4 ,v ,%ort ,sp>ks4--,"s v int]e/+ exp]im5ts on ! pot5tial diff]5ce requir$ to produce exce$+ly %ort sp>ks h be5 made by ,e>h>t1 ,hobbs & ,k9sley2 ! l5g? ( ^! sp>ks 0 comp>able ) ! wave l5g? ( sodium light4 ,) sp>ks ( ^! l5g?s x 0 f\nd t x 0 possible to get a dis*>ge ) less ?an #ccj volts1 ! m9imum pot5tial diff]5ce 9 air4 ,! results ( ^! obs]v]s %[ t !re is no dim9ution 9 ! m9imum pot5tial diff]5ce requir$ to produce dis*>ge until ! sp>k l5g? gets s small t ! av]age electric =ce betwe5 ! electrodes am\nts to ab\t "o million volts p] c5timetre4 ,:5 ! =ce rises to ?is value a dis*>ge takes place ev5 ?\gh ! pot5tial diff]5ce is mu* less ?an #ccj volts2 9 "s ( ,e>h>t's exp]im5ts x 0 only ab\t #b volts4 ,?is k9d ( dis*>ge is det]m9$ n by ! condition t ! pot5tial diff]5ce %\ld h a giv5 value1 b t ! electric =ce %\ld h a giv5 value4 ,ano!r po9t 9 :i* ?is dis*>ge diff]s f ! ord9>y "o is t x is influ5c$ entirely by ! nature ( ! electrodes & n by ! nature or pressure ( ! gas betwe5 !m1 :]eas ! ord9>y dis*>ge is 9 _m cases n affect$ appreciably by *anges 9 ! metal ( ! electrodes1 b is always affect$ by *anges 9 ! pressure & "* ( ! gas betwe5 !m4 ,k9sley f\nd t :5 "o ( ^! small sp>ks pass$ betwe5 ! electrodes a k9d ( metallic bridge 0 =m$ betwe5 !m1 s t !y 7 9 metallic connexion1 & t ! di/ance betwe5 !m _h to be consid]ably increas$ be=e ! bridge 0 brok54 ,almy 7,phil4 ,mag41 ,sept4 #aijh71 :o us$ v small electrodes1 0 unable to get a dis*>ge ) less ?an ! m9imum sp>k pot5tial ev5 :5 ! sp>k l5g? 0 r$uc$ to "o-?ird ( ! wave l5g? ( sodium light4 ,he sugge/s t ! dis*>ges obta9$ ) l>g] electrodes = small] voltages are due to ! electrodes be+ dragg$ toge!r by ! electro/atic attraction betwe5 !m4 ,con/itution ( ! ,electric ,sp>k4--,s*u/] & ,hemsale* 7,phil4 ,trans4 #aic1 p4 #ahi71 ,hemsale* 7,comptes ,r5dus1 #acj1 p4 #hih2 #acb1 p4 #iag2 ,j\r4 de ,phys4 #c4 #i1 p4 #dc1 & ,s*5ck1 ,a/rophy4 ,j\r4 #ad1 p4 #aaf7 h by spectroscopic me?ods obta9$ v int]e/+ results ab\t ! con/itution ( ! sp>k4 ,! me?od employ$ by ,s*u/] & ,hemsale* 0 z foll[s3 ,suppose we photograph ! spectrum ( a horizontal sp>k on a film :i* is on ! rim ( a :eel rotat+ ab\t a horizontal axis ) great velocity4 ,if ! lum9osity travell$ ) inf9ite spe$ f "o electrode to ! o!r1 ! image on ! film w\ld be a horizontal l9e4 ,if1 h[ev]1 ! spe$ ) :i* ! lum9osity travell$ betwe5 ! electrodes 0 comp>able ) ! spe$ ( ! film1 ! l9e w\ld be incl9$ to ! horizontal1 & by measur+ ! incl9ations we c\ld f9d ! spe$ at :i* ! lum9osity travell$4 ,9 ?is way ,s*u/] & ,hemsale* %[$ t :5 an oscillat+ dis*>ge pass$ betwe5 metallic t]m9als 9 air1 ! fir/ sp>k passes ?r\gh ! air alone1 no l9es ( ! metal appe>+ 9 its spectrum4 ,?is fir/ sp>k vaporizes "s ( ! metal & ! subsequ5t sp>ks pass+ ma9ly ?r\gh ! metallic vap\r2 ! appe>ance ( ! l9es 9 ! film %[s t ! velocity ( ! lum9\s "p ( ! vap\r 0 f9ite4 ,! velocity ( ! vap\r ( metals ( l[ atomic weight 0 9 g5]al great] ?an t ( ! vap\r ( heavi] metals4 ,?us ! velocity ( alum9ium vap\r 0 #ahij metres p] second1 t ( z9c & cadmium only ab\t #ede4 ,p]haps ! mo/ int]e/+ po9t 9 ! inve/igation 0 ! discov]y t ! velocities correspond+ to diff]5t l9es 9 ! spectrum ( ! same metal 7 9 "s cases diff]5t4 ,?us ) bismu? "s ( ! l9es indicat$ a velocity ( #adbj metres p] second1 o!rs a velocity ( only #eej1 :ile "o 7lambda #cgic7 %[$ a /ill small] velocity4 ,^! results are 9 accordance ) a view sugge/$ by o!r ph5om5a t _m ( ! l9es 9 a spectrum produc$ by an electrical dis*>ge orig9ate f sy/ems =m$ dur+ ! dis*>ge & n f ! normal atom or molecule4 ,s*u/] & ,hemsale* f\nd t by ins]t+ a coil ) l>ge self induction 9 ! prim>y circuit !y c\ld oblit]ate ! air l9es 9 ! dis*>ge4 ,s*5ck1 by obs]v+ ! appe>ance pres5t$ :5 an alt]nat+ curr5t1 produc$ by dis*>g+ ,leyd5 j>s1 0 exam9$ 9 a rapidly rotat+ mirror1 f\nd x %[$ ! foll[+ /ages3 7#a7 a ?9 bright l9e1 foll[$ 9 "s cases at int]vals ( half ! p]iod ( ! dis*>ge by fa9t] l9es2 7#b7 bright curv$ /ream]s />t+ f ! negative t]m9al1 & dim9i%+ rapidly 9 spe$ z !y rec$$ f ! ca?ode2 7#c7 a diffus$ gl[ la/+ = a mu* long] p]iod ?an ei!r ( ! prec$+4 ,^! con/itu5ts gave out q diff]5t spectra4 ,! /ructure ( ! dis*>ge is mu* m easily /udi$ :5 ! pressure ( ! gas is l[1 z ! v>i\s p>ts :i* make up ! dis*>ge are m widely sep>at$ f ea* o!r4 ,we h already describ$ ! g5]al appe>ance ( ! dis*>ge ?r\gh gases at l[ pressures 7see p4 #feg74 ,!re is1 h[ev]1 "o =m ( dis*>ge :i* is s /rik+ & beautiful t x des]ves m detail$ consid]ation4 ,9 ?is type ( dis*>ge1 kn[n z ! /riat$ dis*>ge1 ! positive column is made up ( alt]nate bright & d>k pat*es kn[n z /riations4 ,"s ( ^! are repres5t$ 9 fig4 #ag1 :i* is tak5 f a pap] by ,de la ,rue & ,mll] 7,phil4 ,trans41 #ahgh1 ,pt4 #a74 ,?is type ( dis*>ge only occurs :5 ! curr5t & ! pressure ( ! gas are betwe5 c]ta9 limits4 ,x is mo/ beautifully %[n :5 a ,wehnelt ca?ode is us$ & ! curr5t is produc$ by /orage cells1 z ?is all[s u to use l>ge curr5ts & to ma9ta9 a /eady pot5tial diff]5ce betwe5 ! electrodes4 ,! /riations are 9 consequ5ce v bright & /eady4 ,! facts :i* h be5 e/abli%$ ab\t ^! /riations are z foll[s3 ,! di/ance betwe5 ! bright p>ts ( ! /riations is great] at l[ pressures ?an at high2 x dep5ds also ^u ! diamet] ( ! tube1 increas+ z ! diamet] ( ! tube increases4 ,if ! dis*>ge tube is wide at "o place & n>r[ 9 ano!r ! /riations w be clos] toge!r 9 ! n>r[ p>ts ?an 9 ! wide4 ,! di/ance betwe5 ! /riations dep5ds on ! curr5t ?r\gh ! tube4 ,! relation is n a v simple "o1 z an increase ( curr5t sometimes increases :ile "u o!r circum/ances x decreases ! di/ance betwe5 ! /riations 7see ,will[s1 ,proc4 ,camb4 ,phil4 ,soc4 #aj1 p4 #cjb74 ,! electric =ce is n uni=m along ! /riat$ dis*>ge1 b is great] 9 ! bright ?an 9 ! d>k p>ts ( ! /riation4 ,an example is %[n 9 fig4 #af1 due to ,h4 ,a4 ,wilson1 :i* %[s ! di/ribution ( electric =ce at e place 9 a /riat$ dis*>ge4 ,9 exp]im5ts made by ,j4 ,j4 ,?omson 7,phil4 ,mag41 ,oct4 #aiji71 us+ a ,wehnelt ca?ode1 ! v>iations 9 ! electric =ce 7 m pron\nc$ ?an ^? %[n 9 fig4 #af4 ,! electric =ce 9 ?is case *ang$ s greatly t x actually became negative j on ! ca?ode side ( ! bright "p ( ! /riation4 ,j inside ! /riation on ! anode side x rose to a v high value1 !n cont9ually dim9i%$ t[>ds ! bright side ( ! next /riation :5 x aga9 increas$4 ,?is di/ribution ( electric =ce implies t !re is great excess ( negative electricity at ! bright head ( ! /riation1 & a small excess ( positive ev]y:]e else4 ,! temp]ature ( ! gas is high] 9 ! bright ?an 9 ! d>k p>ts ( ! /riations4 ,wood 7,wi$4 ,ann4 #di1 p4 #bch71 :o has made a v c>eful /udy ( ! di/ribution ( temp]ature 9 a dis*>ge tube1 f9ds t 9 ^? tubes ! temp]ature v>ies 9 ! same way z ! electric =ce1 b t ?is temp]ature 7:i* x mu/ be rememb]$ is ! av]age temp]ature ( all ! molecules & n m]ely ( ^? :i* are tak+ "p 9 ! dis*>ge7 is by no means high2 9 no "p ( ! dis*>ge did ! temp]ature 9 8 exp]im5ts exce$ #ajj ,c4 ,illu/ration3 ,,fig4 #ag4 ,!ory ( ! ,/riations4--,we may reg>d ! heap+ up ( ! negative *>ges at int]vals along ! dis*>ge z ! fundam5tal feature 9 ! /riations1 & ?is heap+ up may be expla9$ z foll[s4 ,imag9e a corpuscle project$ ) consid]able velocity f a place :]e ! electric field is /rong1 su* z ! neighb\rhood ( ! ca?ode2 z x moves t[>ds ! anode ?r\gh ! gas x w collide ) ! molecules1 ionize !m & lose en]gy & velocity4 ,?us unless ! corpuscle is act$ on by a field /rong en\gh to supply x ) ! en]gy x loses by collision1 its spe$ w gradually dim9i%4 ,fur!r1 :5 its en]gy falls bel[ a c]ta9 value x w unite ) a molecule & become "p ( a negative ion1 in/ead ( a corpuscle2 at ?is /age !re w be a sudd5 & v l>ge dim9ution 9 its velocity4 ,let u n[ foll[ ! c\rse ( a /ream ( corpuscles />t+ f ! ca?ode & approa*+ ! anode4 ,if ! spe$ falls (f z ! /ream proce$s1 ! corpuscles 9 ! re> w ga9 on ^? 9 front & ! d5sity ( ! /ream 9 ! front w be increas$4 ,if at a c]ta9 place ! velocity receives a sudd5 *eck by ! corpuscles becom+ load$ ) a molecule1 ! d5sity ( ! negative electricity w increase at ?is place ) great rapidity1 & "h !re w be a great accumulation ( negative electricity1 z at ! bright head on ! ca?ode side ( a /riation4 ,n[ ?is accumulation ( negative electricity w produce a l>ge electric =ce on ! anode side2 ?is w drive corpuscles =w>d ) great velocity & ionize ! gas4 ,^! corpuscles w behave l ^? %ot f ! ca?ode & w accumulate aga9 at "s di/ance f _! orig91 =m+ ! bright head ( ! next /riation1 :5 ! process w be repeat$4 ,on ?is view ! bright heads ( ! /riations act l electrodes1 & ! dis*>ge passes f "o bright head to ! next z by a numb] ( /epp+ /ones1 & n directly f ca?ode to anode4 ,! lum9osity at ! head ( ! /riations is due to ! recomb9ation ( ! ions4 ,^! ions h acquir$ consid]able en]gy f ! electric field1 & ?is en]gy w be available = supply+ ! en]gy radiat$ away z light4 ,! recomb9ation ( ions :i* d n possess consid]able am\nts ( en]gy does n seem to give rise to lum9osity4 ,?us1 9 an ioniz$ gas n expos$ to an electric field1 al?\gh we h recomb9ation betwe5 ! ions1 we ne$ n h lum9osity4 ,we h at pres5t no exact data z to ! am\nt ( en]gy :i* mu/ be giv5 to an ion to make x lum9\s on recomb9ation2 x also c]ta9ly v>ies ) ! nature ( ! ion2 ?us ev5 ) hot ,wehnelt ca?odes ,j4 ,j4 ,?omson has nev] be5 able to make ! dis*>ge ?r\gh air lum9\s ) a pot5tial less ?an f #af to #ag volts4 ,! m]cury lamps1 h[ev]1 9 :i* ! dis*>ge passes ?r\gh m]cury vap\r are lum9\s ) a pot5tial diff]5ce ( ab\t #ab volts4 ,x foll[s t if ! prec$+ !ory be "r ! pot5tial diff]5ce betwe5 two bright /riations mu/ be great en\gh to make ! corpuscles ionize by collision & also to give en\gh en]gy to ! ions to make !m lum9\s :5 !y recomb9e4 ,! diff]5ce ( pot5tial betwe5 ! bright p>ts ( successive /riations has be5 measur$ by ,hohn 7,phys4 ,zeit4 #i1 p4 #eeh72 x v>ies ) ! pressure & ) ! gas4 ,! smalle/ value giv5 by ,hohn is ab\t #ae volts4 ,9 "s exp]im5ts made by ,j4 ,j4 ,?omson1 :5 ! pressure ( ! gas 0 v l[1 ! diff]5ce ( pot5tial betwe5 two adjac5t d>k spaces 0 z l[ z #c4ge volts4 ,! ,arc ,dis*>ge4--,! dis*>ges we h hi!rto consid]$ h be5 *>act]iz$ by l>ge pot5tial diff]5ces & small curr5ts4 ,9 ! arc dis*>ge we get v l>ge curr5ts ) comp>atively small pot5tial diff]5ces4 ,we may get ! arc dis*>ge by tak+ a batt]y ( cells l>ge en\gh to give a pot5tial diff]5ce ( #fj to #hj volts1 & connect+ ! cells ) two c>bon t]m9als1 :i* are put 9 contact1 s t a curr5t ( electricity fl[s r\nd ! circuit4 ,if ! t]m9als1 :ile ! curr5t is on1 are drawn ap>t1 a bright dis*>ge1 :i* may c>ry a curr5t ( _m amp]es1 passes f "o to ! o!r4 ,?is arc dis*>ge1 z x is call$1 is *>act]iz$ by int5se heat & by ! brilliant lum9osity ( ! t]m9als4 ,?is makes x a p[]ful s\rce ( light4 ,! temp]ature ( ! positive t]m9al is mu* high] ?an t ( ! negative4 ,accord+ to ,violle 7,comptes ,r5dus1 #aae1 p4 #abgc7 ! temp]ature ( ! tip ( ! =m] is ab\t #cejj ,c1 & t ( ! latt] #bgjj ,c4 ,! temp]ature ( ! arc itself he f\nd to be high] ?an t ( ei!r ( its t]m9als4 ,z ! arc passes1 ! positive t]m9al gets holl[$ out into a crat]-l %ape1 b ! negative t]m9al rema9s po9t$4 ,bo? t]m9als lose weight4 ,! appe>ance ( ! t]m9als is %[n 9 fig4 #ah1 giv5 by ,mrs ,ayrton 7,proc4 ,in/4 ,elec4 ,eng4 #bh1 p4 #djj72 a1 b repres5t ! t]m9als :5 ! arc is quiet1 & c :5 x is accompani$ by a hiss+ s\nd4 ,! intr9sic brightness ( ! positive crat] does n increase ) an increase 9 ! curr5t2 an increas$ curr5t produces an increase 9 ! area ( ! lum9\s crat]1 b ! am\nt ( light giv5 out by ea* unit ( area ( lum9\s surface is unalt]$4 ,?is indicates t ! temp]ature ( ! crat] is con/ant2 x is probably t at :i* c>bon volatilizes4 ,w4 ,e4 ,wilson 7,proc4 ,roy4 ,soc4 #eh1 p4 #agd2 #fj1 p4 #cgg7 has %[n t at pressures ( sev]al atmosph]es ! intr9sic brightness ( ! crat] is consid]ably dim9i%$4 ,illu/ration3 ,,fig4 #ah4 ,illu/ration3 ,,fig4 #ai4 ,! connexion betwe5 ,v1 ! pot5tial diff]5ce betwe5 ! t]m9als1 & l1 ! l5g? ( ! arc1 is some:at analog\s to t :i* holds = ! sp>k dis*>ge4 ,frhli* 7,electrote*4 ,zeit4 #d1 p4 #aej7 gives = ?is connexion ! relation ,v m nl1 :]e m & n are con/ants4 ,mrs ,ayrton 7,! ,electric ,arc1 *ap4 iv47 f9ds t bo? m & n dep5d ^u ! curr5t pass+ betwe5 ! t]m9als1 & gives z ! relation betwe5 ,v & l1 ,v alpha beta_/,i 7gamma delta_/,i7l1 :]e alpha1 beta1 gamma1 delta are con/ants & ,i ! curr5t4 ,! relation betwe5 curr5t & pot5tial diff]5ce 0 made ! subject ( a s]ies ( exp]im5ts by ,ayrton 7,electrician1 #a1 p4 #cai2 xi4 p4 #dah71 "s ( ^: results are repres5t$ 9 fig4 #ai4 ,= a quiet arc an increase 9 curr5t is accompani$ by a fall 9 pot5tial diff]5ce1 :ile = ! hiss+ arc ! pot5tial diff]5ce is indep5d5t ( ! curr5t4 ,! quantities m & n :i* occur 9 ,frhli*'s equation h be5 det]m9$ by sev]al exp]im5t]s4 ,= c>bon electrodes 9 air at atmosph]ic pressure m is ab\t #ci volts1 v>y+ some:at ) ! size & purity ( ! c>bons2 x is dim9i%$ by soak+ ! t]m9als 9 salt solution4 ,! value ( n giv5 by diff]5t obs]v]s v>ies consid]ably1 rang+ f 4#gf to #b volts :5 l is measur$ 9 millimetres2 x dep5ds ^u ! curr5t1 dim9i%+ z ! curr5t increases4 ,:5 metallic t]m9als are us$ in/ead ( c>bons1 ! value ( m dep5ds ^u ! nature ( ! metal1 m 9 g5]al be+ l>g] ! high] ! temp]ature at :i* ! metal volatilizes4 ,?us v4 ,lang 7,wi$4 ,ann4 #ca1 p4 #chd7 f\nd ! foll[+ values = m 9 air at atmosph]ic pressure3--,c #ce2 ,pt #bg4d2 ,fe #be2 ,ni #bf4ah2 ,cu #bc4hf2 ,ag #ae4bc2 ,zn #ai4hf2 ,cd #aj4bh4 ,le*] 7,wi$4 ,ann4 #cc1 p4 #fji7 gives ,pt #bh1 ,fe #bj1 ,ag #h1 :ile ,arons 7,wi$4 ,ann4 #ca1 p4 #chd7 f\nd = ,hg ! value #ab4h2 9 ?is case ! fall ( pot5tial along ! arc itself 0 abnormally small4 ,9 comp>+ ^! values x is important to rememb] t ,le*] 7loc4 cit47 has %[n t ) ,fe or ,pt t]m9als ! arc dis*>ge is int]mitt5t4 ,arons has %[n t ?is is also ! case ) ,hg t]m9als1 b no int]mitt5ce has be5 detect$ ) t]m9als ( ,c1 ,ag or ,cu4 ,! prec$+ measurem5ts ref] to mean pot5tials1 & no conclusions z to ! actual pot5tial diff]5ces at any "t c be drawn :5 ! dis*>ge is discont9u\s1 unless we "k ! law ( discont9uity4 ,! ease ) :i* an arc is su/a9$ dep5ds greatly on ! nature ( ! electrodes2 :5 !y are brass1 z9c1 cadmium1 or magnesium x is exce$+ly difficult to get ! arc4 ,illu/ration3 ,,fig4 #bj4 ,illu/ration3 ,,fig4 #ba4 ,! pot5tial diff]5ce betwe5 ! t]m9als is affect$ by ! pressure ( ! gas4 ,! mo/ ext5sive s]ies ( exp]im5ts on ?is po9t is t made by ,duncan1 ,r[l&1 & ,tod 7,electrician1 #ca1 p4 #fj71 ^: results are repres5t$ 9 fig4 #bj4 ,we see f ^! curves t = v %ort arcs ! pot5tial diff]5ce increases cont9u\sly ) ! pressure1 b = long] ones !re is a critical pressure at :i* ! pot5tial diff]5ce is a m9imum1 & t ?is critical pressure seems to increase ) ! l5g? ( arc4 ,! nature ( ! gas also affects ! pot5tial diff]5ce4 ,! magnitude ( ?is effect may be ga!r$ f ! foll[+ values giv5 by ,arons 7,ann4 d] ,phys4 #a1 p4 #gjj7 = ! pot5tial diff]5ce requir$ to produce an arc #a4e mm4 long1 c>ry+ a curr5t ( #d4e amp]es1 betwe5 t]m9als ( diff]5t metals 9 air & pure nitrog54 ---------------------------- ,t]m9al4 ,air4 ,nitrog54 ---------------------------- ,ag #ba 8 ,zn #bc #ba ,cd #be #ba ,cu #bg #cj ,fe #bi #bj ,pt #cf #cj ,al #ci #bg ,pb 44 #ah ,mg 44 #bb ---------------------------- ,?us1 ) ! dis*>ge = an arc ( giv5 l5g? & curr5t1 ! nature ( ! t]m9als is ! mo/ important factor 9 det]m9+ ! pot5tial diff]5ce4 ,! effects produc$ by ! pressure & nature ( ! surr\nd+ gas1 al?\gh q appreciable1 are n ( s mu* importance1 :ile 9 ! sp>k dis*>ge ! nature ( ! t]m9als is ( no importance1 ev]y?+ dep5d+ ^u ! nature & pressure ( ! gas4 ,! pot5tial gradi5t 9 ! arc is v f> f be+ uni=m4 ,) c>bon t]m9als ,lugg9 7,wi54 ,b]4 #ih1 p4 #aaib7 f\nd t1 ) a curr5t ( #ae amp]es1 !re 0 a fall ( pot5tial ( #cc4g close to ! anode1 & "o #h4g close to ! ca?ode1 s t ! curve repres5t+ ! di/ribution ( pot5tial betwe5 ! t]m9als w\ld be some:at l t %[n 9 fig4 #ba4 ,we h se5 t a some:at analog\s di/ribution ( pot5tial holds 9 ! case ( conduction ?r\gh flames1 ?\gh 9 t case ! greate/ drop ( pot5tial is 9 g5]al at ! ca?ode & n at ! anode4 ,! diff]5ce betwe5 ! *anges ( pot5tial at ! anode & ca?ode is n s l>ge ) ,fe & ,cu t]m9als z ) c>bon ones2 ) m]cury t]m9als1 ,arons 7,wi$4 ,ann4 #eh1 p4 #gc7 f\nd ! anode fall to be #g4d volts1 ! ca?ode fall #e4d volts4 ,! case ( ! arc :5 ! ca?ode is a pool ( m]cury & ! anode a metal wire plac$ 9 a vessel f :i* ! air has be5 exhau/$ is "o :i* has attract$ mu* att5tion1 & important inve/igations on ?is po9t h be5 made by ,hewitt 7,electrician1 #eb1 p4 #ddg71 ,wills 7,electrician1 #ed1 p4 #bf71 ,/>k1 ,rets*9sky & ,s*naposnik(f 7,ann4 d] ,phys4 #ah1 p4 #bac7 & ,pollak 7,ann4 d] ,phys4 #ai1 p4 #bag74 ,9 ?is arrangem5t ! m]cury is vaporiz$ by ! heat1 & ! dis*>ge :i* passes ?r\gh ! m]cury vap\r gives an exce$+ly bright light1 :i* has be5 l>gely us$ = light+ factories1 c4 ,! arrangem5t c also be us$ z a rectifi]1 = a curr5t w only pass ?r\gh x :5 ! m]cury pool is ! ca?ode4 ,?us if su* a lamp is connect$ ) an alt]nat+ curr5t circuit1 x lets ?r\gh ! curr5t 9 "o direction & /ops t 9 ! o!r1 ?us furni%+ a curr5t :i* is always 9 "o direction4 ,!ory ( ! ,arc ,dis*>ge4--,an inc&esc5t body su* z a piece ( c>bon ev5 :5 at a temp]ature f> bel[ t ( ! t]m9als 9 an arc1 emits corpuscles at a rate correspond+ to a curr5t ( ! ord] ( #a amp]e p] squ>e c5timetre ( inc&esc5t surface1 & z ! rate ( increase ( emission ) ! temp]ature is v rapid1 x is probably at ! rate ( _m amp]es p] squ>e c5timetre at ! temp]ature ( ! negative c>bon 9 ! arc4 ,if !n a piece ( c>bon 7 ma9ta9$ at ?is temp]ature by "s ext]nal means1 & us$ z a ca?ode1 a curr5t c\ld be s5t f x to ano!r electrode :e!r ! second electrode 7 cold or hot4 ,if1 h[ev]1 ^! negatively electrifi$ corpuscles did n produce o!r ions ei!r by collision ) ! gas ?r\gh :i* !y move or ) ! anode1 ! spaces betwe5 ca?ode & anode w\ld h a negative *>ge1 :i* w\ld t5d to /op ! corpuscles leav+ ! ca?ode & w\ld require a l>ge pot5tial diff]5ce betwe5 anode & ca?ode to produce any consid]able curr5t4 ,if1 h[ev]1 !re is ionization ei!r 9 ! gas or at ! anode1 ! positive ions w diffuse into ! region ( ! dis*>ge until !y are s5sibly equal 9 numb] to ! negative ions4 ,:5 ?is is ! case ! back electromotive =ce is de/roy$ & ! same pot5tial diff]5ce w c>ry a mu* l>g] curr5t4 ,! arc dis*>ge may be reg>d$ z analog\s to ! dis*>ge betwe5 inc&esc5t t]m9als1 ! only diff]5ce be+ t 9 ! arc ! t]m9als are ma9ta9$ 9 ! /ate ( inc&esc5ce by ! curr5t & n by ext]nal means4 ,on ?is view ! ca?ode is bomb>d$ by positive ions :i* heat x to su* a temp]ature t negative corpuscles suffici5t to c>ry ! curr5t are emitt$ by x4 ,^! corpuscles bomb>d ! anode & keep x inc&esc5t4 ,!y ionize also1 ei!r directly by collision or indirectly by heat+ ! anode1 ! gas & vap\r ( ! metal ( :i* ! anode is made1 & produce 9 ?is way ! supply ( positive ions :i* keep ! ca?ode hot4 ,dis*>ge f a ,po9t4--,a v int]e/+ case ( electric dis*>ge is t betwe5 a %>ply po9t$ electrode1 su* z a ne$le1 & a metal surface ( consid]able area4 ,at atmosph]ic pressures ! lum9osity is conf9$ to ! imm$iate neighb\rhood ( ! po9t4 ,if ! sign ( ! pot5tial ( ! po9t does n *ange1 ! dis*>ge is c>ri$ by ions ( "o sign--t ( ! *>ge on ! po9t$ electrode4 ,! velocity ( ^! ions "u a giv5 pot5tial gradi5t has be5 measur$ by ,*attock 7,phil4 ,mag4 #cb1 p4 #bhe71 & f\nd to agree ) t ( ! ions produc$ by ,rntg5 or uranium radiation1 :ile ,t[ns5d 7,phil4 ,trans4 #aie1 p4 #bei7 has %[n t ! *>ge on ^! ions is ! same z t on ! ions /ream+ f ! po9t4 ,if ! po9t$ electrode be plac$ at "r angles to a metal plane s]v+ z ! o!r electrode1 ! dis*>ge takes place :51 = a giv5 di/ance ( ! po9t f ! plane1 ! pot5tial diff]5ce betwe5 ! electrodes exce$s a def9ite value dep5d+ ^u ! pressure & nature ( ! gas ?r\gh :i* ! dis*>ge passes2 its value also dep5ds ^u :e!r1 beg9n+ ) a small pot5tial diff]5ce1 we gradually increase x until dis*>ge comm5ces1 or1 beg9n+ ) a l>ge pot5tial diff]5ce1 we decrease x until ! dis*>ge /ops4 ,! value f\nd by ! latt] me?od is less ?an t by ! =m]4 ,accord+ to ,*attock's measurem5ts ! pot5tial diff]5ce ,v = dis*>ge betwe5 ! po9t & ! plate is giv5 by ! l9e> relation ,v a bl1 :]e l is ! di/ance ( ! po9t f ! plate & a & b are con/ants4 ,f v4 ,ob]may]'s 7,wi54 ,b]4 #ajj1 #b1 p4 #abg7 exp]im5ts1 9 :i* ! di/ance l 0 great] ?an 9 ,*attock's1 x w\ld seem t ! pot5tial = l>g] di/ances does n increase q s rapidly ) l z is indicat$ by ,*attock's relation4 ,! pot5tial requir$ to produce ?is dis*>ge is mu* less ?an t requir$ to produce a sp>k ( l5g? l betwe5 p>allel plates2 ?us f ,*attock's exp]im5ts to produce ! po9t dis*>ge :5 l 4#e cm4 9 air at atmosph]ic pressure requires a pot5tial diff]5ce ( ab\t #chjj volts :5 ! po9t$ electrode is positive1 :ile to produce a sp>k at ! same di/ance betwe5 plane electrodes w\ld require a pot5tial diff]5ce ( ab\t #ae1jjj volts4 ,*attock %[$ t ) ! same po9t$ electrode ! value ( ! electric int5sity at ! po9t 0 ! same :atev] ! di/ance ( ! po9t f ! plane4 ,! value ( ! electric int5sity dep5d$ ^u ! %>pness ( ! po9t4 ,:5 ! end ( ! po9t$ electrode is a hemisph]e ( radius a1 ,*attock %[$ t = ! same gas at ! same pressure ! electric int5sity f :5 dis*>ge takes place is r\ghly proportion$ to a-#j4h4 ,! value ( ! electric int5sity at ! po9t$ electrode is mu* great] ?an its value at a plane electrode = long sp>ks2 b we mu/ rememb] t at a di/ance f a po9t$ electrode equal to a small multiple ( ! radius ( curvature ( its extremity ! electric int5sity falls v f> bel[ t requir$ to produce dis*>ge 9 a uni=m field1 s t ! dis*>ge f a po9t$ electrode ought to be comp>$ ) a sp>k ^: l5g? is comp>able ) ! radius ( curvature ( ! po9t4 ,= su* %ort sp>ks ! electric int5sity is v high4 ,! electric int5sity requir$ to produce ! dis*>ge f a gas dim9i%es z ! pressure ( ! gas dim9i%es1 b n ne>ly s rapidly z ! electric int5sity = long sp>ks4 ,"h aga9 ! dis*>ge f a po9t is comp>able ) %ort sp>ks1 :i*1 z we h se51 are mu* less s5sitive to pressure *anges ?an long] ones4 ,! m9imum pot5tial at :i* ! electricity /reams f ! po9t does n dep5d ^u ! mat]ial ( :i* ! po9t is made2 x v>ies1 h[ev]1 consid]ably ) ! nature ( ! gas4 ,! foll[+ are ! results ( "s exp]im5ts on ?is po9t4 ,^? 9 ! fir/ two columns are due to ,rntg51 ^? 9 ! ?ird & f\r? to ,pre*t3-- ---------------------------------------- --------------- ,dis*>ge ,pot5tial4 ,po9t 4 ,pressure #gfj4 ,gas4 ---------------------------------------- ------- ,pressure #bje4 ,pressure #aaj4 ,po9t 4 ,po9t -4 ---------------------------------------- ------------- ,volts4 ,volts4 ,volts4 ,volts4 ,h#b #abif #aagd #babe #aeej ,o#b #bdjb #aige #bhjj #bcej ,,co #bfcd #bajj 44 44 ,,*#d #bggg #bcag 44 44 ,,no #cahh #bedc 44 44 ,,co#b #cbhg #bfee #cdge #bajj ,n#b 44 44 #bfjj #bjjj ,air 44 44 #bgej #bjej ---------------------------------------- ------------- ,we see f ?is table t 9 ! case ( ! dis*>ge f a positively electrifi$ po9t ! great] ! molecul> weight ( ! gas ! great] ! pot5tial requir$ = dis*>ge4 ,rntg5 conclud$ f 8 exp]im5ts t ! dis*>g+ pot5tial f a positive po9t 9 diff]5t gases at ! same pressure v>ies inv]sely z ! mean free pa? ( ! molecules ( ! gas4 ,9 ! same gas1 h[ev]1 at diff]5t pressures ! dis*>g+ pot5tial does n v>y s quickly ) ! pressure z does ! mean free pa?4 ,9 ,pre*t's exp]im5ts1 9 :i* diff]5t gases 7 us$1 ! v>iations 9 ! dis*>g+ pot5tial are n s great z ! v>iations 9 ! mean free pa? ( ! gases4 ,! curr5t ( electrifi$ air fl[+ f ! po9t :5 ! electricity is escap+--! well-kn[n electrical w9d--is accompani$ by a reaction on ! po9t :i* t5ds to drive x backw>ds4 ,?is reaction has be5 measur$ by ,arrh5ius 7,wi$4 ,ann4 #fc1 p4 #cje71 :o f9ds t :5 positive electricity is escap+ f a po9t 9 air ! reaction on ! po9t = a giv5 curr5t v>ies inv]sely z ! pressure ( ! gas1 & = diff]5t gases 7air1 hydrog5 & c>bonic acid7 inv]sely z ! squ>e root ( ! molecul> weight ( ! gas4 ,! reaction :5 negative electricity is escap+ is mu* less4 ,! proportion betwe5 ! reactions = positive & negative curr5ts dep5ds on ! pressure ( ! gas4 ,?us = equal positive & negative curr5ts 9 air at a pressure ( #gj cm4 ! reaction = a positive po9t 0 #a4i times t ( a negative "o1 at #dj cm4 pressure #b4f times1 at #bj cm4 pressure #c4b times1 at #aj4c cm4 pressure #g times1 & at #e4a cm4 pressure #ae times ! reaction = ! negative po9t4 ,inve/igation %[s t ! reaction %\ld be proportional to ! quoti5t ( ! curr5t by ! velocity acquir$ by an ion "u unit pot5tial gradi5t4 ,n[ ?is velocity is inv]sely proportional to ! pressure1 s t ! reaction %\ld on ?is view be directly proportional to ! pressure4 ,?is agrees ) ,arrh5ius' results :5 ! po9t is positive4 ,aga91 ! velocities ( an ion 9 hydrog51 air & c>bonic acid at ! same pressure are approximately inv]sely proportional to ! squ>e roots ( _! molecul> weights1 s t ! reaction %\ld be directly proportional to ?is quantity4 ,?is also agrees ) ,arrh5ius' results = ! dis*>ge f a positive po9t4 ,! velocity ( ! negative ion is great] ?an t ( a positive "o "u ! same pot5tial gradi5t1 s t ! reaction = ! negative po9t %\ld be less ?an t = a positive "o1 b ! excess ( ! positive reaction ov] ! negative is mu* great] ?an t ( ! velocity ( ! negative ion ov] ! velocity ( ! positive4 ,!re is1 h[ev]1 reason to believe t a consid]able cond5sation takes place ar\nd ! negative ion z a nucleus aft] x is =m$1 s t ! velocity ( ! negative ion "u a giv5 pot5tial gradi5t w be great] imm$iately aft] ! ion is =m$ ?an :5 x has exi/$ = "s "t4 ,! measurem5ts :i* h be5 made ( ! velocities ( ! ions relate to ^? :i* h be5 "s "t 9 exi/5ce1 b a l>ge "p ( ! reaction w be due to ! newly-=m$ ions mov+ ) a great] velocity1 & ?us giv+ a small] reaction ?an t calculat$ f ! obs]v$ velocity4 ,) a giv5 pot5tial diff]5ce betwe5 ! po9t & ! neighb\r+ conductor ! curr5t issu+ f ! po9t is great] :5 ! po9t is negative ?an :5 x is positive1 except 9 oxyg51 :5 x is less4 ,w>burg 7,sitz4 ,akad4 d4 ,wiss5s*4 zu ,b]l91 #ahii1 #ej1 p4 #ggj7 has %[n t ! addition ( a small quantity ( oxyg5 to nitrog5 produces a great dim9ution 9 ! curr5t f a negative po9t1 b has v little effect on ! dis*>ge f a positive po9t4 ,?us ! removal ( a trace ( oxyg5 made a leak f a negative po9t #ej times :at x 0 be=e4 ,exp]im5ts ) hydrog5 & helium %[$ t impurities 9 ^! gases _h a great effect on ! curr5t :5 ! po9t 0 negative1 & b little :5 x 0 positive4 ,?is sugge/s t ! impurities1 by cond5s+ r\nd ! negative ions z nuclei1 s]i\sly dim9i% _! velocity4 ,if a po9t is *>g$ up to a high & rapidly alt]nat+ pot5tial1 su* z c be produc$ by ! electric oscillations />t$ :5 a ,leyd5 j> is dis*>g$1 !n 9 hydrog51 nitrog51 ammonia & c>bonic acid gas a conductor plac$ 9 ! neighb\rhood ( ! po9t gets a negative *>ge1 :ile 9 air & oxyg5 x gets a positive "o4 ,!re are two consid]ations :i* are ( importance 9 connexion ) ?is effect4 ,! fir/ is ! velocity ( ! ions 9 ! electric field1 & ! second ! ease ) :i* ! ions c give up _! *>ges to ! metal po9t4 ,! great] velocity ( ! negative ions w\ld1 if ! pot5tial 7 rapidly alt]nat+1 cause an excess ( negative ions to be left 9 ! surr\nd+ gas4 ,?is is ! case 9 hydrog54 ,if1 h[ev]1 ! metal _h a mu* great] t5d5cy to unite ) negative ?an ) positive ions1 su* z we %\ld expect to be ! case 9 oxyg51 ?is w\ld act 9 ! opposite direction1 & t5d to leave an excess ( positive ions 9 ! gas4 ,! ,*>act]i/ic ,curve = ,dis*>ge ?r\gh ,gases4--,:5 a curr5t ( electricity passes ?r\gh a metallic conductor ! relation betwe5 ! curr5t & ! pot5tial diff]5ce is ! exce$+ly simple "o express$ by ,ohm's law2 ! curr5t is proportional to ! pot5tial diff]5ce4 ,:5 ! curr5t passes ?r\gh a gas !re is no su* simple relation4 ,?us we h already m5tion$ cases :]e ! curr5t increas$ z ! pot5tial increas$ al?\gh n 9 ! same proportion1 :ile z we h se5 9 c]ta9 /ages ( ! arc dis*>ge ! pot5tial diff]5ce dim9i%es z ! curr5t increases4 ,?us ! problem ( f9d+ ! curr5t :i* a giv5 batt]y w produce :5 "p ( ! circuit consi/s ( a gas dis*>ge is mu* m complicat$ ?an :5 ! circuit consi/s entirely ( metallic conductors4 ,if1 h[ev]1 we measure ! pot5tial diff]5ce betwe5 ! electrodes 9 ! gas :5 diff]5t curr5ts are s5t ?r\gh x1 we c plot a curve1 call$ ! *>act]i/ic curve1 ^: ord9ates are ! pot5tial diff]5ces betwe5 ! electrodes 9 ! gas & ! abscissae ! correspond+ curr5ts4 ,by ! aid ( ?is curve we c calculate ! curr5t produc$ :5 a giv5 batt]y is connect$ up to ! gas by leads ( kn[n resi/ance4 ,= let ,e#j be ! electromotive =ce ( ! batt]y1 ,r ! resi/ance ( ! leads1 i ! curr5t1 ! pot5tial diff]5ce betwe5 ! t]ms 9 ! gas w be ,e#j - ,ri4 ,let ,,abc 7fig4 #bb7 be ! *>act]i/ic curve1 ! ord9ates be+ ! pot5tial diff]5ce betwe5 ! t]m9als 9 ! gas1 & ! abscissae ! curr5t4 ,draw ! l9e ,,lm ^: equation is ,e ,e#j - ,ri1 !n ! po9ts :]e ?is l9e cuts ! *>act]i/ic curves w give possible values ( i & ,e1 ! curr5t ?r\gh ! dis*>ge tube & ! pot5tial diff]5ce betwe5 ! t]m9als4 ,"s ( ^! po9ts may1 h[ev]1 correspond to an un/able position & be impossible to realize4 ,! foll[+ me?od gives u a crit]ion by :i* we c di/+ui% ! /able f ! un/able positions4 ,if ! curr5t is increas$ by deltai1 ! electromotive =ce :i* has to be ov]come by ! batt]y is ,rdeltai d,e_/di deltai4 ,if ,r d,e_/di is positive !re w be an unbalanc$ electromotive =ce r\nd ! circuit t5d+ to /op ! curr5t4 ,?us ! increase 9 ! curr5t w be /opp$ & ! condition w be a /able "o4 ,if1 h[ev]1 ,r d,e_/di is negative !re w be an unbalanc$ electromotive =ce t5d+ to increase ! curr5t /ill fur!r2 ?us ! curr5t w g on increas+ & ! condition w be un/able4 ,?us = /ability ,r d,e_/di mu/ be positive1 a condition fir/ giv5 by ,kaufmann 7,ann4 d] ,phys4 #aa1 p4 #aeh74 ,! geometrical int]pretation ( ?is condition is t ! /raight l9e ,,lm mu/1 at ! po9t :]e x cuts ! *>act]i/ic curve1 be /eep] ?an ! tang5t to *>act]i/ic curve4 ,?us ( ! po9ts ,,abc :]e ! l9e cuts ! curve 9 fig4 #bb1 ,a & ,c correspond to /able /ates & ,b to an un/able "o4 ,! /ate ( ?+s repres5t$ by a po9t ,p on ! *>act]i/ic curve :5 ! slope is d[nw>d _c be /able unless !re is 9 ! ext]nal circuit a resi/ance great] ?an t repres5t$ by ! tang5t ( ! incl9ation ( ! tang5t to ! curve at ,p to ! horizontal axis4 ,illu/ration3 ,,fig4 #bb4 ,if we keep ! ext]nal electromotive =ce ! same & gradually increase ! resi/ance 9 ! leads1 ! l9e ,,lm w become /eep] & /eep]4 ,c w move to ! left s t ! curr5t w dim9i%2 :5 ! l9e gets s /eep t x t\*es ! curve at ,c'1 any fur!r increase 9 ! resi/ance w produce an abrupt *ange 9 ! curr5t2 = n[ ! /ate ( ?+s repres5t$ by a po9t ne> ,a' is ! only /able /ate4 ,?us if ! ,,bc "p ( ! curve correspond$ to a lum9\s dis*>ge & ! ,a "p to a d>k dis*>ge1 we see t if ! electromotive =ce is kept con/ant !re is a m9imum value ( ! curr5t = ! lum9\s dis*>ge4 ,if ! curr5t is r$uc$ bel[ ?is value1 ! dis*>ge ceases to be lum9\s1 & !re is an abrupt dim9ution 9 ! curr5t4 ,ca?ode ,rays4--,:5 ! gas 9 ! dis*>ge tube is at a v l[ pressure "s rem>kable ph5om5a occur 9 ! neighb\rhood ( ! ca?ode4 ,^! seem to h be5 fir/ obs]v$ by ,plck] 7,pogg4 ,ann4 #ajg1 p4 #gg2 #aaf1 p4 #de7 :o notic$ on ! walls ( ! glass tube ne> ! ca?ode a gre5i% phosphoresc5ce1 :i* he reg>d$ z due to rays proce$+ f ! ca?ode1 /rik+ aga9/ ! sides ( ! tube1 & !n travell+ back to ! ca?ode4 ,he f\nd t ! action ( a magnet on ^! rays 0 n ! same z ! action on ! "p ( ! dis*>ge ne> ! positive electrode4 ,hittorf 7,pogg4 ,ann4 #acf1 p4 #h7 %[$ t ! ag5t produc+ ! phosphoresc5ce 0 int]cept$ by a solid1 :e!r conductor or insulator1 plac$ betwe5 ! ca?ode & ! sides ( ! tube4 ,he reg>d$ ! phosphoresc5ce z caus$ by a motion />t+ f ! ca?ode & travell+ 9 /raight l9es ?r\gh ! gas4 ,gold/e9 7,monat4 d] ,b]l4 ,akad41 #ahgf1 p4 #bd7 confirm$ ?is discov]y ( ,hittorf's1 & fur!r %[$ t a di/9ct1 ?\gh n v %>p1 %ad[ is ca/ by a small object plac$ ne> a l>ge plane ca?ode4 ,?is is a pro( t ! rays produc+ ! phosphoresc5ce mu/ be emitt$ almo/ normally f ! ca?ode1 & n1 l ! rays ( light f a lum9\s surface1 9 all directions1 = su* rays w\ld n produce a p]ceptible %ad[ if a small body 7 plac$ ne> ! plane4 ,gold/e9 reg>d$ ! phosphoresc5ce z due to waves 9 ! e!r1 = ^: propagation ! gas 0 n necess>y4 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 i4 p4 #ace2 pt4 ii4 pp4 #ehg1 #ffa71 :o made _m rem>kable rese>*es 9 ?is subject1 took a diff]5t view4 ,he reg>d$ ! rays z /reams ( negatively electrifi$ p>ticles project$ normally f ! ca?ode ) great velocity1 &1 :5 ! pressure is suffici5tly l[1 rea*+ ! sides ( ! tube1 & by _! impact produc+ phosphoresc5ce & heat4 ,! rays on ?is view are deflect$ by a magnet1 because a magnet ex]ts a =ce on a *>g$ mov+ body4 ,^! rays /rik+ aga9/ glass make x phosphoresc5t4 ,! col\r ( ! phosphoresc5ce dep5ds on ! k9d ( glass2 ?us ! light f soda glass is a yell[i% gre51 & t f lead glass blue4 ,_m o!r bodies phosphoresce :5 expos$ to ^! rays1 & 9 p>ticul> ! phosphoresc5ce ( "s gems1 su* z rubies & diamonds1 is exce$+ly vivid4 ,! spectrum ( ! phosphoresc5t light is g5]ally cont9u\s1 b ,crookes %[$ t ! phosphoresc5ce ( "s ( ! r>e e>?s1 su* z yttrium1 gives a spectrum ( bright b&s1 & he f\nd$ on ?is fact a spectroscopic me?od ( great importance4 ,gold/e9 7,wi$4 ,ann4 #ed1 p4 #cga7 discov]$ t ! haloid salts ( ! alkali metals *ange col\r "u ! rays1 sodium *loride1 = example1 becom+ violet4 ,! coloration is a surface "o1 & has be5 trac$ by ,e4 ,wi$emann & ,s*midt 7,wi$4 ,ann4 #ed1 p4 #fah7 to ! =mation ( a sub*loride4 ,*lorides ( t91 m]cury & lead also *ange col\r 9 ! same way4 ,e4 ,wi$emann 7,wi$4 ,ann4 #ef1 p4 #bja7 discov]$ ano!r rem>kable effect1 :i* he call$ !rmo-lum9esc5ce2 he f\nd t _m bodies aft] be+ expos$ to ! ca?ode rays possess = "s "t ! p[] ( becom+ lum9\s :5 _! temp]ature is rais$ to a po9t f> bel[ t at :i* !y become lum9\s 9 ! normal /ate4 ,sub/ances belong+ to ! class call$ by van 't ,h(f solid solutions exhibit ?is prop]ty ( !rmo-lum9esc5ce to a rem>kable ext5t4 ,!y are =m$ :5 two salts1 "o greatly 9 excess ( ! o!r1 are simultane\sly precipitat$ f a solution4 ,a trace ( ,mn,s,o#d 9 ,ca,s,o#d %[s v brilliant !rmo-lum9esc5ce4 ,! impact ( ca?ode rays produces aft] a "t p]ceptible *anges 9 ! glass4 ,crookes 7,phil4 ,trans4 pt4 ii4 #ahgi1 p4 #fde7 f\nd t aft] glass has be5 phosphoresc+ = "s "t "u ! ca?ode rays x seems to get tir$1 & ! phosphoresc5ce is n s bright z x 0 initially4 ,?us1 = example1 :5 ! %ad[ ( a ,maltese cross is ?r[n on ! walls ( ! tube z 9 fig4 #bc1 if aft] ! dis*>ge has be5 go+ on = "s "t ! cross is %ak5 d[n or a new ca?ode us$ ^: l9e ( fire does n cut ! cross1 ! patt]n ( ! cross w /ill be se5 on ! glass1 b x w n[ be bright] in/ead ( d>k] ?an ! surr\nd+ portion4 ,! portions %ield$ by ! cross1 n be+ tir$ by be+ made to phosphoresce = a long "t1 respond m vigor\sly to ! /imulus ?an ^? portions :i* h n be5 protect$4 ,sk9n] 7,proc4 ,camb4 ,phil4 ,soc4 ix4 p4 #cga7 & ,?omson f\nd on ! glass :i* _h be5 expos$ to ! rays gelat9\s filam5ts1 app>5tly silica1 result+ f ! r$uction ( ! glass4 ,a r$uc+ action 0 also notic$ by ,vill>d 7,j\rn4 de phys4 #c1 viii4 p4 #adj7 & ,wehnelt 7,wi$4 ,ann4 #fg1 p4 #dba74 ,x c be well %[n by lett+ ! rays fall on a plate ( oxidiz$ copp]1 :5 ! "p /ruck by ! rays w become bright4 ,! rays heat bodies on :i* !y fall1 & if !y are conc5trat$ by us+ z a ca?ode a portion ( a sph]ical surface1 ! heat at ! c5tre becomes s great t a piece ( plat9um wire c be melt$ or a diamond *>r$4 ,measurem5ts ( ! heat+ effects ( ! rays h be5 made by ,?omson 7,phil4 ,mag4 #e1 #dd1 p4 #bic7 & ,cady 7,ann4 d] ,phys4 #a1 p4 #fgh74 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 i4 p4 #aeb7 %[$ t a vane m\nt$ z 9 a radiomet] is set 9 rotation by ! rays1 ! direction ( ! rotation be+ ! same z w\ld be produc$ by a /ream ( p>ticles proce$+ f ! ca?ode4 ,! movem5t is n due to ! mom5tum imp>t$ to ! vanes by ! rays1 b to ! diff]5ce 9 temp]ature betwe5 ! sides ( ! vanes1 ! rays mak+ ! side aga9/ :i* !y /rike hott] ?an ! o!r4 ,illu/ration3 ,,fig4 #bc4 ,effect ( a ,magnet4--,! rays are deflect$ by a magnet1 s t ! di/ribution ( phosphoresc5ce ov] ! glass & ! %ape & position ( ! %ad[s ca/ by bodies 9 ! tube are alt]$ by ! proximity ( a magnet4 ,! laws ( magnetic deflection ( ^! rays h be5 inve/igat$ by ,plck] 7,pogg4 ,ann4 #ajc1 p4 #hh71 ,hittorf 7,pogg4 ,ann4 #acf1 p4 #bac71 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 #a1 p4 #eeg71 & ,s*u/] 7,proc4 ,roy4 ,soc4 #dg1 p4 #ebf74 ,! deflection is ! same z t ( negatively electrifi$ p>ticles travell+ along ! pa? ( ! rays4 ,su* p>ticles w\ld 9 a magnetic field be act$ on by a =ce at "r angles to ! direction ( motion ( ! p>ticle & also to ! magnetic =ce1 ! magnitude ( ! =ce be+ proportional to ! product ( ! velocity ( ! p>ticle1 ! magnetic =ce1 & ! s9e ( ! angle betwe5 ^! vectors4 ,9 ?is case we h se5 t if ! p>ticle is n act$ on by an electro/atic field1 ! pa? 9 a uni=m magnetic field is a spiral1 :i*1 if ! magnetic =ce is at "r angles to ! direction ( projection ( ! p>ticle1 becomes a circle 9 ! plane at "r angles to ! magnetic =ce1 ! radius be+ mv_/,he1 :]e m1 v1 e are respectively ! mass1 velocity & *>ge on ! p>ticle1 & ,h is ! magnetic =ce4 ,! small] ! diff]5ce ( pot5tial betwe5 ! electrodes ( ! dis*>ge tube ! great] ! deflection produc$ by a magnetic field ( giv5 /r5g?1 & z ! diff]5ce ( pot5tial rapidly increases ) dim9ution ( pressure1 aft] a c]ta9 pressure has be5 pass$1 ! high] ! exhau/ion ( ! tube ! less ! magnetic deflection ( ! rays4 ,birkel& 7,comptes r5dus1 #ahif1 p4 #dib7 has %[n t :5 ! dis*>ge is f an induction coil ! ca?ode rays produc$ 9 ! tube at any "o "t are n equally deflect$ by a magnet1 b t a n>r[ pat* ( phosphoresc5ce :5 deflect$ by a magnet is split up into sev]al di/9ct pat*es1 giv+ rise to :at ,birkel& calls ! magnetic spectrum4 ,/rutt 7,phil4 ,mag4 #dh1 p4 #dgh7 has %[n t ?is magnetic spectrum does n occur if ! dis*>ge ( a l>ge numb] ( cells is employ$ in/ead ( ! coil4 ,?omson 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #bdc7 has %[n t if ! pot5tial diff]5ce betwe5 ! electrodes is kept ! same ! magnetic deflection is indep5d5t ( ! nature ( ! gas fill+ ! dis*>ge tube2 ?is 0 te/$ ) gases s diff]5t z air1 hydrog51 c>bonic acid & me?yl iodide4 ,*>ge ( ,negative ,electricity c>ri$ by ! ,rays4--,we h se5 t ! rays are deflect$ by a magnet1 z if !y 7 p>ticles *>g$ ) negative electricity4 ,p]r9 7,comptes r5dus1 #aba1 p4 #aacj7 %[$ by direct exp]im5t t a /ream ( negative electricity is associat$ ) ! rays4 ,a modification made by ,?omson ( ,p]r9's exp]im5t is sket*$ 9 fig4 #bd 7,phil4 ,mag4 #dh1 p4 #dgh74 ,illu/ration3 ,,fig4 #bd4 ,! rays />t f ! ca?ode ,a1 & pass ?r\gh a slit 9 a solid brass rod ,b fitt+ tightly into ! neck ( ! tube4 ,?is rod is connect$ ) e>? & us$ z ! anode4 ,! rays aft] pass+ ?r\gh ! slit travel ?r\gh ! vessel ,c4 ,d & ,e are two insulat$ metal cyl9d]s insulat$ f ea* o!r1 & ea* hav+ a slit cut 9 its face s z to enable ! rays to pass into ! inside ( ! inn] cyl9d]1 :i* is connect$ ) an electromet]1 ! out] cyl9d] be+ connect$ ) ! e>?4 ,! two cyl9d]s are plac$ on ! f> side ( ! vessel1 b out ( ! direct l9e ( fire ( ! rays4 ,:5 ! rays g /raight ?r\gh ! slit !re is only a v small negative *>ge communicat$ to ! inn] cyl9d]1 b :5 !y are deflect$ by a magnet s t ! phosphoresc5t pat* falls on ! slit 9 ! out] cyl9d] ! inn] cyl9d] receives a v l>ge negative *>ge1 ! increase co9cid+ v %>ply ) ! appe>ance ( ! phosphoresc5t pat* on ! slit4 ,:5 ! pat* is s mu* deflect$ by ! magnet t x falls bel[ ! slit1 ! negative *>ge 9 ! cyl9d] aga9 disappe>s4 ,?is exp]im5t %[s t ! ca?ode rays are accompani$ by a /ream ( negative electrification4 ,! same app>atus c be us$ to %[ t ! passage ( ca?ode rays ?r\gh a gas makes x a conductor ( electricity4 ,= if ! induction coil is kept runn+ & a /ream ( ! rays kept /eadily go+ into ! inn] cyl9d]1 ! pot5tial ( ! inn] cyl9d] rea*es a def9ite negative value bel[ :i* x does n fall1 h[ev] long ! rays may be kept go+4 ,! cyl9d] rea*es a /eady /ate 9 :i* ! ga9 ( negative electricity f ! ca?ode rays is equal to ! loss by leakage ?r\gh ! conduct+ gas1 ! conductivity be+ produc$ by ! passage ( ! rays ?r\gh x4 ,if ! inn] cyl9d] is *>g$ up initially ) a great] negative *>ge ?an corresponds to ! /eady /ate1 on turn+ ! rays on to ! cyl9d] ! negative *>ge w decrease & n increase until x rea*es ! /eady /ate4 ,! conductivity produc$ by ! passage ( ca?ode rays ?r\gh a gas dim9i%es rapidly ) ! pressure4 ,:5 rays pass ?r\gh a gas at a l[ pressure1 !y are deflect$ by an electric field2 :5 ! pressure ( ! gas is high] ! conductivity x acquires :5 ! ca?ode rays pass ?r\gh x is s l>ge t ! pot5tial gradi5t _c rea* a suffici5tly high value to produce an appreciable deflection4 ,?us ! ca?ode rays c>ry a *>ge ( negative electricity2 ! exp]im5t describ$ on page #hge 7fig4 #ac7 %[s t !y are deflect$ by an electric field z if !y 7 negatively electrifi$1 & are act$ on by a magnetic =ce 9 j ! way ?is =ce w\ld act on a negatively electrifi$ body mov+ along ! pa? ( ! rays4 ,!re is !re=e e reason = believ+ t !y are *>ges ( negative electricity 9 rapid motion4 ,by measur+ ! deflection produc$ by magnetic & electric fields we c det]m9e ! velocity ) :i* ^! p>ticles mov$ & ! ratio ( ! mass ( ! p>ticle to ! *>ge c>ri$ by x4 ,we may conclude f ! exp]im5ts t ! value ( m_/e = ! p>ticles con/itut+ ! ca?ode rays is ( ! ord] #a_/a4g #ajg1 & we h se5 t m_/e has ! same value 9 all ! o!r cases ( negative ions 9 a gas at l[ pressure = :i* x has be5 measur$--viz4 = ! ions produc$ :5 ultra-violet light falls on a metal plate1 or :5 an inc&esc5t c>bon filam5t is surr\nd$ by a gas at a l[ pressure1 & = ! beta p>ticles giv5 out by radio-active bodies4 ,we h also se5 t ! value ( ! *>ge on ! gase\s ion1 9 all cases 9 :i* x has be5 measur$--viz4 ! ions produc$ by ,rntg5 & uranium radiation1 by ultra-violet light1 & by ! dis*>ge ( electrification f a po9t--is ! same 9 magnitude z ! *>ge c>ri$ by ! hydrog5 atom 9 ! electrolysis ( solutions4 ,! mass ( ! hydrog5 alone is1 h[ev]1 #aj-d times ?is *>ge1 :ile ! mass ( ! c>ri]s ( negative electrification is only #a_/a4g #ajg times ! *>ge2 h5ce ! mass ( ! c>ri]s ( ! negative electrification is only #a_/agjj ( ! mass ( ! hydrog5 atom4 ,we are ?us1 by ! /udy ( ! electric dis*>ge1 =c$ to recognize ! exi/5ce ( masses v mu* small] ?an ! smalle/ mass hi!rto recogniz$4 ,direct det]m9ations ( ! velocity ( ! ca?ode rays h be5 made by ,j4 ,j4 ,?omson 7,phil4 ,mag4 #ch1 p4 #ceh71 :o measur$ ! int]val betwe5 ! appe>ance ( phosphoresc5ce on two pieces ( glass plac$ at a kn[n di/ance ap>t1 & by ,maiorana 7,nuovo ,cim5to1 #d1 #f1 p4 #ccf7 & ,battelli & ,/efan9i 7,phys4 ,zeit4 #a1 p4 #ea71 :o measur$ ! int]val betwe5 ! arrival ( ! negative *>ge c>ri$ by ! rays at two places sep>at$ by a kn[n di/ance4 ,! values ( ! velocity got 9 ?is way are mu* small] ?an ! values got by ! indirect me?ods previ\sly describ$3 ?us ,j4 ,j4 ,?omson at a fairly high pressure f\nd ! velocity to be #b #ajg cm4_/sec4 ,maiorana f\nd values rang+ betwe5 #ajg & #f #ajg cm4_/sec1 & ,battelli & ,/efan9i values rang+ f #f #ajf to #a4b #ajg4 ,9 ^! me?ods x is v difficult to elim9ate ! effect ( ! int]val :i* elapses betwe5 ! arrival ( ! rays & ! atta9m5t by ! means ( detection1 su* z ! phosphoresc5ce ( ! glass or ! deflection ( ! electromet]1 ( suffici5t int5sity to affect ! s5ses4 ,illu/ration3 ,,fig4 #be4 ,transmission ( ,ca?ode ,rays ?r\gh ,solids--,l5>d ,rays4--,x 0 = a long "t believ$ t all solids 7 absolutely opaque to ^! rays1 z ,crookes & ,gold/e9 _h prov$ t v ?9 glass1 & ev5 a film ( collodion1 ca/ int5sely black %ad[s4 ,h]tz 7,wi$4 ,ann4 #de1 p4 #bh71 h[ev]1 %[$ t beh9d a piece ( gold-leaf or alum9ium foil an appreciable am\nt ( phosphoresc5ce occurr$ on ! glass1 & t ! phosphoresc5ce mov$ :5 a magnet 0 br\ght ne>4 ,a mo/ important advance 0 next made by ,l5>d 7,wi$4 ,ann4 #ea1 p4 #bbe71 :o got ! ca?ode rays to pass f ! inside ( a dis*>ge tube to ! air outside4 ,= ?is purpose he us$ a tube l t %[n 9 fig4 #be4 ,! ca?ode ,k is an alum9ium disc #a4b cm4 9 diamet] fa/5$ to a /iff wire1 :i* is surr\nd$ by a glass tube4 ,! anode ,a is a brass /rip p>tly surr\nd+ ! ca?ode4 ,! end ( ! tube 9 front ( ! ca?ode is clos$ by a /rong metal cap1 fa/5$ 9 ) m>9e glue1 9 ! middle ( :i* a hole #a4g mm4 9 diamet] is bor$1 & cov]$ ) a piece ( v ?9 alum9ium foil ab\t 4#jjbf mm4 9 ?ickness4 ,! alum9ium w9d[ is 9 metallic contact ) ! cap1 & ?is & ! anode are connect$ ) ! e>?4 ,! tube is !n exhau/$ until ! ca?ode rays /rike aga9/ ! w9d[4 ,diffuse light spreads f ! w9d[ into ! air outside ! tube1 & c be trac$ 9 a d>k room = a di/ance ( sev]al c5timetres4 ,f ! w9d[1 too1 proce$ rays :i*1 l ! ca?ode rays1 c produce phosphoresc5ce1 = c]ta9 bodies phosphoresce :5 plac$ 9 ! neighb\rhood ( ! w9d[4 ,?is effect is conv5i5tly obs]v$ by ! plat9o-cryanide scre5s us$ to detect ,rntg5 radiation4 ,! prop]ties ( ! rays outside ! tube resemble 9 all respects ^? ( ca?ode rays2 !y are deflect$ by a magnet & by an electric field1 !y ionize ! gas ?r\gh :i* !y pass & make x a conductor ( electricity1 & !y affect a photographic plate & *ange ! col\r ( ! haloid salts ( ! alkali metals4 ,z1 h[ev]1 x is conv5i5t to di/+ui% betwe5 ca?ode rays outside & inside ! tube1 we %all call ! =m] ,l5>d rays4 ,9 air at atmosph]ic pressure ! ,l5>d rays spread out v diffusely4 ,if ! alum9ium w9d[1 in/ead ( op5+ into ! air1 op5s into ano!r tube :i* c be exhau/$1 x is f\nd t ! l[] ! pressure ( ! gas 9 ?is tube ! f>!r ! rays travel & ! less diffuse !y are4 ,by fill+ ! tube ) diff]5t gases ,l5>d %[$ t ! great] ! d5sity ( ! gas ! great] is ! absorption ( ^! rays4 ,?us !y travel f>!r 9 hydrog5 ?an 9 any o!r gas at ! same pressure4 ,l5>d %[$1 too1 t if he adju/$ ! pressure s t ! d5sity ( ! gas 9 ?is tube 0 ! same--if1 = example1 ! pressure :5 ! tube 0 fill$ ) oxyg5 0 #a_/af ( ! pressure :5 x 0 fill$ ) hydrog5--! absorption 0 con/ant :atev] ! nature ( ! gas4 ,beck] 7,ann4 d] ,phys4 #ag1 p4 #cha7 has %[n t ?is law is only approximately true1 ! absorption by hydrog5 be+ abnormally l>ge1 & by ! in]t monatomic gases1 su* z helium & argon1 abnormally small4 ,! di/ance to :i* ! ,l5>d rays p5etrate into ?is tube dep5ds ^u ! pressure 9 ! dis*>ge tube2 if ! exhau/ion 9 ! latt] is v high1 s t !re is a l>ge pot5tial diff]5ce betwe5 ! ca?ode & ! anode1 & !re=e a high velocity = ! ca?ode rays1 ! ,l5>d rays w p5etrate f>!r ?an :5 ! pressure 9 ! dis*>ge tube is high] & ! velocity ( ! ca?ode rays small]4 ,l5>d %[$ t ! great] ! p5etrat+ p[] ( 8 rays ! small] 0 _! magnetic deflection1 & !re=e ! great] _! velocity2 ?us ! great] ! velocity ( ! ca?ode rays ! great] is ! velocity ( ! ,l5>d rays to :i* !y give rise4 ,= v sl[ ca?ode rays ! absorption by diff]5t gases dep>ts altoge!r f ! d5sity law1 s mu* s t ! absorption ( ^! rays by hydrog5 is great] ?an t by air 7,l5>d1 ,ann4 d] ,phys4 #ab1 p4 #gcb74 ,l5>d 7,wi$4 ,ann4 #ef1 p4 #bee7 /udi$ ! passage ( 8 rays ?r\gh solids z well z ?r\gh gases1 & arriv$ at ! v int]e/+ result t ! absorption ( a sub/ance dep5ds only ^u its d5sity1 & n ^u its *emical composition or physical /ate2 9 o!r words1 ! am\nt ( absorption ( ! rays :5 !y trav]se a giv5 di/ance dep5ds only on ! quantity ( matt] !y cut ?r\gh 9 ! di/ance4 ,mc,clelland 7,proc4 ,roy4 ,soc4 #fa1 p4 #bbg7 %[$ t ! rays c>ry a *>ge ( negative electricity1 & ,m',l5nan measur$ ! am\nt ( ionization rays ( giv5 int5sity produc$ 9 diff]5t gases1 f9d+ t if ! pressure is adju/$ s t ! d5sity ( ! diff]5t gases is ! same ! numb] ( ions p] cubic c5timetre is also ! same4 ,9 ?is case1 z ,l5>d has %[n1 ! absorption is ! same1 s t ) ! ,l5>d rays1 z ) uranium & probably ) ,rntg5 rays1 equal absorption corresponds to equal ionization4 ,a conv5i5t me?od = produc+ ,l5>d rays ( great int5sity has be5 describ$ by ,des ,c\dres 7,wi$4 ,ann4 #fb1 p4 #acd74 ,diffuse ,reflection ( ,ca?ode ,rays4--,:5 ca?ode rays fall ^u a surface1 :e!r ( an insulator or a conductor1 ca?ode rays />t f ! surface 9 all directions4 ,?is ph5om5on1 :i* 0 discov]$ by ,gold/e9 7,wi$4 ,ann4 #fb1 p4 #acd71 has be5 inve/igat$ by ,/>ke 7,wi$4 ,ann4 #ff1 p4 #di2 ,ann4 d] ,phys4 #aaa1 p4 #ge71 ,au/9 & ,/>ke 7,ann4 d] ,phys4 #i1 p4 #bga71 ,campbell-,sw9ton 7,proc4 ,roy4 ,soc4 #fd1 p4 #cgg71 ,m]ritt 7,phys4 ,rev4 #g1 p4 #bag7 & ,gehrcke 7,ann4 d] ,phys4 #h1 p4 #ha72 x is (t5 reg>d$ z analog\s to ! diffuse reflection ( light f su* a surface z gypsum1 & is spok5 ( z ! diffuse reflection ( ! ca?ode rays4 ,accord+ to ,m]ritt & ,au/9 & ,/>ke ! deviation 9 a magnetic field ( ^! reflect$ rays is ! same z t ( ! incid5t rays4 ,! exp]im5ts1 h[ev]1 7 conf9$ to rays reflect$ s t ! angle ( reflection 0 ne>ly equal to t ( incid5ce4 ,gehrcke %[$ t among ! reflect$ rays !re 7 a l>ge numb] :i* _h a mu* small] velocity ?an ! incid5t ones4 ,accord+ to ,campbell-,sw9ton ! diffuse reflection is accompani$ by a c]ta9 am\nt ( specul> reflection4 ,l5>d1 :o us$ sl[] ca?ode rays ?an ,au/9 & ,/>ke1 c\ld n detect 9 ! scatt]$ rays any ) velocities comp>able ) t ( ! incid5t rays2 he obta9$ copi\s supplies ( sl[ rays ^: spe$ did n dep5d on ! angle ( incid5ce ( ! prim>y rays 7,ann4 d] ,phys4 #ae1 p4 #dhe74 ,:5 ! angle ( incid5ce is v oblique ! surface /ruck by ! rays gets positively *>g$1 %[+ t ! second>y rays are m num]\s ?an ! prim>y4 ,repulsion ( two ,ca?ode ,/reams4--,gold/e9 discov]$ t if 9 a tube !re are two ca?odes connect$ toge!r1 ! ca?odic rays f "o ca?ode are deflect$ :5 !y pass ne> ! o!r4 ,exp]im5ts be>+ on ?is subject h be5 made by ,crookes & ,wi$emann & ,eb]t4 ,! ph5om5a may be describ$ by say+ t ! repulsion ( ! rays f a ca?ode ,a by a ca?ode ,b is only appreciable :5 ! rays f ,a pass ?r\gh ! ,crookes d>k space r\nd ,b4 ,?is is :at we %\ld expect if we rememb] t ! electric field 9 ! d>k space is f> /rong] ?an 9 ! re/ ( ! dis*>ge1 & t ! gas 9 ! o!r p>ts ( ! tube is r5d]$ a conductor by ! passage ?r\gh x ( ! ca?ode rays1 & !re=e incapable ( transmitt+ electro/atic repulsion4 ,scatt]+ ( ! ,negative ,electrodes4--,9 addition to ! ca?ode rays1 portions ( metal />t normally f ! ca?ode & =m a metallic deposit on ! walls ( ! tube4 ,! am\nt ( ?is deposit v>ies v mu* ) ! metal4 ,crookes 7,proc4 ,roy4 ,soc4 #ej1 p4 #hh7 f\nd t ! quantities ( metal torn f electrodes ( ! same size1 9 equal times1 by ! same curr5t1 are 9 ! ord] ,pd1 ,au1 ,ag1 ,pb1 ,sn1 ,pt1 ,cu1 ,cd1 ,ni1 ,91 ,fe4444 ,9 air !re is v little deposit f an ,al ca?ode1 b x is abundant 9 tubes fill$ ) ! monatomic gases1 m]cury vap\r1 argon or helium4 ,! scatt]+ increases z ! d5sity ( ! gas dim9i%es4 ,! p>ticles ( metal are at l[ pressures deflect$ by a magnet1 ?\gh n ne>ly to ! same ext5t z ! ca?ode rays4 ,accord+ to ,gr&qui/1 ! loss ( weight ( ! ca?ode 9 a giv5 "t is proportional to ! squ>e ( ! curr5t2 x is !re=e n1 l ! loss ( ! ca?ode 9 ord9>y electrolysis1 proportional to ! quantity ( curr5t :i* passes ?r\gh x4 ,illu/ration3 ,,fig4 #bf4 ,positive ,rays or ,canal/rahl54--,gold/e9 7,b]l4 ,sitzungsb4 #ci1 p4 #fia7 f\nd t ) a p]=at$ ca?ode c]ta9 rays occurr$ beh9d ! ca?ode :i* 7 n appreciably deflect$ by a magnet2 ^! he call$ ,canal/rahl51 b we %all1 = reasons :i* w appe> lat]1 call !m positive rays4 ,_! appe>ance is well %[n 9 fig4 #bf1 tak5 f a pap] by ,wehnelt 7,wi$4 ,ann4 #fg1 p4 #dba7 9 :i* !y are repres5t$ at ,b4 ,gold/e9 f\nd t _! col\r dep5ds on ! gas 9 :i* !y are =m$1 be+ gold-col\r 9 air & nitrog51 rose-col\r 9 hydrog51 yell[i% rose 9 oxyg51 & gre5i% gray 9 c>bonic acid4 ,! col\r ( ! lum9osity due to positive rays is n 9 g5]al ! same z t due to anode rays2 ! diff]5ce is exceptionally well m>k$ 9 helium1 :]e ! ca?ode ray lum9osity is blue :ile t due to ! positive rays is r$4 ,! lum9osity produc$ :5 ! rays /rike aga9/ solids is also q di/9ct4 ,! ca?ode rays make ! body emit a cont9u\s spectrum1 :ile ! spectrum produc$ by ! positive rays (t5 %[s bright l9es4 ,?us li?ium *loride "u ca?ode rays gives out a /eely blue light & ! spectrum is cont9u\s1 :ile "u ! positive rays ! salt gives out a brilliant r$ light & ! spectrum %[s ! r$ helium l9e4 ,x is rem>kable t ! l9es on ! spectra ( ! alkali metals are mu* m easily produc$ :5 ! positive rays fall on ! oxide ( ! metal ?an :5 !y fall on ! metal itself4 ,?us :5 ! positive rays fall on a pool ( ! liquid alloy ( sodium & potassium ! specks ( oxide on ! surface %9e ) a bright yell[ light :ile ! unt>ni%$ "p ( ! surface is q d>k4 ,w4 ,wi5 7,wi$4 ,ann4 #fe1 p4 #dde7 measur$ ! values ( e_/m = ! p>ticles =m+ ! positive rays4 ,o!r measurem5ts h be5 made by ,ew]s 7,wi$4 ,ann4 #fi1 p4 #afg7 & ,j4 ,j4 ,?omson 7,phil4 ,mag4 #ac1 p4 #efa74 ,! diff]5ces betwe5 ! values ( e_/m = ! ca?ode & positive rays are v rem>kable4 ,= ca?ode rays ^: velocity does n approa* t ( light1 e_/m is always equal to #a4g #ajh1 :ile = ! positive rays ! greate/ value ( ?is quantity yet obs]v$ is #ajd1 :i* is also ! value ( e_/m = ! hydrog5 ions 9 ! electrolysis ( dilute solutions4 ,9 "s exp]im5ts made by ,j4 ,j4 ,?omson 7,phil4 ,mag41 #ad1 p4 #cei7 x 0 f\nd t :5 ! pressure ( ! gas 0 n too l[ ! bright spot produc$ by ! impact ( a p5cil ( ^! rays on a phosphoresc5t scre5 is deflect$ by electric & magnetic =ces into a cont9u\s b& ext5d+ on bo? sides ( ! undeflect$ position4 ,! portion on "o side is 9 g5]al mu* fa9t] ?an t on ! o!r4 ,! direction ( ?is deflection %[s t x is produc$ by p>ticles *>g$ ) negative electricity1 :ile ! bright] b& is due to p>ticles *>g$ ) positive electricity4 ,! negatively electrifi$ p>ticles :i* produce ! b& c4c are n corpuscles1 = f ! electric & magnetic deflections we c f9d ! value ( e_/m4 ,z ?is proves to be equal to #ajd1 we see t ! mass ( ! c>ri] ( ! negative *>ge is comp>able ) t ( an atom1 & s v mu* great] ?an t ( a corpuscle4 ,at v l[ pressures "p ( ! phosphoresc5ce disappe>s1 :ile ! upp] portion breaks up into two pat*es 7fig4 #bg74 ,= "o ( ^! ! maximum value ( e_/m is #ajd & = ! o!r #e #aj4 ,at l[ pressures ! appe>ance ( ! pat*es & ! values ( e_/m are ! same :e!r ! tube is fill$ orig9ally ) air1 hydrog5 or helium4 ,9 "s ( ! exp]im5ts ! tube 0 exhau/$ until ! pressure 0 too l[ to all[ ! dis*>ge to pass4 ,a v small quantity ( ! gas "u inve/igation 0 !n admitt$ into ! tube1 j suffici5t to all[ ! dis*>ge to pass1 & ! deflection ( ! phosphoresc5t pat* measur$4 ,! foll[+ gases 7 admitt$ into ! tube1 air1 c>bonic oxide1 oxyg51 hydrog51 helium1 argon & neon1 b :atev] ! gas ! appe>ance ( ! phosphoresc5ce 0 ! same2 9 e case !re 7 two pat*es1 = "o ( :i* e_/m #ajd & = ! o!r e_/m #e #aj4 ,9 helium at high] pressures ano!r pat* 0 obs]v$1 = :i* e_/m #b4e #ajh4 ,! cont9u\s b& into :i* ! phosphoresc5t spot is drawn out :5 ! pressure is n exce$+ly l[1 :i* involves ! exi/5ce ( p>ticles = :i* ! mean value ( e_/m v>ies f z]o to #ajd1 c be expla9$ z foll[s4 ,! rays on _! way to ! phosphoresc5t scre5 h to pass ?r\gh gas :i* is ioniz$ by ! passage ?r\gh x ( ! positive rays2 ?is gas w !re=e conta9 free corpuscles4 ,! p>ticles :i* con/itute ! rays />t ) a *>ge ( positive electricity4 ,"s ( ^! p>ticles 9 _! j\rney ?r\gh ! gas attract a corpuscle ^: negative *>ge neutralizes ! positive *>ge on ! p>ticle4 ,! p>ticles :5 9 ?is neutral /ate may be ioniz$ by collision & reacquire a positive *>ge1 or by attract+ ano!r p>ticle may become negatively *>g$1 & ?is process may be repeat$ sev]al times on _! j\rney to ! phosphoresc5t scre54 ,?us "s ( ! p>ticles1 in/ead ( be+ positively *>g$ = ! :ole ( ! "t !y are expos$ to ! electric & magnetic =ces1 may be = a "p ( t "t )\t a *>ge or ev5 h a negative *>ge4 ,! deflection ( a p>ticle is proportional to ! av]age value ( its *>ge :il/ "u ! influ5ce ( ! deflect+ =ces4 ,?us if a p>ticle is )\t a *>ge = a "p ( ! "t1 its deflection w be less ?an t ( a p>ticle :i* has reta9$ its positive *>ge = ! :ole ( its j\rney1 :ile ! few p>ticles :i* h a negative *>ge = a long] "t ?an !y h a positive w be deflect$ 9 ! opposite direction to ! ma9 portion & w produce ! tail 7fig4 #bg74 ,illu/ration3 ,fig4 #bg4 ,a simil> explanation w apply to ! positive rays discov]$ by ,vill>d 7,comptes r5dus1 #adc1 p4 #fgd7 & ,j4 ,j4 ,?omson 7,phil4 ,mag4 #ac1 p4 #cei71 :i* travel 9 ! opposite direction to ! rays we h be5 consid]+1 i4e4 !y travel away f ! ca?ode & 9 ! direction ( ! ca?ode's rays2 ^! rays are sometimes call$ retrograde rays4 ,^! z f> z has be5 obs]v$ h always ! same maximum value ( e_/m1 i4e4 #ajd1 & !re are a consid]able numb] ( negative ones always mix$ ) !m4 ,! maximum velocity ( bo? ! positive & retrograde rays is ab\t #b #ajh cm4_/sec4 & v>ies v little ) ! pot5tial diff]5ce betwe5 ! electrodes 9 ! tube 9 :i* !y are produc$ 7,j4 ,j4 ,?omson1 ,phil4 ,mag41 ,dec4 #aiji74 ,! positive rays %[1 :5 ! pressure is n v l[1 ! l9e spectrum ( ! gas ?r\gh :i* !y pass4 ,an exce$+ly valuable set ( obs]vations on ?is po9t h be5 made by ,/>k & 8 pupils 7,physik4 ,zeit4 #f1 p4 #hib2 ,ann4 d] ,phys4 #ba1 pp4 #dj1 #deg74 ,/>k has %[n t 9 _m gases1 notably hydrog51 ! spectrum %[s ! ,doppl] effect1 & he has be5 able to calculate 9 ?is way ! velocity ( ! positive rays4 ,anode ,rays4--,gehrcke & ,rei*5he9 7,ann4 d] ,phys4 #be1 p4 #hfa7 h f\nd t :5 ! anode consi/s ( a mixture ( sodium & li?ium *loride rais$ to a high temp]ature ei!r by ! dis*>ge itself or by an indep5d5t heat+ circuit1 v conspicu\s rays come f ! anode :5 ! pressure ( ! gas 9 ! dis*>ge tube is v l[1 & a l>ge coil is us$ to produce ! dis*>ge4 ,! det]m9ation ( e_/m = ^! rays %[$ t !y are positively *>g$ atoms ( sodium or li?ium1 mov+ ) v consid]able velocity2 9 "s ( ,gehrcke's exp]im5ts ! maximum velocity 0 z great z #a4h #ajg cm4_/sec4 ?\gh ! av]age 0 ab\t #ajg cm4_/sec4 ,^! velocities are less ?an ^? ( ! positive rays ^: maximum velocity is ab\t #b #ajh cm4_/sec4 7,j4 ,j4 ,t47 ,,footnotes3 #a ,! values = nickel & bismu? giv5 9 ! table are mu* high] ?an lat] values obta9$ ) pure electrolytic nickel & bismu?4 #b ,! value "h giv51 namely #ab4hhe1 = ! electric mass-resi/ivity ( liquid m]cury z det]m9$ by ,mat?iess5 is n[ kn[n to be too high by ne>ly #a4 ,! value at pres5t accept$ is #ab4ghi ohms p] metre-gramme at #j ,c4 #c ,! value 7#afcj7 "h giv5 = h>d-drawn copp] is ab\t high] ?an ! value n[ adopt$1 namely1 #afbf4 ,! diff]5ce is due to ! fact t ei!r ,j5k9 or ,mat?iess5 did n employ precisely ! value at pres5t employ$ = ! d5sity ( h>d-drawn & anneal$ copp] 9 calculat+ ! volume-resi/ivities f ! mass-resi/ivities4 #d ,mat?iess5's value = nickel is mu* great] ?an t obta9$ 9 m rec5t rese>*es4 7,see ,mat?iess5 & ,vogt1 ,phil4 ,trans41 #ahfc1 & ,j4 ,a4 ,flem+1 ,proc4 ,roy4 ,soc41 ,decemb] #ahii47 #e ,mat?iess5's value = m]cury is ne>ly #a great] ?an ! value adopt$ at pres5t z ! mean ( ! be/ results1 namely #id1jgj4 #f ,! samples ( silv]1 copp] & nickel employ$ = ^! te/s 7 prep>$ electrolytically by ,sir ,j4 ,w4 ,swan1 & 7 exce$+ly pure & s(t4 ,! value = volume-resi/ivity ( nickel z giv5 9 ! above table 7f exp]im5ts by ,j4 ,a4 ,flem+1 ,proc4 ,roy4 ,soc41 ,decemb] #ahii7 is mu* less 7ne>ly #dj7 ?an ! value giv5 by ,mat?iess5's rese>*es4 #g ,! electrolytic bismu? "h us$ 0 prep>$ by ,h>tmann & ,braun1 & ! resi/ivity tak5 by ,j4 ,a4 ,flem+4 ,! value is ne>ly #bj less ?an t giv5 by ,mat?iess54 #h ,9 #ahii a committee 0 =m$ ( repres5tatives f eight ( ! lead+ manufactur]s ( insulat$ copp] cables ) delegates f ! ,po/ ,(fice & ,in/itution ( ,electrical ,eng9e]s1 to consid] ! "q ( ! values to be assign$ to ! resi/ivity ( h>d-drawn & anneal$ copp]4 ,! sitt+s ( ! committee 7 held 9 ,london1 ! secret>y be+ ,a4 ,h4 ,h[>d4 ,! values giv5 9 ! above p>agraphs are 9 accordance ) ! decision ( ?is committee1 & its recomm5dations h be5 accept$ by ! ,g5]al ,po/ ,(fice & ! lead+ manufactur]s ( insulat$ copp] wire & cables4 #i ,plat9oid is an alloy introduc$ by ,m>t9o1 said to be simil> 9 composition to ,g]man silv]1 b ) a little tung/5 add$4 ,x v>ies a good deal 9 composition accord+ to manufacture1 & ! resi/ivity ( diff]5t specim5s is n id5tical4 ,its electric prop]ties 7 fir/ made kn[n by ,j4 ,t4 ,bottomley1 9 a pap] read at ! ,royal ,society1 ,may #e1 #ahhe4 #aj ,an equival5t gramme molecule is a weight 9 grammes equal num]ically to ! *emical equival5t ( ! salt4 ,= in/ance1 "o equival5t gramme molecule ( sodium *loride is a mass ( #eh4e grammes4 ,na,cl #eh4e4 #aa ,f4 ,kohlraus* & ,l4 ,holborn1 ,das ,leitv]mg5 d] ,elektrolyte 7,leipzig1 #ahih74 #ab ,x %\ld be notic$ t ! velocities calculat$ 9 ,kohlraus*'s !ory & obs]v$ exp]im5tally are ! av]age velocities1 & involve bo? ! factors m5tion$ above2 !y include ! "t wa/$ by ! ions 9 comb9ation ) ea* o!r1 &1 except at great dilution1 are less ?an ! velocity ) :i* ! ions move :5 free f ea* o!r4