,transcriber's notes3 7#a7 ,numbers following letters 7without space7 like ,c#b were originally printed in subscript4 ,when letters are subscripted1 they are preceded by an underscore1 like ,cn4 7#b7 ,characters following a carat 77 were originally printed in superscript4 7#c7 ,letters topped by ,macron are represented as x4 7#d7 oo stands for infinity2 int for integral2 alpha1 beta1 etc4 for greek letters4 7#e7 ,the following typographical errors have been corrected3 ,page #hga3 an equation which is very useful1 because it enables us1 if we know the distribution4 'because' amended from 'becaus'4 ,page #hij3 ,the colour of the luminosity due to positive rays is not in general the same as that due to anode rays4 'positive' amended from 'postive'4 ,page #hij3 ,anode ,rays4--,gehrcke and ,reichenhein 7,ann4 der ,phys4 #be1 p4 #hfa7 have found that when the anode consists of a mixture of sodium and lithium chloride4 'mixture' amended from 'mixure'4 ,,encyclopaedia ,,britannica ,a ,,dictionary ,,of ,,arts1 ,,sciences1 ,,literature ,,and ,,general ,,information ,,eleventh ,,edition ,,volume ,,vi1 ,,slice ,,viii ,conduction1 ,electric ,article in ,this ,slice3 ,,conduction1 ,,electric ,,conduction1 ,,electric4 ,the electric conductivity of a substance is that property in virtue of which all its parts come spontaneously to the same electric potential if the substance is kept free from the operation of electric force4 ,accordingly1 the reciprocal quality1 electric resistivity1 may be defined as a quality of a substance in virtue of which a difference of potential can exist between different portions of the body when these are in contact with some constant source of electromotive force1 in such a manner as to form part of an electric circuit4 ,all material substances possess in some degree1 large or small1 electric conductivity1 and may for the sake of convenience be broadly divided into five classes in this respect4 ,between these1 however1 there is no sharply-marked dividing line1 and the classification must therefore be accepted as a more or less arbitrary one4 ,these divisions are3 7#a7 metallic conductors1 7#b7 non-metallic conductors1 7#c7 dielectric conductors1 7#d7 electrolytic conductors1 7#e7 gaseous conductors4 ,the first class comprises all metallic substances1 and those mixtures or combinations of metallic substances known as alloys4 ,the second includes such non-metallic bodies as carbon1 silicon1 many of the oxides and peroxides of the metals1 and probably also some oxides of the non-metals1 sulphides and selenides4 ,many of these substances1 for instance carbon and silicon1 are well-known to have the property of existing in several allotropic forms1 and in some of these conditions1 so far from being fairly good conductors1 they may be almost perfect non-conductors4 ,an example of this is seen in the case of carbon in its three allotropic conditions--charcoal1 graphite and diamond4 ,as charcoal it possesses a fairly well-marked but not very high conductivity in comparison with metals2 as graphite1 a conductivity about one-four-hundredth of that of iron2 but as diamond so little conductivity that the substance is included amongst insulators or non-conductors4 ,the third class includes those substances which are generally called insulators or non-conductors1 but which are better denominated dielectric conductors2 it comprises such solid substances as mica1 ebonite1 shellac1 india-rubber1 gutta-percha1 paraffin1 and a large number of liquids1 chiefly hydrocarbons4 ,these substances differ greatly in insulating power1 and according as the conductivity is more or less marked1 they are spoken of as bad or good insulators4 ,amongst the latter many of the liquid gases hold a high position4 ,thus1 liquid oxygen and liquid air have been shown by ,sir ,james ,dewar to be almost perfect non-conductors of electricity4 ,the behaviour of substances which fall into these three classes is discussed below in section ,i41 dealing with metallic conduction4 ,the fourth class1 namely the electrolytic conductors comprises all those substances which undergo chemical decomposition when they form part of an electric circuit traversed by an electric current4 ,they are discussed in section ,,ii41 dealing with electrolytic conduction4 ,the fifth and last class of conductors includes the gases4 ,the conditions under which this class of substance becomes possessed of electric conductivity are considered in section ,,iii41 on conduction in gases4 ,in connexion with metallic conductors1 it is a fact of great interest and considerable practical importance1 that1 although the majority of metals when in a finely divided or powdered condition are practically non-conductors1 a mass of metallic powder or filings may be made to pass suddenly into a conductive condition by being exposed to the influence of an electric wave4 ,the same is true of the loose contact of two metallic conductors4 ,thus if a steel point1 such as a needle1 presses very lightly against a metallic plate1 say of aluminium1 it is found that this metallic contact1 if carefully adjusted1 is non-conductive1 but that if an electric wave is created anywhere in the neighbourhood1 this non-conducting contact passes into a conductive state4 ,this fact1 investigated and discovered independently by ,d4 ,e4 ,hughes1 ,c4 ,onesti1 ,e4 ,branly1 ,o4 ,j4 ,lodge and others1 is applied in the construction of the coherer1 or sensitive tube employed as a detector or receiver in that form of wireless telegraphy chiefly developed by ,marconi4 ,further references to it are made in the articles ,,electric ,,waves and ,,telegraphy3 ,wireless4 ,international ,ohm4--,the practical unit of electrical resistance was legally defined in ,great ,britain by the authority of the queen in council in #ahid1 as the resistance offered to an invariable electric current by a column of mercury at the temperature of melting ice1 #ad4deba grammes in mass1 of a constant cross-sectional area1 and a length #ajf4c centimetres4 ,the same unit has been also legalized as a standard in ,france1 ,germany and the ,united ,states1 and is denominated the ,international or ,standard ,ohm4 ,it is intended to represent as nearly as possible a resistance equal to #aj absolute ,c4,g4,s4 units of electric resistance4 ,convenient multiples and subdivisions of the ohm are the microhm and the megohm1 the former being a millionth part of an ohm1 and the latter a million ohms4 ,the resistivity of substances is then numerically expressed by stating the resistance of one cubic centimetre of the substance taken between opposed faces1 and expressed in ohms1 microhms or megohms1 as may be most convenient4 ,the reciprocal of the ohm is called the mho1 which is the unit of conductivity1 and is defined as the conductivity of a substance whose resistance is one ohm4 ,the absolute unit of conductivity is the conductivity of a substance whose resistivity is one absolute ,c4,g4,s4 unit1 or one-thousandth-millionth part of an ohm4 ,resistivity is a quality in which material substances differ very widely4 ,the metals and alloys1 broadly speaking1 are good conductors1 and their resistivity is conveniently expressed in microhms per cubic centimetre1 or in absolute ,c4,g4,s4 units4 ,very small differences in density and in chemical purity make1 however1 immense differences in electric resistivity2 hence the values given by different experimentalists for the resistivity of known metals differ to a considerable extent4 ,i4 ,,conduction ,,in ,,solids ,it is found convenient to express the resistivity of metals in two different ways3 7#a7 ,we may state the resistivity of one cubic centimetre of the material in microhms or absolute units taken between opposed faces4 ,this is called the volume-resistivity2 7#b7 we may express the resistivity by stating the resistance in ohms offered by a wire of the material in question of uniform cross-section one metre in length1 and one gramme in weight4 ,this numerical measure of the resistivity is called the mass-resistivity4 ,the mass-resistivity of a body is connected with its volume-resistivity and the density of the material in the following manner3--,the mass-resistivity1 expressed in microhms per metre-gramme1 divided by #aj times the density is numerically equal to the volume-resistivity per centimetre-cube in absolute ,c4,g4,s4 units4 ,the mass-resistivity per metre-gramme can always be obtained by measuring the resistance and the mass of any wire of uniform cross-section of which the length is known1 and if the density of the substance is then measured1 the volume-resistivity can be immediately calculated4 ,if ,r is the resistance in ohms of a wire of length l1 uniform cross-section s1 and density d1 then taking rho for the volume-resistivity we have #aji,r rhol_/s2 but lsd ,m1 where ,m is the mass of the wire4 ,hence #aji,r rhodl_/,m4 ,if l #ajj and ,m #a1 then ,r rho' resistivity in ohms per metre-gramme1 and #ajirho' #aj1jjj;drho1 or rho #ajerho'_/d1 and rho' #aj1jjj,,mr_/l4 ,the following rules1 therefore1 are useful in connexion with these measurements4 ,to obtain the mass-resistivity per metre-gramme of a substance in the form of a uniform metallic wire3--,multiply together #aj1jjj times the mass in grammes and the total resistance in ohms1 and then divide by the square of the length in centimetres4 ,again1 to obtain the volume-resistivity in ,c4,g4,s4 units per centimetre-cube1 the rule is to multiply the mass-resistivity in ohms by #ajj1jjj and divide by the density4 ,these rules1 of course1 apply only to wires of uniform cross-section4 ,in the following ,tables ,i41 ,,ii4 and ,,iii4 are given the mass and volume resistivity of ordinary metals and certain alloys expressed in terms of the international ohm or the absolute ,c4,g4,s4 unit of resistance1 the values being calculated from the experiments of ,a4 ,matthiessen 7#ahca-ahgj7 between #ahfj and #ahfe1 and from later results obtained by ,j4 ,a4 ,fleming and ,sir ,james ,dewar in #ahic4 ,,table ,i4--,electric ,mass-,resistivity of ,various ,metals at #j ,c41 or ,resistance per ,metre-gramme in ,international ,ohms at #j ,c4 7,matthiessen47 ---------------------------------------- --------------- ,resistance at #j ,c4 in ,international ,approximate ,metal4 ,ohms of a ,wire ,temperature #a ,metre long and ,coefficient ,weighing near #bj ,c4 #a ,gramme4 ---------------------------------------- --------------- ,silver 7annealed7 4#aebc #j4jjcgg ,silver 7hard-drawn7 4#afeg 44 ,copper 7annealed7 4#adba #j4jjchh ,copper 7hard-drawn7 4#addi 7,matthiessen's ,standard7 ,gold 7annealed7 4#djbe #j4jjcfe ,gold 7hard-drawn7 4#djid 44 ,aluminium 7annealed7 4#jgeg 44 ,zinc 7pressed7 4#djac 44 ,platinum 7annealed7 #a4iccg 44 ,iron 7annealed7 4#gfe 44 ,nickel 7annealed7 #a4jeha 44 ,tin 7pressed7 4#ifah #j4jjcfe ,lead 7pressed7 #b4bbfh #j4jjchg ,antimony 7pressed7 #b4cghg #j4jjchi ,bismuth 7pressed7 #ab4heeda #j4jjced ,mercury 7liquid7 #ab4hheb #j4jjjgb ---------------------------------------- --------------- ,the data commonly used for calculating metallic resistivities were obtained by ,a4 ,matthiessen1 and his results are set out in the ,table ,,ii4 which is taken from ,cantor lectures given by ,fleeming ,jenkin in #ahff at or about the date when the researches were made4 ,the figures given by ,jenkin have1 however1 been reduced to international ohms and ,c4,g4,s4 units by multiplying by 7pi_/#d7 #j4ihff #aje #gg1dhe4 ,subsequently numerous determinations of the resistivity of various pure metals were made by ,fleming and ,dewar1 whose results are set out in ,table ,,iii4 ,,table ,,ii4--,electric ,volume-,resistivity of ,various ,metals at #j ,c41 or ,resistance per ,centimetre-cube in ,c4,g4,s4 ,units at #j ,c4 ---------------------------------------- -- ,volume-,resistivity4 ,metal4 at #j ,c4 in ,c4,g4,s4 ,units ---------------------------------------- -- ,silver 7annealed7 #a1ejb ,silver 7hard-drawn7 #a1fbi ,copper 7annealed7 #a1eid ,copper 7hard-drawn7 #a1fcjc ,gold 7annealed7 #b1jeb ,gold 7hard-drawn7 #b1jij ,aluminium 7annealed7 #c1jjf ,zinc 7pressed7 #e1fba ,platinum 7annealed7 #i1jce ,iron 7annealed7 #aj1efh ,nickel 7annealed7 #ab1dbid ,tin 7pressed7 #ac1agh ,lead 7pressed7 #ai1ehj ,antimony 7pressed7 #ce1dah ,bismuth 7pressed7 #acj1hgb ,mercury 7liquid7 #id1hife ---------------------------------------- -- ,,table ,,iii4--,electric ,volume-,resistivity of ,various ,metals at #j ,c41 or ,resistance per ,centimetre-cube at #j ,c4 in ,c4,g4,s4 ,units4 7,fleming and ,dewar1 ,phil4 ,mag41 ,september #ahic47 ---------------------------------------- ---------------------- ,resistance ,mean ,temperature ,metal4 at #j ,c4 per ,coefficient ,centimetre-cube between #j ,c4 in ,c4,g4,s4 ,units4 and #ajj ,c4 ---------------------------------------- ---------------------- ,silver 7electrolytic and well annealed7#f #a1dfh #j4jjdjj ,copper 7electrolytic and well annealed7#f #a1efa #j4jjdbh ,gold 7annealed7 #b1aig #j4jjcgg ,aluminium 7annealed7 #b1ffe #j4jjdce ,magnesium 7pressed7 #d1cee #j4jjcha ,zinc #e1gea #j4jjdjf ,nickel 7electrolytic7#f #f1ice #j4jjfah ,iron 7annealed7 #i1jfe #j4jjfbe ,cadmium #aj1jbc #j4jjdai ,palladium #aj1bai #j4jjced ,platinum 7annealed7 #aj1iag #j4jjcffi ,tin 7pressed7 #ac1jdh #j4jjddj ,thallium 7pressed7 #ag1fcc #j4jjcih ,lead 7pressed7 #bj1chj #j4jjdaa ,bismuth 7electrolytic7#g #aaj1jjj #j4jjdcc ---------------------------------------- ---------------------- ,resistivity of ,mercury4--,the volume-resistivity of pure mercury is a very important electric constant1 and since #ahhj many of the most competent experimentalists have directed their attention to the determination of its value4 ,the experimental process has usually been to fill a glass tube of known dimensions1 having large cup-like extensions at the ends1 with pure mercury1 and determine the absolute resistance of this column of metal4 ,for the practical details of this method the following references may be consulted3--,the ,specific ,resistance of ,mercury1 ,lord ,rayleigh and ,mrs ,sidgwick1 ,phil4 ,trans41 #ahhc1 part i4 p4 #agc1 and ,r4 ,t4 ,glazebrook1 ,phil4 ,mag41 #ahhe1 p4 #bj2 ,on the ,specific ,resistance of ,mercury1 ,r4 ,t4 ,glazebrook and ,t4 ,c4 ,fitzpatrick1 ,phil4 ,trans41 #ahhh1 p4 #agi1 or ,proc4 ,roy4 ,soc41 #ahhh1 p4 #dd1 or ,electrician1 #ahhh1 #ba1 p4 #ech2 ,recent ,determinations of the ,absolute ,resistance of ,mercury1 ,r4 ,t4 ,glazebrook1 ,electrician1 #ahij1 #be1 pp4 #edc and #ehh4 ,also see ,j4 ,v4 ,jones1 ,on the ,determination of the ,specific ,resistance of ,mercury in ,absolute ,measure1 ,phil4 ,trans41 #ahia1 ,a1 p4 #b4 ,table ,,iv4 gives the values of the volume-resistivity of mercury as determined by various observers1 the constant being expressed 7a7 in terms of the resistance in ohms of a column of mercury one millimetre in cross-section and #ajj centimetres in length1 taken at #j ,c42 and 7b7 in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at #j ,c4 ,the result of all the most careful determinations has been to show that the resistivity of pure mercury at #j ,c4 is about #id1jgj ,c4,g4,s4 electromagnetic units of resistance1 and that a column of mercury #ajf4c centimetres in length having a cross-sectional area of one square millimetre would have a resistance at #j ,c4 of one international ohm4 ,these values have accordingly been accepted as the official and recognized values for the specific resistance of mercury1 and the definition of the ohm4 ,the table also states the methods which have been adopted by the different observers for obtaining the absolute value of the resistance of a known column of mercury1 or of a resistance coil afterwards compared with a known column of mercury4 ,a column of figures is added showing the value in fractions of an international ohm of the ,british ,association ,unit 7,b4,a4,u471 formerly supposed to represent the true ohm4 ,the real value of the ,b4,a4,u4 is now taken as 4#ihff of an international ohm4 ,,table ,,iv4--,determinations of the ,absolute ,value of the ,volume-,resistivity of ,mercury and the ,mercury ,equivalent of the ,ohm4 ---------------------------------------- -------------------------------- ,value of ,value of ,value of#ajj ,centi-,ohm in ,observer4 ,date4 ,method4 ,b4,a4,u4 metres of ,centi- in ,ohms4,mercury metres of in ,ohms4 ,mercury4 ---------------------------------------- -------------------------------- ,lord ,rayleigh #ahhb ,rotating coil 4#ihfea 4#idacc #ajf4ca ,lord ,rayleigh #ahhc ,lorenz method 4#ihfgg 44 #ajf4bg ,g4 ,wiedemann #ahhd ,rotation through #ahj 44 44 #ajf4ai ,e4 ,e4 ,n4 ,mascart #ahhd ,induced current 4#ihfaa 4#idjif #ajf4cc ,h4 ,a4 ,rowland #ahhg ,mean of several 4#ihfdd 4#idjga #ajf4cb methods ,f4 ,kohlrausch #ahhg ,damping of magnets 4#ihffj 4#idjfa #ajf4cb ,r4 ,t4 ,glazebrook #ahhb ,induced currents 4#ihffe 4#idjgd #ajf4bi #ahhh ,wuilleumeier #ahij 4#ihfhf 4#idjgg #ajf4ca ,duncan and ,wilkes #ahij ,lorenz 4#ihfcd 4#idjfg #ajf4cd ,j4 ,v4 ,jones #ahia ,lorenz 44 4#idjfg #ajf4ca --------------------------- ,mean value 4#ihfec ,streker #ahhe ,an absolute determin- 4#idjef #ajf4cb ,hutchinson #ahhh ation of resistance 4#idjgd #ajf4cj ,e4 ,salvioni #ahij was not made4 ,the 4#idjed #ajf4cc ,e4 ,salvioni 44 value 4#ihfef has 4#idjgf #ajf4cj been used ------------------- ,mean value 4#idjgf #ajf4ca ,h4 ,f4 ,weber #ahhd ,induced current ,absolute measure- #aje4cg ,h4 ,f4 ,weber 44 ,rotating coil ments compared #ajf4af ,a4 ,roiti #ahhd ,mean effect of with ,german silver #aje4hi induced current wire coils issued ,f4 ,himstedt #ahhe by ,siemens and #aje4ih ,streker ,f4 ,e4 ,dorn #ahhi ,damping of a magnet #ajf4bd ,wild #ahhc ,damping of a magnet #ajf4jc ,l4 ,v4 ,lorenz #ahhe ,lorenz method #aje4ic ---------------------------------------- --------------------------------- ,for a critical discussion of the methods which have been adopted in the absolute determination of the resistivity of mercury1 and the value of the ,british ,association unit of resistance1 the reader may be referred to the ,british ,association ,reports for #ahij and #ahib 7,report of ,electrical ,standards ,committee71 and to the ,electrician1 #be1 p4 #def1 and #bi1 p4 #dfb4 ,a discussion of the relative value of the results obtained between #ahhb and #ahij was given by ,r4 ,t4 ,glazebrook in a paper presented to the ,british ,association at ,leeds1 #ahij4 ,resistivity of ,copper4--,in connexion with electro-technical work the determination of the conductivity or resistivity values of annealed and hard-drawn copper wire at standard temperatures is a very important matter4 ,matthiessen devoted considerable attention to this subject between the years #ahfj and #ahfd 7see ,phil4 ,trans41 #ahfj1 p4 #aej71 and since that time much additional work has been carried out4 ,matthiessen's value1 known as ,matthiessen's ,standard1 for the mass-resistivity of pure hard-drawn copper wire1 is the resistance of a wire of pure hard-drawn copper one metre long and weighing one gramme1 and this is equal to #j4addic international ohms at #j ,c4 ,for many purposes it is more convenient to express temperature in ,fahrenheit degrees1 and the recommendation of the #ahii committee on copper conductors#h is as follows3--,matthiessen's standard for hard-drawn conductivity commercial copper shall be considered to be the resistance of a wire of pure hard-drawn copper one metre long1 weighing one gramme which at #fj ,f4 is #j4aecheh international ohms4 ,matthiessen also measured the mass-resistivity of annealed copper1 and found that its conductivity is greater than that of hard-drawn copper by about #b4be to #b4e ,as annealed copper may vary considerably in its state of annealing1 and is always somewhat hardened by bending and winding1 it is found in practice that the resistivity of commercial annealed copper is about #a less than that of hard-drawn copper4 ,the standard now accepted for such copper1 on the recommendation of the #ahii ,committee1 is a wire of pure annealed copper one metre long1 weighing one gramme1 whose resistance at #j ,c4 is #j4adba international ohms1 or at #fj ,f41 #j4aejhbb international ohms4 ,the specific gravity of copper varies from about #h4hi to #h4ie1 and the standard value accepted for high conductivity commercial copper is #h4iab1 corresponding to a weight of #eee lb per cubic foot at #fj ,f4 ,hence the volume-resistivity of pure annealed copper at #j ,c4 is #a4eid microhms per c4c41 or #aeid ,c4,g4,s4 units1 and that of pure hard-drawn copper at #j ,c4 is #a4fbf microhms per c4c41 or #afbf ,c4,g4,s4 units4 ,since ,matthiessen's researches1 the most careful scientific investigation on the conductivity of copper is that of ,t4 ,c4 ,fitzpatrick1 carried out in #ahij4 7,brit4 ,assoc4 ,report1 #ahij1 ,appendix #c1 p4 #abj47 ,fitzpatrick confirmed ,matthiessen's chief result1 and obtained values for the resistivity of hard-drawn copper which1 when corrected for temperature variation1 are in entire agreement with those of ,matthiessen at the same temperature4 ,the volume resistivity of alloys is1 generally speaking1 much higher than that of pure metals4 ,table ,v4 shows the volume resistivity at #j ,c4 of a number of well-known alloys1 with their chemical composition4 ,,table ,v4--,volume-,resistivity of ,alloys of known ,composition at #j ,c4 in ,c4,g4,s4 ,units per ,centimetre-cube4 ,mean ,temperature ,coefficients taken at #ae ,c4 7,fleming and ,dewar47 ---------------------------------------- ------------------------ ,resistivity,temperature,composition in per ,alloys4 at #j ,c4 ,coefficient cents4 at #ae ,c4 ---------------------------------------- ------------------------ ,platinum-silver #ca1ehb 4#jjjbdc ,pt #cc1 ,ag #ff ,platinum-iridium #cj1hif 4#jjjhbb ,pt #hj1 ,ir #bj ,platinum-rhodium #ba1adb 4#jjadc ,pt #ij1 ,rd #aj ,gold-silver #f1bhj 4#jjabd ,au #ij1 ,ag #aj ,manganese-steel #fg1adh 4#jjabg ,mn #ab1 ,fe #gh ,nickel-steel #bi1deb 4#jjbja ,ni #d4ce1 remaining percentage chiefly iron1 but uncertain ,german silver #bi1ihb 4#jjjbgc ,cu#e,zn#c,ni#b ,platinoid#i #da1gca 4#jjjca ,manganin #df1fgh 4#jjjj ,cu #hd1 ,mn #ab1 ,ni #d ,aluminium-silver #d1fda 4#jjbch ,al #id1 ,ag #f ,aluminium-copper #b1ijd 4#jjcha ,al #id1 ,cu #f ,copper-aluminium #h1hdg 4#jjjhig ,cu #ig1 ,al #c ,copper-nickel-aluminium #ad1iab 4#jjjfdc ,cu #hg1 ,ni #f4e1 ,al #f4e ,titanium-aluminium #c1hhg 4#jjbij ---------------------------------------- ------------------------ ,generally speaking1 an alloy having high resistivity has poor mechanical qualities1 that is to say1 its tensile strength and ductility are small4 ,it is possible to form alloys having a resistivity as high as #ajj microhms per cubic centimetre2 but1 on the other hand1 the value of an alloy for electro-technical purposes is judged not merely by its resistivity1 but also by the degree to which its resistivity varies with temperature1 and by its capability of being easily drawn into fine wire of not very small tensile strength4 ,some pure metals when alloyed with a small proportion of another metal do not suffer much change in resistivity1 but in other cases the resultant alloy has a much higher resistivity4 ,thus an alloy of pure copper with #c of aluminium has a resistivity about #e times that of copper2 but if pure aluminium is alloyed with #f of copper1 the resistivity of the product is not more than #bj greater than that of pure aluminium4 ,the presence of a very small proportion of a non-metallic element in a metallic mass1 such as oxygen1 sulphur or phosphorus1 has a very great effect in increasing the resistivity4 ,certain metallic elements also have the same power2 thus platinoid has a resistivity #cj greater than ,german silver1 though it differs from it merely in containing a trace of tungsten4 ,the resistivity of non-metallic conductors is in all cases higher than that of any pure metal4 ,the resistivity of carbon1 for instance1 in the forms of charcoal or carbonized organic material and graphite1 varies from #fjj to #fjjj microhms per cubic centimetre1 as shown in ,table ,,vi43-- ,,table ,,vi4--,electric ,volume-,resistivity in ,microhms per ,centimetre-cube of ,various ,forms of ,carbon at #ae ,c4 ---------------------------------------- ---------------- ,substance4 ,resistivity4 ---------------------------------------- ---------------- ,arc lamp carbon rod #hjjj ,jablochkoff candle carbon #djjj ,carr carbon #cdjj ,carbonized bamboo #fjjj ,carbonized parchmentized thread #djjj to #ejjj ,ordinary carbon filament from glow-lamp treated or flashed #bdjj to #bejj ,deposited or secondary carbon #fjj to #ijj ,graphite #djj to #ejj ---------------------------------------- ---------------- ,the resistivity of liquids is1 generally speaking1 much higher than that of any metals1 metallic alloys or non-metallic conductors4 ,thus fused lead chloride1 one of the best conducting liquids1 has a resistivity in its fused condition of #j4cgf ohm per centimetre-cube1 or #cgf1jjj microhms per centimetre-cube1 whereas that of metallic alloys only in few cases exceeds #ajj microhms per centimetre-cube4 ,the resistivity of solutions of metallic salts also varies very largely with the proportion of the diluent or solvent1 and in some instances1 as in the aqueous solutions of mineral acids2 there is a maximum conductivity corresponding to a certain dilution4 ,the resistivity of many liquids1 such as alcohol1 ether1 benzene and pure water1 is so high1 in other words1 their conductivity is so small1 that they are practically insulators1 and the resistivity can only be appropriately expressed in megohms per centimetre-cube4 ,in ,table ,,vii4 are given the names of a few of these badly-conducting liquids1 with the values of their volume-resistivity in megohms per centimetre-cube3-- ,,table ,,vii4--,electric ,volume-,resistivity of ,various ,badly-,conducting ,liquids in ,megohms per ,centimetre-cube4 ---------------------------------------- ------------------------ ,resistivity ,substance4 in ,megohms ,observer4 per c4c4 ---------------------------------------- ------------------------ ,ethyl alcohol #j4e ,pfeiffer4 ,ethyl ether #a4age to #c4gfj ,w4 ,kohlrausch4 ,benzene #d4gjj ,absolutely pure water #be4j at #ah ,c4 ,value estimated approximates probably to by ,f4 ,kohlrausch and ,a4 ,heydweiler4 ,all very dilute aqueous #a4jj at #ah ,c4 ,from results by salt solutions having a ,f4 ,kohlrausch concentration of about and others4 #j4jjjja of an equivalent gramme molecule#aj per litre approximate to ---------------------------------------- ------------------------ ,the resistivity of all those substances which are generally called dielectrics or insulators is also so high that it can only be appropriately expressed in millions of megohms per centimetre-cube1 or in megohms per quadrant-cube1 the quadrant being a cube the side of which is #aji cms4 7see ,table ,,viii474 ,effects of ,heat4--,temperature affects the resistivity of these different classes of conductors in different ways4 ,in all cases1 so far as is yet known1 the resistivity of a pure metal is increased if its temperature is raised1 and decreased if the temperature is lowered1 so that if it could be brought to the absolute zero of temperature 7-#bgc ,c47 its resistivity would be reduced to a very small fraction of its resistance at ordinary temperatures4 ,with metallic alloys1 however1 rise of temperature does not always increase resistivity3 it sometimes diminishes it1 so that many alloys are known which have a maximum resistivity corresponding to a certain temperature1 and at or near this point they vary very little in resistance with temperature4 ,such alloys have1 therefore1 a negative temperature-variation of resistance at and above fixed temperatures4 ,prominent amongst these metallic compounds are alloys of iron1 manganese1 nickel and copper1 some of which were discovered by ,edward ,weston1 in the ,united ,states4 ,one well-known alloy of copper1 manganese and nickel1 now called manganin1 which was brought to the notice of electricians by the careful investigations made at the ,berlin ,physikalisch-,technische ,reichsanstalt1 is characterized by having a zero temperature coefficient at or about a certain temperature in the neighbourhood of #ae ,c4 ,hence within a certain range of temperature on either side of this critical value the resistivity of manganin is hardly affected at all by temperature4 ,similar alloys can be produced from copper and ferro-manganese4 ,an alloy formed of #hj copper and #bj manganese in an annealed condition has a nearly zero temperature-variation of resistance between #bj ,c4 and #ajj ,c4 ,in the case of non-metals the action of temperature is generally to diminish the resistivity as temperature rises1 though this is not universally so4 ,the interesting observation has been recorded by ,j4 ,w4 ,howell1 that treated carbon filaments and graphite are substances which have a minimum resistance corresponding to a certain temperature approaching red heat 7,electrician1 vol4 xxxviii4 p4 #hce74 ,at and beyond this temperature increased heating appears to increase their resistivity2 this phenomenon may1 however1 be accompanied by a molecular change and not be a true temperature variation4 ,in the case of dielectric conductors and of electrolytes1 the action of rising temperature is to reduce resistivity4 ,many of the so-called insulators1 such as mica1 ebonite1 indiarubber1 and the insulating oils1 paraffin1 c41 decrease in resistivity with great rapidity as the temperature rises4 ,with guttapercha a rise in temperature from #j ,c4 to #bd ,c4 is sufficient to reduce the resistivity of one-twentieth part of its value at #j ,c41 and the resistivity of flint glass at #adj ,c4 is only one-hundredth of what it is at #fj ,c4 ,,table ,,viii4--,electric ,volume-,resistivity of ,dielectrics reckoned in ,millions of ,megohms 7,mega-megohms7 per ,centimetre-cube1 and in ,megohms per ,quadrant-cube1 i4e4 a ,cube whose ,side is #aji cms4 ---------------------------------------- --------------------- ,resistivity4 -------------------------- ,tempera- ,substance4 ,mega-megohms ,megohms per tura per c4c4 ,quadrant-cube4 ,cent4 ---------------------------------------- -------------------- ,bohemian glass #fa 4#jfa #fj ,mica #hd 4#jhd #bj ,gutta-percha #dej 4#de #bd ,flint glass #a1jbj #a4jb #fj ,glover's vulcanized indiarubber #a1fcj #a4fc #ae ,siemens' ordinary pure vulcanized indiarubber #b1bhj #b4bh #ae ,shellac #i1jjj #i4j #bh ,indiarubber #aj1ijj #aj4i #bd ,siemens' high-insulating fibrous material #aa1ijj #aa4i #ae ,siemens' special high-insulating indiarubber4 #af1agj #af4ag #ae ,flint glass #bj1jjj #bj4j #bj ,ebonite #bh1jjj #bh4 #df ,paraffin #cd1jjj #cd4 #df ---------------------------------------- -------------------- ,a definition may here be given of the meaning of the term ,temperature ,coefficient4 ,if1 in the first place1 we suppose that the resistivity 7rhot7 at any temperature 7t7 is a simple linear function of the resistivity 7rho#j7 at #j ,c41 then we can write rhot rho#j7a alphat71 or alpha 7rhot - rho#j7_/rho#jt4 ,the quantity alpha is then called the temperature-coefficient1 and its reciprocal is the temperature at which the resistivity would become zero4 ,by an extension of this notion we can call the quantity drho_/rhodt the temperature coefficient corresponding to any temperature t at which the resistivity is rho4 ,in all cases the relation between the resistivity of a substance and the temperature is best set out in the form of a curve called a temperature-resistance curve4 ,if a series of such curves are drawn for various pure metals1 temperature being taken as abscissa and resistance as ordinate1 and if the temperature range extends from the absolute zero of temperature upwards1 then it is found that these temperature-resistance lines are curved lines having their convexity either upwards or downwards4 ,in other words1 the second differential coefficient of resistance with respect to temperature is either a positive or negative quantity4 ,an extensive series of observations concerning the form of the resistivity curves for various pure metals over a range of temperature extending from -#bjj ,c4 to #bjj ,c4 was carried out in #ahib and #ahic by ,fleming and ,dewar 7,phil4 ,mag4 ,oct4 #ahib and ,sept4 #ahic74 ,the resistance observations were taken with resistance coils constructed with wires of various metals obtained in a state of great chemical purity4 ,the lengths and mean diameters of the wires were carefully measured1 and their resistance was then taken at certain known temperatures obtained by immersing the coils in boiling aniline1 boiling water1 melting ice1 melting carbonic acid in ether1 and boiling liquid oxygen1 the temperatures thus given being #ahd4e ,c41 #ajj ,c41 #j ,c41 -#gh4b ,c4 and -#ahb4e ,c4 ,the resistivities of the various metals were then calculated and set out in terms of the temperature4 ,from these data a chart was prepared showing the temperature-resistance curves of these metals throughout a range of #djj degrees4 ,the exact form of these curves through the region of temperature lying between -#bjj ,c4 and -#bgc ,c4 is not yet known4 ,as shown on the chart1 the curves evidently do not converge to precisely the same point4 ,it is1 however1 much less probable that the resistance of any metal should vanish at a temperature above the absolute zero than at the absolute zero itself1 and the precise path of these curves at their lower ends cannot be delineated until means are found for fixing independently the temperature of some regions in which the resistance of metallic wires can be measured4 ,sir ,j4 ,dewar subsequently showed that for certain pure metals it is clear that the resistance would not vanish at the absolute zero but would be reduced to a finite but small value 7see ,electric ,resistance ,thermometry at the ,temperature of ,boiling ,hydrogen1 ,proc4 ,roy4 ,soc4 #aijd1 #gc1 p4 #bdd74 ,the resistivity curves of the magnetic metals are also remarkable for the change of curvature they exhibit at the magnetic critical temperature4 ,thus ,j4 ,hopkinson and ,d4 ,k4 ,morris 7,phil4 ,mag4 ,september #ahig1 p4 #bac7 observed the remarkable alteration that takes place in the iron resistance temperature curve in the neighbourhood of #ghj ,c4 ,at that temperature the direction of the curvature of the curve changes so that it becomes convex upwards instead of convex downwards1 and in addition the value of the temperature coefficient undergoes a great reduction4 ,the mean temperature coefficient of iron in the neighbourhood of #j ,c4 is #j4jjeg2 at #gfe ,c4 it rises to a maximum value #j4jbjd2 but at #ajjj ,c4 it falls again to a lower value1 #j4jjbdd4 ,a similar rise to a maximum value and subsequent fall are also noted in the case of the specific heat of iron4 ,the changes in the curvature of the resistivity curves are undoubtedly connected with the molecular changes that occur in the magnetic metals at their critical temperatures4 ,a fact of considerable interest in connexion with resistivity is the influence exerted by a strong magnetic field in the case of some metals1 notably bismuth4 ,it was discovered by ,a4 ,righi and confirmed by ,s4 ,a4 ,leduc 7,journ4 de ,phys4 #ahhf1 #e1 p4 #aaf1 and #ahhg1 #f1 p4 #ahi7 that if a pure bismuth wire is placed in a magnetic field transversely to the direction of the magnetic field1 its resistance is considerably increased4 ,this increase is greatly affected by the temperature of the metal 7,dewar and ,fleming1 ,proc4 ,roy4 ,soc4 #ahig1 #fj1 p4 #dbg74 ,the temperature coefficient of pure copper is an important constant1 and its value as determined by ,messrs ,clark1 ,forde and ,taylor in terms of ,fahrenheit temperature is rhot rho#cb #a #j4jjbcgjh7t - #cb7 #j4jjjjjcdedh7t - #cb74 ,time ,effects4--,in the case of dielectric conductors1 commonly called insulators1 such as indiarubber1 guttapercha1 glass and mica1 the electric resistivity is not only a function of the temperature but also of the time during which the electromotive force employed to measure it is imposed4 ,thus if an indiarubber-covered cable is immersed in water and the resistance of the dielectric between the copper conductor and the water measured by ascertaining the current which can be caused to flow through it by an electromotive force1 this current is found to vary very rapidly with the time during which the electromotive force is applied4 ,apart from the small initial effect due to the electrostatic capacity of the cable1 the application of an electromotive force to the dielectric produces a current through it which rapidly falls in value1 as if the electric resistance of the dielectric were increasing4 ,the current1 however1 does not fall continuously but tends to a limiting value1 and it appears that if the electromotive force is kept applied to the cable for a prolonged time1 a small and nearly constant current will ultimately be found flowing through it4 ,it is customary in electro-technical work to consider the resistivity of the dielectric as the value it has after the electromotive force has been applied for one minute1 the standard temperature being #ge ,f4 ,this1 however1 is a purely conventional proceeding1 and the number so obtained does not necessarily represent the true or ohmic resistance of the dielectric4 ,if the electromotive force is increased1 in the case of a large number of ordinary dielectrics the apparent resistance at the end of one minute's electrification decreases as the electromotive force increases4 ,practical ,standards4--,the practical measurement of resistivity involves many processes and instruments 7see ,,wheatstone',s ,,bridge and ,,ohmmeter74 ,broadly speaking1 the processes are divided into ,comparison ,methods and ,absolute ,methods4 ,in the former a comparison is effected between the resistance of a material in a known form and some standard resistance4 ,in the ,absolute ,methods the resistivity is determined without reference to any other substance1 but with reference only to the fundamental standards of length1 mass and time4 ,immense labour has been expended in investigations concerned with the production of a standard of resistance and its evaluation in absolute measure4 ,in some cases the absolute standard is constructed by filling a carefully-calibrated tube of glass with mercury1 in order to realize in a material form the official definition of the ohm2 in this manner most of the principal national physical laboratories have been provided with standard mercury ohms4 7,for a full description of the standard mercury ohm of the ,berlin ,physikalisch-,technische ,reichsanstalt1 see the ,electrician1 xxxvii4 #efi47 ,for practical purposes it is more convenient to employ a standard of resistance made of wire4 ,opinion is not yet perfectly settled on the question whether a wire made of any alloy can be considered to be a perfectly unalterable standard of resistance1 but experience has shown that a platinum silver alloy 7#ff silver1 #cc platinum71 and also the alloy called manganin1 seem to possess the qualities of permanence essential for a wire-resistance standard4 ,a comparison made in #ahib and #ahid of all the manganin wire copies of the ohm made at the ,reichsanstalt in ,berlin1 showed that these standards had remained constant for two years to within one or two parts in #ajj1jjj4 ,it appears1 however1 that in order that manganin may remain constant in resistivity when used in the manufacture of a resistance coil1 it is necessary that the alloy should be aged by heating it to a temperature of #adj ,c4 for ten hours2 and to prevent subsequent changes in resistivity1 solders containing zinc must be avoided1 and a silver solder containing #ge of silver employed in soldering the manganin wire to its connexions4 ,the authorities of the ,berlin ,reichsanstalt have devoted considerable attention to the question of the best form for a wire standard of electric resistance4 ,in that now adopted the resistance wire is carefully insulated and wound on a brass cylinder1 being doubled on itself to annul inductance as much as possible4 ,in the coil two wires are wound on in parallel1 one being much finer than the other1 and the final adjustment of the coil to an exact value is made by shortening the finer of the two4 ,a standard of resistance for use in a laboratory now generally consists of a wire of manganin or platinum-silver carefully insulated and enclosed in a brass case4 ,thick copper rods are connected to the terminals of the wire in the interior of the case1 and brought to the outside1 being carefully insulated at the same time from one another and from the case4 ,the coil so constructed can be placed under water or paraffin oil1 the temperature of which can be exactly observed during the process of taking a resistance measurement4 ,equalization of the temperature of the surrounding medium is effected by the employment of a stirrer1 worked by hand or by a small electric motor4 ,the construction of a standard of electrical resistance consisting of mercury in a glass tube is an operation requiring considerable precautions1 and only to be undertaken by those experienced in the matter4 ,opinions are divided on the question whether greater permanence in resistance can be secured by mercury-in-glass standards of resistance or by wire standards1 but the latter are at least more portable and less fragile4 ,a full description of the construction of a standard wire-resistance coil on the plan adopted by the ,berlin ,physikalisch-,technische ,reichsanstalt is given in the ,report of the ,british ,association ,committee on ,electrical ,standards1 presented at the ,edinburgh ,meeting in #ahib4 ,for the design and construction of standards of electric resistances adapted for employment in the comparison and measurement of very low or very high resistances1 the reader may be referred to standard treatises on electric measurements4 ,,bibliography4--,see also ,j4 ,a4 ,fleming1 ,a ,handbook for the ,electrical ,laboratory and ,testing ,room1 vol4 i4 7,london1 #aija72 ,reports of the ,british ,association ,committee on ,electrical ,standards1 edited by ,fleeming ,jenkin 7,london1 #ahgc72 ,a4 ,matthiessen and ,c4 ,vogt1 ,on the ,influence of ,temperature on the ,conducting ,power of ,alloys1 ,phil4 ,trans41 #ahfd1 #aed1 p4 #afg1 and ,phil4 ,mag41 #ahfe1 #bi1 p4 #cfc2 ,a4 ,matthiessen and ,m4 ,holtzmann1 ,on the ,effect of the ,presence of ,metals and ,metalloids upon the ,electric ,conducting ,power of ,pure ,copper1 ,phil4 ,trans41 #ahfj1 #aej1 p4 #he2 ,t4 ,c4 ,fitzpatrick1 ,on the ,specific ,resistance of ,copper1 ,brit4 ,assoc4 ,report1 #ahij1 p4 #abj1 or ,electrician1 #ahij1 #be1 p4 #fjh2 ,r4 ,appleyard1 ,the ,conductometer and ,electrical ,conductivity2 ,clark1 ,forde and ,taylor1 ,temperature ,coefficients of ,copper 7,london1 #aija74 7,j4 ,a4 ,f47 ,,ii4 ,,conduction ,,in ,,liquids ,through liquid metals1 such as mercury at ordinary temperatures and other metals at temperatures above their melting points1 the electric current flows as in solid metals without changing the state of the conductor1 except in so far as heat is developed by the electric resistance4 ,but another class of liquid conductors exists1 and in them the phenomena are quite different4 ,the conductivity of fused salts1 and of solutions of salts and acids1 although less than that of metals1 is very great compared with the traces of conductivity found in so-called non-conductors4 ,in fused salts and conducting solutions the passage of the current is always accompanied by definite chemical changes2 the substance of the conductor or electrolyte is decomposed1 and the products of the decomposition appear at the electrodes1 i4e4 the metallic plates by means of which the current is led into and out of the solution4 ,the chemical phenomena are considered in the article ,,electrolysis2 we are here concerned solely with the mechanism of this electrolytic conduction of the current4 ,to explain the appearance of the products of decomposition at the electrodes only1 while the intervening solution is unaltered1 we suppose that1 under the action of the electric forces1 the opposite parts of the electrolyte move in opposite directions through the liquid4 ,these opposite parts1 named ions by ,faraday1 must therefore be associated with electric charges1 and it is the convective movement of the opposite streams of ions carrying their charges with them that1 on this view1 constitutes the electric current4 ,in metallic conduction it is found that the current is proportional to the applied electromotive force--a relation known by the name of ,ohm's law4 ,if we place in a circuit with a small electromotive force an electrolytic cell consisting of two platinum electrodes and a solution1 the initial current soon dies away1 and we shall find that a certain minimum electromotive force must be applied to the circuit before any considerable permanent current passes4 ,the chemical changes which are initiated on the surfaces of the electrodes set up a reverse electromotive force of polarization1 and1 until this is overcome1 only a minute current1 probably due to the slow but steady removal of the products of decomposition from the electrodes by a process of diffusion1 will pass through the cell4 ,thus it is evident that1 considering the electrolytic cell as a whole1 the passage of the current through it cannot conform to ,ohm's law4 ,but the polarization is due to chemical changes1 which are confined to the surfaces of the electrodes2 and it is necessary to inquire whether1 if the polarization at the electrodes be eliminated1 the passage of the current through the bulk of the solution itself is proportional to the electromotive force actually applied to that solution4 ,rough experiment shows that the current is proportional to the excess of the electromotive force over a constant value1 and thus verifies the law approximately1 the constant electromotive force to be overcome being a measure of the polarization4 ,a more satisfactory examination of the question was made by ,f4 ,kohlrausch in the years #ahgc to #ahgf4 ,ohm's law states that the current ,c is proportional to the electromotive force ,e1 or ,c k,r1 where k is a constant called the conductivity of the circuit4 ,the equation may also be written as ,c ,e_/,r1 where ,r is a constant1 the reciprocal of k1 known as the resistance of the circuit4 ,the essence of the law is the proportionality between ,c and ,e1 which means that the ratio ,e_/,c is a constant4 ,but ,e_/,c ,r1 and thus the law may be tested by examining the constancy of the measured resistance of a conductor when different currents are passing through it4 ,in this way ,ohm's law has been confirmed in the case of metallic conduction to a very high degree of accuracy4 ,a similar principle was applied by ,kohlrausch to the case of electrolytes1 and he was the first to show that an electrolyte possesses a definite resistance which has a constant value when measured with different currents and by different experimental methods4 ,measurement of the ,resistance of ,electrolytes4--,there are two effects of the passage of an electric current which prevent the possibility of measuring electrolytic resistance by the ordinary methods with the direct currents which are used in the case of metals4 ,the products of the chemical decomposition of the electrolyte appear at the electrodes and set up the opposing electromotive force of polarization1 and unequal dilution of the solution may occur in the neighbourhood of the two electrodes4 ,the chemical and electrolytic aspects of these phenomena are treated in the article ,,electrolysis1 but from our present point of view also it is evident that they are again of fundamental importance4 ,the polarization at the surface of the electrodes will set up an opposing electromotive force1 and the unequal dilution of the solution will turn the electrolyte into a concentration cell and produce a subsidiary electromotive force either in the same direction as that applied or in the reverse according as the anode or the cathode solution becomes the more dilute4 ,both effects thus involve internal electromotive forces1 and prevent the application of ,ohm's law to the electrolytic cell as a whole4 ,but the existence of a definite measurable resistance as a characteristic property of the system depends on the conformity of the system to ,ohm's law1 and it is therefore necessary to eliminate both these effects before attempting to measure the resistance4 ,the usual and most satisfactory method of measuring the resistance of electrolytes consists in eliminating the effects of polarization by the use of alternating currents1 that is1 currents that are reversed in direction many times a second4#aa ,the chemical action produced by the first current is thus reversed by the second current in the opposite direction1 and the polarization caused by the first current on the surface of the electrodes is destroyed before it rises to an appreciable value4 ,the polarization is also diminished in another way4 ,the electromotive force of polarization is due to the deposition of films of the products of chemical decomposition on the surface of the electrodes1 and only reaches its full value when a continuous film is formed4 ,if the current be stopped before such a film is completed1 the reverse electromotive force is less than its full value4 ,a given current flowing for a given time deposits a definite amount of substance on the electrodes1 and therefore the amount per unit area is inversely proportional to the area of the electrodes--to the area of contact1 that is1 between the electrode and the liquid4 ,thus1 by increasing the area of the electrodes1 the polarization due to a given current is decreased4 ,now the area of free surface of a platinum plate can be increased enormously by coating the plate with platinum black1 which is metallic platinum in a spongy state1 and with such a plate as electrode the effects of polarization are diminished to a very marked extent4 ,the coating is effected by passing an electric current first one way and then the other between two platinum plates immersed in a #c solution of platinum chloride to which a trace of lead acetate is sometimes added4 ,the platinized plates thus obtained are quite satisfactory for the investigation of strong solutions4 ,they have the power1 however1 of absorbing a certain amount of salt from the solutions and of giving it up again when water or more dilute solution is placed in contact with them4 ,the measurement of very dilute solutions is thus made difficult1 but1 if the plates be heated to redness after being platinized1 a grey surface is obtained which possesses sufficient area for use with dilute solutions and yet does not absorb an appreciable quantity of salt4 ,any convenient source of alternating current may be used4 ,the currents from the secondary circuit of a small induction coil are satisfactory1 or the currents of an alternating electric light supply may be transformed down to an electromotive force of one or two volts4 ,with such currents it is necessary to consider the effects of self-induction in the circuit and of electrostatic capacity4 ,in balancing the resistance of the electrolyte1 resistance coils may be used in which self-induction and the capacity are reduced to a minimum by winding the wire of the coil backwards and forwards in alternate layers4 ,illustration3 ,,fig4 #a4 ,with these arrangements the usual method of measuring resistance by means of ,wheatstone's bridge may be adapted to the case of electrolytes4 ,with alternating currents1 however1 it is impossible to use a galvanometer in the usual way4 ,the galvanometer was therefore replaced by ,kohlrausch by a telephone1 which gives a sound when an alternating current passes through it4 ,the most common plan of the apparatus is shown diagrammatically in fig4 #a4 ,the electrolytic cell and a resistance box form two arms of the bridge1 and the sliding contact is moved along the metre wire which forms the other two arms till no sound is heard in the telephone4 ,the resistance of the electrolyte is to that of the box as that of the right-hand end of the wire is to that of the left-hand end4 ,a more accurate method of using alternating currents1 and one more pleasant to use1 gets rid of the telephone 7,phil4 ,trans41 #aijj1 #aid1 p4 #cba74 ,the current from one or two voltaic cells is led to an ebonite drum turned by a motor or a hand-wheel and cord4 ,on the drum are fixed brass strips with wire brushes touching them in such a manner that the current from the brushes is reversed several times in each revolution of the drum4 ,the wires from the brushes are connected with the ,wheatstone's bridge4 ,a moving coil galvanometer is used as indicator1 its connexions being reversed in time with those of the battery by a slightly narrower set of brass strips fixed on the other end of the ebonite commutator4 ,thus any residual current through the galvanometer is direct and not alternating4 ,the high moment of inertia of the coil makes the period of swing slow compared with the period of alternation of the current1 and the slight periodic disturbances are thus prevented from affecting the galvanometer4 ,when the measured resistance is not altered by increasing the speed of the commutator or changing the ratio of the arms of the bridge1 the disturbing effects may be considered to be eliminated4 ,illustration3 ,,fig4 #b4 ,illustration3 ,,fig4 #c4 ,the form of vessel chosen to contain the electrolyte depends on the order of resistance to be measured4 ,for dilute solutions the shape of cell shown in fig4 #b will be found convenient1 while for more concentrated solutions1 that indicated in fig4 #c is suitable4 ,the absolute resistances of certain solutions have been determined by ,kohlrausch by comparison with mercury1 and1 by using one of these solutions in any cell1 the constant of that cell may be found once for all4 ,from the observed resistance of any given solution in the cell the resistance of a centimetre cube--the so-called specific resistance--may be calculated4 ,the reciprocal of this1 or the conductivity1 is a more generally useful constant2 it is conveniently expressed in terms of a unit equal to the reciprocal of an ohm4 ,thus ,kohlrausch found that a solution of potassium chloride1 containing one-tenth of a gram equivalent 7#g4df grams7 per litre1 has at #ah ,c4 a specific resistance of #hi4cg ohms per centimetre cube1 or a conductivity of #a4aai #aj-b mhos or #a4aai #aj-aa ,c4,g4,s4 units4 ,as the temperature variation of conductivity is large1 usually about #b per degree1 it is necessary to place the resistance cell in a paraffin or water bath1 and to observe its temperature with some accuracy4 ,another way of eliminating the effects of polarization and of dilution has been used by ,w4 ,stroud and ,j4 ,b4 ,henderson 7,phil4 ,mag41 #ahig #e1 #dc1 p4 #ai74 ,two of the arms of a ,wheatstone's bridge are composed of narrow tubes filled with the solution1 the tubes being of equal diameter but of different length4 ,the other two arms are made of coils of wire of equal resistance1 and metallic resistance is added to the shorter tube till the bridge is balanced4 ,direct currents of somewhat high electromotive force are used to work the bridge4 ,equal currents then flow through the two tubes2 the effects of polarization and dilution must be the same in each1 and the resistance added to the shorter tube must be equal to the resistance of a column of liquid the length of which is equal to the difference in length of the two tubes4 ,a somewhat different principle was adopted by ,e4 ,bouty in #ahhd4 ,if a current be passed through two resistances in series by means of an applied electromotive force1 the electric potential falls from one end of the resistances to the other1 and1 if we apply ,ohm's law to each resistance in succession1 we see that1 since for each of them ,e ,,cr1 and ,c the current is the same through both1 ,e the electromotive force or fall of potential between the ends of each resistance must be proportional to the resistance between them4 ,thus by measuring the potential difference between the ends of the two resistances successively1 we may compare their resistances4 ,if1 on the other hand1 we can measure the potential difference in some known units1 and similarly measure the current flowing1 we can determine the resistance of a single electrolyte4 ,the details of the apparatus may vary1 but its principle is illustrated in the following description4 ,a narrow glass tube is fixed horizontally into side openings in two glass vessels1 and an electric current passed through it by means of platinum electrodes and a battery of considerable electromotive force4 ,in this way a steady fall of electric potential is set up along the length of the tube4 ,to measure the potential difference between the ends of the tube1 tapping electrodes are constructed1 e4g4 by placing zinc rods in vessels with zinc sulphate solution and connecting these vessels 7by means of thin siphon tubes also filled with solution7 with the vessels at the ends of the long tube which contains the electrolyte to be examined4 ,whatever be the contact potential difference between zinc and its solution1 it is the same at both ends1 and thus the potential difference between the zinc rods is equal to that between the liquid at the two ends of the tube4 ,this potential difference may be measured without passing any appreciable current through the tapping electrodes1 and thus the resistance of the liquid deduced4 ,equivalent ,conductivity of ,solutions4--,as is the case in the other properties of solutions1 the phenomena are much more simple when the concentration is small than when it is great1 and a study of dilute solutions is therefore the best way of getting an insight into the essential principles of the subject4 ,the foundation of our knowledge was laid by ,kohlrausch when he had developed the method of measuring electrolyte resistance described above4 ,he expressed his results in terms of equivalent conductivity1 that is1 the conductivity 7k7 of the solution divided by the number 7m7 of gram-equivalents of electrolyte per litre4 ,he finds that1 as the concentration diminishes1 the value of k_/m approaches a limit1 and eventually becomes constant1 that is to say1 at great dilution the conductivity is proportional to the concentration4 ,kohlrausch first prepared very pure water by repeated distillation and found that its resistance continually increased as the process of purification proceeded4 ,the conductivity of the water1 and of the slight impurities which must always remain1 was subtracted from that of the solution made with it1 and the result1 divided by m1 gave the equivalent conductivity of the substance dissolved4 ,this procedure appears justifiable1 for as long as conductivity is proportional to concentration it is evident that each part of the dissolved matter produces its own independent effect1 so that the total conductivity is the sum of the conductivities of the parts2 when this ceases to hold1 the concentration of the solution has in general become so great that the conductivity of the solvent may be neglected4 ,the general result of these experiments can be represented graphically by plotting k_/m as ordinates and root #cm as abscissae1 root #cm being a number proportional to the reciprocal of the average distance between the molecules1 to which it seems likely that the molecular conductivity may be related4 ,the general types of curve for a simple neutral salt like potassium or sodium chloride and for a caustic alkali or acid are shown in fig4 #d4 ,the curve for the neutral salt comes to a limiting value2 that for the acid attains a maximum at a certain very small concentration1 and falls again when the dilution is carried farther4 ,it has usually been considered that this destruction of conductivity is due to chemical action between the acid and the residual impurities in the water4 ,at such great dilution these impurities are present in quantities comparable with the amount of acid which they convert into a less highly conducting neutral salt4 ,in the case of acids1 then1 the maximum must be taken as the limiting value4 ,the decrease in equivalent conductivity at great dilution is1 however1 so constant that this explanation seems insufficient4 ,the true cause of the phenomenon may perhaps be connected with the fact that the bodies in which it occurs1 acids and alkalis1 contain the ions1 hydrogen in the one case1 hydroxyl in the other1 which are present in the solvent1 water1 and have1 perhaps because of this relation1 velocities higher than those of any other ions4 ,the values of the molecular conductivities of all neutral salts are1 at great dilution1 of the same order of magnitude1 while those of acids at their maxima are about three times as large4 ,the influence of increasing concentration is greater in the case of salts containing divalent ions1 and greatest of all in such cases as solutions of ammonia and acetic acid1 which are substances of very low conductivity4 ,illustration3 ,,fig4 #d4 ,theory of ,moving ,ions4--,kohlrausch found that1 when the polarization at the electrodes was eliminated1 the resistance of a solution was constant however determined1 and thus established ,ohm's ,law for electrolytes4 ,the law was confirmed in the case of strong currents by ,g4 ,f4 ,fitzgerald and ,f4 ,t4 ,trouton 7,b4,a4 ,report1 #ahhf1 p4 #cab74 ,now1 ,ohm's ,law implies that no work is done by the current in overcoming reversible electromotive forces such as those of polarization4 ,thus the molecular interchange of ions1 which must occur in order that the products may be able to work their way through the liquid and appear at the electrodes1 continues throughout the solution whether a current is flowing or not4 ,the influence of the current on the ions is merely directive1 and1 when it flows1 streams of electrified ions travel in opposite directions1 and1 if the applied electromotive force is enough to overcome the local polarization1 give up their charges to the electrodes4 ,we may therefore represent the facts by considering the process of electrolysis to be a kind of convection4 ,faraday's classical experiments proved that when a current flows through an electrolyte the quantity of substance liberated at each electrode is proportional to its chemical equivalent weight1 and to the total amount of electricity passed4 ,accurate determinations have since shown that the mass of an ion deposited by one electromagnetic unit of electricity1 i4e4 its electro-chemical equivalent1 is #a4jcf #aj-d its chemical equivalent weight4 ,thus the amount of electricity associated with one gram-equivalent of any ion is #ajd_/a4jcf #ifec units4 ,each monovalent ion must therefore be associated with a certain definite charge1 which we may take to be a natural unit of electricity2 a divalent ion carries two such units1 and so on4 ,a cation1 i4e4 an ion giving up its charge at the cathode1 as the electrode at which the current leaves the solution is called1 carries a positive charge of electricity2 an anion1 travelling in the opposite direction1 carries a negative charge4 ,it will now be seen that the quantity of electricity flowing per second1 i4e4 the current through the solution1 depends on 7#a7 the number of the ions concerned1 7#b7 the charge on each ion1 and 7#c7 the velocity with which the ions travel past each other4 ,now1 the number of ions is given by the concentration of the solution1 for even if all the ions are not actively engaged in carrying the current at the same instant1 they must1 on any dynamical idea of chemical equilibrium1 be all active in turn4 ,the charge on each1 as we have seen1 can be expressed in absolute units1 and therefore the velocity with which they move past each other can be calculated4 ,this was first done by ,kohlrausch 7,gttingen ,nachrichten1 #ahgf1 p4 #bac1 and ,das ,leitvermgen der ,elektrolyte1 ,leipzig1 #ahih7 about #ahgi4 ,in order to develop ,kohlrausch's theory1 let us take1 as an example1 the case of an aqueous solution of potassium chloride1 of concentration n gram-equivalents per cubic centimetre4 ,there will then be n gram-equivalents of potassium ions and the same number of chlorine ions in this volume4 ,let us suppose that on each gram-equivalent of potassium there reside e units of electricity1 and on each gram-equivalent of chlorine ions -e units4 ,if u denotes the average velocity of the potassium ion1 the positive charge carried per second across unit area normal to the flow is n e u4 ,similarly1 if v be the average velocity of the chlorine ions1 the negative charge carried in the opposite direction is n e v4 ,but positive electricity moving in one direction is equivalent to negative electricity moving in the other1 so that1 before changes in concentration sensibly supervene1 the total current1 ,c1 is ne7u v74 ,now let us consider the amounts of potassium and chlorine liberated at the electrodes by this current4 ,at the cathode1 if the chlorine ions were at rest1 the excess of potassium ions would be simply those arriving in one second1 namely1 nu4 ,but since the chlorine ions move also1 a further separation occurs1 and nv potassium ions are left without partners4 ,the total number of gram-equivalents liberated is therefore n7u v74 ,by ,faraday's law1 the number of grams liberated is equal to the product of the current and the electro-chemical equivalent of the ion2 the number of gram-equivalents therefore must be equal to eta,c1 where eta denotes the electro-chemical equivalent of hydrogen in ,c4,g4,s4 units4 ,thus we get n7u v7 eta,c etane7u v71 and it follows that the charge1 e1 on #a gram-equivalent of each kind of ion is equal to #a_/;eta4 ,we know that ,ohm's ,law holds good for electrolytes1 so that the current ,c is also given by kd,p_/dx1 where k denotes the conductivity of the solution1 and d,p_/dx the potential gradient1 i4e4 the change in potential per unit length along the lines of current flow4 ,thus n -----7u v7 kd,p_/dx2 eta therefore k d,p u v eta - --4 n dx ,now eta is #a4jcf #aj-d1 and the concentration of a solution is usually expressed in terms of the number1 m1 of gram-equivalents per litre instead of per cubic centimetre4 ,therefore k d,p u v #a4jcf #aj-a - -- --4 m dx ,when the potential gradient is one volt 7#ajh ,c4,g4,s4 units7 per centimetre this becomes u v #a4jcf #aj-g k_/m4 ,thus by measuring the value of k_/m1 which is known as the equivalent conductivity of the solution1 we can find u v1 the velocity of the ions relative to each other4 ,for instance1 the equivalent conductivity of a solution of potassium chloride containing one-tenth of a gram-equivalent per litre is #aaai #aj-ac ,c4,g4,s4 units at #ah ,c4 ,therefore u v #a4jcf #ajg #aaai #aj-ac #a4aei #aj-c #j4jjaaei cm4 per sec4 ,in order to obtain the absolute velocities u and v1 we must find some other relation between them4 ,let us resolve u into 7u v7 in one direction1 say to the right1 and 7u - v7 to the left4 ,similarly v can be resolved into 7vu7 to the left and 7v-u7 to the right4 ,on pairing these velocities we have a combined movement of the ions to the right1 with a speed of 7u - v7 and a drift right and left1 past each other1 each ion travelling with a speed of 7u v71 constituting the electrolytic separation4 ,if u is greater than v1 the combined movement involves a concentration of salt at the cathode1 and a corresponding dilution at the anode1 and vice versa4 ,the rate at which salt is electrolysed1 and thus removed from the solution at each electrode1 is 7u v74 ,thus the total loss of salt at the cathode is 7u v7 - 7u - v7 or v1 and at the anode1 7v u7 - 7v - u71 or u4 ,therefore1 as is explained in the article ,,electrolysis1 by measuring the dilution of the liquid round the electrodes when a current passed1 ,w4 ,hittorf 7,pogg4 ,ann41 #ahec-ahei1 #hi1 p4 #agg2 #ih1 p4 #a2 #ajc1 p4 #a2 #ajf1 pp4 #ccg and #eac7 was able to deduce the ratio of the two velocities1 for simple salts when no complex ions are present1 and many further experiments have been made on the subject 7see ,das ,leitvermgen der ,elektrolyte74 ,by combining the results thus obtained with the sum of the velocities1 as determined from the conductivities1 ,kohlrausch calculated the absolute velocities of different ions under stated conditions4 ,thus1 in the case of the solution of potassium chloride considered above1 ,hittorf's experiments show us that the ratio of the velocity of the anion to that of the cation in this solution is 4#ea 3 4#di4 ,the absolute velocity of the potassium ion under unit potential gradient is therefore #j4jjjefg cm4 per sec41 and that of the chlorine ion #j4jjjeib cm4 per sec4 ,similar calculations can be made for solutions of other concentrations1 and of different substances4 ,table ,,ix4 shows ,kohlrausch's values for the ionic velocities of three chlorides of alkali metals at #ah ,c1 calculated for a potential gradient of #a volt per cm42 the numbers are in terms of a unit equal to #aj-f cm4 per 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 ---------------------------------------- ------------------ ,these numbers show clearly that there is an increase in ionic velocity as the dilution proceeds4 ,moreover1 if we compare the values for the chlorine ion obtained from observations on these three different salts1 we see that as the concentrations diminish the velocity of the chlorine ion becomes the same in all of them4 ,a similar relation appears in other cases1 and1 in general1 we may say that at great dilution the velocity of an ion is independent of the nature of the other ion present4 ,this introduces the conception of specific ionic velocities1 for which some values at #ah ,c4 are given by ,kohlrausch in ,table ,x43-- ,table ,x4 ------------------------------------ ,k #ff #aj-e cms4 per 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 ------------------------------------ ,having obtained these numbers we can deduce the conductivity of the dilute solution of any salt1 and the comparison of the calculated with the observed values furnished the first confirmation of ,kohlrausch's theory4 ,some exceptions1 however1 are known4 ,thus acetic acid and ammonia give solutions of much lower conductivity than is indicated by the sum of the specific ionic velocities of their ions as determined from other compounds4 ,an attempt to find in ,kohlrausch's theory some explanation of this discrepancy shows that it could be due to one of two causes4 ,either the velocities of the ions must be much less in these solutions than in others1 or else only a fractional part of the number of molecules present can be actively concerned in conveying the current4 ,we shall return to this point later4 ,friction on the ,ions4--,it is interesting to calculate the magnitude of the forces required to drive the ions with a certain velocity4 ,if we have a potential gradient of #a volt per centimetre the electric force is #ajh in ,c4,g4,s4 units4 ,the charge of electricity on #a gram-equivalent of any ion is #a_/4jjjajcf #ifec units1 hence the mechanical force acting on this mass is #ifec #ajh dynes4 ,this1 let us say1 produces a velocity u2 then the force required to produce unit velocity is ,,pa #i4fec #ajaa_/u dynes #i4hd #aje_/u kilograms-weight4 ,if the ion have an equivalent weight ,a1 the force producing unit velocity when acting on #a gram is ,p#a #i4hd #aje_/;,au kilograms-weight4 ,thus the aggregate force required to drive #a gram of potassium ions with a velocity of #a centimetre per second through a very dilute solution must be equal to the weight of #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 ------------- ----------------- ,since the ions move with uniform velocity1 the frictional resistances brought into play must be equal and opposite to the driving forces1 and therefore these numbers also represent the ionic friction coefficients in very dilute solutions at #ah ,c4 ,direct ,measurement of ,ionic ,velocities4--,sir ,oliver ,lodge was the first to directly measure the velocity of an ion 7,b4,a4 ,report1 #ahhf1 p4 #chi74 ,in a horizontal glass tube connecting two vessels filled with dilute sulphuric acid he placed a solution of sodium chloride in solid agar-agar jelly4 ,this solid solution was made alkaline with a trace of caustic soda in order to bring out the red colour of a little phenol-phthalein added as indicator4 ,an electric current was then passed from one vessel to the other4 ,the hydrogen ions from the anode vessel of acid were thus carried along the tube1 and1 as they travelled1 decolourized the phenol-phthalein4 ,by this method the velocity of the hydrogen ion through a jelly solution under a known potential gradient was observed to about #j4jjbf cm4 per sec1 a number of the same order as that required by ,kohlrausch's theory4 ,direct determinations of the velocities of a few other ions have been made by ,w4 ,c4 ,d4 ,whetham 7,phil4 ,trans4 vol4 #ahd1 ,a1 p4 #ccg2 vol4 #ahf1 ,a1 p4 #ejg2 ,phil4 ,mag41 ,october #ahid74 ,two solutions having one ion in common1 of equivalent concentrations1 different densities1 different colours1 and nearly equal specific resistances1 were placed one over the other in a vertical glass tube4 ,in one case1 for example1 decinormal solutions of potassium carbonate and potassium bichromate were used4 ,the colour of the latter is due to the presence of the bichromate group1 ,cr#b,o#g4 ,when a current was passed across the junction1 the anions ,,co#c and ,cr#b,o#g travelled in the direction opposite to that of the current1 and their velocity could be determined by measuring the rate at which the colour boundary moved4 ,similar experiments were made with alcoholic solutions of cobalt salts1 in which the velocities of the ions were found to be much less than in water4 ,the behaviour of agar jelly was then investigated1 and the velocity of an ion through a solid jelly was shown to be very little less than in an ordinary liquid solution4 ,the velocities could therefore be measured by tracing the change in colour of an indicator or the formation of a precipitate4 ,thus decinormal jelly solutions of barium chloride and sodium chloride1 the latter containing a trace of sodium sulphate1 were placed in contact4 ,under the influence of an electromotive force the barium ions moved up the tube1 disclosing their presence by the trace of insoluble barium sulphate formed4 ,again1 a measurement of the velocity of the hydrogen ion1 when travelling through the solution of an acetate1 showed that its velocity was then only about the one-fortieth part of that found during its passage through chlorides4 ,from this1 as from the measurements on alcohol solutions1 it is clear that where the equivalent conductivities are very low the effective velocities of the ions are reduced in the same proportion4 ,another series of direct measurements has been made by ,orme ,masson 7,phil4 ,trans4 vol4 #aib1 ,a1 p4 #cca74 ,he placed the gelatine solution of a salt1 potassium chloride1 for example1 in a horizontal glass tube1 and found the rate of migration of the potassium and chlorine ions by observing the speed at which they were replaced when a coloured anion1 say1 the ,cr#b,o#g from a solution of potassium bichromate1 entered the tube at one end1 and a coloured cation1 say1 the ,cu from copper sulphate1 at the other4 ,the coloured ions are specifically slower than the colourless ions which they follow1 and in this case it follows that the coloured solution has a higher resistance than the colourless4 ,for the same current1 therefore1 the potential gradient is higher in the coloured solution and lower in the colourless one4 ,thus a coloured ion which gets in front of the advancing boundary finds itself acted on by a smaller force and falls back into line1 while a straggling colourless ion is pushed forward again4 ,hence a sharp boundary is preserved4 ,b4 ,d4 ,steele has shown that with these sharp boundaries the use of coloured ions is unnecessary1 the junction line being visible owing to the difference in the optical refractive indices of two colourless solutions4 ,once the boundary is formed1 too1 no gelatine is necessary1 and the motion can be watched through liquid aqueous solutions 7see ,r4 ,b4 ,denison and ,b4 ,d4 ,steele1 ,phil4 ,trans41 #aijf74 ,all the direct measurements which have been made on simple binary electrolytes agree with ,kohlrausch's results within the limits of experimental error4 ,his theory1 therefore1 probably holds good in such cases1 whatever be the solvent1 if the proper values are given to the ionic velocities1 i4e4 the values expressing the velocities with which the ions actually move in the solution of the strength taken1 and under the conditions of the experiment4 ,if we know the specific velocity of any one ion1 we can deduce1 from the conductivity of very dilute solutions1 the velocity of any other ion with which it may be associated1 a proceeding which does not involve the difficult task of determining the migration constant of the compound4 ,thus1 taking the specific ionic velocity of hydrogen as #j4jjjcb cm4 per second1 we can find1 by determining the conductivity of dilute solutions of any acid1 the specific velocity of the acid radicle involved4 ,or again1 since we know the specific velocity of silver1 we can find the velocities of a series of acid radicles at great dilution by measuring the conductivity of their silver salts4 ,by such methods ,w4 ,ostwald1 ,g4 ,bredig and other observers have found the specific velocities of many ions both of inorganic and organic compounds1 and examined the relation between constitution and ionic velocity4 ,the velocity of elementary ions is found to be a periodic function of the atomic weight1 similar elements lying on corresponding portions of a curve drawn to express the relation between these two properties4 ,such a curve much resembles that giving the relation between atomic weight and viscosity in solution4 ,for complex ions the velocity is largely an additive property2 to a continuous additive change in the composition of the ion corresponds a continuous but decreasing change in the velocity4 ,the following table gives ,ostwald's results for the formic acid series3-- ,table ,,xii4 ---------------------------------------- ------------- ,velocity4 ,difference for ,,ch#b4 ---------------------------------------- ------------- ,formic 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 ,valeric ,h#i;,c#e,o#b #bh4h - #b4j ,caprionic ,h#aa;,c#f,o#b #bg4d - #a4d ---------------------------------------- ------------- ,nature of ,electrolytes4--,we have as yet said nothing about the fundamental cause of electrolytic activity1 nor considered why1 for example1 a solution of potassium chloride is a good conductor1 while a solution of sugar allows practically no current to pass4 ,all the preceding account of the subject is1 then1 independent of any view we may take of the nature of electrolytes1 and stands on the basis of direct experiment4 ,nevertheless1 the facts considered point to a very definite conclusion4 ,the specific velocity of an ion is independent of the nature of the opposite ion present1 and this suggests that the ions themselves1 while travelling through the liquid1 are dissociated from each other4 ,further evidence1 pointing in the same direction1 is furnished by the fact that since the conductivity is proportional to the concentration at great dilution1 the equivalent-conductivity1 and therefore the ionic velocity1 is independent of it4 ,the importance of this relation will be seen by considering the alternative to the dissociation hypothesis4 ,if the ions are not permanently free from each other their mobility as parts of the dissolved molecules must be secured by continual interchanges4 ,the velocity with which they work their way through the liquid must then increase as such molecular rearrangements become more frequent1 and will therefore depend on the number of solute molecules1 i4e4 on the concentration4 ,on this supposition the observed constancy of velocity would be impossible4 ,we shall therefore adopt as a wording hypothesis the theory1 confirmed by other phenomena 7see ,,electrolysis71 that an electrolyte consists of dissociated ions4 ,it will be noticed that neither the evidence in favour of the dissociation theory which is here considered1 nor that described in the article ,,electrolysis1 requires more than the effective dissociation of the ions from each other4 ,they may well be connected in some way with solvent molecules1 and there are several indications that an ion consists of an electrified part of the molecule of the dissolved salt with an attendant atmosphere of solvent round it4 ,the conductivity of a salt solution depends on two factors--7#a7 the fraction of the salt ionized2 7#b7 the velocity with which the ions1 when free from each other1 move under the electric forces4#ab ,when a solution is heated1 both these factors may change4 ,the coefficient of ionization usually1 though not always1 decreases2 the specific ionic velocities increase4 ,now the rate of increase with temperature of these ionic velocities is very nearly identical with the rate of decrease of the viscosity of the liquid4 ,if the curves obtained by observations at ordinary temperatures be carried on they indicate a zero of fluidity and a zero of ionic velocity about the same point1 #ch4e ,c4 below the freezing point of water 7,kohlrausch1 ,sitz4 preuss4 ,akad4 ,wiss41 #aija1 #db1 p4 #ajbf74 ,such relations suggest that the frictional resistance to the motion of an ion is due to the ordinary viscosity of the liquid1 and that the ion is analogous to a body of some size urged through a viscous medium rather than to a particle of molecular dimensions finding its way through a crowd of molecules of similar magnitude4 ,from this point of view ,w4 ,k4 ,bousfield has calculated the sizes of ions on the assumption that ,stokes's theory of the motion of a small sphere through a viscous medium might be applied 7,zeits4 phys4 ,chem41 #aije1 #ec1 p4 #beg2 ,phil4 ,trans4 ,a1 #aijf1 #bjf1 p4 #aja74 ,the radius of the potassium or chlorine ion with its envelope of water appears to be about #a4b #aj-h centimetres4 ,for the bibliography of electrolytic conduction see ,,electrolysis4 ,the books which deal more especially with the particular subject of the present article are ,das ,leitvermgen der ,elektrolyte1 by ,f4 ,kohlrausch and ,l4 ,holborn 7,leipzig1 #ahih71 and ,the ,theory of ,solution and ,electrolysis1 by ,w4 ,c4 ,d4 ,whetham 7,cambridge1 #aijb74 7,w4 ,c4 ,d4 ,w47 ,,iii4 ,,electric ,,conduction ,,through ,,gases ,a gas such as air when it is under normal conditions conducts electricity to a small but only to a very small extent1 however small the electric force acting on the gas may be4 ,the electrical conductivity of gases not exposed to special conditions is so small that it was only definitely established in the early years of the #bjth century1 although it had engaged the attention of physicists for more than a hundred years4 ,it had been known for a long time that a body charged with electricity slowly lost its charge even when insulated with the greatest care1 and though long ago some physicists believed that part of the leak of electricity took place through the air1 the general view seems to have been that it was due to almost unavoidable defects in the insulation or to dust in the air1 which after striking the charged body was repelled from it and went off with some of the charge4 ,c4 ,a4 ,coulomb1 who made some very careful experiments which were published in #aghe 7,mm4 de l',acad4 des ,sciences1 #aghe1 p4 #fab71 came to the conclusion that after allowing for the leakage along the threads which supported the charged body there was a balance over1 which he attributed to leakage through the air4 ,his view was that when the molecules of air come into contact with a charged body some of the electricity goes on to the molecules1 which are then repelled from the body carrying their charge with them4 ,we shall see later that this explanation is not tenable4 ,c4 ,matteucci 7,ann4 chim4 phys41 #ahej1 #bh1 p4 #cij7 in #ahej also came to the conclusion that the electricity from a charged body passes through the air2 he was the first to prove that the rate at which electricity escapes is less when the pressure of the gas is low than when it is high4 ,he found that the rate was the same whether the charged body was surrounded by air1 carbonic acid or hydrogen4 ,subsequent investigations have shown that the rate in hydrogen is in general much less than in air4 ,thus in #ahgb ,e4 ,g4 ,warburg 7,pogg4 ,ann41 #ahgb1 #ade1 p4 #egh7 found that the leak through hydrogen was only about one-half of that through air3 he confirmed ,matteucci's observations on the effect of pressure on the rate of leak1 and also found that it was the same whether the gas was dry or damp4 ,he was inclined to attribute the leak to dust in the air1 a view which was strengthened by an experiment of ,j4 ,w4 ,hittorf's 7,wied4 ,ann41 #ahgi1 #g1 p4 #eie71 in which a small carefully insulated electroscope1 placed in a small vessel filled with carefully filtered gas1 retained its charge for several days2 we know now that this was due to the smallness of the vessel and not to the absence of dust1 as it has been proved that the rate of leak in small vessels is less than in large ones4 ,great light was thrown on this subject by some experiments on the rates of leak from charged bodies in closed vessels made almost simultaneously by ,h4 ,geitel 7,phys4 ,zeit41 #aijj1 #b1 p4 #aaf7 and ,c4 ,t4 ,r4 ,wilson 7,proc4 ,camb4 ,phil4 ,soc41 #aijj1 #aa1 p4 #cb74 ,these observers established that 7#a7 the rate of escape of electricity in a closed vessel is much smaller than in the open1 and the larger the vessel the greater is the rate of leak2 and 7#b7 the rate of leak does not increase in proportion to the differences of potential between the charged body and the walls of the vessel3 the rate soon reaches a limit beyond which it does not increase1 however much the potential difference may be increased1 provided1 of course1 that this is not great enough to cause sparks to pass from the charged body4 ,on the assumption that the maximum leak is proportional to the volume1 ,wilson's experiments1 which were made in vessels less than #a litre in volume1 showed that in dust-free air at atmospheric pressure the maximum quantity of electricity which can escape in one second from a charged body in a closed volume of ,v cubic centimetres is about #aj-h,v electrostatic units4 ,e4 ,rutherford and ,s4 ,t4 ,allan 7,phys4 ,zeit41 #aijb1 #c1 p4 #bbe71 working in ,montreal1 obtained results in close agreement with this4 ,working between pressures of from #dc to #gdc millimetres of mercury1 ,wilson showed that the maximum rate of leak is very approximately proportional to the pressure2 it is thus exceedingly small when the pressure is low--a result illustrated in a striking way by an experiment of ,sir ,w4 ,crookes 7,proc4 ,roy4 ,soc41 #ahgi1 #bh1 p4 #cdg7 in which a pair of gold leaves retained an electric charge for several months in a very high vacuum4 ,subsequent experiments have shown that it is only in very small vessels that the rate of leak is proportional to the volume and to the pressure2 in large vessels the rate of leak per unit volume is considerably smaller than in small ones4 ,in small vessels the maximum rate of leak in different gases1 is1 with the exception of hydrogen1 approximately proportional to the density of the gas4 ,wilson's results on this point are shown in the following table 7,proc4 ,roy4 ,soc41 #aija1 #fj1 p4 #bgg73-- ---------------------------------------- ---------- ,gas4 ,relative ,rate of ,leak4 ,rate of ,leak4 ,sp4 ,gr4 ---------------------------------------- ---------- ,air #a4jj #a ,h#b 4#ahd #b4g ,,co#b #a4fi #a4aj ,,so#b #b4fd #a4ba ,,ch#c;,cl #d4g #a4ji ,ni7,,co7#d #e4a 4#hfg ---------------------------------------- ---------- ,the rate of leak of electricity through gas contained in a closed vessel depends to some extent on the material of which the walls of the vessel are made2 thus it is greater1 other circumstances being the same1 when the vessel is made of lead than when it is made of aluminium4 ,it also varies1 as ,campbell and ,wood 7,phil4 ,mag4 #f1 #ac1 p4 #bfe7 have shown1 with the time of the day1 having a well-marked minimum at about #c o'clock in the morning3 it also varies from month to month4 ,rutherford 7,phys4 ,rev41 #aijc1 #af1 p4 #ahc71 ,cooke 7,phil4 ,mag41 #aijc #f1 #f1 p4 #djc7 and ,m',clennan and ,burton 7,phys4 ,rev41 #aijc1 #af1 p4 #ahd7 have shown that the leak in a closed vessel can be reduced by about #cj by surrounding the vessel with sheets of thick lead1 but that the reduction is not increased beyond this amount1 however thick the lead sheets may be4 ,this result indicates that part of the leak is due to a very penetrating kind of radiation1 which can get through the thin walls of the vessel but is stopped by the thick lead4 ,a large part of the leak we are describing is due to the presence of radioactive substances such as radium and thorium in the earth's crust and in the walls of the vessel1 and to the gaseous radioactive emanations which diffuse from them into the atmosphere4 ,this explains the very interesting effect discovered by ,j4 ,elster and ,h4 ,geitel 7,phys4 ,zeit41 #aija1 #b1 p4 #efj71 that the rate of leak in caves and cellars when the air is stagnant and only renewed slowly is much greater than in the open air4 ,in some cases the difference is very marked2 thus they found that in the cave called the ,baumannshhle in the ,harz mountains the electricity escaped at seven times the rate it did in the air outside4 ,in caves and cellars the radioactive emanations from the walls can accumulate and are not blown away as in the open air4 ,the electrical conductivity of gases in the normal state is1 as we have seen1 exceedingly small1 so small that the investigation of its properties is a matter of considerable difficulty2 there are1 however1 many ways by which the electrical conductivity of a gas can be increased so greatly that the investigation becomes comparatively easy4 ,among such methods are raising the temperature of the gas above a certain point4 ,gases drawn from the neighbourhood of flames1 electric arcs and sparks1 or glowing pieces of metal or carbon are conductors1 as are also gases through which ,rntgen or cathode rays or rays of positive electricity are passing2 the rays from the radioactive metals1 radium1 thorium1 polonium and actinium1 produce the same effect1 as does also ultra-violet light of exceedingly short wave-length4 ,the gas1 after being made a conductor of electricity by any of these means1 is found to possess certain properties2 thus it retains its conductivity for some little time after the agent which made it a conductor has ceased to act1 though the conductivity diminishes very rapidly and finally gets too small to be appreciable4 ,illustration3 ,,fig4 #e4 ,this and several other properties of conducting gas may readily be proved by the aid of the apparatus represented in fig4 #e4 ,v is a testing vessel in which an electroscope is placed4 ,two tubes ,a and ,c are fitted into the vessel1 ,a being connected with a water pump1 while the far end of ,c is in the region where the gas is exposed to the agent which makes it a conductor of electricity4 ,let us suppose that the gas is made conducting by ,rntgen rays produced by a vacuum tube which is placed in a box1 covered except for a window at ,b with lead so as to protect the electroscope from the direct action of the rays4 ,if a slow current of air is drawn by the water pump through the testing vessel1 the charge on the electroscope will gradually leak away4 ,the leak1 however1 ceases when the current of air is stopped4 ,this result shows that the gas retains its conductivity during the time taken by it to pass from one end to the other of the tube ,c4 ,the gas loses its conductivity when filtered through a plug of glass-wool1 or when it is made to bubble through water4 ,this can readily be proved by inserting in the tube ,c a plug of glass-wool or a water trap2 then if by working the pump a little harder the same current of air is produced as before1 it will be found that the electroscope will now retain its charge1 showing that the conductivity can1 as it were1 be filtered out of the gas4 ,the conductivity can also be removed from the gas by making the gas traverse a strong electric field4 ,we can show this by replacing the tube ,c by a metal tube with an insulated wire passing down the axis of the tube4 ,if there is no potential difference between the wire and the tube then the electroscope will leak when a current of air is drawn through the vessel1 but the leak will stop if a considerable difference of potential is maintained between the wire and the tube3 this shows that a strong electric field removes the conductivity from the gas4 ,the fact that the conductivity of the gas is removed by filtering shows that it is due to something mixed with the gas which is removed from it by filtration1 and since the conductivity is also removed by an electric field1 the cause of the conductivity must be charged with electricity so as to be driven to the sides of the tube by the electric force4 ,since the gas as a whole is not electrified either positively or negatively1 there must be both negative and positive charges in the gas1 the amount of electricity of one sign being equal to that of the other4 ,we are thus led to the conclusion that the conductivity of the gas is due to electrified particles being mixed up with the gas1 some of these particles having charges of positive electricity1 others of negative4 ,these electrified particles are called ions1 and the process by which the gas is made a conductor is called the ionization of the gas4 ,we shall show later that the charges and masses of the ions can be determined1 and that the gaseous ions are not identical with those met with in the electrolysis of solutions4 ,illustration3 ,,fig4 #f4 ,one very characteristic property of conduction of electricity through a gas is the relation between the current through the gas and the electric force which gave rise to it4 ,this relation is not in general that expressed by ,ohm's law1 which always1 as far as our present knowledge extends1 expresses the relation for conduction through metals and electrolytes4 ,with gases1 on the other hand1 it is only when the current is very small that ,ohm's law is true4 ,if we represent graphically by means of a curve the relation between the current passing between two parallel metal plates separated by ionized gas and the difference of potential between the plates1 the curve is of the character shown in fig4 #f when the ordinates represent the current and the abscissae the difference of potential between the plates4 ,we see that when the potential difference is very small1 i4e4 close to the origin1 the curve is approximately straight1 but that soon the current increases much less rapidly than the potential difference1 and that a stage is reached when no appreciable increase of current is produced when the potential difference is increased2 when this stage is reached the current is constant1 and this value of the current is called the saturation value4 ,when the potential difference approaches the value at which sparks would pass through the gas1 the current again increases with the potential difference2 thus the curve representing the relation between the current and potential difference over very wide ranges of potential difference has the shape shown in fig4 #g2 curves of this kind have been obtained by von ,schweidler 7,wien4 ,ber41 #ahii1 #ajh1 p4 #bgc71 and ,j4 ,e4 ,s4 ,townsend 7,phil4 ,mag41 #aija #f1 #a1 p4 #aih74 ,we shall discuss later the causes of the rise in the current with large potential differences1 when we consider ionization by collision4 ,the general features of the earlier part of the curve are readily explained on the ionization hypothesis4 ,on this view the ,rntgen rays or other ionizing agent acting on the gas between the plates1 produces positive and negative ions at a definite rate4 ,let us suppose that q positive and q negative ions are by this means produced per second between the plates2 these under the electric force will tend to move1 the positive ones to the negative plate1 the negative ones to the positive4 ,some of these ions will reach the plate1 others before reaching the plate will get so near one of the opposite sign that the attraction between them will cause them to unite and form an electrically neutral system2 when they do this they end their existence as ions4 ,the current between the plates is proportional to the number of ions which reach the plates per second4 ,now it is evident that we cannot go on taking more ions out of the gas than are produced2 thus we cannot1 when the current is steady1 have more than q positive ions driven to the negative plate per second1 and the same number of negative ions to the positive4 ,if each of the positive ions carries a charge of e units of positive electricity1 and if there is an equal and opposite charge on each negative ion1 then the maximum amount of electricity which can be given to the plates per second is qe1 and this is equal to the saturation current4 ,thus if we measure the saturation current1 we get a direct measure of the ionization1 and this does not require us to know the value of any quantity except the constant charge on the ion4 ,if we attempted to deduce the amount of ionization by measurements of the current before it was saturated1 we should require to know in addition the velocity with which the ions move under a given electric force1 the time that elapses between the liberation of an ion and its combination with one of the opposite sign1 and the potential difference between the plates4 ,thus if we wish to measure the amount of ionization in a gas we should be careful to see that the current is saturated4 ,illustration3 ,,fig4 #g4 ,the difference between conduction through gases and through metals is shown in a striking way when we use potential differences large enough to produce the saturation current4 ,suppose we have got a potential difference between the plates more than sufficient to produce the saturation current1 and let us increase the distance between the plates4 ,if the gas were to act like a metallic conductor this would diminish the current1 because the greater length would involve a greater resistance in the circuit4 ,in the case we are considering the separation of the plates will increase the current1 because now there is a larger volume of gas exposed to the rays2 there are therefore more ions produced1 and as the saturation current is proportional to the number of ions the saturation current is increased4 ,if the potential difference between the plates were much less than that required to saturate the current1 then increasing the distance would diminish the current2 the gas for such potential differences obeys ,ohm's law and the behaviour of the gaseous resistance is therefore similar to that of a metallic one4 ,in order to produce the saturation current the electric field must be strong enough to drive each ion to the electrode before it has time to enter into combination with one of the opposite sign4 ,thus when the plates in the preceding example are far apart1 it will take a larger potential difference to produce this current than when the plates are close together4 ,the potential difference required to saturate the current will increase as the square of the distance between the plates1 for if the ions are to be delivered in a given time to the plates their speed must be proportional to the distance between the plates4 ,but the speed is proportional to the electric force acting on the ion2 hence the electric force must be proportional to the distance between the plates1 and as in a uniform field the potential difference is equal to the electric force multiplied by the distance between the plates1 the potential difference will vary as the square of this distance4 ,the potential difference required to produce saturation will1 other circumstances being the same1 increase with the amount of ionization1 for when the number of ions is large and they are crowded together1 the time which will elapse before a positive one combines with a negative will be smaller than when the number of ions is small4 ,the ions have therefore to be removed more quickly from the gas when the ionization is great than when it is small2 thus they must move at a higher speed and must therefore be acted upon by a larger force4 ,when the ions are not removed from the gas1 they will increase until the number of ions of one sign which combine with ions of the opposite sign in any time is equal to the number produced by the ionizing agent in that time4 ,we can easily calculate the number of free ions at any time after the ionizing agent has commenced to act4 ,let q be the number of ions 7positive or negative7 produced in one cubic centimetre of the gas per second by the ionizing agent1 n#a1 n#b1 the number of free positive and negative ions respectively per cubic centimetre of the gas4 ,the number of collisions between positive and negative ions per second in one cubic centimetre of the gas is proportional to n#an#b4 ,if a certain fraction of the collisions between the positive and negative ions result in the formation of an electrically neutral system1 the number of ions which disappear per second on a cubic centimetre will be equal to alphan#a n#b1 where alpha is a quantity which is independent of n#a1 n#b2 hence if t is the time since the ionizing agent was applied to the gas1 we have dn#a_/;dt q - alphan#a n#b1 dn#b_/;dt q - alphan#a n#b4 ,thus n#a - n#b is constant1 so if the gas is uncharged to begin with1 n#a will always equal n#b4 ,putting n#a n#b n we have dn_/dt q - alphan 7#a71 the solution of which is1 since n #j when t #j1 k7epsilon#bkalphat - #a7 n ---------------------------- 7#b7 epsilon#bkalphat #a if k q_/alpha4 ,now the number of ions when the gas has reached a steady state is got by putting t equal to infinity in the preceding equation1 and is therefore given by the equation n#j k root7q_/alpha74 ,we see from equation 7#a7 that the gas will not approximate to its steady state until #bkalphat is large1 that is until t is large compared with #a_/bkalpha or with #a_/broot7qalpha74 ,we may thus take #a_/broot7qalpha7 as a measure of the time taken by the gas to reach a steady state when exposed to an ionizing agent2 as this time varies inversely as rootq we see that when the ionization is feeble it may take a very considerable time for the gas to reach a steady state4 ,thus in the case of our atmosphere where the production of ions is only at the rate of about #cj per cubic centimetre per second1 and where1 as we shall see1 alpha is about #aj-f1 it would take some minutes for the ionization in the air to get into a steady state if the ionizing agent were suddenly applied4 ,we may use equation 7#a7 to determine the rate at which the ions disappear when the ionizing agent is removed4 ,putting q#j in that equation we get dn_/alphat -alphan4 ,hence n n#j_/7a n#j;alphat7 7#c71 where n#j is the number of ions when t #j4 ,thus the number of ions falls to one-half its initial value in the time #a_/n#j;alpha4 ,the quantity alpha is called the coefficient of recombination1 and its value for different gases has been determined by ,rutherford 7,phil4 ,mag4 #ahig #e1 #dd1 p4 #dbb71 ,townsend 7,phil4 ,trans41 #aijj1 #aic1 p4 #abi71 ,mc,clung 7,phil4 ,mag41 #aijb #f1 #c1 p4 #bhc71 ,langevin 7,ann4 chim4 phys4 #g1 #bh1 p4 #bhi71 ,retschinsky 7,ann4 d4 ,phys41 #aije1 #ag1 p4 #eah71 ,hendred 7,phys4 ,rev41 #aije1 #ba1 p4 #cad74 ,the values of alpha_/e1 e being the charge on an ion in electrostatic measure as determined by these observers for different gases1 is given in the following table3-- ---------------------------------------- ----------------- ,townsend4 ,mc,clung4 ,langevin4,retschinsky4 ,hendred4 ---------------------------------------- ----------------- ,air #cdbj #cchj #cbjj #dadj #cejj ,o#b #cchj ,,co#b #cejj #cdij #cdjj ,h#b #cjbj #bidj ---------------------------------------- ----------------- ,the gases in these experiments were carefully dried and free from dust2 the apparent value of alpha is much increased when dust or small drops of water are present in the gas1 for then the ions get caught by the dust particles1 the mass of a particle is so great compared with that of an ion that they are practically immovable under the action of the electric field1 and so the ions clinging to them escape detection when electrical methods are used4 ,taking e as #c4e #aj-aj1 we see that alpha is about #a4b #aj-f1 so that the number of recombinations in unit time between n positive and n negative ions in unit volume is #a4b #aj-fn4 ,the kinetic theory of gases shows that if we have n molecules of air per cubic centimetre1 the number of collisions per second is #a4b #aj-ajn at a temperature of #j ,c4 ,thus we see that the number of recombinations between oppositely charged ions is enormously greater than the number of collisions between the same number of neutral molecules4 ,we shall see that the difference in size between the ion and the molecule is not nearly sufficient to account for the difference between the collisions in the two cases2 the difference is due to the force between the oppositely charged ions1 which drags ions into collisions which but for this force would have missed each other4 ,several methods have been used to measure alpha4 ,in one method air1 exposed to some ionizing agent at one end of a long tube1 is slowly sucked through the tube and the saturation current measured at different points along the tube4 ,these currents are proportional to the values of n at the place of observation3 if we know the distance of this place from the end of the tube when the gas was ionized and the velocity of the stream of gas1 we can find t in equation 7#c71 and knowing the value of n we can deduce the value of alpha from the equation #a_/n#a - #a_/n#b alpha7t#a - t#b71 where n#a1 n#b are the values of n at the times t#a1 t#b respectively4 ,in this method the tubes ought to be so wide that the loss of ions by diffusion to the sides of the tube is negligible4 ,there are other methods which involve the knowledge of the speed with which the ions move under the action of known electric forces2 we shall defer the consideration of these methods until we have discussed the question of these speeds4 ,in measuring the value of alpha it should be remembered that the theory of the methods supposes that the ionization is uniform throughout the gas4 ,if the total ionization throughout a gas remains constant1 but instead of being uniformly distributed is concentrated in patches1 it is evident that the ions will recombine more quickly in the second case than in the first1 and that the value of alpha will be different in the two cases4 ,this probably explains the large values of alpha obtained by ,retschinsky1 who ionized the gas by the alpha rays from radium1 a method which produces very patchy ionization4 ,variation of alpha with the ,pressure of the ,gas4--,all observers agree that there is little variation in alpha with the pressures for pressures of between #e and #a atmospheres2 at lower pressures1 however1 the value of alpha seems to diminish with the pressure3 thus ,langevin 7,ann4 chim4 phys41 #aijc1 #bh1 p4 #bhg7 found that at a pressure of #a_/e of an atmosphere the value of alpha was about #a_/e of its value at atmospheric pressure4 ,variation of alpha with the ,temperature4--,erikson 7,phil4 ,mag41 ,aug4 #aiji7 has shown that the value of alpha for air increases as the temperature diminishes1 and that at the temperature of liquid air -#ahj ,c41 it is more than twice as great as at #ab ,c4 ,since1 as we have seen1 the recombination is due to the coming together of the positive and negative ions under the influence of the electrical attraction between them1 it follows that a large electric force sufficient to overcome this attraction would keep the ions apart and hence diminish the coefficient of recombination4 ,simple considerations1 however1 will show that it would require exceedingly strong electric fields to produce an appreciable effect4 ,the value of alpha indicates that for two oppositely charged ions to unite they must come within a distance of about #a4e #aj-f centimetres2 at this distance the attraction between them is e #ajab_/b4be1 and if ,x is the external electric force1 the force tending to pull them apart cannot be greater than ,xe2 if this is to be comparable with the attraction1 ,x must be comparable with e #ajab_/b4be1 or putting e #d #aj-aj1 with #a4h #aj2 this is #ed1jjj volts per centimetre1 a force which could not be applied to gas at atmospheric pressure without producing a spark4 ,diffusion of the ,ions4--,the ionized gas acts like a mixture of gases1 the ions corresponding to two different gases1 the non-ionized gas to a third4 ,if the concentration of the ions is not uniform1 they will diffuse through the non-ionized gas in such a way as to produce a more uniform distribution4 ,a very valuable series of determinations of the coefficient of diffusion of ions through various gases has been made by ,townsend 7,phil4 ,trans41 #aijj1 ,a1 #aic1 p4 #abi74 ,the method used was to suck the ionized gas through narrow tubes2 by measuring the loss of both the positive and negative ions after the gases had passed through a known length of tube1 and allowing for the loss by recombination1 the loss by diffusion and hence the coefficient of diffusion could be determined4 ,the following tables give the values of the coefficients of diffusion ,d on the ,c4,g4,s4 system of units as determined by ,townsend3-- ,table ,i4--,coefficients of ,diffusion 7,d7 in ,dry ,gases4 ---------------------------------------- ----------------- ,gas4 ,d for ions4,d for -ions4,mean ,value ,ratio of ,d for of ,d4 - to ,d for 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--,coefficients of ,diffusion in ,moist ,gases4 ---------------------------------------- ----------------- ,gas4 ,d for ions4,d for -ions4,mean ,value ,ratio of ,d for of ,d4 - to ,d for 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 ---------------------------------------- ----------------- ,it is interesting to compare with these coefficients the values of ,d when various gases diffuse through each other4 ,d for hydrogen through air is 4#fcd1 for oxygen through air 4#agg1 for the vapour of isobutyl amide through air 4#jdb4 ,we thus see that the velocity of diffusion of ions through air is much less than that of the simple gas1 but that it is quite comparable with that of the vapours of some complex organic compounds4 ,the preceding tables show that the negative ions diffuse more rapidly than the positive1 especially in dry gases4 ,the superior mobility of the negative ions was observed first by ,zeleny 7,phil4 ,mag41 #ahih #e1 #df1 p4 #abj71 who showed that the velocity of the negative ions under an electric force is greater than that of the positive4 ,it will be noticed that the difference between the mobility of the negative and the positive ions is much more pronounced in dry gases than in moist4 ,the difference in the rates of diffusion of the positive and negative ions is the reason why ionized gas1 in which1 to begin with1 the positive and negative charges were of equal amounts1 sometimes becomes electrified even although the gas is not acted upon by electric forces4 ,thus1 for example1 if such gas be blown through narrow tubes1 it will be positively electrified when it comes out1 for since the negative ions diffuse more rapidly than the positive1 the gas in its passage through the tubes will lose by diffusion more negative than positive ions and hence will emerge positively electrified4 ,zeleny snowed that this effect does not occur when1 as in carbonic acid gas1 the positive and negative ions diffuse at the same rates4 ,townsend 7loc4 cit47 showed that the coefficient of diffusion of the ions is the same whether the ionization is produced by ,rntgen rays1 radioactive substances1 ultra-violet light1 or electric sparks4 ,the ions produced by chemical reactions and in flames are much less mobile2 thus1 for example1 ,bloch 7,ann4 chim4 phys41 #aije #h1 #d1 p4 #be7 found that for the ions produced by drawing air over phosphorus the value of alpha_/e was between #a and #f instead of over #cjjj1 the value when the air was ionized by ,rntgen rays4 ,velocity of ,ions in an ,electric ,field4--,the velocity of ions in an electric field1 which is of fundamental importance in conduction1 is very closely related to the coefficient of diffusion4 ,measurements of this velocity for ions produced by ,rntgen rays have been made by ,rutherford 7,phil4 ,mag4 #e1 #dd1 p4 #dbb71 ,zeleny 7,phil4 ,mag4 #e1 #df1 p4 #abj71 ,langevin 7,ann4 ,chim4 ,phys41 #aijc1 #bh1 p4 #bhi71 ,phillips 7,proc4 ,roy4 ,soc4 #gh1 ,a1 p4 #afg71 and ,wellisch 7,phil4 ,trans41 #aiji1 #bji1 p4 #bdi74 ,the ions produced by radioactive substance have been investigated by ,rutherford 7,phil4 ,mag4 #e1 #dg1 p4 #aji7 and by ,franck and ,pohl 7,verh4 deutsch4 phys4 ,gesell41 #aijg1 #i1 p4 #fi71 and the negative ions produced when ultra-violet light falls on a metal plate by ,rutherford 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #dja74 ,h4 ,a4 ,wilson 7,phil4 ,trans4 #aib1 p4 #d,o#i71 ,marx 7,ann4 de ,phys4 #aa1 p4 #gfe71 ,moreau 7,journ4 de ,phys4 #d1 #aa1 p4 #eeh2 ,ann4 ,chim4 ,phys4 #g1 #cj1 p4 #e7 and ,gold 7,proc4 ,roy4 ,soc4 #gi1 p4 #dc7 have investigated the velocities of ions produced by putting various salts into flames2 ,mc,clelland 7,phil4 ,mag4 #df1 p4 #bi7 the velocity of the ions in gases sucked from the neighbourhood of flames and arcs2 ,townsend 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #cde7 and ,bloch 7loc4 cit47 the velocity of ions produced by chemical reaction2 and ,chattock 7,phil4 ,mag4 #e1 #dh1 p4 #dja7 the velocity of the ions produced when electricity escapes from a sharp needle point into a gas4 ,several methods have been employed to determine these velocities4 ,the one most frequently employed is to find the electromotive intensity required to force an ion against the stream of gas moving with a known velocity parallel to the lines of electric force4 ,thus1 of two perforated plane electrodes vertically over each other1 suppose the lower to be positively1 the upper negatively electrified1 and suppose that the gas is streaming vertically downwards with the velocity ,v2 then unless the upward velocity of the positive ion is greater than ,v1 no positive electricity will reach the upper plate4 ,if we increase the strength of the field between the plates1 and hence the upward velocity of the positive ion1 until the positive ions just begin to reach the upper plate1 we know that with this strength of field the velocity of the positive ion is equal to ,v4 ,by this method1 which has been used by ,rutherford1 ,zeleny and ,h4 ,a4 ,wilson1 the velocity of ions in fields of various strengths has been determined4 ,the arrangement used by ,zeleny is represented in fig4 #h4 ,p and ,q are square brass plates4 ,they are bored through their centres1 and to the openings the tubes ,r and ,s are attached1 the space between the plates being covered in so as to form a closed box4 ,k is a piece of wire gauze completely covering the opening in ,q2 ,t is an insulated piece of wire gauze nearly but not quite filling the opening in the plate ,p1 and connected with one pair of quadrants of an electrometer ,e4 ,a plug of glass wool ,g filters out the dust from a stream of gas which enters the vessel by the tube ,d and leaves it by ,f2 this plug also makes the velocity of the flow of the gas uniform across the section of the tube4 ,the ,rntgen rays to ionize the gas were produced by a bulb at ,o1 the bulb and coil being in a lead-covered box1 with an aluminium window through which the rays passed4 ,q is connected with one pole of a battery of cells1 ,p and the other pole of the battery are put to earth4 ,the changes in the potential of ,t are due to ions giving up their charges to it4 ,with a given velocity of air-blast the potential of ,t was found not to change unless the difference of potential between ,p and ,q exceeded a critical value4 ,the field corresponding to this critical value thus made the ions move with the known velocity of the blast4 ,illustration3 ,,fig4 #h4 ,illustration3 ,,fig4 #i4 ,another method which has been employed by ,rutherford and ,mc,clelland is based on the action of an electric field in destroying the conductivity of gas streaming through it4 ,suppose that ,,bab1 ,,dcd 7fig4 #i7 are a system of parallel plates boxed in so that a stream of gas1 after flowing between ,,bb1 passes between ,,dd without any loss of gas in the interval4 ,suppose the plates ,,dd are insulated1 and connected with one pair of quadrants of an electrometer1 by charging up ,c to a sufficiently high potential we can drive all the positive ions which enter the system ,,dcd against the plates ,d2 this will cause a deflexion of the electrometer1 which in one second will be proportional to the number of positive ions which have entered the system in that time4 ,if we charge ,a up to a high potential1 ,b being put to earth1 we shall find that the deflexion of the electrometer connected with ,,dd is less than it was when ,a and ,b were at the same potential1 because some of the positive ions in their passage through ,,bab are driven against the plates ,b4 ,if u is the velocity along the lines of force in the uniform electric field between ,a and ,b1 and t the time it takes for the gas to pass through ,,bab1 then all the positive ions within a distance ut of the plates ,b will be driven up against these plates1 and thus if the positive ions are equally distributed through the gas1 the number of positive ions which emerge from the system when the electric field is on will bear to the number which emerge when the field is off the ratio of #a - ut_/l to unity1 where l is the distance between ,a and ,b4 ,this ratio is equal to the ratio of the deflexions in one second of the electrometer attached to ,d1 hence the observations of this instrument give #a - ut_/l4 ,if we know the velocity of the gas and the length of the plates ,a and ,b1 we can determine t1 and since l can be easily measured1 we can find u1 the velocity of the positive ion in a field of given strength4 ,by charging ,a and ,c negatively instead of positively we can arrive at the velocity of the negative ion4 ,in practice it is more convenient to use cylindrical tubes with coaxial wires instead of the systems of parallel plates1 though in this case the calculation of the velocity of the ions from the observations is a little more complicated1 inasmuch as the electric field is not uniform between the tubes4 ,illustration3 ,,fig4 #aj4 ,a method which gives very accurate results1 though it is only applicable in certain cases1 is the one used by ,rutherford to measure the velocity of the negative ions produced close to a metal plate by the incidence on the plate of ultra-violet light4 ,the principle of the method is as follows3--,,ab 7fig4 #aj7 is an insulated horizontal plate of well-polished zinc1 which can be moved vertically up and down by means of a screw2 it is connected with one pair of quadrants of an electrometer1 the other pair of quadrants being put to earth4 ,,cd is a base-plate with a hole ,,ef in it2 this hole is covered with fine wire gauze1 through which ultra-violet light passes and falls on the plate ,,ab4 ,the plate ,,cd is connected with an alternating current dynamo1 which produces a simply-periodic potential difference between ,,ab and ,,cd1 the other pole being put to earth4 ,suppose that at any instant the plate ,,cd is at a higher potential than ,,ab1 then the negative ions from ,,ab will move towards ,,cd1 and will continue to do so as long as the potential of ,,cd is higher than that of ,,ab4 ,if1 however1 the potential difference changes sign before the negative ions reach ,,cd1 these ions will go back to ,,ab4 ,thus ,,ab will not lose any negative charge unless the distance between the plates ,,ab and ,,cd is less than the distance traversed by the negative ion during the time the potential of ,,cd is higher than that of ,,ab4 ,by altering the distance between the plates until ,,cd just begins to lose a negative charge1 we find the velocity of the negative ion under unit electromotive intensity4 ,for suppose the difference of potential between ,,ab and ,,cd is equal to a sin pt1 then if d is the distance between the plates1 the electric intensity is equal to a sin pt_/d2 if we suppose the velocity of the ion is proportional to the electric intensity1 and if u is the velocity for unit electric intensity1 the velocity of the negative ion will be ua sin pt_/d4 ,hence if x represent the distance of the ion from ,,ab dx ua --- --- sin pt d,t d ua x ----7#a - cos pt71 if x #j when t #j4 pd ,thus the greatest distance the ion can get from the plate is equal to #b;au_/pd1 and if the distance between the plates is gradually reduced to this value1 the plate ,,ab will begin to lose a negative charge2 hence when this happens d #b;au_/pd1 or u pd_/#b;a1 an equation by means of which we can find u4 ,in this form the method is not applicable when ions of both signs are present4 ,franck and ,pohl 7,verh4 deutsch4 physik4 ,gesell4 #aijg1 #i1 p4 #fi7 have by a slight modification removed this restriction4 ,the modification consists in confining the ionization to a layer of gas below the gauze ,,ef4 ,if the velocity of the positive ions is to be determined1 these ions are forced through the gauze by applying to the ionized gas a small constant electric force acting upwards2 if negative ions are required1 the constant force is reversed4 ,after passing through the gauze the ions are acted upon by alternating forces as in ,rutherford's method4 ,langevin 7,ann4 chim4 phys41 #aijc1 #bh1 p4 #bhi7 devised a method of measuring the velocity of the ions which has been extensively used2 it has the advantage of not requiring the rate of ionization to remain uniform4 ,the general idea is as follows4 ,suppose that we expose the gas between two parallel plates ,a1 ,b to ,rntgen rays or some other ionizing agent1 then stop the rays and apply a uniform electric field to the region between the plates4 ,if the force on the positive ion is from ,a to ,b1 the plate ,b will receive a positive charge of electricity4 ,after the electric force has acted for a time ,t reverse it4 ,b will now begin to receive negative electricity and will go on doing so until the supply of negative ions is exhausted4 ,let us consider how the quantity of positive electricity received by ,b will vary with ,t4 ,to fix our ideas1 suppose the positive ions move more slowly than the negative2 let ,t#b and ,t#a be respectively the times taken by the positive and negative ions to move under the electric field through a distance equal to ,,ab1 the distance between the planes4 ,then if ,t is greater than ,t#b all the ions will have been driven from between the plates before the field is reversed1 and therefore the positive charge received by ,b will not depend upon ,t4 ,next let ,t be less than ,t#b but greater than ,t#a2 then at the time when the field is reversed all the negative ions will have been driven from between the plates1 so that the positive charge received by ,b will not be neutralized by the arrival of fresh ions coming to it after the reversal of the field4 ,the number of positive ions driven against the plate ,b will be proportional to ,t4 ,thus if we measure the value of the positive charge on ,b for a series of values of ,t1 each value being less than the preceding1 we shall find that until ,t reaches a certain value the charge remains constant1 but as soon as we reduce the time below this value the charge diminishes4 ,the value of ,t when the diminution in the field begins is ,t#b1 the time taken for a positive ion to cross from ,a to ,b under the electric field2 thus from ,t#b we can calculate the velocity of the positive ion in this field4 ,if we still further diminish ,t1 we shall find that we reach a value when the diminution of the positive charge on ,b with the time suddenly becomes much more rapid2 this change occurs when ,t falls below ,t#a the time taken for the negative ions to go from one plate to the other1 for now when the field is reversed there are still some negative ions left between the plates1 and these will be driven against ,b and rob it of some of the positive charge it had acquired before the field was reversed4 ,by observing the time when the increase in the rate of diminution of the positive charge with the time suddenly sets in we can determine ,t#a1 and hence the velocity of the negative ions4 ,the velocity of the ions produced by the discharge of electricity from a fine point was determined by ,chattock by an entirely different method4 ,in this case the electric field is so strong and the velocity of the ion so great that the preceding methods are not applicable4 ,suppose ,p represents a vertical needle discharging electricity into air1 consider the force acting on the ions included between two horizontal planes ,a1 ,b4 ,if ,p is the density of the electrification1 and ,z the vertical component of the electric intensity1 ,f the resultant force on the ions between ,a and ,b is vertical and equal to _/ _/ _/ ,zrhodxdydz4 _/_/_/ ,let us suppose that the velocity of the ion is proportional to the electric intensity1 so that if w is the vertical velocity of the ions1 which are supposed all to be of one sign1 w ,,rz4 ,substituting this value of ,z1 the vertical force on the ions between ,a and ,b is equal to #a _/ _/ _/ - wrhodxdydz4 ,r _/_/_/ ,but integralintegralwrhodxdy iota1 where iota is the current streaming from the point4 ,this current1 which can be easily measured by putting a galvanometer in series with the discharging point1 is independent of z1 the vertical distance of a plane between ,a and ,b below the charging point4 ,hence we have iota _/ iota ,f ------ dz ------z4 ,r _/ ,r ,this force must be counterbalanced by the difference of gaseous pressures over the planes ,a and ,b2 hence if p,b and p,a denote respectively the pressures over ,b and ,a1 we have iota p,b - p,a ------ z4 ,r ,hence by the measurement of these pressures we can determine ,r1 and hence the velocity with which an ion moves under a given electric intensity4 ,there are other methods of determining the velocities of the ions1 but as these depend on the theory of the conduction of electricity through a gas containing charged ions1 we shall consider them in our discussion of that theory4 ,by the use of these methods it has been shown that the velocities of the ions in a given gas are the same whether the ionization is produced by ,rntgen rays1 radioactive substances1 ultra-violet light1 or by the discharge of electricity from points4 ,when the ionization is produced by chemical action the ions are very much less mobile1 moving in the same electric field with a velocity less than one-thousandth part of the velocity of the first kind of ions4 ,on the other hand1 as we shall see later1 the velocity of the negative ions in flames is enormously greater than that of even the first kind of ion under similar electric fields and at the same pressure4 ,but when these negative ions get into the cold part of the flame1 they move sluggishly with velocities of the order of those possessed by the second kind4 ,the results of the various determinations of the velocities of the ions are given in the following table4 ,the velocities are in centimetres per second under an electric force of one volt per centimetre1 the pressure of the gas being #a atmosphere4 ,v denotes the velocity of the positive ion1 ,v- that of the negative4 ,v is the mean velocity of the positive and negative ions4 ,velocities of ,ions4--,ions produced by ,rntgen ,rays4 ---------------------------------------- ----------------- ,gas4 ,v4 ,v-4 ,v4 ,observer4 ---------------------------------------- ----------------- ,air 44 44 #a4f ,rutherford ,air 7dry7 #a4cf #a4hg 44 ,zeleny #a4fj #a4gj 44 ,langevin #a4ci #a4gh 44 ,phillips #a4ed #a4gh 44 ,wellisch ,air 7moist7 #a4cg #a4ha 44 ,zeleny ,oxygen 7dry7 #a4cf #a4hj 44 ,oxygen 7moist7 #a4bi #a4eb 44 ,carbonic acid 7dry7 #j4gf #j4ha 44 #j4hf #j4ij 44 ,langevin #j4ha #j4he 44 ,wellisch ,carbonic acid 7moist7 #j4hb #j4ge 44 ,zeleny ,hydrogen 7dry7 #f4gj #g4ie 44 ,nitrogen 44 44 #a4f ,rutherford ,sulphur dioxide #j4dd #j4da 44 ,wellisch ,hydrochloric acid 44 44 #a4bg ,rutherford ,chlorine 44 44 #a4j ,helium 7dry7 #e4ji #f4ca 44 ,franck and ,pohl ,carbon monoxide #a4aj #a4ad 44 ,wellisch ,nitrous oxide #j4hb #j4ij 44 ,ammonia #j4gd #j4hj 44 ,aldehyde #j4ca #j4cj 44 ,ethyl alcohol #j4cd #j4bg 44 ,acetone #j4ca #j4bi 44 ,ethyl chloride #j4cc #j4ca 44 ,pentane #j4cf #j4ce 44 ,methyl acetate #j4cc #j4cf 44 ,ethyl formate #j4cj #j4ca 44 ,ethyl ether #j4bi #j4ca 44 ,ethyl acetate #j4ca #j4bh 44 ,methyl bromide #j4bi #j4bh 44 ,methyl iodide #j4ba #j4bb 44 ,carbon tetrachloride #j4cj #j4ca 44 ,ethyl iodide #j4ag #j4af 44 ---------------------------------------- ----------------- ,ions produced by ,ultra-,violet ,light4 ,air #a4d ,rutherford ,hydrogen #c4i ,rutherford ,carbonic acid #j4gh ,rutherford ,ions in ,gases sucked from ,flames4 ,velocities varying from 4#jd to 4#bc ,mc,clelland ,ions in ,flames containing ,salts4 ,negative ions #ab4i cm4_/sec4 ,gold ions for salts of ,li1 ,na1 ,k1 ,rb1 ,cs #fb ,h4 ,a4 ,wilson #bjj ,marx #hj ,moreau ,ions liberated by ,chemical ,action4 ,velocities of the order of #j4jjje cm4_/sec4 ,bloch ,ions from ,point ,discharge4 ---------------------------------------- ---- ,hydrogen #e4d #g4dc #f4da ,chattock ,carbonic acid #j4hc #j4ibe #j4hh ,chattock ,air #a4cb #a4hj #a4ee ,chattock ,oxygen #a4cj #a4he #a4eg ,chattock ---------------------------------------- ---- ,it will be seen from this table that the greater mobility of the negative ions is very much more marked in the case of the lighter and simpler gases than in that of the heavier and more complicated ones2 with the vapours of organic substances there seems but little difference between the mobilities of the positive and negative ions1 indeed in one or two cases the positive one seems slightly but very slightly the more mobile of the two4 ,in the case of the simple gases the difference is much greater when the gases are dry than when they are moist4 ,it has been shown by direct experiment that the velocities are directly proportional to the electric force4 ,variation of ,velocities with ,pressure4--,until the pressure gets low the velocities of the ions1 negative as well as positive1 vary inversely as the pressure4 ,langevin 7loc4 cit47 was the first to show that at very low pressures the velocity of the negative ions increases more rapidly as the pressure is diminished than this law indicates4 ,if the nature of the ion did not change with the pressure1 the kinetic theory of gases indicates that the velocity would vary inversely as the pressure1 so that ,langevin's results indicate a change in the nature of the negative ion when the pressure is diminished below a certain value4 ,langevin's results are given in the following table1 where p represents the pressure measured in centimetres of mercury1 ,v and ,v- the velocities of the positive and negative ions in air under unit electrostatic force1 i4e4 #cjj volts per centimetre3-- ---------------------------------------- ---- ,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 ---------------------------------------- ,the increase in the case of p,v- indicates that the structure of the negative ion gets simpler as the pressure is reduced4 ,wallisch in some experiments made at the ,cavendish ,laboratory found that the diminution in the value of p,v- at low pressures is much more marked in some gases than in others1 and in some gases he failed to detect it2 but it must be remembered that it is difficult to get measurements at pressures of only a few millimetres1 as the amount of ionization is so exceedingly small at such pressures that the quantities to be observed are hardly large enough to admit of accurate measurements by the methods available at higher pressures4 ,effect of ,temperature on the ,velocity of the ,ions4--,phillips 7,proc4 ,roy4 ,soc41 #aijf1 #gh1 p4 #afg7 investigated1 using ,langevin's method1 the velocities of the and - ions through air at atmospheric pressure at temperatures ranging from that of boiling liquid air to #daa ,c42 ,r#a and ,r#b are the velocities of the and - ions respectively when the force is a volt per centimetre4 ----------------------------------- ,r#a4 ,r#b4 ,temperature ,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 that except in the case of the lowest temperature1 that of liquid air1 where there is a great drop in the velocity1 the velocities of the ions are proportional to the absolute temperature4 ,on the hypothesis of an ion of constant size we should1 from the kinetic theory of gases1 expect the velocity to be proportional to the square root of the absolute temperature1 if the charge on the ion did not affect the number of collisions between the ion and the molecules of the gas through which it is moving4 ,if the collisions were brought about by the electrical attraction between the ions and the molecules1 the velocity would be proportional to the absolute temperature4 ,h4 ,a4 ,wilson 7,phil4 ,trans4 #aib1 p4 #dii71 in his experiments on the conduction of flames and hot gases into which salts had been put1 found that the velocity of the positive ions in flames at a temperature of #bjjj ,c4 containing the salts of the alkali metals was #fb cm4_/sec4 under an electric force of one volt per centimetre1 while the velocity of the positive ions in a stream of hot air at #ajjj ,c4 containing the same salts was only #g cm4_/sec4 under the same force4 ,the great effect of temperature is also shown in some experiments of ,mc,clelland 7,phil4 ,mag4 #e1 #df1 p4 #bi7 on the velocities of the ions in gases drawn from ,bunsen flames and arcs2 he found that these depended upon the distance the gas had travelled from the flame4 ,thus1 the velocity of the ions at a distance of #e4e cm4 from the ,bunsen flame when the temperature was #bcj ,c4 was 4#bc cm4_/sec4 for a volt per centimetre2 at a distance of #aj cm4 from the flame when the temperature was #afj ,c4 the velocity was 4#ba cm4_/sec2 while at a distance of #ad4e cm4 from the flame when the temperature was #aje ,c4 the velocity was only 4#jd cm4_/sec4 ,if the temperature of the gas at this distance from the flame was raised by external means1 the velocity of the ions increased4 ,we can derive some information as to the constitution of the ions by calculating the velocity with which a molecule of the gas would move in the electric field if it carried the same charge as the ion4 ,from the theory of the diffusion of gases1 as developed by ,maxwell1 we know that if the particles of a gas ,a are surrounded by a gas ,b1 then1 if the partial pressure of ,a is small1 the velocity u with which its particles will move when acted upon by a force ,xe is given by the equation ,xe u ------- ,d1 7p#a_/,n#a7 where ,d represents the coefficient of inter-diffusion of ,a into ,b1 and ,n#a the number of particles of ,a per cubic centimetre when the pressure due to ,a is p#a4 ,let us calculate by this equation the velocity with which a molecule of hydrogen would move through hydrogen if it carried the charge carried by an ion1 which we shall prove shortly to be equal to the charge carried by an atom of hydrogen in the electrolysis of solutions4 ,since p#a_/,n#a is independent of the pressure1 it is equal to ,pi_/,n1 where ,pi is the atmospheric pressure and ,n the number of molecules in a cubic centimetre of gas at atmospheric pressure4 ,now ,ne #a4bb #ajaj1 if e is measured in electrostatic units2 ,pi #ajf and ,d in this case is the coefficient of diffusion of hydrogen into itself1 and is equal to #a4g4 ,substituting these values we find u #a4ig #ajd,x4 ,if the potential gradient is #a volt per centimetre1 ,x #a_/cjj4 ,substituting this value for ,x1 we find u #ff cm4_/sec1 for the velocity of a hydrogen molecule4 ,we have seen that the velocity of the ion in hydrogen is only about #e cm4_/sec1 so that the ion moves more slowly than it would if it were a single molecule4 ,one way of explaining this is to suppose that the ion is bigger than the molecule1 and is in fact an aggregation of molecules1 the charged ion acting as a nucleus around which molecules collect like dust round a charged body4 ,this view is supported by the effect produced by moisture in diminishing the velocity of the negative ion1 for1 as ,c4 ,t4 ,r4 ,wilson 7,phil4 ,trans4 #aic1 p4 #bhi7 has shown1 moisture tends to collect round the ions1 and condenses more easily on the negative than on the positive ion4 ,in connexion with the velocities of ions in the gases drawn from flames1 we find other instances which suggest that condensation takes place round the ions4 ,an increase in the size of the system is not1 however1 the only way by which the velocity might fall below that calculated for the hydrogen molecule1 for we must remember that the hydrogen molecule1 whose coefficient of diffusion is #a4g1 is not charged1 while the ion is4 ,the forces exerted by the ion on the other molecules of hydrogen are not the same as those which would be exerted by a molecule of hydrogen1 and as the coefficient of diffusion depends on the forces between the molecules1 the coefficient of diffusion of a charged molecule into hydrogen might be very different from that of an uncharged one4 ,wellisch 7loc4 cit47 has shown that the effect of the charge on the ion is sufficient in many cases to explain the small velocity of the ions1 even if there were no aggregation4 ,mixture of ,gases4--,the ionization of a mixture of gases raises some very interesting questions4 ,if we ionize a mixture of two very different gases1 say hydrogen and carbonic acid1 and investigate the nature of the ions by measuring their velocities1 the question arises1 shall we find two kinds of positive and two kinds of negative ions moving with different velocities1 as we should do if some of the positive ions were positively charged hydrogen molecules1 while others were positively charged molecules of carbonic acid2 or shall we find only one velocity for the positive ions and one for the negative8 ,many experiments have been made on the velocity of ions in mixtures of two gases1 but as yet no evidence has been found of the existence of two different kinds of either positive or negative ions in such mixtures1 although some of the methods for determining the velocities of the ions1 especially ,langevin's1 ought to give evidence of this effect1 if it existed4 ,the experiments seem to show that the positive 7and the same is true for the negative7 ions in a mixture of gases are all of the same kind4 ,this conclusion is one of considerable importance1 as it would not be true if the ions consisted of single molecules of the gas from which they are produced4 ,recombination4--,several methods enable us to deduce the coefficient of recombination of the ions when we know their velocities4 ,perhaps the simplest of these consists in determining the relation between the current passing between two parallel plates immersed in ionized gas and the potential difference between the plates4 ,for let q be the amount of ionization1 i4e4 the number of ions produced per second per unit volume of the gas1 ,a the area of one of the plates1 and d the distance between them2 then if the ionization is constant through the volume1 the number of ions of one sign produced per second in the gas is q,ad4 ,now if i is the current per unit area of the plate1 e the charge on an ion1 i,a_/e ions of each sign are driven out of the gas by the current per second4 ,in addition to this source of loss of ions there is the loss due to the recombination2 if n is the number of positive or negative ions per unit volume1 then the number which recombine per second is alphan per cubic centimetre1 and if n is constant through the volume of the gas1 as will approximately be the case if the current through the gas is only a small fraction of the saturation current1 the number of ions which disappear per second through recombination is alphan,ad4 ,hence1 since when the gas is in a steady state the number of ions produced must be equal to the number which disappear1 we have q,ad i,a_/e alphan,ad1 q i_/ed alphan#b4 ,if u#a and u#b are the velocities with which the positive and negative ions move1 nu#a;e and nu#b;e are respectively the quantities of positive electricity passing in one direction through unit area of the gas per second1 and of negative in the opposite direction1 hence i nu#a;e nu#b;e4 ,if ,x is the electric force acting on the gas1 k#a and k#b the velocities of the positive and negative ions under unit force1 u#a k#a,x1 u#b k#b,x2 hence n i_/7k#a k#b7,xe1 and we have i alphai q -- --------------4 ed 7k#a k#b7;e,x ,but qed is the saturation current per unit area of the plate2 calling this ,i1 we have dalphai ,i - i ------------- e7k#a k#b7,x or idalpha ,x ------------------4 e7,i - i77k#a k#b7 ,hence if we determine corresponding values of ,x and i we can deduce the value of alpha_/e if we also know 7k#a k#b74 ,the value of ,i is easily determined1 as it is the current when ,x is very large4 ,the preceding result only applies when i is small compared with ,i1 as it is only in this case that the values of n and ,x are uniform throughout the volume of the gas4 ,another method which answers the same purpose is due to ,langevin 7,ann4 ,chim4 ,phys41 #aijc1 #bh1 p4 #bhi72 it is as follows4 ,let ,a and ,b be two parallel planes immersed in a gas1 and let a slab of the gas bounded by the planes a1 b parallel to ,a and ,b be ionized by an instantaneous flash of ,rntgen rays4 ,if ,a and ,b are at different electric potentials1 then all the positive ions produced by the rays will be attracted by the negative plate and all the negative ions by the positive1 if the electric field were exceedingly large they would reach these plates before they had time to recombine1 so that each plate would receive ,n#j ions if the flash of ,rntgen rays produced ,n#j positive and ,n#j negative ions4 ,with weaker fields the number of ions received by the plates will be less as some of them will recombine before they can reach the plates4 ,we can find the number of ions which reach the plates in this case in the following way3--,in consequence of the movement of the ions the slab of ionized gas will broaden out and will consist of three portions1 one in which there are nothing but positive ions1--this is on the side of the negative plate1--another on the side of the positive plate in which there are nothing but negative ions1 and a portion between these in which there are both positive and negative ions2 it is in this layer that recombination takes place1 and here if n is the number of positive or negative ions at the time t after the flash of ,rntgen rays1 n n#j_/7a alphan#jt74 ,with the same notation as before1 the breadth of either of the outer layers will in time dt increase by ,x7k#a k#b7;dt1 and the number of ions in it by ,x7k#a k#b7ndt2 these ions will reach the plate1 the outer layers will receive fresh ions until the middle one disappears1 which it will do after a time l_/,x7k#a k#b71 where l is the thickness of the slab ab of ionized gas2 hence ,n1 the number of ions reaching either plate1 is given by the 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 the charge received by the plate1 ,x _/ ,q#j;epsilon ,q ,ne -------------- log 7 #a ----------- 71 #dpiepsilon #dpi,x _/ where ,q#j n#jle is the charge received by the plate when the electric force is large enough to prevent recombination1 and epsilon alpha#dpie7,r#a ,r#b74 ,we can from this result deduce the value of epsilon and hence the value of alpha when ,r#a,r#b is known4 ,distribution of ,electric ,force when a ,current is passing through an ,ionized ,gas4--,let the two plates be at right angles to the axis of x2 then we may suppose that between the plates the electric intensity ,x is everywhere parallel to the axis of x4 ,the velocities of both the positive and negative ions are assumed to be proportional to ,x4 ,let k#a,x1 k#b,x represent these velocities respectively2 let n#a1 n#b be respectively the number of positive and negative ions per unit volume at a point fixed by the co-ordinate x2 let q be the number of positive or negative ions produced in unit time per unit volume at this point2 and let the number of ions which recombine in unit volume in unit time be alphan#an#b2 then if e is the charge on the ion1 the volume density of the electrification is 7n#a - n#b7;e1 hence d,x -- #dpi7n#a - n#b7;e 7#a74 dx ,if ,i is the current through unit area of the gas and if we neglect any diffusion except that caused by the electric field1 n#a;ek#a,x n#b;ek#b,x ,i 7#b74 ,from equations 7#a7 and 7#b7 we have #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 _/ and from these equations we can1 if we know the distribution of electric intensity between the plates1 calculate the number of positive and negative ions4 ,in a steady state the number of positive and negative ions in unit volume at a given place remains constant1 hence neglecting the loss by diffusion1 we have 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 and ,k#b are constant1 we have from 7#a71 7#e7 and 7#f7 d,x _/ #a #a ---- #hpie7q - alphan#an#b77 --- --- 7 7#g71 dx k#a k#b _/ an equation which is very useful1 because it enables us1 if we know the distribution of ,x1 to find whether at any point in the gas the ionization is greater or less than the recombination of the ions4 ,we see that q - alphan#an#b1 which is the excess of ionization over recombination1 is proportional to d,x_/dx4 ,thus when the ionization exceeds the recombination1 i4e4 when q - alphan#an#b is positive1 the curve for ,x is convex to the axis of x1 while when the recombination exceeds the ionization the curve for ,x will be concave to the axis of x4 ,thus1 for example1 fig4 #aa represents the curve for ,x observed by ,graham 7,wied4 ,ann4 #fd1 p4 #di7 in a tube through which a steady current is passing4 ,interpreting it by equation 7#g71 we infer that ionization was much in excess of recombination at ,a and ,b1 slightly so along ,c1 while along ,d the recombination exceeded the ionization4 ,substituting in equation 7#g7 the values of n#a1 n#b given in 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 _/ ,illustration3 ,fig4 #aa4 ,this equation can be solved 7see ,thomson1 ,phil4 ,mag4 xlvii4 ,p4 #bec71 when q is constant and k#a k#b4 ,from the solution it appears that if ,x#a be the value of x close to one of the plates1 and ,x#j the value midway between them1 #a ,x#a_/,x#j ------------------ beta - #b_/;beta where beta #hpiek#a_/;alpha4 ,since e #d #aj-aj1 alpha #b #aj-f1 and k#a for air at atmospheric pressure #dej1 beta is about #b4c for air at atmospheric pressure and it becomes much greater at lower pressures4 ,thus ,x#a_/,x#j is always greater than unity1 and the value of the ratio increases from unity to infinity as beta increases from zero to infinity4 ,as beta does not involve either q or ,i1 the ratio of ,x#a to ,x#j is independent of the strength of the current and of the intensity of the ionization4 ,no general solution of equation 7#h7 has been found when k#a is not equal to k#b1 but we can get an approximation to the solution when q is constant4 ,the equations 7#a71 7#b71 7#c71 7#d7 are satisfied by the 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 ,these solutions cannot1 however1 hold right up to the surface of the plates1 for across each unit of area1 at a point ,p1 k#a;,i_/7k#ak#b7;e positive ions pass in unit time1 and these must all come from the region between ,p and the positive plate4 ,if lambda is the distance of ,p from this plate1 this region cannot furnish more than qlambda positive ions1 and only this number if there are no recombinations4 ,hence the solution cannot hold when qlambda is less than k#a;,i_/7k#a k#b7;e1 or where lambda is less than k#a;,i_/7k#a k#b7qe4 ,similarly the solution cannot hold nearer to the negative plate than the distance k#b;,i_/7k#a k#b7qe4 ,illustration3 ,,fig4 #ab4 ,the force in these layers will be greater than that in the middle of the gas1 and so the loss of ions by recombination will be smaller in comparison with the loss due to the removal of the ions by the current4 ,if we assume that in these layers the loss of ions by recombination can be neglected1 we can by the method of the next article find an expression for the value of the electric force at any point in the layer4 ,this1 in conjunction with the value _/alpha ,i ,x#j 7 ------- 7 ---------- q _/ e7k#a k#b7 for the gas outside the layer1 will give the value of ,x at any point between the plates4 ,it follows from this investigation that if ,x#a and ,x#b are the values of ,x at the positive and negative plates respectively1 and ,x#j the value of ,x outside the layer1 _/ 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_/ where epsilon alpha_/#dpie7k#a k#b74 ,langevin found that for air at a pressure of #aeb mm4 epsilon #j4ja1 at #cge mm4 epsilon #j4jf1 and at #gfj mm4 epsilon #j4bg4 ,thus at fairly low pressures #a_/;epsilon is large1 and we have 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 ,therefore ,x#a_/,x#b k#a_/k#b1 or the force at the positive plate is to that at the negative plate as the velocity of the positive ion is to that of the negative ion4 ,thus the force at the negative plate is greater than that at the positive4 ,the falls of potential ,v#a1 ,v#b at the two layers when #a_/;epsilon is large can be shown to be given by the 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_/ hence ,v#a_/,v#b k#a_/k#b1 so that the potential falls at the electrodes are proportional to the squares of the velocities of the ions4 ,the change in potential across the layers is proportional to the square of the current1 while the potential change between the layers is proportional to the current1 the total potential difference between the plates is the sum of these changes1 hence the relation between ,v and i will be of the form ,v ,ai ,bi4 ,mie 7,ann4 der4 ,phys41 #aijd1 #ac1 ,p4 #heg7 has by the method of successive approximations obtained solutions of equation 7#h7 7i47 when the current is only a small fraction of the saturation current1 7ii47 when the current is nearly saturated4 ,the results of his investigations are represented in fig4 #ab1 which represents the distribution of electric force along the path of the current for various values of the current expressed as fractions of the saturation current4 ,it will be seen that until the current amounts to about one-fifth of the maximum current1 the type of solution is the one just indicated1 i4e4 the electric force is constant except in the neighbourhood of the electrodes when it increases rapidly4 ,though we are unable to obtain a general solution of the equation 7#h71 there are some very important special cases in which that equation can be solved without difficulty4 ,we shall consider two of these1 the first being that when the current is saturated4 ,in this case there is no loss of ions by recombination1 so that using the same notation as before we have d --7n#ak#a,x7 q1 dx d --7n#bk#b,x7 -q4 dx ,the solutions of which if q is constant are n#ak#a,x qx1 n#bk#b,x ,i_/e - qx q7l - x71 if l is the distance between the plates1 and x #j at the positive electrode4 ,since 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 where ,c is a quantity to be determined by the condition that _/ l ,xdx ,v1 _/#j where ,v is the given potential difference between the plates4 ,when the force is a minimum d,x_/dx #j1 hence at this point lk#a lk#b x -------1 l - x -------4 k#a k#b k#a k#b ,hence the ratio of the distances of this point from the positive and negative plates respectively is equal to the ratio of the velocities of the positive and negative ions4 ,the other case we shall consider is the very important one in which the velocity of the negative ion is exceedingly large compared with the positive2 this is the case in flames where1 as ,gold 7,proc4 ,roy4 ,soc4 #ig1 p4 #dc7 has shown1 the velocity of the negative ion is many thousand times the velocity of the positive2 it is also very probably the case in all gases when the pressure is low4 ,we may get the solution of this case either by putting k#a_/k#b #j in equation 7#h71 or independently as follows3--,using the same notation as before1 we have 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 ,in this case practically all the current is carried by the negative ions so that i n#bk#b,xe1 and therefore q alphan#an#b4 ,thus n#b i_/k#b,xe1 n#a qk#b,xe_/alphai4 ,thus d,x #dpiek#bq,x #dpii -- ----------- - ------1 dx alphai k#b,x or d,x #hpiek#bq,x #hpii -- - ------------ - ------4 dx alphai k#b ,the solution of this equation is alpha i ,x ------- ----- ,cepsilon7#hpiek#bqx_/alphai7 q k#b;e ,here x is measured from the positive electrode2 it is more convenient in this case1 however1 to measure it from the negative electrode4 ,if x be the distance from the negative electrode at which the electric force is ,x1 we have from equation 7#g7 alpha i ,x ------- ----- ,cepsilon7#hpiek#bqx_/alphai7 q k#b;e ,to find the value of ,c we see by equation 7#g7 that d,x k#ak#b #a --- ------- ------ q - alphan#an#b2 d,x k#a k#b #hpie hence d,x k#ak#b #a x#a _/ x#a --- ------- ------ 7q - alphan#an#b7;dx4 d,x k#a k#b #hpie _/#j ,the right hand side of this equation is the excess of ionization over recombination in the region extending from the cathode to x#a2 it must therefore1 when things are in a steady state1 equal the excess of the number of negative ions which leave this region over those which enter it4 ,the number which leave is i_/e and the number which enter is i#j_/;e1 if it is the current of negative ions coming from unit area of the cathode1 as hot metal cathodes emit large quantities of negative electricity i#j may in some cases be considerable1 thus the right hand side of equation is 7i - i#j7_/;e4 ,when x#a is large d,x_/dx #j2 hence we have from equation alphai7i - i#j7 k#a k#b ,c ---------------- -------1 qk#ak#b;e k#b and since k#a is small compared with k#b1 we have alphai _/ k#b i - i#j ,x --------- 7#a -- ------ epsilon-#hpiek#bqx_/alphai 74 qk#b;e k#a i _/ ,from the values which have been found for k#b and alpha1 we know that #hpiek#b_/;alpha is a large quantity1 hence the second term inside the bracket will be very small when eqx is equal to or greater than i2 thus this term will be very small outside a layer of gas next the cathode of such thickness that the number of ions produced on it would be sufficient1 if they were all utilized for the purpose1 to carry the current2 in the case of flames this layer is exceedingly thin unless the current is very large4 ,the value of the electric force in the uniform part of the field is equal to i_/k#b;eroot7alpha_/q71 while when i#j #j1 the force at the cathode itself bears to the uniform force the ratio of 7k#a k#b7 to k#a4 ,as k#a is many thousand times k#b the force increases with great rapidity as we approach the cathode2 this is a very characteristic feature of the passage of electricity through flames and hot gases4 ,thus in an experiment made by ,h4 ,a4 ,wilson with a flame #ah cm4 long1 the drop of potential within #a centimetre of the cathode was about five times the drop in the other #ag cm4 of the tube4 ,the relation between the current and the potential difference when the velocity of the negative ion is much greater than the positive is very easily obtained4 ,since the force is uniform and equal to i_/k#b;eroot7alpha_/q71 until we get close to the cathode the fall of potential in this part of the discharge will be very approximately equal to i_/k#b;eroot7alphal_/q71 where l is the distance between the electrodes4 ,close to the cathode1 the electric force when i#j is not nearly equal to i is approximately given by the equation i _/alpha ,x --------- 7---------7 epsilon-#dpiek#bqx_/alphai1 e7k#ak#b7 q _/ 1 and the fall of potential at the cathode is equal approximately to oo _/ ,x dx1 _/#j that is to i _/alpha alpha i --------- 7---------7 ----------4 e7k#ak#b7 q _/ #dpiek#bq ,the potential difference between the plates is the sum of the fall of potential in the uniform part of the discharge plus the fall at the cathode1 hence _/alpha i _/ ialpha #a ,v 7---------7 --- 7 il --------- ------------ 74 q _/ ek#b #dpieq root7k#ak#b7_/ ,the fall of potential at the cathode is proportional to the square of the current1 while the fall in the rest of the circuit is directly proportional to the current4 ,in the case of flames or hot gases1 the fall of potential at the cathode is much greater than that in the rest of the circuit1 so that in such cases the current through the gas varies nearly as the square root of the potential difference4 ,the equation we have just obtained is of the form ,v ,ai ,bi1 and ,h4 ,a4 ,wilson has shown that a relation of this form represents the results of his experiments on the conduction of electricity through flames4 ,the expression for the fall of potential at the cathode is inversely proportional to q7#c_/b71 q being the number of ions produced per cubic centimetre per second close to the cathode2 thus any increase in the ionization at the cathode will diminish the potential fall at the cathode1 and as practically the whole potential difference between the electrodes occurs at the cathode1 a diminution in the potential fall there will be much more important than a diminution in the electric force in the uniform part of the discharge1 when the force is comparatively insignificant4 ,this consideration explains a very striking phenomenon discovered many years ago by ,hittorf1 who found that if he put a wire carrying a bead of a volatile salt into the flame1 it produced little effect upon the current1 unless it were placed close to the cathode where it gave rise to an enormous increase in the current1 sometimes increasing the current more than a hundredfold4 ,the introduction of the salt increases very largely the number of ions produced1 so that q is much greater for a salted flame than for a plain one4 ,thus ,hittorf's result coincides with the conclusions we have drawn from the theory of this class of conduction4 ,the fall of potential at the cathode is proportional to i - i#j1 where i#j is the stream of negative electricity which comes from the cathode itself1 thus as i#j increases the fall of potential at the cathode diminishes and the current sent by a given potential difference through the gas increases4 ,now all metals give out negative particles when heated1 at a rate which increases very rapidly with the temperature1 but at the same temperature some metals give out more than others4 ,if the cathode is made of a metal which emits large quantities of negative particles1 7i - i#j7 will for a given value of i be smaller than if the metal only emitted a small number of particles2 thus the cathode fall will be smaller for the metal with the greater emissitivity1 and the relation between the potential difference and the current will be different in the two cases4 ,these considerations are confirmed by experience1 for it has been found that the current between electrodes immersed in a flame depends to a great extent upon the metal of which the electrodes are made4 ,thus ,pettinelli 7,acc4 dei ,lincei #e1 v4 p4 #aah7 found that1 ceteris paribus1 the current between two carbon electrodes was about #ejj times that between two iron ones4 ,if one electrode was carbon and the other iron1 the current when the carbon was cathode and the iron anode was more than #ajj times the current when the electrodes were reversed4 ,the emission of negative particles by some metallic oxides1 notably those of calcium and barium1 has been shown by ,wehnelt 7,ann4 der ,phys4 #aa1 p4 #dbe7 to be far greater than that of any known metal1 and the increase of current produced by coating the cathodes with these oxides is exceedingly large2 in some cases investigated by ,tufts and ,stark 7,physik4 ,zeits41 #aijh1 #e1 p4 #bdh7 the current was increased many thousand times by coating the cathode with lime4 ,no appreciable effect is produced by putting lime on the anode4 ,conduction when all the ,ions are of one ,sign4--,there are many important cases in which the ions producing the current come from one electrode or from a thin layer of gas close to the electrode1 no ionization occurring in the body of the gas or at the other electrode4 ,among such cases may be mentioned those where one of the electrodes is raised to incandescence while the other is cold1 or when the negative electrode is exposed to ultra-violet light4 ,in such cases if the electrode at which the ionization occurs is the positive electrode1 all the ions will be positively charged1 while if it is the negative electrode the ions will all be charged negatively4 ,the theory of this case is exceedingly simple4 ,suppose the electrodes are parallel planes at right angles to the axis of x2 let ,x be the electric force at a distance x from the electrode where the ionization occurs1 n the number of ions 7all of which are of one sign7 at this place per cubic centimetre1 k the velocity of the ion under unit electric force1 e the charge on an ion1 and i the current per unit area of the electrode4 ,then we have d,x_/dx #dpine1 and if u is the velocity of the ion neu i4 ,but u k,x1 hence we have k,x_/#dpi d,x_/dx i1 and since the right hand side of this equation does not depend upon x1 we get k,x_/#hpi ix ,c1 where ,c is a constant to be determined4 ,if l is the distance between the plates1 and ,v the potential difference between them1 _/ l #a _/#hpi ,v ,xdx --- _/ ----- 7 il ,c 7#c_/b - ,c#c_/b 4 _/#j i _/ k ,we shall show that when the current is far below the saturation value1 ,c is very small compared with il1 so that the preceding equation becomes ,v #hpili_/k 7#a74 ,to show that for small currents ,c is small compared with il1 consider the case when the ionization is confined to a thin layer1 thickness d close to the electrode1 in that layer let n#j be the value of n1 then we have q alphan#j i_/ed4 ,if ,x#j be the value of ,x when x #j1 k,x#jn#j;e i1 and1 k,x#j i alpha i ,c ----- ----------- -------- -------- 7#b74 #hpi n#jke#hpi #hpike q i_/ed ,since alpha_/#hpike is1 as we have seen1 less than unity1 ,c will be small compared with il1 if i_/7eq i_/d7 is small compared with l4 ,if ,i#j is the saturation current1 q ,i#j_/;ed1 so that the former expression id_/7,i#j i71 if i is small compared with ,i#j1 this expression is small compared with d1 and therefore a fortiori compared with l1 so that we are justified in this case in using equation 7#a74 ,from equation 7#b7 we see that the current increases as the square of the potential difference4 ,here an increase in the potential difference produces a much greater percentage increase than in conduction through metals1 where the current is proportional to the potential difference4 ,when the ionization is distributed through the gas1 we have seen that the current is approximately proportional to the square root of the potential1 and so increases more slowly with the potential difference than currents through metals4 ,from equation 7#a7 the current is inversely proportional to the cube of the distance between the electrodes1 so that it falls off with great rapidity as this distance is increased4 ,we may note that for a given potential difference the expression for the current does not involve q1 the rate of production of the ions at the electrode1 in other words1 if we vary the ionization the current will not begin to be affected by the strength of the ionization until this falls so low that the current is a considerable fraction of the saturation current4 ,for the same potential difference the current is proportional to k1 the velocity under unit electric force of the ion which carries the current4 ,as the velocity of the negative ion is greater than that of the positive1 the current when the ionization is confined to the neighbourhood of one of the electrodes will be greater when that electrode is made cathode than when it is anode4 ,thus the current will appear to pass more easily in one direction than in the opposite4 ,since the ions which carry the current have to travel all the way from one electrode to the other1 any obstacle which is impervious to these ions will1 if placed between the electrodes1 stop the current to the electrode where there is no ionization4 ,a plate of metal will be as effectual as one made of a non-conductor1 and thus we get the remarkable result that by interposing a plate of an excellent conductor like copper or silver between the electrode1 we can entirely stop the current4 ,this experiment can easily be tried by using a hot plate as the electrode at which the ionization takes place3 then if the other electrode is cold the current which passes when the hot plate is cathode can be entirely stopped by interposing a cold metal plate between the electrodes4 ,methods of counting the ,number of ,ions4--,the detection of the ions and the estimation of their number in a given volume is much facilitated by the property they possess of promoting the condensation of water-drops in dust-free air supersaturated with water vapour4 ,if such air contains no ions1 then it requires about an eightfold supersaturation before any water-drops are formed2 if1 however1 ions are present ,c4 ,t4 ,r4 ,wilson 7,phil4 ,trans4 #ahi1 p4 #bfe7 has shown that a sixfold supersaturation is sufficient to cause the water vapour to condense round the ions and to fall down as raindrops4 ,the absence of the drops when no ions are present is due to the curvature of the drop combined with the surface tension causing1 as ,lord ,kelvin showed1 the evaporation from a small drop to be exceeding rapid1 so that even if a drop of water were formed the evaporation would be so great in its early stages that it would rapidly evaporate and disappear4 ,it has been shown1 however 7,j4 ,j4 ,thomson1 ,application of ,dynamics to ,physics and ,chemistry1 p4 #afd2 ,conduction of ,electricity through ,gases1 #bnd ed4 p4 #agi71 that if a drop of water is charged with electricity the effect of the charge is to diminish the evaporation2 if the drop is below a certain size the effect the charge has in promoting condensation more than counterbalances the effect of the surface tension in promoting evaporation4 ,thus the electric charge protects the drop in the most critical period of its growth4 ,the effect is easily shown experimentally by taking a bulb connected with a piston arranged so as to move with great rapidity4 ,when the piston moves so as to increase the volume of the air contained in the bulb the air is cooled by expansion1 and if it was saturated with water vapour before it is supersaturated after the expansion4 ,by altering the throw of the piston the amount of supersaturation can be adjusted within very wide limits4 ,let it be adjusted so that the expansion produces about a sixfold supersaturation2 then if the gas is not exposed to any ionizing agents very few drops 7and these probably due to the small amount of ionization which we have seen is always present in gases7 are formed4 ,if1 however1 the bulb is exposed to strong ,rntgen rays expansion produces a dense cloud which gradually falls down and disappears4 ,if the gas in the bulb at the time of its exposure to the ,rntgen rays is subject to a strong electric field hardly any cloud is formed when the gas is suddenly expanded4 ,the electric field removes the charged ions from the gas as soon as they are formed so that the number of ions present is greatly reduced4 ,this experiment furnishes a very direct proof that the drops of water which form the cloud are only formed round the ions4 ,this method gives us an exceedingly delicate test for the presence of ions1 for there is no difficulty in detecting ten or so raindrops per cubic centimetre2 we are thus able to detect the presence of this number of ions4 ,this result illustrates the enormous difference between the delicacy of the methods of detecting ions and those for detecting uncharged molecules2 we have seen that we can easily detect ten ions per cubic centimetre1 but there is no known method1 spectroscopic or chemical1 which would enable us to detect a billion 7#ajab7 times this number of uncharged molecules4 ,the formation of the water-drops round the charged ions gives us a means of counting the number of ions present in a cubic centimetre of gas2 we cool the gas by sudden expansion until the supersaturation produced by the cooling is sufficient to cause a cloud to be formed round the ions1 and the problem of finding the number of ions per cubic centimetre of gas is thus reduced to that of finding the number of drops per cubic centimetre in the cloud4 ,unless the drops are very few and far between we cannot do this by direct counting2 we can1 however1 arrive at the result in the following way4 ,from the amount of expansion of the gas we can calculate the lowering produced in its temperature and hence the total quantity of water precipitated4 ,the water is precipitated as drops1 and if all the drops are the same size the number per cubic centimetre will be equal to the volume of water deposited per cubic centimetre1 divided by the volume of one of the drops4 ,hence we can calculate the number of drops if we know their size1 and this can be determined by measuring the velocity with which they fall under gravity through the air4 ,the theory of the fall of a heavy drop of water through a viscous fluid shows that v 7#b_/i7;ga_/mu1 where a is the radius of the drop1 g the acceleration due to gravity1 and mu the coefficient of viscosity of the gas through which the drop falls4 ,hence if we know v we can deduce the value of a and hence the volume of each drop and the number of drops4 ,charge on ,ion4--,by this method we can determine the number of ions per unit volume of an ionized gas4 ,knowing this number we can proceed to determine the charge on an ion4 ,to do this let us apply an electric force so as to send a current of electricity through the gas1 taking care that the current is only a small fraction of the saturating current4 ,then if u is the sum of the velocities of the positive and negative ions produced in the electric field applied to the gas1 the current through unit area of the gas is neu1 where n is the number of positive or negative ions per cubic centimetre1 and e the charge on an ion4 ,we can easily measure the current through the gas and thus determine neu2 we can determine n by the method just described1 and u1 the velocity of the ions under the given electric field1 is known from the experiments of ,zeleny and others4 ,thus since the product neu1 and two of the factors n1 u are known1 we can determine the other factor e1 the charge on the ion4 ,this method was used by ,j4 ,j4 ,thomson1 and details of the method will be found in ,phil4 ,mag4 #e1 #df1 p4 #ebh2 #e1 #dh1 p4 #edg2 #f1 #e1 p4 #cdf4 ,the result of these measurements shows that the charge on the ion is the same whether the ionization is by ,rntgen rays or by the influence of ultra-violet light on a metal plate4 ,it is the same whether the gas ionized is hydrogen1 air or carbonic acid1 and thus is presumably independent of the nature of the gas4 ,the value of e formed by this method was #c4d #aj-aj electrostatic units4 ,h4 ,a4 ,wilson 7,phil4 ,mag4 #f1 #e1 p4 #dbi7 used another method4 ,drops of water1 as we have seen1 condense more easily on negative than on positive ions4 ,it is possible1 therefore1 to adjust the expansion so that a cloud is formed on the negative but not on the positive ions4 ,wilson arranged the experiments so that such a cloud was formed between two horizontal plates which could be maintained at different potentials4 ,the charged drops between the plates were acted upon by a uniform vertical force which affected their rate of fall4 ,let ,x be the vertical electric force1 e the charge on the drop1 v#a the rate of fall of the drop when this force acts1 and v the rate of fall due to gravity alone4 ,then since the rate of fall is proportionate to the force on the drop1 if a is the radius of the drop1 and rho its density1 then ,xe 7#d_/c7pirhoga v#a ---------------------- ---1 #d_/cpirhoga v or ,xe 7#d_/c7pirhoga7v#a - v7_/v4 ,but v #b_/i;garho_/mu1 so that _/ _/ mu v7#c_/b77v#a - v7 ,xe _/ #b4ipi - _/ ------ ---------------4 _/ grho v ,thus if ,x1 v1 v#a are known e can be determined4 ,wilson by this method found that e was #c4a #aj-aj electrostatic units4 ,a few of the ions carried charges #b;e or #c;e4 ,townsend has used the following method to compare the charge carried by a gaseous ion with that carried by an atom of hydrogen in the electrolysis of solution4 ,we have u_/,d ,ne_/,pi1 where ,d is the coefficient of diffusion of the ions through the gas1 u the velocity of the ion in the same gas when acted on by unit electric force1 ,n the number of molecules in a cubic centimetre of the gas when the pressure is ,pi dynes per square centimetre1 and e the charge in electrostatic units4 ,this relation is obtained on the hypothesis that ,n ions in a cubic centimetre produce the same pressure as ,n uncharged molecules4 ,we know the value of ,d from ,townsend's experiments and the values of u from those of ,zeleny4 ,we get the following values for ,ne #aj-aj3-- ---------------------------------------- ----------------- ,moist ,gas4 ,moist ,gas4 ---------------------------------------- --------------- ,gas4 ,positive ,negative ,positive ,negative ,ions4 ,ions4 ,ions4 ,ions4 ---------------------------------------- --------------- ,air #a4bh #a4bi #a4df #a4ca ,oxygen #a4cd #a4bg #a4fc #a4cf ,carbonic acid #a4ja 4#hg 4#ii 4#ic ,hydrogen #a4bd #a4ah #a4fc #a4be ---------------------------------------- --------------- ,mean #a4bb #a4ae #a4dc #a4ba ---------------------------------------- --------------- ,since #a4bb cubic centimetres of hydrogen at the temperature #ae ,c4 and pressure #gfj mm4 of mercury are liberated by the passage through acidulated water of one electromagnetic unit of electricity or #c #ajaj electrostatic units1 and since in one cubic centimetre of the gas there are #b4df ,n atoms of hydrogen1 we have1 if ,e is the charge in electrostatic units1 on the atom of hydrogen in the electrolysis of solutions #b4df,,ne #c #ajaj1 or ,,ne #a4bb #ajaj4 ,the mean of the values of ,ne in the preceding table is #a4bd #ajaj4 ,hence we may conclude that the charge of electricity carried by a gaseous ion is equal to the charge carried by the hydrogen atom in the electrolysis of solutions4 ,the values of ,ne for the different gases differ more than we should have expected from the probable accuracy of the determination of ,d and the velocity of the ions3 ,townsend 7,proc4 ,roy4 ,soc4 #hj1 p4 #bjg7 has shown that when the ionization is produced by ,rntgen rays some of the positive ions carry a double charge and that this accounts for the values of ,ne being greater for the positive than for the negative ions4 ,since we know the value of e1 viz4 #c4e #aj-aj1 and1 also ,ne1 #a4bd #ajaj1 we find ,n the number of molecules in a cubic centimetre of gas at standard temperature and pressure to be equal to #c4e #ajai4 ,this method of obtaining ,n is the only one which does not involve any assumption as to the shape of the molecules and the forces acting between them4 ,another method of determining the charge carried by an ion has been employed by ,rutherford 7,proc4 ,roy4 ,soc4 #ha1 pp4 #ada1 #afb71 in which the positively electrified particles emitted by radium are made use of4 ,the method consists of3 7#a7 ,counting the number of alpha particles emitted by a given quantity of radium in a known time4 7#b7 ,measuring the electric charge emitted by this quantity in the same time4 ,to count the number of the alpha particles the radium was so arranged that it shot into an ionization chamber a small number of alpha particles per minute2 the interval between the emission of individual particles was several seconds4 ,when an alpha particle passed into the vessel it ionized the gas inside and so greatly increased its conductivity2 thus1 if the gas were kept exposed to an electric field1 the current through the gas would suddenly increase when an alpha particle passed into the vessel4 ,although each alpha particle produces about thirty thousand ions1 this is hardly large enough to produce the conductivity appreciable without the use of very delicate apparatus2 to increase the conductivity ,rutherford took advantage of the fact that ions1 especially negative ones1 when exposed to a strong electric field1 produce other ions by collision against the molecules of the gas through which they are moving4 ,by suitably choosing the electric field and the pressure in the ionization chamber1 the #cj1jjj ions produced by each alpha particle can be multiplied to such an extent that an appreciable current passes through the ionization chamber on the arrival of each alpha particle4 ,an electrometer placed in series with this vessel will show by its deflection when an alpha particle enters the chamber1 and by counting the number of deflections per minute we can determine the number of alpha particles given out by the radium in that time4 ,another method of counting this number is to let the particles fall on a phosphorescent screen1 and count the number of scintillations on the screen in a certain time4 ,rutherford has shown that these two methods give concordant results4 ,the charge of positive electricity given out by the radium was measured by catching the alpha particles in a ,faraday cylinder placed in a very highly exhausted vessel1 and measuring the charge per minute received by this cylinder4 ,in this way ,rutherford showed that the charge on the alpha particle was #i4d #aj-aj electrostatic units4 ,now e_/m for the alpha particle #e #aj1 and there is evidence that the alpha particle is a charged atom of helium2 since the atomic weight of helium is #d and e_/m for hydrogen is #ajd1 it follows that the charge on the helium atom is twice that on the hydrogen1 so that the charge on the hydrogen atom is #d4g #aj-aj electrostatic units4 ,calculation of the ,mass of the ,ions at ,low ,pressures4--,although at ordinary pressures the ion seems to have a very complex structure and to be the aggregate of many molecules1 yet we have evidence that at very low pressures the structure of the ion1 and especially of the negative one1 becomes very much simpler4 ,this evidence is afforded by determination of the mass of the atom4 ,we can measure the ratio of the mass of an ion to the charge on the ion by observing the deflections produced by magnetic and electric forces on a moving ion4 ,if an ion carrying a charge e is moving with a velocity v1 at a point where the magnetic force is ,h1 a mechanical force acts on the ion1 whose direction is at right angles both to the direction of motion of the ion and to the magnetic force1 and whose magnitude is ev,h sin theta1 where theta is the angle between v and ,h4 ,suppose then that we have an ion moving through a gas whose pressure is so low that the free path of the ion is long compared with the distance through which it moves whilst we are experimenting upon it2 in this case the motion of the ion will be free1 and will not be affected by the presence of the gas4 ,since the force is always at right angles to the direction of motion of the ion1 the speed of the ion will not be altered by the action of this force2 and if the ion is projected with a velocity v in a direction at right angles to the magnetic force1 and if the magnetic force is constant in magnitude and direction1 the ion will describe a curve in a plane at right angles to the magnetic force4 ,if rho is the radius of curvature of this curve1 m the mass of the ion1 mv_/rho must equal the normal force acting on the ion1 i4e4 it must be equal to ,hev1 or rho mv_/,he4 ,thus the radius of curvature is constant2 the path is therefore a circle1 and if we can measure the radius of this circle we know the value of mv_/,he4 ,in the case of the rapidly moving negative ions projected from the cathode in a highly exhausted tube1 which are known as cathode rays1 the path of the ions can be readily determined since they make many substances luminous when they impinge against them4 ,thus by putting a screen of such a substance in the path of the rays the shape of the path will be determined4 ,let us now suppose that the ion is acted upon by a vertical electric force ,x and is free from magnetic force1 if it be projected with a horizontal velocity v1 the vertical deflection y after a time t is et_/m1 or if l is the horizontal distance travelled over by the ion in this time we have since l vt1 ,xe l y -- --4 m v ,thus if we measure y and l we can deduce e_/mv4 ,from the effect of the magnetic force we know e_/mv4 ,combining these results we can find both e_/m and v4 ,illustration3 ,,fig4 #ac4 ,the method by which this determination is carried out in practice is illustrated in fig4 #ac4 ,the cathode rays start from the electrode ,c in a highly exhausted tube1 pass through two small holes in the plugs ,a and ,b1 the holes being in the same horizontal line4 ,thus a pencil of rays emerging from ,b is horizontal and produces a bright spot at the far end of the tube4 ,in the course of their journey to the end of the tube they pass between the horizontal plates ,e and ,d1 by connecting these plates with an electric battery a vertical electric field is produced between ,e and ,d and the phosphorescent spot is deflected4 ,by measuring this deflection we determine e_/mv4 ,the tube is now placed in a uniform magnetic field1 the lines of magnetic force being horizontal and at right angles to the plane of the paper4 ,the magnetic force makes the rays describe a circle in the plane of the paper1 and by measuring the vertical deflection of the phosphorescent patch at the end of the tube we can determine the radius of this circle1 and hence the value of e_/mv4 ,from the two observations the value of e_/m and v can be calculated4 ,another method of finding e_/m for the negative ion which is applicable in many cases to which the preceding one is not suitable1 is as follows3 ,let us suppose that the ion starts from rest and moves in a field where the electric and magnetic forces are both uniform1 the electric force ,x being parallel to the axis of x1 and the magnetic force ,z parallel to the axis of z2 then if x1 y1 are the co-ordinates of the ion at the time t1 the equations of motion of the ion are-- dx dy m --- ,xe - ,he -- 1 dt dt dy dx m --- ,he --4 dt dt ,the solution of these equations1 if x1 y1 dx_/dt1 dy_/dt all vanish when t #j1 is ,xm _/ _/ e x --- #a - cos7 -- ,ht 7 e,h m _/ _/ ,xm _/e _/ e y --- -- ,ht - sin7 -- ,ht 7 4 e,h m m _/ _/ ,these equations show that the path of the ion is a cycloid1 the generating circle of which has a diameter equal to #b,xm_/e,h1 and rolls on the line x #j4 ,suppose now that we have a number of ions starting from the plane x #j1 and moving towards the plane x a4 ,the particles starting from x #j describe cycloids1 and the greatest distance they can get from the plane is equal to the diameter of the generating circle of the cycloid1 i4e4 to #b,xm_/e,h4 7,after reaching this distance they begin to approach the plane47 ,hence if a is less than the diameter of the generating circle1 all the particles starting from x #j will reach the plane x a1 if this is unlimited in extent2 while if a is greater than the diameter of the generating circle none of the particles which start from x #j will reach the plane x a4 ,thus1 if x #j is a plane illuminated by ultra-violet light1 and consequently the seat of a supply of negative ions1 and x a a plane connected with an electrometer1 then if a definite electric intensity is established between the planes1 i4e4 if ,x be fixed1 so that the rate of emission of negative ions from the illuminated plate is given1 and if a is less than #b,xm_/e,h1 all the ions which start from x #j will reach x a4 ,that is1 the rate at which this plane receives an electric charge will be the same whether there is a magnetic field between the plate or not1 but if a is greater than #b,xm_/e,h1 then no particle which starts from the plate x #j will reach the plate x a1 and this plate will receive no charge4 ,thus the supply of electricity to the plate has been entirely stopped by the magnetic field4 ,thus1 on this theory1 if the distance between the plates is less than a certain value1 the magnetic force should produce no effect on the rate at which the electrometer plate receives a charge1 while if the distance is greater than this value the magnetic force would completely stop the supply of electricity to the plate4 ,the actual phenomena are not so abrupt as this theory indicates4 ,we find that when the plates are very near together the magnetic force produces a very slight effect1 and this an increase in the rate of charging of the plate4 ,on increasing the distance we come to a stage where the magnetic force produces a great diminution in the rate of charging4 ,it does not1 however1 stop it abruptly1 there being a considerable range of distance1 in which the magnetic force diminishes but does not destroy the current4 ,at still greater distances the current to the plate under the magnetic force is quite inappreciable compared with that when there is no magnetic force4 ,we should get this gradual instead of abrupt decay of the current if some of the particles1 instead of all starting from rest1 started with a finite velocity2 in that case the first particles stopped would be those which started from rest4 ,this would be when a #b,xm_/e,h4 ,thus if we measure the value of a when the magnetic force first begins to affect the leak to the electrometer we determine #b,xm_/e,h1 and as we can easily measure ,x and ,h1 we can deduce the value of m_/e4 ,by these methods ,thomson determined the value of e_/m for the negative ions produced when ultra-violet light falls on a metal plate1 as well as for the negative ions produced by an incandescent carbon filament in an atmosphere of hydrogen 7,phil4 ,mag4 #e1 #dh1 p4 #edg7 as well as for the cathode rays4 ,it was found that the value of e_/m for the negative ions was the same in all these cases1 and that it was a constant quantity independent of the nature of the gas from which the ions are produced and the means used to produce them4 ,it was found1 too1 that this value was more than a thousand times the value of e_/,m1 where e is the charge carried by an atom of hydrogen in the electrolysis of solutions1 and ,m the mass of an atom of hydrogen4 ,we have seen that this charge is the same as that carried by the negative ion in gases2 thus since e_/m is more than a thousand times e_/,m1 it follows that ,m must be more than a thousand times m4 ,thus the mass of the negative ion is exceedingly small compared with the mass of the atom of hydrogen1 the smallest mass recognized in chemistry4 ,the production of negative ions thus involves the splitting up of the atom1 as from a collection of atoms something is detached whose mass is less than that of a single atom4 ,it is important to notice in connexion with this subject that an entirely different line of argument1 based on the ,zeeman effect 7see ,,magneto-,,optics71 leads to the recognition of negatively electrified particles for which e_/m is of the same order as that deduced from the consideration of purely electrical phenomena4 ,these small negatively electrified particles are called corpuscles4 ,the latest determinations of e_/m for corpuscles available are the following3-- ,observer4 e_/m4 ,classen 7,ber4 deut4 phys4 ,ges4 #f1 p4 #gjj7 #a4ggbh #ajg ,bucherer 7,ann4 der ,phys41 #bh1 p4 #eac7 #a4gfc #ajg ,it follows from electrical theory that when the corpuscles are moving with a velocity comparable with that of light their masses increase rapidly with their velocity4 ,this effect has been detected by ,kauffmann 7,gtt4 ,nach41 ,nov4 #h1 #aija71 who used the corpuscles shot out from radium1 some of which move with velocities only a few per cent less than that of light4 ,other experiments on this point have been made by ,bucherer 7,ann4 der ,phys4 #bh1 p4 #eac74 ,conductivity ,produced by ,ultra-,violet ,light4--,so much use has been made in recent times of ultra-violet light for producing ions that it is desirable to give some account of the electrical effects produced by light4 ,the discovery by ,hertz 7,wied4 ,ann4 #ca1 p4 #ihc7 in #ahhg1 that the incidence of ultra-violet light on a spark gap facilitates the passage of a spark1 led to a series of investigations by ,hallwachs1 ,hoor1 ,righi and ,stoletow1 on the effect of ultra-violet light on electrified bodies4 ,these researches have shown that a freshly cleaned metal surface1 charged with negative electricity1 rapidly loses its charge1 however small1 when exposed to ultra-violet light1 and that if the surface is insulated and without charge initially1 it acquires a positive charge under the influence of the light4 ,the magnitude of this positive charge may be very much increased by directing a blast of air on the plate4 ,this1 as ,zeleny 7,phil4 ,mag4 #e1 #de1 p4 #bgb7 showed1 has the effect of blowing from the neighbourhood of the plate negatively electrified gas1 which has similar properties to the charged gas obtained by the separation of ions from a gas exposed to ,rntgen rays or uranium radiation4 ,if the metal plate is positively electrified1 there is no loss of electrification caused by ultra-violet light4 ,this has been questioned1 but a very careful examination of the question by ,elster and ,geitel 7,wied4 ,ann4 #eg1 p4 #bd7 has shown that the apparent exceptions are due to the accidental exposure to reflected ultra-violet light of metal surfaces in the neighbourhood of the plate negatively electrified by induction1 so that the apparent loss of charge is due to negative electricity coming up to the plate1 and not to positive electricity going away from it4 ,the ultra-violet light may be obtained from an arc-lamp1 the effectiveness of which is increased if one of the terminals is made of zinc or aluminium1 the light from these substances being very rich in ultra-violet rays2 it may also be got very conveniently by sparking with an induction coil between zinc or cadmium terminals4 ,sunlight is not rich in ultra-violet light1 and does not produce anything like so great an effect as the arc light4 ,elster and ,geitel1 who have investigated with great success the effects of light on electrified bodies1 have shown that the more electro-positive metals lose negative charges when exposed to ordinary light1 and do not need the presence of the ultra-violet rays4 ,thus they found that amalgams of sodium or potassium enclosed in a glass vessel lose a negative charge when exposed to daylight1 though the glass stops the small amount of ultra-violet light left in sunlight after its passage through the atmosphere4 ,if sodium or potassium be employed1 or1 what is more convenient1 the mercury-like liquid obtained by mixing sodium and potassium in the proportion of their combining weights1 they found that negative electricity was discharged by an ordinary petroleum lamp4 ,if the still more electro-positive metal rubidium is used1 the discharge can be produced by the light from a glass rod just heated to redness2 but there is no discharge till the glass is luminous4 ,elster and ,geitel arrange the metals in the following order for the facility with which negative electrification is discharged by light3 rubidium1 potassium1 alloy of sodium and potassium1 sodium1 lithium1 magnesium1 thallium1 zinc4 ,with copper1 platinum1 lead1 iron1 cadmium1 carbon and mercury the effects with ordinary light are too small to be appreciable4 ,the order is the same as that in ,volta's electro-chemical series4 ,with ultra-violet light the different metals show much smaller differences in their power of discharging negative electricity than they do with ordinary light4 ,elster and ,geitel found that the ratio of the photo-electric effects of two metals exposed to approximately monochromatic light depended upon the wave-length of the light1 different metals showing a maximum sensitiveness in different parts of the spectrum4 ,this is shown by the following table for the alkaline metals4 ,the numbers in the table are the rates of emission of negative electricity under similar circumstances4 ,the rate of emission under the light from a petroleum lamp was taken as unity3-- ,blue4 ,yellow4 ,orange4 ,red4 ,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 ,the table shows that the absorption of light by the metal has great influence on the photo-electric effect1 for while potassium is more sensitive in blue light than sodium1 the strong absorption of yellow light by sodium makes it more than five times more sensitive to this light than potassium4 ,stoletow1 at an early period1 called attention to the connexion between strong absorption and photo-electric effects4 ,he showed that water1 which does not absorb to any great extent either the ultra-violet or visible rays1 does not show any photo-electric effect1 while strongly coloured solutions1 and especially solutions of fluorescent substances such as methyl green or methyl violet1 do so to a very considerable extent2 indeed1 a solution of methyl green is more sensitive than zinc4 ,hallwachs 7,wied4 ,ann4 #cg1 p4 #fff7 proved that in liquids showing photo-electric effects there is always strong absorption2 we may1 however1 have absorption without these effects4 ,phosphorescent substances1 such as calcium sulphide show this effect1 as also do various specimens of fluor-spar4 ,as phosphorescence and fluorescence are probably accompanied by a very intense absorption by the surface layers1 the evidence is strong that to get the photo-electric effects we must have strong absorption of some kind of light1 either visible or ultra-violet4 ,illustration3 ,,fig4 #ad4 ,if a conductor ,a is placed near a conductor ,b exposed to ultra-violet light1 and if ,b is made the negative electrode and a difference of potential established between ,a and ,b1 a current of electricity will flow between the conductors4 ,the relation between the magnitude of the current and the difference of potential when ,a and ,b are parallel plates has been investigated by ,stoletow 7,journal de physique1 #ahij1 #aa1 p4 #dfi71 von ,schweidler 7,wien4 ,ber41 #ahii1 #ajh1 p4 #bgc7 and ,varley 7,phil4 ,trans4 ,a41 #aijd1 #bjb1 p4 #dci74 ,the results of some of ,varley's experiments are represented in the curves shown in fig4 #ad1 in which the ordinates are the currents and the abscissae the potentials4 ,it will be seen that when the pressure is exceedingly low the current is independent of the potential difference and is equal to the negative charge carried off in unit time by the corpuscles emitted from the surface exposed to the light4 ,at higher pressures the current rises far above these values and increases rapidly with the potential difference4 ,this is due to the corpuscles emitted by the illuminated surface acquiring under the electric field such high velocities that when they strike against the molecules of the gas through which they are passing they ionize them1 producing fresh ions which can carry on additional current4 ,the relation between the current and the potential difference in this case is in accordance with the results of the theory of ionization by collision4 ,the corpuscles emitted from a body under the action of ultra-violet light start from the surface with a finite velocity4 ,the velocity is not the same for all the corpuscles1 nor indeed could we expect that it should be3 for as ,ladenburg has shown 7,ann4 der ,phys41 #aijc1 #ab1 p4 #eeh7 the seat of their emission is not confined to the surface layer of the illuminated metal but extends to a layer of finite1 though small1 thickness4 ,thus the particles which start deep down will have to force their way through a layer of metal before they reach the surface1 and in doing so will have their velocities retarded by an amount depending on the thickness of this layer4 ,the variation in the velocity of the corpuscles is shown in the following table1 due to ,lenard 7,ann4 der ,phys41 #aijb1 #h1 p4 #adi74 ---------------------------------------- ------------------------- ,carbon4 ,platinum4 ,aluminium4 ---------------------------------------- ------------------------- ,corpuscles emitted with velocities between #ab and #h #ajg cm sec4 #j4jjj #j4jjj #j4jjd between #h and #d #ajg cm sec4 #j4jdi #j4aee #j4aea between #d and #j #ajg cm sec4 #j4fg #j4fe #j4di ,corpuscles only emitted with the help of an external electric #j4bh #j4ba #j4ce field4 ----------------------------- #a4jj #a4jj #a4jj ---------------------------------------- ------------------------- ,if the illuminated surface is completely surrounded by an envelope of the same metal insulated from and completely shielded from the light1 the emission of the negative corpuscles from the illuminated surface would go on until the potential difference ,v between this surface and the envelope became so great that the corpuscles with the greatest velocity lost their energy before reaching the envelope1 i4e4 if m is the mass1 e the charge on a corpuscle1 v the greatest velocity of projection1 until ,ve mv4 ,the values found for ,v by different observers are not very consistent4 ,lenard found that ,v for aluminium was about #c volts and for platinum #b4 ,millikan and ,winchester 7,phil4 ,mag41 ,july #aijg7 found for aluminium ,v 4#gch4 ,the apparatus used by them was so complex that the interpretation of their results is difficult4 ,an extremely interesting fact discovered by ,lenard is that the velocity with which the corpuscles are emitted from the metal is independent of the intensity of the incident light4 ,the quantity of corpuscles increases with the intensity1 but the velocity of the individual corpuscles does not4 ,it is worthy of notice that in other cases when negative corpuscles are emitted from metals1 as for example when the metals are exposed to cathode rays1 ,canal-strahlen1 or ,rntgen rays1 the velocity of the emitted corpuscles is independent of the intensity of the primary radiation which excites them4 ,the velocity is not1 however1 independent of the nature of the primary rays4 ,thus when light is used to produce the emission of corpuscles the velocity1 as ,ladenburg has shown1 depends on the wave length of the light1 increasing as the wave length diminishes4 ,the velocity of corpuscles emitted under the action of cathode rays is greater than that of those ejected by light1 while the incidence of ,rntgen rays produces the emission of corpuscles moving much more rapidly than those in the cases already mentioned1 and the harder the primary rays the greater is the velocity of the corpuscles4 ,the importance of the fact that the velocity and therefore the energy of the corpuscles emitted from the metal is independent of the intensity of the incident light can hardly be overestimated4 ,it raises the most fundamental questions as to the nature of light and the constitution of the molecules4 ,what is the source of the energy possessed by these corpuscles8 ,is it the light1 or in the stores of internal energy possessed by the molecule8 ,let us follow the consequences of supposing that the energy comes from the light4 ,then1 since the energy is independent of the intensity of the light1 the electric forces which liberate the corpuscles must also be independent of that intensity4 ,but this cannot be the case if1 as is usually assumed in the electromagnetic theory1 the wave front consists of a uniform distribution of electric force without structure1 for in this case the magnitude of the electric force is proportional to the square root of the intensity4 ,on the emission theory of light a difficulty of this kind would not arise1 for on that theory the energy in a luminiferous particle remains constant as the particle pursues its flight through space4 ,thus any process which a single particle is able to effect by virtue of its energy will be done just as well a thousand miles away from the source of light as at the source itself1 though of course in a given space there will not be nearly so many particles to do this process far from the source as there are close in4 ,thus1 if one of the particles when it struck against a piece of metal caused the ejection of a corpuscle with a given velocity1 the velocity of emission would not depend on the intensity of the light4 ,there does not seem any reason for believing that the electromagnetic theory is inconsistent with the idea that on this theory1 as on the emission theory1 the energy in the light wave may instead of being uniformly distributed through space be concentrated in bundles which occupy only a small fraction of the volume traversed by the light1 and that as the wave travels out the bundles get farther apart1 the energy in each remaining undiminished4 ,some such view of the structure of light seems to be required to account for the fact that when a plate of metal is struck by a wave of ultra-violet light1 it would take years before the corpuscles emitted from the metal would equal in number the molecules on the surface of the metal plate1 and yet on the ordinary theory of light each one of these is without interruption exposed to the action of the light4 ,the fact discovered by ,e4 ,ladenburg 7,verh4 d4 deutsch4 physik4 ,ges4 #i1 p4 #ejd7 that the velocity with which the corpuscles are emitted depends on the wave length of the light suggests that the energy in each bundle depends upon the wave length and increases as the wave length diminishes4 ,these considerations illustrate the evidence afforded by photo-electric effects on the nature of light2 these effects may also have a deep significance with regard to the structure of matter4 ,the fact that the energy of the individual corpuscles is independent of the intensity of the light might be explained by the hypothesis that the energy of the corpuscles does not come from the light but from the energy stored up in the molecules of the metal exposed to the light4 ,we may suppose that under the action of the light some of the molecules are thrown into an unstable state and explode1 ejecting corpuscles2 the light in this case acts only as a trigger to liberate the energy in the atom1 and it is this energy and not that of the light which goes into the corpuscles4 ,in this way the velocity of the corpuscles would be independent of the intensity of the light4 ,but it may be asked1 is this view consistent with the result obtained by ,ladenburg that the velocity of the corpuscles depends upon the nature of the light8 ,if light of a definite wave length expelled corpuscles with a definite and uniform velocity1 it would be very improbable that the emission of the corpuscles is due to an explosion of the atoms4 ,the experimental facts as far as they are known at present do not allow us to say that the connexion between the velocity of the corpuscles and the wave length of the light is of this definite character1 and a connexion such as a gradual increase of average velocity as the wave length of the light diminishes1 would be quite consistent with the view that the corpuscles are ejected by the explosion of the atom4 ,for in a complex thing like an atom there may be more than one system which becomes unstable when exposed to light4 ,let us suppose that there are two such systems1 ,a and ,b1 of which ,b ejects the corpuscles with the greater velocity4 ,if ,b is more sensitive to the short waves1 and ,a to the long ones1 then as the wave length of the light diminishes the proportion of the corpuscles which come from ,b will increase1 and as these are the faster1 the average velocity of the corpuscles emitted will also increase4 ,and although the potential acquired by a perfectly insulated piece of metal when exposed to ultra-violet light would depend only on the velocity of the fastest corpuscles and not upon their number1 in practice perfect insulation is unattainable1 and the potential actually acquired is determined by the condition that the gain of negative electricity by the metal through lack of insulation1 is equal to the loss by the emission of negatively electrified corpuscles4 ,the potential acquired will fall below that corresponding to perfect insulation by an amount depending on the number of the faster corpuscles emitted1 and the potential will rise if the proportion of the rapidly moving corpuscles is increased1 even though there is no increase in their velocity4 ,it is interesting to compare other cases in which corpuscles are emitted with the case of ultra-violet light4 ,when a metal or gas is bombarded by cathode rays it emits corpuscles and the velocity of these is found to be independent of the velocity of the cathode rays which excite them2 the velocity is greater than for corpuscles emitted under ultra-violet light4 ,again1 when bodies are exposed to ,rntgen rays they emit corpuscles moving with a much greater velocity than those excited by cathode rays1 but again the velocity does not depend upon the intensity of the rays although it does to some extent on their hardness4 ,in the case of cathode and ,rntgen rays1 the velocity with which the corpuscles are emitted seems1 as far as we know at present1 to vary slightly1 but only slightly1 with the nature of the substance on which the rays fall4 ,may not this indicate that the first effect of the primary rays is to detach a neutral doublet1 consisting of a positive and negative charge1 this doublet being the same from whatever system it is detached8 ,and that the doublet is unstable and explodes1 expelling the negative charge with a high velocity1 and the positive one1 having a much larger charge1 with a much smaller velocity1 the momentum of the negative charge being equal to that of the positive4 ,up to now we have been considering the effects produced when light is incident on metals4 ,lenard found 7and the result has been confirmed by the experiments of ,j4 ,j4 ,thomson and ,lyman7 that certain kinds of ultra-violet light ionize a gas when they pass through4 ,the type of ultra-violet light which produces this effect is so easily absorbed that it is stopped by a layer a few millimetres thick of air at atmospheric pressure4 ,ionization by ,collision4--,when the ionization of the gas is produced by external agents such as ,rntgen rays or ultra-violet light1 the electric field produces a current by setting the positive ions moving in one direction1 and the negative ones in the opposite2 it makes use of ions already made and does not itself give rise to ionization4 ,in many cases1 however1 such as in electric sparks1 there are no external agents to produce ionization and the electric field has to produce the ions as well as set them in motion4 ,when the ionization is produced by external means the smallest electric field is able to produce a current through the gas2 when1 however1 these external means are absent no current is produced unless the strength of the electric field exceeds a certain critical value1 which depends not merely upon the nature of the gas but also upon the pressure and the dimensions of the vessel in which it is contained4 ,the variation of the electric field required to produce discharge can be completely explained if we suppose that the ionization of the gas is produced by the impact with its molecules of corpuscles1 and in certain cases of positive ions1 which under the influence of the electric field have acquired considerable kinetic energy4 ,we have direct evidence that rapidly moving corpuscles are able to ionize molecules against which they strike1 for the cathode rays consist of such corpuscles1 and these when they pass through a gas produce large amounts of ionization4 ,suppose then that we have in a gas exposed to an electric field a few corpuscles4 ,these will be set in motion by the field and will acquire an amount of energy in proportion to the product of the electric force1 their charge1 and the distance travelled in the direction of the electric field between two collisions with the molecules of the gas4 ,if this energy is sufficient to give them the ionizing property possessed by cathode rays1 then when a corpuscle strikes against a molecule it will detach another corpuscle2 this under the action of the electric field will acquire enough energy to produce corpuscles on its own account1 and so as the corpuscles move through the gas their number will increase in geometrical progression4 ,thus1 though there were but few corpuscles to begin with1 there may be great ionization after these have been driven some distance through the gas by the electric field4 ,the number of ions produced by collisions can be calculated by the following method4 ,let the electric force be parallel to the axis of x1 and let n be the number of corpuscles per unit volume at a place fixed by the co-ordinate x2 then in unit time these corpuscles will make nu_/lambda collisions with the molecules1 if u is the velocity of a corpuscle and lambda the mean free path of a corpuscle4 ,when the corpuscles are moving fast enough to produce ions by collision their velocities are very much greater than those they would possess at the same temperature if they were not acted on by electrical force1 and so we may regard the velocities as being parallel to the axis of x and determined by the electric force and the mean free path of the corpuscles4 ,we have to consider how many of the nu_/lambda collisions which take place per second will produce ions4 ,we should expect that the ionization of a molecule would require a certain amount of energy1 so that if the energy of the corpuscle fell below this amount no ionization would take place1 while if the energy of the corpuscle were exceedingly large1 every collision would result in ionization4 ,we shall suppose that a certain fraction of the number of collisions result in ionization and that this fraction is a function of the energy possessed by the corpuscle when it collides against the molecules4 ,this energy is proportional to ,xelambda when ,x is the electric force1 e the charge on the corpuscle1 and lambda the mean free path4 ,if the fraction of collisions which produce ionization is int7,xelambda71 then the number of ions produced per cubic centimetre per second is int7,xelambda7nu_/lambda4 ,if the collisions follow each other with great rapidity so that a molecule has not had time to recover from one collision before it is struck again1 the effect of collisions might be cumulative1 so that a succession of collisions might give rise to ionization1 though none of the collisions would produce an ion by itself4 ,in this case int would involve the frequency of the collisions as well as the energy of the corpuscle2 in other words1 it might depend on the current through the gas as well as upon the intensity of the electric field4 ,we shall1 however1 to begin with1 assume that the current is so small that this cumulative effect may be neglected4 ,let us now consider the rate of increase1 dn_/dt1 in the number of corpuscles per unit volume4 ,in consequence of the collisions1 int7,xelambda7nu_/lambda corpuscles are produced per second2 in consequence of the motion of the corpuscles1 the number which leave unit volume per second is greater than those which enter it by 7d_/dx77nu72 while in a certain number of collisions a corpuscle will stick to the molecule and will thus cease to be a free corpuscle4 ,let the fraction of the number of collisions in which this occurs be beta4 ,thus the gain in the number of corpuscles is int7,xelambda7nu_/lambda1 while the loss is 7d_/dx77nu7 beta7nu7_/lambda2 hence dn nu d betanu -- int7,xelambda7 -------- - --7nu7 - --------4 dt lambda dx lambda ,when things are in a steady state dn_/dt #j1 and we have d #a _/ --7nu7 --------7 int7,xelambda7 - beta 7nu4 dx lambda _/ ,if the current is so small that the electrical charges in the gas are not able to produce any appreciable variations in the field1 ,x will be constant and we get nu ,cepsilonalphax1 where alpha int7,xelambda7 - beta_/lambda4 ,if we take the origin from which we measure x at the cathode1 ,c is the value of nu at the cathode1 i4e4 it is the number of corpuscles emitted per unit area of the cathode per unit time2 this is equal to i#j_/;e if i#j is the quantity of negative electricity coming from unit area of the cathode per second1 and e the electric charge carried by a corpuscle4 ,hence we have nue i#j;epsilonalphax4 ,if l is the distance between the anode and the cathode1 the value of nue1 when x l1 is the current passing through unit area of the gas1 if we neglect the electricity carried by negatively electrified carriers other than corpuscles4 ,hence i i#j;epsilonalphal4 ,thus the current between the plates increases in geometrical progression with the distance between the plates4 ,by measuring the variation of the current as the distance between the plates is increased1 ,townsend1 to whom we owe much of our knowledge on this subject1 determined the values of alpha for different values of ,x and for different pressures for air1 hydrogen and carbonic acid gas 7,phil4 ,mag4 #f1 #a1 p4 #aih74 ,since lambda varies inversely as the pressure1 we see that alpha may be written in the form pphi7,x_/p7 or alpha_/,x ,f7,x_/p74 ,the following are some of the values of alpha found by ,townsend for air4 ---------------------------------------- ------------------- ,x ,volts ,pressure ,pressure ,pressure ,pressure ,pressure per 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 from this table that for a given value of ,x1 alpha for small pressures increases as the pressure increases2 it attains a maximum at a particular pressure1 and then diminishes as the pressure increases4 ,the increase in the pressure increases the number of collisions1 but diminishes the energy acquired by the corpuscle in the electric field1 and thus diminishes the change of any one collision resulting in ionization4 ,if we suppose the field is so strong that at some particular pressure the energy acquired by the corpuscle is well above the value required to ionize at each collision1 then it is evident that increasing the number of collisions will increase the amount of ionization1 and therefore alpha1 and alpha cannot begin to diminish until the pressure has increased to such an extent that the mean free path of a corpuscle is so small that the energy acquired by the corpuscle from the electric field falls below the value when each collision results in ionization4 ,the value of p1 when ,x is given1 for which alpha is a maximum1 is proportional to ,x2 this follows at once from the fact that alpha is of the form ,x,f7,x_/p74 ,the value of ,x_/p for which ,f7,x_/p7 is a maximum is seen from the preceding table to be about #dbj1 when ,x is expressed in volts per centimetre and p in millimetres of mercury4 ,the maximum value of ,f7,x_/p7 is about #a_/fj4 ,since the current passing between two planes at a distance l apart is i#j;epsilonalphal or i#j;epsilon,xl,f7,x_/p71 and since the force between the plates is supposed to be uniform1 ,xl is equal to ,v1 the potential between the plates2 hence the current between the plates is i#j;epsilon,vl,f7,x_/p71 and the greatest value it can have is i#j;epsilon,v_/#fj4 ,thus the ratio between the current between the plates when there is ionization and when there is none cannot be greater than epsilon,v_/#fj1 when ,v is measured in volts4 ,this result is based on ,townsend's experiments with very weak currents2 we must remember1 however1 that when the collisions are so frequent that the effects of collisions can accumulate1 alpha may have much larger values than when the current is small4 ,in some experiments made by ,j4 ,j4 ,thomson with intense currents from cathodes covered with hot lime1 the increase in the current when the potential difference was #fj volts1 instead of being e times the current when there was no ionization1 as the preceding theory indicates1 was several hundred times that value1 thus indicating a great increase in alpha with the strength of the current4 ,townsend has shown that we can deduce from the values of alpha the mean free path of a corpuscle4 ,for if the ionization is due to the collisions with the corpuscles1 then unless one collision detaches more than one corpuscle the maximum number of corpuscles produced will be equal to the number of collisions4 ,when each collision results in the production of a corpuscle1 alpha #a_/lambda and is independent of the strength of the electric field4 ,hence we see that the value of alpha1 when it is independent of the electric field1 is equal to the reciprocal of the free path4 ,thus from the table we infer that at a pressure of #ag mm4 the mean free path is #a_/cbe cm42 hence at #a mm4 the mean free path of a corpuscle is #a_/ai cm4 ,townsend has shown that this value of the mean free path agrees well with the value #a_/ba cm4 deduced from the kinetic theory of gases for a corpuscle moving through air4 ,by measuring the values of alpha for hydrogen and carbonic acid gas ,townsend and ,kirby 7,phil4 ,mag4 #f1 #a1 p4 #fcj7 showed that the mean free paths for corpuscles in these gases are respectively #a_/aa4e and #a_/bi cm4 at a pressure of #a mm4 ,these results again agree well with the values given by the kinetic theory of gases4 ,if the number of positive ions per unit volume is m and v is the velocity1 we have nuemve i1 where i is the current through unit area of the gas4 ,since nue i#j;epsilonnx and i i#j;epsilonnl1 when l is the distance between the plates1 we see that nu _/ mv epsilon7nx7 _/ 7epsilon7nl7 - epsilon7nx771 n v epsilon7nx7 -- -- -------------------------------4 m u epsilon7ne7 - epsilon7nx7 ,since v_/u is a very small quantity we see that n will be less than m except when epsilonnl - epsilonnx is small1 i4e4 except close to the anode4 ,thus there will be an excess of positive electricity from the cathode almost up to the anode1 while close to the anode there will be an excess of negative4 ,this distribution of electricity will make the electric force diminish from the cathode to the place where there is as much positive as negative electricity1 where it will have its minimum value1 and then increase up to the anode4 ,the expression i i#j;epsilonalphal applies to the case when there is no source of ionization in the gas other than the collisions2 if in addition to this there is a source of uniform ionization producing q ions per cubic centimetre1 we can easily show that qe i i#j;epsilonalphal -------7ealphal - #a74 alpha ,with regard to the minimum energy which must be possessed by a corpuscle to enable it to produce ions by collision1 ,townsend 7loc4 cit47 came to the conclusion that to ionize air the corpuscle must possess an amount of energy equal to that acquired by the fall of its charge through a potential difference of about #b volts4 ,this is also the value arrived at by ,h4 ,a4 ,wilson by entirely different considerations4 ,stark1 however1 gives #ag volts as the minimum for ionization4 ,the energy depends upon the nature of the gas2 recent experiments by ,dawes and ,gill and ,pedduck 7,phil4 ,mag41 ,aug4 #aijh7 have shown that it is smaller for helium than for air1 hydrogen1 or carbonic acid gas4 ,if there is no external source of ionization and no emission of corpuscles from the cathode1 then it is evident that even if some corpuscles happened to be present in the gas when the electric field were applied1 we could not get a permanent current by the aid of collisions made by these corpuscles4 ,for under the electric field1 the corpuscles would be driven from the cathode to the anode1 and in a short time all the corpuscles originally present in the gas and those produced by them would be driven from the gas against the anode1 and if there was no source from which fresh corpuscles could be introduced into the gas the current would cease4 ,the current1 however1 could be maintained indefinitely if the positive ions in their journey back to the cathode also produced ions by collisions1 for then we should have a kind of regenerative process by which the supply of corpuscles could be continually renewed4 ,to maintain the current it is not necessary that the ionization resulting from the positive ions should be anything like as great as that from the negative1 as the investigation given below shows a very small amount of ionization by the positive ions will suffice to maintain the current4 ,the existence of ionization by collision with positive ions has been proved by ,townsend4 ,another method by which the current could be and is maintained is by the anode emitting corpuscles under the impact of the positive ions driven against it by the electric field4 ,j4 ,j4 ,thomson has shown by direct experiment that positively electrified particles when they strike against a metal plate cause the metal to emit corpuscles 7,j4 ,j4 ,thomson1 ,proc4 ,camb4 ,phil4 ,soc4 #ac1 p4 #bab2 ,austin1 ,phys4 ,rev4 #bb1 p4 #cab74 ,if we assume that the number of corpuscles emitted by the plate in one second is proportional to the energy in the positive ions which strike the plate in that second1 we can readily find an expression for the difference of potential which will maintain without any external ionization a current of electricity through the gas4 ,as this investigation brings into prominence many of the most important features of the electric discharge1 we shall consider it in some detail4 ,let us suppose that the electrodes are parallel plates of metal at right angles to the axis of x1 and that at the cathode x #j and at the anode x d1 d being thus the distance between the plates4 ,let us also suppose that the current of electricity flowing between the plates is so small that the electrification between the plates due to the accumulation of ions is not sufficient to disturb appreciably the electric field1 which we regard as uniform between the plates1 the electric force being equal to ,v_/d1 where ,v is the potential difference between the plates4 ,the number of positive ions produced per second in a layer of gas between the planes x and xdx is alphanudx4 ,here n is the number of corpuscles per unit volume1 alpha the coefficient of ionization 7for strong electric field alpha #a_/lambda'1 where lambda' is the mean free path of a corpuscle71 and u the velocity of a corpuscle parallel to x4 ,we have seen that nu i#j;epsilonalphax1 where i#j is the number of corpuscles emitted per second by unit area of the cathode4 ,thus the number of positive ions produced in the layer is alphai#j;epsilonalphax dx4 ,if these went straight to the cathode without a collision1 each of them would have received an amount of kinetic energy ,vex_/d when they struck the cathode1 and the energy of the group of ions would be ,vex_/dalphai#j;epsilondx dx4 ,the positive ions will1 however1 collide with the molecules of the gas through which they are passing1 and this will diminish the energy they possess when they reach the cathode4 ,the diminution in the energy will increase in geometrical proportion with the length of path travelled by the ion and will thus be proportional to epsilon-betax1 beta will be proportional to the number of collisions and will thus be proportional to the pressure of the gas4 ,thus the kinetic energy possessed by the ions when they reach the cathode will be epsilon-betax ,v7ex_/d7 alphai#j;epsilonalphax dx1 and ,e1 the total amount of energy in the positive ions which reach the cathode in unit time1 will be given by the 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 the number of corpuscles emitted by the cathode in unit time is proportional to this energy we have i#j k,e1 where k is a constant2 hence by equation 7#a7 we have 7beta-alpha7 d ,v ----------------- --1 kealpha ,i where ,i #a - epsilon-7beta-alpha7d 7#a d7beta - alpha774 ,since both beta and alpha are proportional to the pressure1 ,i and 7beta - alpha7d_/alpha are both functions of pd1 the product of the pressure and the spark length1 hence we see that ,v is expressed by an equation of the form #a ,v -- int7pd7 7#b71 ke where int7pd7 denotes a function of pd1 and neither p nor d enter into the expression for ,v except in this product4 ,thus the potential difference required to produce discharge is constant as long as the product of the pressure and spark length remains constant2 in other words1 the spark potential is constant as long as the mass of the gas between the electrodes is constant4 ,thus1 for example1 if we halve the pressure the same potential difference will produce a spark of twice the length4 ,this law1 which was discovered by ,paschen for fairly long sparks 7,annalen1 #cg1 p4 #gi71 and has been shown by ,carr 7,phil4 ,trans41 #aijc7 to hold for short ones1 is one of the most important properties of the electric discharge4 ,we see from the expression for ,v that when 7beta - alpha7d is very large ,v 7beta - alpha7d_/kealpha4 ,thus ,v becomes infinite when d is infinite4 ,again when 7beta - alpha7d is very small we find ,v #a_/kealphad2 thus ,v is again infinite when d is nothing4 ,there must therefore be some value of d intermediate between zero and infinity for which ,v is a minimum4 ,this value is got by finding in the usual way the value of d1 which makes the expression for ,v given in equation 7#a7 a minimum4 ,we find that d must satisfy the equation _/ #a epsilon-7beta-alpha7d #a 7beta - alpha7d 7beta - alphad74 _/ ,we find by a process of trial and error that 7beta-alpha7d #a4h is approximately a solution of this equation2 hence the distance for minimum potential is #a4h_/7;beta - alpha74 ,since beta and alpha are both proportional to the pressure1 we see that the critical spark length varies inversely as the pressure4 ,if we substitute this value in the expression for ,v we find that ,v1 the minimum spark potential1 is given by beta - alpha #b4b ,v ---------------- ---4 alpha ke ,since beta and alpha are each proportional to the pressure1 the minimum potential is independent of the pressure of the gas4 ,on this view the minimum potential depends upon the metal of which the cathode is made1 since k measures the number of corpuscles emitted per unit time by the cathode when struck by positive ions carrying unit energy1 and unless beta bears the same ratio to alpha for all gases the minimum potential will also vary with the gas4 ,the measurements which have been made of the cathode fall of potential1 which as we shall see is equal to the minimum potential required to produce a spark1 show that this quantity varies with the material of which the cathode is made and also with the nature of the gas4 ,since a metal plate1 when bombarded by positive ions1 emits corpuscles1 the effect we have been considering must play a part in the discharge2 it is not1 however1 the only effect which has to be considered1 for as ,townsend has shown1 positive ions when moving above a certain speed ionize the gas1 and cause it to emit corpuscles4 ,it is thus necessary to take into account the ionization of the positive ions4 ,let m be the number of positive ions per unit volume1 and w their velocity1 the number of collisions which occur in one second in one cubic centimetre of the gas will be proportional to mwp1 where p is the pressure of the gas4 ,let the number of ions which result from these collisions be gammamw2 gamma will be a function of p and of the strength of the electric field4 ,let as before n be the number of corpuscles per cubic centimetre1 u their velocity1 and alphanu the number of ions which result in one second from the collisions between the corpuscles and the gas4 ,the number of ions produced per second per cubic centimetre is equal to alphanu gammamw2 hence when things are in a steady state d --7nu7 alphanu gammamw 1 dx and e7nu mw7 i1 where e is the charge on the ion and i the current through the gas4 ,the solution of these equations when the field is uniform between the plates1 is enu ,cepsilon7alpha-gamma7x - gammai_/7alpha - gamma71 emw -,cepsilon7alpha-gamma7x alphai_/7alpha - gamma71 where ,c is a constant of integration4 ,if there is no emission of positive ions from the anode enu i1 when x d4 ,determining ,c from this condition we find i _/ enu ----------------- alphaepsilon7alpha-gamma77x-d7 - gamma 1 alpha - gamma _/ alphai _/ emw ----------------- #a - epsilon7alpha-gamma77x-d7 4 alpha - gamma _/ ,if the cathode did not emit any corpuscles owing to the bombardment by positive ions1 the condition that the charge should be maintained is that there should be enough positive ions at the cathode to carry the current i4e4 that emw i2 when x #j1 the condition gives i _/ ----------------- alphaepsilon-7alpha-gamma7d - gamma #j1 alpha - gamma _/ or epsilonalphad_/alpha epsilongammad_/gamma4 ,since alpha and gamma are both of the form pf7,x_/p7 and ,x ,v_/d1 we see that ,v will be a function of pd1 in agreement with ,paschen's law4 ,if we take into account both the ionization of the gas and the emission of corpuscles by the metal we can easily show that alpha-gammaepsilon7alpha-gamma7d kalpha,ve #a ---------------------------------------- ----- ---------- ------------------------- - alpha - gamma d 7betagamma-alpha7 _/ #a d epsilon-7betagamma-alpha7d ------------------------ ---------------------- 1 7betagamma-alpha7 betagamma-alpha_/ where k and beta have the same meaning as in the previous investigation4 ,when d is large1 epsilon7alpha-gamma7d is also large2 hence in order that the left-hand side of this equation should not be negative gamma must be less than alpha_/epsilon 7alpha-gamma7d2 as this diminishes as d increases we see that when the sparks are very long discharge will take place1 practically as soon as gamma has a finite value1 i4e4 as soon as the positive ions begin to produce fresh ions by their collisions4 ,in the preceding investigation we have supposed that the electric field between the plates was uniform2 if it were not uniform we could get discharges produced by very much smaller differences of potential than are necessary in a uniform field4 ,for to maintain the discharge it is not necessary that the positive ions should act as ionizers all along their path2 it is sufficient that they should do so in the neighbourhood of cathode4 ,thus if we have a strong field close to the cathode we might still get the discharge though the rest of the field were comparatively weak4 ,such a distribution of electric force requires1 however1 a great accumulation of charged ions near the cathode2 until these ions accumulate the field will be uniform4 ,if the uniform field existing in the gas before the discharge begins were strong enough to make the corpuscles produce ions by collision1 but not strong enough to make the positive ions act as ionizers1 there would be some accumulation of ions1 and the amount of this accumulation would depend upon the number of free corpuscles originally present in the gas1 and upon the strength of the electric field4 ,if the accumulation were sufficient to make the field near the cathode so strong that the positive ions could produce fresh ions either by collision with the cathode or with the gas1 the discharge would pass though the gas2 if not1 there will be no continuous discharge4 ,as the amount of the accumulation depends on the number of corpuscles present in the gas1 we can understand how it is that after a spark has passed1 leaving for a time a supply of corpuscles behind it1 it is easier to get a discharge to pass through the gas than it was before4 ,illustration3 ,fig4 #ae4 ,the inequality of the electric field in the gas when a continuous discharge is passing through it is very obvious when the pressure of the gas is low4 ,in this case the discharge presents a highly differentiated appearance of which a type is represented in fig4 #ae4 ,starting from the cathode we have a thin velvety luminous glow in contact with the surface2 this glow is often called the first cathode layer4 ,next this we have a comparatively dark space whose thickness increases as the pressure diminishes2 this is called the ,crookes's dark space1 or the second cathode layer4 ,next this we have a luminous position called the negative glow or the third cathode layer4 ,the boundary between the second and third layers is often very sharply defined4 ,next to the third layer we have another dark space called the ,faraday dark space4 ,next to this and reaching up to the anode is another region of luminosity1 called the positive column1 sometimes 7as in fig4 #ae1 a7 continuous1 sometimes 7as in fig4 #ae1 b7 broken up into light or dark patches called striations4 ,the dimensions of the ,faraday dark space and the positive column vary greatly with the current passing through the gas and with its pressure2 sometimes one or other of them is absent4 ,these differences in appearances are accompanied by great difference in the strength of the electric field4 ,the magnitude of the electric force at different parts of the discharge is represented in fig4 #af1 where the ordinates represent the electric force at different parts of the tube1 the cathode being on the right4 ,we see that the electric force is very large indeed between the negative glow and the cathode1 much larger than in any other part of the tube4 ,it is not constant in this region1 but increases as we approach the cathode4 ,the force reaches a minimum either in the negative glow itself or in the part of the ,faraday dark space just outside1 after which it increases towards the positive column4 ,in the case of a uniform positive column the electric force along it is constant until we get quite close to the anode1 when a sudden change1 called the anode fall1 takes place in the potential4 ,illustration3 ,discharge in ,hydrogen ,pressure #b4be m4m4 ,current #j4efhaj-c ampere ,,fig4 #af4 ,the difference of potential between the cathode and the negative glow is called the cathode potential fall and is found to be constant for wide variations in the pressure of the gas and the current passing through4 ,it increases1 however1 considerably when the current through the gas exceeds a certain critical value1 depending among other things on the size of the cathode4 ,this cathode fall of potential is shown by experiment to be very approximately equal to the minimum potential difference4 ,the following table contains a comparison of the measurements of the cathode fall of potentials in various gases made by ,warburg 7,wied4 ,ann41 #ahhg1 #ca1 p4 #ede1 and #ahij1 #dj1 p4 #a71 ,capstick 7,proc4 ,roy4 ,society1 #ahih1 #fc1 p4 #cef71 and ,strutt 7,phil4 ,trans41 #aijj1 #aic1 p4 #cgg71 and the measurements by ,strutt of the smallest difference of potential which will maintain a spark through these gases4 ---------------------------------------- --------------------------- ,cathode fall in ,volts4 ,least potential ,gas4 ---------------------------------------- difference ,platinum ,electrodes4 ,aluminium required to ,electrodes4maintain a ,spark4 ---------------------------------------- ------------------------ ,warburg4 ,capstick4,strutt4 ,warburg4 ,strutt4 ---------------------------------------- ------------------------ ,air #cdj-cej 44 44 44 #cda ,h#b about #cjj #bih 44 #afh #cjb-cjh ,o#b 44 #cfi 44 44 44 ,n#b #bcj if free #bcb 44 #bjg #bea from oxygen ,hg vapour #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 ---------------------------------------- ------------------------ ,thus in the cases in which the measurements could be made with the greatest accuracy the agreement between the cathode fall and the minimum potential difference is very close4 ,the cathode fall depends on the material of which the terminals are made1 as is shown by the following table due to ,mey 7,verh4 deutsch4 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 ---------------------------------------- - ,the dependence of the minimum potential required to produce a spark upon the metal of which the cathode is made has not been clearly established1 some observers being unable to detect any difference between the potential required to spark between electrodes of aluminium and those of brass1 while others thought they had detected such a difference4 ,it is only with sparks not much longer than the critical spark length that we could hope to detect this difference4 ,when the current through the gas exceeds a certain critical value depending among other things on the size of the cathode1 the cathode fall of potential increases rapidly and at the same time the thickness of the dark spaces diminishes4 ,we may regard the part of the discharge between the cathode and the negative glow as a discharge taking place under minimum potential difference through a distance equal to the critical spark length4 ,an inspection of fig4 #af will show that we cannot regard the electric field as constant even for this small distance2 it thus becomes a matter of interest to know what would be the effect on the minimum potential difference required to produce a spark if there were sufficient ions present to produce variations in the electric field analogous to those represented in fig4 #af4 ,if the electric force at a distance x from the cathode were proportional to epsilon-px we should have a state of things much resembling the distribution of electric force near the cathode4 ,if we apply to this distribution the methods used above for the case when the force was uniform1 we shall find that the minimum potential is less and the critical spark length greater than when the electric force is uniform4 ,potential ,difference required to produce a ,spark of given ,length4--,we may regard the region between the cathode and the negative glow as a place for the production of corpuscles1 these corpuscles finding their way from this region through the negative glow4 ,the parts of this glow towards the anode we may regard as a cathode1 from which1 as from a hot lime cathode1 corpuscles are emitted4 ,let us now consider what will happen to these corpuscles shot out from the negative glow with a velocity depending on the cathode fall of potential and independent of the pressure4 ,these corpuscles will collide with the molecules of the gas1 and unless there is an external electric field to maintain their velocity they will soon come to rest and accumulate in front of the negative glow4 ,the electric force exerted by this cloud of corpuscles will diminish the strength of the electric field in the region between the cathode and the negative glow1 and thus tend to stop the discharge4 ,to keep up the discharge we must have a sufficiently strong electric field between the negative glow and the anode to remove the corpuscles from this region as fast as they are sent into it from the cathode4 ,if1 however1 there is no production of ions in the region between the negative glow and the anode1 all the ions in this region will have come from near the cathode and will be negatively charged2 this negative electrification will diminish the electric force on the cathode side of it and thus tend to stop the discharge4 ,this back electric field could1 however1 be prevented by a little ionization in the region between the anode and glow1 for this would afford a supply of positive ions1 and thus afford an opportunity for the gas in this region to have in it as many positive as negative ions2 in this case it would not give rise to any back electromotive force4 ,the ionization which produces these positive ions may1 if the field is intense1 be due to the collisions of corpuscles1 or it may be due to radiation analogous to ultra-violet1 or soft ,rntgen rays1 which have been shown by experiment to accompany the discharge4 ,thus in the most simple conditions for discharge we should have sufficient ionization to keep up the supply of positive ions1 and an electric field strong enough to keep the velocity of the negative corpuscle equal to the value it has when it emerges from the negative glow4 ,thus the force must be such as to give a constant velocity to the corpuscle1 and since the force required to move an ion with a given velocity is proportional to the pressure1 this force will be proportional to the pressure of the gas4 ,let us call this force ap2 then if l is the distance of the anode from the negative glow the potential difference between these points will be alp4 ,the potential difference between the negative glow and the cathode is constant and equals c2 hence if ,v is the potential difference between the anode and cathode1 then ,v c alp1 a relation which expresses the connexion between the potential difference and spark length for spark lengths greater than the critical distance4 ,it is to be remembered that the result we have obtained applies only to such a case as that indicated above1 where the electric force is constant along the positive column4 ,experiments with the discharge through gases at low pressure show the discharge may take other forms4 ,thus the positive column may be striated when the force along it is no longer uniform1 or the positive column may be absent2 the discharge may be changed from one of these forms to another by altering the current4 ,the relation between the potential and the distance between the electrodes varies greatly1 as we might expect1 with the current passing through the gas4 ,the connexion between the potential difference and the spark length has been made the subject of a large number of experiments4 ,the first measurements were made by ,lord ,kelvin in #ahfj 7,collected ,papers on ,electrostatics and ,magnetism1 p4 #bdg72 subsequent experiments have been made by ,baille 7,ann4 de chimie et de physique1 #e1 #be1 p4 #dhf71 ,liebig 7,phil4 ,mag4 #e1 #bd1 p4 #ajf71 ,paschen 7,wied4 ,ann4 #cg1 p4 #gi71 ,peace 7,proc4 ,roy4 ,soc41 #ahib1 #eb1 p4 #ii71 ,orgler 7,ann4 der ,phys4 #a1 p4 #aei71 ,strutt 7,phil4 ,trans4 #aic1 p4 #cgg71 ,bouty 7,comptes rendus1 #aca1 pp4 #dfi1 #ejc71 ,earhart 7,phil4 ,mag4 #f1 #a1 p4 #adg71 ,carr 7,phil4 ,trans41 #aijc71 ,russell 7,phil4 ,mag4 #e1 #fd1 p4 #bcg71 ,hobbs 7,phil4 ,mag4 #f1 #aj1 p4 #fag71 ,kinsley 7,phil4 ,mag4 #f1 #i1 #fib71 ,ritter 7,ann4 der ,phys4 #ad1 p4 #aah74 ,the results of their experiments show that for sparks considerably longer than the critical spark length1 the relation between the potential difference ,v and the spark length l may be expressed when the electrodes are large with great accuracy by the linear relation ,v c blp1 where p is the pressure and c and b are constants depending on the nature of the gas4 ,when the sparks are long the term blp is the most important and the sparking potential is proportional to the spark length4 ,though there are considerable discrepancies between the results obtained by different observers1 these indicate that the production of a long spark between large electrodes in air at atmospheric pressure requires a potential difference of #cj1jjj volts for each centimetre of spark length4 ,in hydrogen only about half this potential difference is required1 in carbonic acid gas the potential difference is about the same as in air1 while ,ritter's experiments show that in helium only about one-tenth of this potential difference is required4 ,in the case when the electric field is not uniform1 as for example when the discharge takes place between spherical electrodes1 ,russell's experiments show that the discharge takes place as soon as the maximum electric force in the field between the electrodes reaches a definite value1 which he found was for air at atmospheric pressure about #ch1jjj volts per centimetre4 ,very ,short ,sparks4--,some very interesting experiments on the potential difference required to produce exceedingly short sparks have been made by ,earhart1 ,hobbs and ,kinsley2 the length of these sparks was comparable with the wave length of sodium light4 ,with sparks of these lengths it was found that it was possible to get a discharge with less than #ccj volts1 the minimum potential difference in air4 ,the results of these observers show that there is no diminution in the minimum potential difference required to produce discharge until the spark length gets so small that the average electric force between the electrodes amounts to about one million volts per centimetre4 ,when the force rises to this value a discharge takes place even though the potential difference is much less than #ccj volts2 in some of ,earhart's experiments it was only about #b volts4 ,this kind of discharge is determined not by the condition that the potential difference should have a given value1 but that the electric force should have a given value4 ,another point in which this discharge differs from the ordinary one is that it is influenced entirely by the nature of the electrodes and not by the nature or pressure of the gas between them1 whereas the ordinary discharge is in many cases not affected appreciably by changes in the metal of the electrodes1 but is always affected by changes in the pressure and character of the gas between them4 ,kinsley found that when one of these small sparks passed between the electrodes a kind of metallic bridge was formed between them1 so that they were in metallic connexion1 and that the distance between them had to be considerably increased before the bridge was broken4 ,almy 7,phil4 ,mag41 ,sept4 #aijh71 who used very small electrodes1 was unable to get a discharge with less than the minimum spark potential even when the spark length was reduced to one-third of the wave length of sodium light4 ,he suggests that the discharges obtained with larger electrodes for smaller voltages are due to the electrodes being dragged together by the electrostatic attraction between them4 ,constitution of the ,electric ,spark4--,schuster and ,hemsalech 7,phil4 ,trans4 #aic1 p4 #ahi71 ,hemsalech 7,comptes ,rendus1 #acj1 p4 #hih2 #acb1 p4 #iag2 ,jour4 de ,phys4 #c4 #i1 p4 #dc1 and ,schenck1 ,astrophy4 ,jour4 #ad1 p4 #aaf7 have by spectroscopic methods obtained very interesting results about the constitution of the spark4 ,the method employed by ,schuster and ,hemsalech was as follows3 ,suppose we photograph the spectrum of a horizontal spark on a film which is on the rim of a wheel rotating about a horizontal axis with great velocity4 ,if the luminosity travelled with infinite speed from one electrode to the other1 the image on the film would be a horizontal line4 ,if1 however1 the speed with which the luminosity travelled between the electrodes was comparable with the speed of the film1 the line would be inclined to the horizontal1 and by measuring the inclinations we could find the speed at which the luminosity travelled4 ,in this way ,schuster and ,hemsalech showed that when an oscillating discharge passed between metallic terminals in air1 the first spark passes through the air alone1 no lines of the metal appearing in its spectrum4 ,this first spark vaporizes some of the metal and the subsequent sparks passing mainly through the metallic vapour2 the appearance of the lines in the film shows that the velocity of the luminous part of the vapour was finite4 ,the velocity of the vapour of metals of low atomic weight was in general greater than that of the vapour of heavier metals4 ,thus the velocity of aluminium vapour was #ahij metres per second1 that of zinc and cadmium only about #ede4 ,perhaps the most interesting point in the investigation was the discovery that the velocities corresponding to different lines in the spectrum of the same metal were in some cases different4 ,thus with bismuth some of the lines indicated a velocity of #adbj metres per second1 others a velocity of only #eej1 while one 7lambda #cgic7 showed a still smaller velocity4 ,these results are in accordance with a view suggested by other phenomena that many of the lines in a spectrum produced by an electrical discharge originate from systems formed during the discharge and not from the normal atom or molecule4 ,schuster and ,hemsalech found that by inserting a coil with large self induction in the primary circuit they could obliterate the air lines in the discharge4 ,schenck1 by observing the appearance presented when an alternating current1 produced by discharging ,leyden jars1 was examined in a rapidly rotating mirror1 found it showed the following stages3 7#a7 a thin bright line1 followed in some cases at intervals of half the period of the discharge by fainter lines2 7#b7 bright curved streamers starting from the negative terminal1 and diminishing rapidly in speed as they receded from the cathode2 7#c7 a diffused glow lasting for a much longer period than either of the preceding4 ,these constituents gave out quite different spectra4 ,the structure of the discharge is much more easily studied when the pressure of the gas is low1 as the various parts which make up the discharge are more widely separated from each other4 ,we have already described the general appearance of the discharge through gases at low pressures 7see p4 #feg74 ,there is1 however1 one form of discharge which is so striking and beautiful that it deserves more detailed consideration4 ,in this type of discharge1 known as the striated discharge1 the positive column is made up of alternate bright and dark patches known as striations4 ,some of these are represented in fig4 #ag1 which is taken from a paper by ,de la ,rue and ,mller 7,phil4 ,trans41 #ahgh1 ,pt4 #a74 ,this type of discharge only occurs when the current and the pressure of the gas are between certain limits4 ,it is most beautifully shown when a ,wehnelt cathode is used and the current is produced by storage cells1 as this allows us to use large currents and to maintain a steady potential difference between the electrodes4 ,the striations are in consequence very bright and steady4 ,the facts which have been established about these striations are as follows3 ,the distance between the bright parts of the striations is greater at low pressures than at high2 it depends also upon the diameter of the tube1 increasing as the diameter of the tube increases4 ,if the discharge tube is wide at one place and narrow in another the striations will be closer together in the narrow parts than in the wide4 ,the distance between the striations depends on the current through the tube4 ,the relation is not a very simple one1 as an increase of current sometimes increases while under other circumstances it decreases the distance between the striations 7see ,willows1 ,proc4 ,camb4 ,phil4 ,soc4 #aj1 p4 #cjb74 ,the electric force is not uniform along the striated discharge1 but is greater in the bright than in the dark parts of the striation4 ,an example is shown in fig4 #af1 due to ,h4 ,a4 ,wilson1 which shows the distribution of electric force at every place in a striated discharge4 ,in experiments made by ,j4 ,j4 ,thomson 7,phil4 ,mag41 ,oct4 #aiji71 using a ,wehnelt cathode1 the variations in the electric force were more pronounced than those shown in fig4 #af4 ,the electric force in this case changed so greatly that it actually became negative just on the cathode side of the bright part of the striation4 ,just inside the striation on the anode side it rose to a very high value1 then continually diminished towards the bright side of the next striation when it again increased4 ,this distribution of electric force implies that there is great excess of negative electricity at the bright head of the striation1 and a small excess of positive everywhere else4 ,the temperature of the gas is higher in the bright than in the dark parts of the striations4 ,wood 7,wied4 ,ann4 #di1 p4 #bch71 who has made a very careful study of the distribution of temperature in a discharge tube1 finds that in those tubes the temperature varies in the same way as the electric force1 but that this temperature 7which it must be remembered is the average temperature of all the molecules and not merely of those which are taking part in the discharge7 is by no means high2 in no part of the discharge did the temperature in his experiments exceed #ajj ,c4 ,illustration3 ,,fig4 #ag4 ,theory of the ,striations4--,we may regard the heaping up of the negative charges at intervals along the discharge as the fundamental feature in the striations1 and this heaping up may be explained as follows4 ,imagine a corpuscle projected with considerable velocity from a place where the electric field is strong1 such as the neighbourhood of the cathode2 as it moves towards the anode through the gas it will collide with the molecules1 ionize them and lose energy and velocity4 ,thus unless the corpuscle is acted on by a field strong enough to supply it with the energy it loses by collision1 its speed will gradually diminish4 ,further1 when its energy falls below a certain value it will unite with a molecule and become part of a negative ion1 instead of a corpuscle2 at this stage there will be a sudden and very large diminution in its velocity4 ,let us now follow the course of a stream of corpuscles starting from the cathode and approaching the anode4 ,if the speed falls off as the stream proceeds1 the corpuscles in the rear will gain on those in front and the density of the stream in the front will be increased4 ,if at a certain place the velocity receives a sudden check by the corpuscles becoming loaded with a molecule1 the density of the negative electricity will increase at this place with great rapidity1 and here there will be a great accumulation of negative electricity1 as at the bright head on the cathode side of a striation4 ,now this accumulation of negative electricity will produce a large electric force on the anode side2 this will drive corpuscles forward with great velocity and ionize the gas4 ,these corpuscles will behave like those shot from the cathode and will accumulate again at some distance from their origin1 forming the bright head of the next striation1 when the process will be repeated4 ,on this view the bright heads of the striations act like electrodes1 and the discharge passes from one bright head to the next as by a number of stepping stones1 and not directly from cathode to anode4 ,the luminosity at the head of the striations is due to the recombination of the ions4 ,these ions have acquired considerable energy from the electric field1 and this energy will be available for supplying the energy radiated away as light4 ,the recombination of ions which do not possess considerable amounts of energy does not seem to give rise to luminosity4 ,thus1 in an ionized gas not exposed to an electric field1 although we have recombination between the ions1 we need not have luminosity4 ,we have at present no exact data as to the amount of energy which must be given to an ion to make it luminous on recombination2 it also certainly varies with the nature of the ion2 thus even with hot ,wehnelt cathodes ,j4 ,j4 ,thomson has never been able to make the discharge through air luminous with a potential less than from #af to #ag volts4 ,the mercury lamps1 however1 in which the discharge passes through mercury vapour are luminous with a potential difference of about #ab volts4 ,it follows that if the preceding theory be right the potential difference between two bright striations must be great enough to make the corpuscles ionize by collision and also to give enough energy to the ions to make them luminous when they recombine4 ,the difference of potential between the bright parts of successive striations has been measured by ,hohn 7,phys4 ,zeit4 #i1 p4 #eeh72 it varies with the pressure and with the gas4 ,the smallest value given by ,hohn is about #ae volts4 ,in some experiments made by ,j4 ,j4 ,thomson1 when the pressure of the gas was very low1 the difference of potential between two adjacent dark spaces was as low as #c4ge volts4 ,the ,arc ,discharge4--,the discharges we have hitherto considered have been characterized by large potential differences and small currents4 ,in the arc discharge we get very large currents with comparatively small potential differences4 ,we may get the arc discharge by taking a battery of cells large enough to give a potential difference of #fj to #hj volts1 and connecting the cells with two carbon terminals1 which are put in contact1 so that a current of electricity flows round the circuit4 ,if the terminals1 while the current is on1 are drawn apart1 a bright discharge1 which may carry a current of many amperes1 passes from one to the other4 ,this arc discharge1 as it is called1 is characterized by intense heat and by the brilliant luminosity of the terminals4 ,this makes it a powerful source of light4 ,the temperature of the positive terminal is much higher than that of the negative4 ,according to ,violle 7,comptes ,rendus1 #aae1 p4 #abgc7 the temperature of the tip of the former is about #cejj ,c1 and that of the latter #bgjj ,c4 ,the temperature of the arc itself he found to be higher than that of either of its terminals4 ,as the arc passes1 the positive terminal gets hollowed out into a crater-like shape1 but the negative terminal remains pointed4 ,both terminals lose weight4 ,the appearance of the terminals is shown in fig4 #ah1 given by ,mrs ,ayrton 7,proc4 ,inst4 ,elec4 ,eng4 #bh1 p4 #djj72 a1 b represent the terminals when the arc is quiet1 and c when it is accompanied by a hissing sound4 ,the intrinsic brightness of the positive crater does not increase with an increase in the current2 an increased current produces an increase in the area of the luminous crater1 but the amount of light given out by each unit of area of luminous surface is unaltered4 ,this indicates that the temperature of the crater is constant2 it is probably that at which carbon volatilizes4 ,w4 ,e4 ,wilson 7,proc4 ,roy4 ,soc4 #eh1 p4 #agd2 #fj1 p4 #cgg7 has shown that at pressures of several atmospheres the intrinsic brightness of the crater is considerably diminished4 ,illustration3 ,,fig4 #ah4 ,illustration3 ,,fig4 #ai4 ,the connexion between ,v1 the potential difference between the terminals1 and l1 the length of the arc1 is somewhat analogous to that which holds for the spark discharge4 ,frhlich 7,electrotech4 ,zeit4 #d1 p4 #aej7 gives for this connexion the relation ,v m nl1 where m and n are constants4 ,mrs ,ayrton 7,the ,electric ,arc1 chap4 iv47 finds that both m and n depend upon the current passing between the terminals1 and gives as the relation between ,v and l1 ,v alpha beta_/,i 7gamma delta_/,i7l1 where alpha1 beta1 gamma1 delta are constants and ,i the current4 ,the relation between current and potential difference was made the subject of a series of experiments by ,ayrton 7,electrician1 #a1 p4 #cai2 xi4 p4 #dah71 some of whose results are represented in fig4 #ai4 ,for a quiet arc an increase in current is accompanied by a fall in potential difference1 while for the hissing arc the potential difference is independent of the current4 ,the quantities m and n which occur in ,frhlich's equation have been determined by several experimenters4 ,for carbon electrodes in air at atmospheric pressure m is about #ci volts1 varying somewhat with the size and purity of the carbons2 it is diminished by soaking the terminals in salt solution4 ,the value of n given by different observers varies considerably1 ranging from 4#gf to #b volts when l is measured in millimetres2 it depends upon the current1 diminishing as the current increases4 ,when metallic terminals are used instead of carbons1 the value of m depends upon the nature of the metal1 m in general being larger the higher the temperature at which the metal volatilizes4 ,thus v4 ,lang 7,wied4 ,ann4 #ca1 p4 #chd7 found the following values for m in air at atmospheric pressure3--,c #ce2 ,pt #bg4d2 ,fe #be2 ,ni #bf4ah2 ,cu #bc4hf2 ,ag #ae4bc2 ,zn #ai4hf2 ,cd #aj4bh4 ,lecher 7,wied4 ,ann4 #cc1 p4 #fji7 gives ,pt #bh1 ,fe #bj1 ,ag #h1 while ,arons 7,wied4 ,ann4 #ca1 p4 #chd7 found for ,hg the value #ab4h2 in this case the fall of potential along the arc itself was abnormally small4 ,in comparing these values it is important to remember that ,lecher 7loc4 cit47 has shown that with ,fe or ,pt terminals the arc discharge is intermittent4 ,arons has shown that this is also the case with ,hg terminals1 but no intermittence has been detected with terminals of ,c1 ,ag or ,cu4 ,the preceding measurements refer to mean potentials1 and no conclusions as to the actual potential differences at any time can be drawn when the discharge is discontinuous1 unless we know the law of discontinuity4 ,the ease with which an arc is sustained depends greatly on the nature of the electrodes2 when they are brass1 zinc1 cadmium1 or magnesium it is exceedingly difficult to get the arc4 ,illustration3 ,,fig4 #bj4 ,illustration3 ,,fig4 #ba4 ,the potential difference between the terminals is affected by the pressure of the gas4 ,the most extensive series of experiments on this point is that made by ,duncan1 ,rowland1 and ,tod 7,electrician1 #ca1 p4 #fj71 whose results are represented in fig4 #bj4 ,we see from these curves that for very short arcs the potential difference increases continuously with the pressure1 but for longer ones there is a critical pressure at which the potential difference is a minimum1 and that this critical pressure seems to increase with the length of arc4 ,the nature of the gas also affects the potential difference4 ,the magnitude of this effect may be gathered from the following values given by ,arons 7,ann4 der ,phys4 #a1 p4 #gjj7 for the potential difference required to produce an arc #a4e mm4 long1 carrying a current of #d4e amperes1 between terminals of different metals in air and pure nitrogen4 ---------------------------- ,terminal4 ,air4 ,nitrogen4 ---------------------------- ,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 ---------------------------- ,thus1 with the discharge for an arc of given length and current1 the nature of the terminals is the most important factor in determining the potential difference4 ,the effects produced by the pressure and nature of the surrounding gas1 although quite appreciable1 are not of so much importance1 while in the spark discharge the nature of the terminals is of no importance1 everything depending upon the nature and pressure of the gas4 ,the potential gradient in the arc is very far from being uniform4 ,with carbon terminals ,luggin 7,wien4 ,ber4 #ih1 p4 #aaib7 found that1 with a current of #ae amperes1 there was a fall of potential of #cc4g close to the anode1 and one #h4g close to the cathode1 so that the curve representing the distribution of potential between the terminals would be somewhat like that shown in fig4 #ba4 ,we have seen that a somewhat analogous distribution of potential holds in the case of conduction through flames1 though in that case the greatest drop of potential is in general at the cathode and not at the anode4 ,the difference between the changes of potential at the anode and cathode is not so large with ,fe and ,cu terminals as with carbon ones2 with mercury terminals1 ,arons 7,wied4 ,ann4 #eh1 p4 #gc7 found the anode fall to be #g4d volts1 the cathode fall #e4d volts4 ,the case of the arc when the cathode is a pool of mercury and the anode a metal wire placed in a vessel from which the air has been exhausted is one which has attracted much attention1 and important investigations on this point have been made by ,hewitt 7,electrician1 #eb1 p4 #ddg71 ,wills 7,electrician1 #ed1 p4 #bf71 ,stark1 ,retschinsky and ,schnaposnikoff 7,ann4 der ,phys4 #ah1 p4 #bac7 and ,pollak 7,ann4 der ,phys4 #ai1 p4 #bag74 ,in this arrangement the mercury is vaporized by the heat1 and the discharge which passes through the mercury vapour gives an exceedingly bright light1 which has been largely used for lighting factories1 c4 ,the arrangement can also be used as a rectifier1 for a current will only pass through it when the mercury pool is the cathode4 ,thus if such a lamp is connected with an alternating current circuit1 it lets through the current in one direction and stops that in the other1 thus furnishing a current which is always in one direction4 ,theory of the ,arc ,discharge4--,an incandescent body such as a piece of carbon even when at a temperature far below that of the terminals in an arc1 emits corpuscles at a rate corresponding to a current of the order of #a ampere per square centimetre of incandescent surface1 and as the rate of increase of emission with the temperature is very rapid1 it is probably at the rate of many amperes per square centimetre at the temperature of the negative carbon in the arc4 ,if then a piece of carbon were maintained at this temperature by some external means1 and used as a cathode1 a current could be sent from it to another electrode whether the second electrode were cold or hot4 ,if1 however1 these negatively electrified corpuscles did not produce other ions either by collision with the gas through which they move or with the anode1 the spaces between cathode and anode would have a negative charge1 which would tend to stop the corpuscles leaving the cathode and would require a large potential difference between anode and cathode to produce any considerable current4 ,if1 however1 there is ionization either in the gas or at the anode1 the positive ions will diffuse into the region of the discharge until they are sensibly equal in number to the negative ions4 ,when this is the case the back electromotive force is destroyed and the same potential difference will carry a much larger current4 ,the arc discharge may be regarded as analogous to the discharge between incandescent terminals1 the only difference being that in the arc the terminals are maintained in the state of incandescence by the current and not by external means4 ,on this view the cathode is bombarded by positive ions which heat it to such a temperature that negative corpuscles sufficient to carry the current are emitted by it4 ,these corpuscles bombard the anode and keep it incandescent4 ,they ionize also1 either directly by collision or indirectly by heating the anode1 the gas and vapour of the metal of which the anode is made1 and produce in this way the supply of positive ions which keep the cathode hot4 ,discharge from a ,point4--,a very interesting case of electric discharge is that between a sharply pointed electrode1 such as a needle1 and a metal surface of considerable area4 ,at atmospheric pressures the luminosity is confined to the immediate neighbourhood of the point4 ,if the sign of the potential of the point does not change1 the discharge is carried by ions of one sign--that of the charge on the pointed electrode4 ,the velocity of these ions under a given potential gradient has been measured by ,chattock 7,phil4 ,mag4 #cb1 p4 #bhe71 and found to agree with that of the ions produced by ,rntgen or uranium radiation1 while ,townsend 7,phil4 ,trans4 #aie1 p4 #bei7 has shown that the charge on these ions is the same as that on the ions streaming from the point4 ,if the pointed electrode be placed at right angles to a metal plane serving as the other electrode1 the discharge takes place when1 for a given distance of the point from the plane1 the potential difference between the electrodes exceeds a definite value depending upon the pressure and nature of the gas through which the discharge passes2 its value also depends upon whether1 beginning with a small potential difference1 we gradually increase it until discharge commences1 or1 beginning with a large potential difference1 we decrease it until the discharge stops4 ,the value found by the latter method is less than that by the former4 ,according to ,chattock's measurements the potential difference ,v for discharge between the point and the plate is given by the linear relation ,v a bl1 where l is the distance of the point from the plate and a and b are constants4 ,from v4 ,obermayer's 7,wien4 ,ber4 #ajj1 #b1 p4 #abg7 experiments1 in which the distance l was greater than in ,chattock's1 it would seem that the potential for larger distances does not increase quite so rapidly with l as is indicated by ,chattock's relation4 ,the potential required to produce this discharge is much less than that required to produce a spark of length l between parallel plates2 thus from ,chattock's experiments to produce the point discharge when l 4#e cm4 in air at atmospheric pressure requires a potential difference of about #chjj volts when the pointed electrode is positive1 while to produce a spark at the same distance between plane electrodes would require a potential difference of about #ae1jjj volts4 ,chattock showed that with the same pointed electrode the value of the electric intensity at the point was the same whatever the distance of the point from the plane4 ,the value of the electric intensity depended upon the sharpness of the point4 ,when the end of the pointed electrode is a hemisphere of radius a1 ,chattock showed that for the same gas at the same pressure the electric intensity f when discharge takes place is roughly proportioned to a-#j4h4 ,the value of the electric intensity at the pointed electrode is much greater than its value at a plane electrode for long sparks2 but we must remember that at a distance from a pointed electrode equal to a small multiple of the radius of curvature of its extremity the electric intensity falls very far below that required to produce discharge in a uniform field1 so that the discharge from a pointed electrode ought to be compared with a spark whose length is comparable with the radius of curvature of the point4 ,for such short sparks the electric intensity is very high4 ,the electric intensity required to produce the discharge from a gas diminishes as the pressure of the gas diminishes1 but not nearly so rapidly as the electric intensity for long sparks4 ,here again the discharge from a point is comparable with short sparks1 which1 as we have seen1 are much less sensitive to pressure changes than longer ones4 ,the minimum potential at which the electricity streams from the point does not depend upon the material of which the point is made2 it varies1 however1 considerably with the nature of the gas4 ,the following are the results of some experiments on this point4 ,those in the first two columns are due to ,rntgen1 those in the third and fourth to ,precht3-- ---------------------------------------- --------------- ,discharge ,potential4 ,point 4 ,pressure #gfj4 ,gas4 ---------------------------------------- ------- ,pressure #bje4 ,pressure #aaj4 ,point 4 ,point -4 ---------------------------------------- ------------- ,volts4 ,volts4 ,volts4 ,volts4 ,h#b #abif #aagd #babe #aeej ,o#b #bdjb #aige #bhjj #bcej ,,co #bfcd #bajj 44 44 ,,ch#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 from this table that in the case of the discharge from a positively electrified point the greater the molecular weight of the gas the greater the potential required for discharge4 ,rntgen concluded from his experiments that the discharging potential from a positive point in different gases at the same pressure varies inversely as the mean free path of the molecules of the gas4 ,in the same gas1 however1 at different pressures the discharging potential does not vary so quickly with the pressure as does the mean free path4 ,in ,precht's experiments1 in which different gases were used1 the variations in the discharging potential are not so great as the variations in the mean free path of the gases4 ,the current of electrified air flowing from the point when the electricity is escaping--the well-known electrical wind--is accompanied by a reaction on the point which tends to drive it backwards4 ,this reaction has been measured by ,arrhenius 7,wied4 ,ann4 #fc1 p4 #cje71 who finds that when positive electricity is escaping from a point in air the reaction on the point for a given current varies inversely as the pressure of the gas1 and for different gases 7air1 hydrogen and carbonic acid7 inversely as the square root of the molecular weight of the gas4 ,the reaction when negative electricity is escaping is much less4 ,the proportion between the reactions for positive and negative currents depends on the pressure of the gas4 ,thus for equal positive and negative currents in air at a pressure of #gj cm4 the reaction for a positive point was #a4i times that of a negative one1 at #dj cm4 pressure #b4f times1 at #bj cm4 pressure #c4b times1 at #aj4c cm4 pressure #g times1 and at #e4a cm4 pressure #ae times the reaction for the negative point4 ,investigation shows that the reaction should be proportional to the quotient of the current by the velocity acquired by an ion under unit potential gradient4 ,now this velocity is inversely proportional to the pressure1 so that the reaction should on this view be directly proportional to the pressure4 ,this agrees with ,arrhenius' results when the point is positive4 ,again1 the velocities of an ion in hydrogen1 air and carbonic acid at the same pressure are approximately inversely proportional to the square roots of their molecular weights1 so that the reaction should be directly proportional to this quantity4 ,this also agrees with ,arrhenius' results for the discharge from a positive point4 ,the velocity of the negative ion is greater than that of a positive one under the same potential gradient1 so that the reaction for the negative point should be less than that for a positive one1 but the excess of the positive reaction over the negative is much greater than that of the velocity of the negative ion over the velocity of the positive4 ,there is1 however1 reason to believe that a considerable condensation takes place around the negative ion as a nucleus after it is formed1 so that the velocity of the negative ion under a given potential gradient will be greater immediately after the ion is formed than when it has existed for some time4 ,the measurements which have been made of the velocities of the ions relate to those which have been some time in existence1 but a large part of the reaction will be due to the newly-formed ions moving with a greater velocity1 and thus giving a smaller reaction than that calculated from the observed velocity4 ,with a given potential difference between the point and the neighbouring conductor the current issuing from the point is greater when the point is negative than when it is positive1 except in oxygen1 when it is less4 ,warburg 7,sitz4 ,akad4 d4 ,wissensch4 zu ,berlin1 #ahii1 #ej1 p4 #ggj7 has shown that the addition of a small quantity of oxygen to nitrogen produces a great diminution in the current from a negative point1 but has very little effect on the discharge from a positive point4 ,thus the removal of a trace of oxygen made a leak from a negative point #ej times what it was before4 ,experiments with hydrogen and helium showed that impurities in these gases had a great effect on the current when the point was negative1 and but little when it was positive4 ,this suggests that the impurities1 by condensing round the negative ions as nuclei1 seriously diminish their velocity4 ,if a point is charged up to a high and rapidly alternating potential1 such as can be produced by the electric oscillations started when a ,leyden jar is discharged1 then in hydrogen1 nitrogen1 ammonia and carbonic acid gas a conductor placed in the neighbourhood of the point gets a negative charge1 while in air and oxygen it gets a positive one4 ,there are two considerations which are of importance in connexion with this effect4 ,the first is the velocity of the ions in the electric field1 and the second the ease with which the ions can give up their charges to the metal point4 ,the greater velocity of the negative ions would1 if the potential were rapidly alternating1 cause an excess of negative ions to be left in the surrounding gas4 ,this is the case in hydrogen4 ,if1 however1 the metal had a much greater tendency to unite with negative than with positive ions1 such as we should expect to be the case in oxygen1 this would act in the opposite direction1 and tend to leave an excess of positive ions in the gas4 ,the ,characteristic ,curve for ,discharge through ,gases4--,when a current of electricity passes through a metallic conductor the relation between the current and the potential difference is the exceedingly simple one expressed by ,ohm's law2 the current is proportional to the potential difference4 ,when the current passes through a gas there is no such simple relation4 ,thus we have already mentioned cases where the current increased as the potential increased although not in the same proportion1 while as we have seen in certain stages of the arc discharge the potential difference diminishes as the current increases4 ,thus the problem of finding the current which a given battery will produce when part of the circuit consists of a gas discharge is much more complicated than when the circuit consists entirely of metallic conductors4 ,if1 however1 we measure the potential difference between the electrodes in the gas when different currents are sent through it1 we can plot a curve1 called the characteristic curve1 whose ordinates are the potential differences between the electrodes in the gas and the abscissae the corresponding currents4 ,by the aid of this curve we can calculate the current produced when a given battery is connected up to the gas by leads of known resistance4 ,for let ,e#j be the electromotive force of the battery1 ,r the resistance of the leads1 i the current1 the potential difference between the terms in the gas will be ,e#j - ,ri4 ,let ,,abc 7fig4 #bb7 be the characteristic curve1 the ordinates being the potential difference between the terminals in the gas1 and the abscissae the current4 ,draw the line ,,lm whose equation is ,e ,e#j - ,ri1 then the points where this line cuts the characteristic curves will give possible values of i and ,e1 the current through the discharge tube and the potential difference between the terminals4 ,some of these points may1 however1 correspond to an unstable position and be impossible to realize4 ,the following method gives us a criterion by which we can distinguish the stable from the unstable positions4 ,if the current is increased by deltai1 the electromotive force which has to be overcome by the battery is ,rdeltai d,e_/di deltai4 ,if ,r d,e_/di is positive there will be an unbalanced electromotive force round the circuit tending to stop the current4 ,thus the increase in the current will be stopped and the condition will be a stable one4 ,if1 however1 ,r d,e_/di is negative there will be an unbalanced electromotive force tending to increase the current still further2 thus the current will go on increasing and the condition will be unstable4 ,thus for stability ,r d,e_/di must be positive1 a condition first given by ,kaufmann 7,ann4 der ,phys4 #aa1 p4 #aeh74 ,the geometrical interpretation of this condition is that the straight line ,,lm must1 at the point where it cuts the characteristic curve1 be steeper than the tangent to characteristic curve4 ,thus of the points ,,abc where the line cuts the curve in fig4 #bb1 ,a and ,c correspond to stable states and ,b to an unstable one4 ,the state of things represented by a point ,p on the characteristic curve when the slope is downward cannot be stable unless there is in the external circuit a resistance greater than that represented by the tangent of the inclination of the tangent to the curve at ,p to the horizontal axis4 ,illustration3 ,,fig4 #bb4 ,if we keep the external electromotive force the same and gradually increase the resistance in the leads1 the line ,,lm will become steeper and steeper4 ,c will move to the left so that the current will diminish2 when the line gets so steep that it touches the curve at ,c'1 any further increase in the resistance will produce an abrupt change in the current2 for now the state of things represented by a point near ,a' is the only stable state4 ,thus if the ,,bc part of the curve corresponded to a luminous discharge and the ,a part to a dark discharge1 we see that if the electromotive force is kept constant there is a minimum value of the current for the luminous discharge4 ,if the current is reduced below this value1 the discharge ceases to be luminous1 and there is an abrupt diminution in the current4 ,cathode ,rays4--,when the gas in the discharge tube is at a very low pressure some remarkable phenomena occur in the neighbourhood of the cathode4 ,these seem to have been first observed by ,plcker 7,pogg4 ,ann4 #ajg1 p4 #gg2 #aaf1 p4 #de7 who noticed on the walls of the glass tube near the cathode a greenish phosphorescence1 which he regarded as due to rays proceeding from the cathode1 striking against the sides of the tube1 and then travelling back to the cathode4 ,he found that the action of a magnet on these rays was not the same as the action on the part of the discharge near the positive electrode4 ,hittorf 7,pogg4 ,ann4 #acf1 p4 #h7 showed that the agent producing the phosphorescence was intercepted by a solid1 whether conductor or insulator1 placed between the cathode and the sides of the tube4 ,he regarded the phosphorescence as caused by a motion starting from the cathode and travelling in straight lines through the gas4 ,goldstein 7,monat4 der ,berl4 ,akad41 #ahgf1 p4 #bd7 confirmed this discovery of ,hittorf's1 and further showed that a distinct1 though not very sharp1 shadow is cast by a small object placed near a large plane cathode4 ,this is a proof that the rays producing the phosphorescence must be emitted almost normally from the cathode1 and not1 like the rays of light from a luminous surface1 in all directions1 for such rays would not produce a perceptible shadow if a small body were placed near the plane4 ,goldstein regarded the phosphorescence as due to waves in the ether1 for whose propagation the gas was not necessary4 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 i4 p4 #ace2 pt4 ii4 pp4 #ehg1 #ffa71 who made many remarkable researches in this subject1 took a different view4 ,he regarded the rays as streams of negatively electrified particles projected normally from the cathode with great velocity1 and1 when the pressure is sufficiently low1 reaching the sides of the tube1 and by their impact producing phosphorescence and heat4 ,the rays on this view are deflected by a magnet1 because a magnet exerts a force on a charged moving body4 ,these rays striking against glass make it phosphorescent4 ,the colour of the phosphorescence depends on the kind of glass2 thus the light from soda glass is a yellowish green1 and that from lead glass blue4 ,many other bodies phosphoresce when exposed to these rays1 and in particular the phosphorescence of some gems1 such as rubies and diamonds1 is exceedingly vivid4 ,the spectrum of the phosphorescent light is generally continuous1 but ,crookes showed that the phosphorescence of some of the rare earths1 such as yttrium1 gives a spectrum of bright bands1 and he founded on this fact a spectroscopic method of great importance4 ,goldstein 7,wied4 ,ann4 #ed1 p4 #cga7 discovered that the haloid salts of the alkali metals change colour under the rays1 sodium chloride1 for example1 becoming violet4 ,the coloration is a surface one1 and has been traced by ,e4 ,wiedemann and ,schmidt 7,wied4 ,ann4 #ed1 p4 #fah7 to the formation of a subchloride4 ,chlorides of tin1 mercury and lead also change colour in the same way4 ,e4 ,wiedemann 7,wied4 ,ann4 #ef1 p4 #bja7 discovered another remarkable effect1 which he called thermo-luminescence2 he found that many bodies after being exposed to the cathode rays possess for some time the power of becoming luminous when their temperature is raised to a point far below that at which they become luminous in the normal state4 ,substances belonging to the class called by van 't ,hoff solid solutions exhibit this property of thermo-luminescence to a remarkable extent4 ,they are formed when two salts1 one greatly in excess of the other1 are simultaneously precipitated from a solution4 ,a trace of ,mn,s,o#d in ,ca,s,o#d shows very brilliant thermo-luminescence4 ,the impact of cathode rays produces after a time perceptible changes in the glass4 ,crookes 7,phil4 ,trans4 pt4 ii4 #ahgi1 p4 #fde7 found that after glass has been phosphorescing for some time under the cathode rays it seems to get tired1 and the phosphorescence is not so bright as it was initially4 ,thus1 for example1 when the shadow of a ,maltese cross is thrown on the walls of the tube as in fig4 #bc1 if after the discharge has been going on for some time the cross is shaken down or a new cathode used whose line of fire does not cut the cross1 the pattern of the cross will still be seen on the glass1 but it will now be brighter instead of darker than the surrounding portion4 ,the portions shielded by the cross1 not being tired by being made to phosphoresce for a long time1 respond more vigorously to the stimulus than those portions which have not been protected4 ,skinner 7,proc4 ,camb4 ,phil4 ,soc4 ix4 p4 #cga7 and ,thomson found on the glass which had been exposed to the rays gelatinous filaments1 apparently silica1 resulting from the reduction of the glass4 ,a reducing action was also noticed by ,villard 7,journ4 de phys4 #c1 viii4 p4 #adj7 and ,wehnelt 7,wied4 ,ann4 #fg1 p4 #dba74 ,it can be well shown by letting the rays fall on a plate of oxidized copper1 when the part struck by the rays will become bright4 ,the rays heat bodies on which they fall1 and if they are concentrated by using as a cathode a portion of a spherical surface1 the heat at the centre becomes so great that a piece of platinum wire can be melted or a diamond charred4 ,measurements of the heating effects of the rays have been made by ,thomson 7,phil4 ,mag4 #e1 #dd1 p4 #bic7 and ,cady 7,ann4 der ,phys4 #a1 p4 #fgh74 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 i4 p4 #aeb7 showed that a vane mounted as in a radiometer is set in rotation by the rays1 the direction of the rotation being the same as would be produced by a stream of particles proceeding from the cathode4 ,the movement is not due to the momentum imparted to the vanes by the rays1 but to the difference in temperature between the sides of the vanes1 the rays making the side against which they strike hotter than the other4 ,illustration3 ,,fig4 #bc4 ,effect of a ,magnet4--,the rays are deflected by a magnet1 so that the distribution of phosphorescence over the glass and the shape and position of the shadows cast by bodies in the tube are altered by the proximity of a magnet4 ,the laws of magnetic deflection of these rays have been investigated by ,plcker 7,pogg4 ,ann4 #ajc1 p4 #hh71 ,hittorf 7,pogg4 ,ann4 #acf1 p4 #bac71 ,crookes 7,phil4 ,trans41 #ahgi1 pt4 #a1 p4 #eeg71 and ,schuster 7,proc4 ,roy4 ,soc4 #dg1 p4 #ebf74 ,the deflection is the same as that of negatively electrified particles travelling along the path of the rays4 ,such particles would in a magnetic field be acted on by a force at right angles to the direction of motion of the particle and also to the magnetic force1 the magnitude of the force being proportional to the product of the velocity of the particle1 the magnetic force1 and the sine of the angle between these vectors4 ,in this case we have seen that if the particle is not acted on by an electrostatic field1 the path in a uniform magnetic field is a spiral1 which1 if the magnetic force is at right angles to the direction of projection of the particle1 becomes a circle in the plane at right angles to the magnetic force1 the radius being mv_/,he1 where m1 v1 e are respectively the mass1 velocity and charge on the particle1 and ,h is the magnetic force4 ,the smaller the difference of potential between the electrodes of the discharge tube the greater the deflection produced by a magnetic field of given strength1 and as the difference of potential rapidly increases with diminution of pressure1 after a certain pressure has been passed1 the higher the exhaustion of the tube the less the magnetic deflection of the rays4 ,birkeland 7,comptes rendus1 #ahif1 p4 #dib7 has shown that when the discharge is from an induction coil the cathode rays produced in the tube at any one time are not equally deflected by a magnet1 but that a narrow patch of phosphorescence when deflected by a magnet is split up into several distinct patches1 giving rise to what ,birkeland calls the magnetic spectrum4 ,strutt 7,phil4 ,mag4 #dh1 p4 #dgh7 has shown that this magnetic spectrum does not occur if the discharge of a large number of cells is employed instead of the coil4 ,thomson 7,proc4 ,camb4 ,phil4 ,soc4 #i1 p4 #bdc7 has shown that if the potential difference between the electrodes is kept the same the magnetic deflection is independent of the nature of the gas filling the discharge tube2 this was tested with gases so different as air1 hydrogen1 carbonic acid and methyl iodide4 ,charge of ,negative ,electricity carried by the ,rays4--,we have seen that the rays are deflected by a magnet1 as if they were particles charged with negative electricity4 ,perrin 7,comptes rendus1 #aba1 p4 #aacj7 showed by direct experiment that a stream of negative electricity is associated with the rays4 ,a modification made by ,thomson of ,perrin's experiment is sketched in fig4 #bd 7,phil4 ,mag4 #dh1 p4 #dgh74 ,illustration3 ,,fig4 #bd4 ,the rays start from the cathode ,a1 and pass through a slit in a solid brass rod ,b fitting tightly into the neck of the tube4 ,this rod is connected with earth and used as the anode4 ,the rays after passing through the slit travel through the vessel ,c4 ,d and ,e are two insulated metal cylinders insulated from each other1 and each having a slit cut in its face so as to enable the rays to pass into the inside of the inner cylinder1 which is connected with an electrometer1 the outer cylinder being connected with the earth4 ,the two cylinders are placed on the far side of the vessel1 but out of the direct line of fire of the rays4 ,when the rays go straight through the slit there is only a very small negative charge communicated to the inner cylinder1 but when they are deflected by a magnet so that the phosphorescent patch falls on the slit in the outer cylinder the inner cylinder receives a very large negative charge1 the increase coinciding very sharply with the appearance of the phosphorescent patch on the slit4 ,when the patch is so much deflected by the magnet that it falls below the slit1 the negative charge in the cylinder again disappears4 ,this experiment shows that the cathode rays are accompanied by a stream of negative electrification4 ,the same apparatus can be used to show that the passage of cathode rays through a gas makes it a conductor of electricity4 ,for if the induction coil is kept running and a stream of the rays kept steadily going into the inner cylinder1 the potential of the inner cylinder reaches a definite negative value below which it does not fall1 however long the rays may be kept going4 ,the cylinder reaches a steady state in which the gain of negative electricity from the cathode rays is equal to the loss by leakage through the conducting gas1 the conductivity being produced by the passage of the rays through it4 ,if the inner cylinder is charged up initially with a greater negative charge than corresponds to the steady state1 on turning the rays on to the cylinder the negative charge will decrease and not increase until it reaches the steady state4 ,the conductivity produced by the passage of cathode rays through a gas diminishes rapidly with the pressure4 ,when rays pass through a gas at a low pressure1 they are deflected by an electric field2 when the pressure of the gas is higher the conductivity it acquires when the cathode rays pass through it is so large that the potential gradient cannot reach a sufficiently high value to produce an appreciable deflection4 ,thus the cathode rays carry a charge of negative electricity2 the experiment described on page #hge 7fig4 #ac7 shows that they are deflected by an electric field as if they were negatively electrified1 and are acted on by a magnetic force in just the way this force would act on a negatively electrified body moving along the path of the rays4 ,there is therefore every reason for believing that they are charges of negative electricity in rapid motion4 ,by measuring the deflection produced by magnetic and electric fields we can determine the velocity with which these particles moved and the ratio of the mass of the particle to the charge carried by it4 ,we may conclude from the experiments that the value of m_/e for the particles constituting the cathode rays is of the order #a_/a4g #ajg1 and we have seen that m_/e has the same value in all the other cases of negative ions in a gas at low pressure for which it has been measured--viz4 for the ions produced when ultra-violet light falls on a metal plate1 or when an incandescent carbon filament is surrounded by a gas at a low pressure1 and for the beta particles given out by radio-active bodies4 ,we have also seen that the value of the charge on the gaseous ion1 in all cases in which it has been measured--viz4 the ions produced by ,rntgen and uranium radiation1 by ultra-violet light1 and by the discharge of electrification from a point--is the same in magnitude as the charge carried by the hydrogen atom in the electrolysis of solutions4 ,the mass of the hydrogen alone is1 however1 #aj-d times this charge1 while the mass of the carriers of negative electrification is only #a_/a4g #ajg times the charge2 hence the mass of the carriers of the negative electrification is only #a_/agjj of the mass of the hydrogen atom4 ,we are thus1 by the study of the electric discharge1 forced to recognize the existence of masses very much smaller than the smallest mass hitherto recognized4 ,direct determinations of the velocity of the cathode rays have been made by ,j4 ,j4 ,thomson 7,phil4 ,mag4 #ch1 p4 #ceh71 who measured the interval between the appearance of phosphorescence on two pieces of glass placed at a known distance apart1 and by ,maiorana 7,nuovo ,cimento1 #d1 #f1 p4 #ccf7 and ,battelli and ,stefanini 7,phys4 ,zeit4 #a1 p4 #ea71 who measured the interval between the arrival of the negative charge carried by the rays at two places separated by a known distance4 ,the values of the velocity got in this way are much smaller than the values got by the indirect methods previously described3 thus ,j4 ,j4 ,thomson at a fairly high pressure found the velocity to be #b #ajg cm4_/sec4 ,maiorana found values ranging between #ajg and #f #ajg cm4_/sec1 and ,battelli and ,stefanini values ranging from #f #ajf to #a4b #ajg4 ,in these methods it is very difficult to eliminate the effect of the interval which elapses between the arrival of the rays and the attainment by the means of detection1 such as the phosphorescence of the glass or the deflection of the electrometer1 of sufficient intensity to affect the senses4 ,illustration3 ,,fig4 #be4 ,transmission of ,cathode ,rays through ,solids--,lenard ,rays4--,it was for a long time believed that all solids were absolutely opaque to these rays1 as ,crookes and ,goldstein had proved that very thin glass1 and even a film of collodion1 cast intensely black shadows4 ,hertz 7,wied4 ,ann4 #de1 p4 #bh71 however1 showed that behind a piece of gold-leaf or aluminium foil an appreciable amount of phosphorescence occurred on the glass1 and that the phosphorescence moved when a magnet was brought near4 ,a most important advance was next made by ,lenard 7,wied4 ,ann4 #ea1 p4 #bbe71 who got the cathode rays to pass from the inside of a discharge tube to the air outside4 ,for this purpose he used a tube like that shown in fig4 #be4 ,the cathode ,k is an aluminium disc #a4b cm4 in diameter fastened to a stiff wire1 which is surrounded by a glass tube4 ,the anode ,a is a brass strip partly surrounding the cathode4 ,the end of the tube in front of the cathode is closed by a strong metal cap1 fastened in with marine glue1 in the middle of which a hole #a4g mm4 in diameter is bored1 and covered with a piece of very thin aluminium foil about 4#jjbf mm4 in thickness4 ,the aluminium window is in metallic contact with the cap1 and this and the anode are connected with the earth4 ,the tube is then exhausted until the cathode rays strike against the window4 ,diffuse light spreads from the window into the air outside the tube1 and can be traced in a dark room for a distance of several centimetres4 ,from the window1 too1 proceed rays which1 like the cathode rays1 can produce phosphorescence1 for certain bodies phosphoresce when placed in the neighbourhood of the window4 ,this effect is conveniently observed by the platino-cryanide screens used to detect ,rntgen radiation4 ,the properties of the rays outside the tube resemble in all respects those of cathode rays2 they are deflected by a magnet and by an electric field1 they ionize the gas through which they pass and make it a conductor of electricity1 and they affect a photographic plate and change the colour of the haloid salts of the alkali metals4 ,as1 however1 it is convenient to distinguish between cathode rays outside and inside the tube1 we shall call the former ,lenard rays4 ,in air at atmospheric pressure the ,lenard rays spread out very diffusely4 ,if the aluminium window1 instead of opening into the air1 opens into another tube which can be exhausted1 it is found that the lower the pressure of the gas in this tube the farther the rays travel and the less diffuse they are4 ,by filling the tube with different gases ,lenard showed that the greater the density of the gas the greater is the absorption of these rays4 ,thus they travel farther in hydrogen than in any other gas at the same pressure4 ,lenard showed1 too1 that if he adjusted the pressure so that the density of the gas in this tube was the same--if1 for example1 the pressure when the tube was filled with oxygen was #a_/af of the pressure when it was filled with hydrogen--the absorption was constant whatever the nature of the gas4 ,becker 7,ann4 der ,phys4 #ag1 p4 #cha7 has shown that this law is only approximately true1 the absorption by hydrogen being abnormally large1 and by the inert monatomic gases1 such as helium and argon1 abnormally small4 ,the distance to which the ,lenard rays penetrate into this tube depends upon the pressure in the discharge tube2 if the exhaustion in the latter is very high1 so that there is a large potential difference between the cathode and the anode1 and therefore a high velocity for the cathode rays1 the ,lenard rays will penetrate farther than when the pressure in the discharge tube is higher and the velocity of the cathode rays smaller4 ,lenard showed that the greater the penetrating power of his rays the smaller was their magnetic deflection1 and therefore the greater their velocity2 thus the greater the velocity of the cathode rays the greater is the velocity of the ,lenard rays to which they give rise4 ,for very slow cathode rays the absorption by different gases departs altogether from the density law1 so much so that the absorption of these rays by hydrogen is greater than that by air 7,lenard1 ,ann4 der ,phys4 #ab1 p4 #gcb74 ,lenard 7,wied4 ,ann4 #ef1 p4 #bee7 studied the passage of his rays through solids as well as through gases1 and arrived at the very interesting result that the absorption of a substance depends only upon its density1 and not upon its chemical composition or physical state2 in other words1 the amount of absorption of the rays when they traverse a given distance depends only on the quantity of matter they cut through in the distance4 ,mc,clelland 7,proc4 ,roy4 ,soc4 #fa1 p4 #bbg7 showed that the rays carry a charge of negative electricity1 and ,m',lennan measured the amount of ionization rays of given intensity produced in different gases1 finding that if the pressure is adjusted so that the density of the different gases is the same the number of ions per cubic centimetre is also the same4 ,in this case1 as ,lenard has shown1 the absorption is the same1 so that with the ,lenard rays1 as with uranium and probably with ,rntgen rays1 equal absorption corresponds to equal ionization4 ,a convenient method for producing ,lenard rays of great intensity has been described by ,des ,coudres 7,wied4 ,ann4 #fb1 p4 #acd74 ,diffuse ,reflection of ,cathode ,rays4--,when cathode rays fall upon a surface1 whether of an insulator or a conductor1 cathode rays start from the surface in all directions4 ,this phenomenon1 which was discovered by ,goldstein 7,wied4 ,ann4 #fb1 p4 #acd71 has been investigated by ,starke 7,wied4 ,ann4 #ff1 p4 #di2 ,ann4 der ,phys4 #aaa1 p4 #ge71 ,austin and ,starke 7,ann4 der ,phys4 #i1 p4 #bga71 ,campbell-,swinton 7,proc4 ,roy4 ,soc4 #fd1 p4 #cgg71 ,merritt 7,phys4 ,rev4 #g1 p4 #bag7 and ,gehrcke 7,ann4 der ,phys4 #h1 p4 #ha72 it is often regarded as analogous to the diffuse reflection of light from such a surface as gypsum1 and is spoken of as the diffuse reflection of the cathode rays4 ,according to ,merritt and ,austin and ,starke the deviation in a magnetic field of these reflected rays is the same as that of the incident rays4 ,the experiments1 however1 were confined to rays reflected so that the angle of reflection was nearly equal to that of incidence4 ,gehrcke showed that among the reflected rays there were a large number which had a much smaller velocity than the incident ones4 ,according to ,campbell-,swinton the diffuse reflection is accompanied by a certain amount of specular reflection4 ,lenard1 who used slower cathode rays than ,austin and ,starke1 could not detect in the scattered rays any with velocities comparable with that of the incident rays2 he obtained copious supplies of slow rays whose speed did not depend on the angle of incidence of the primary rays 7,ann4 der ,phys4 #ae1 p4 #dhe74 ,when the angle of incidence is very oblique the surface struck by the rays gets positively charged1 showing that the secondary rays are more numerous than the primary4 ,repulsion of two ,cathode ,streams4--,goldstein discovered that if in a tube there are two cathodes connected together1 the cathodic rays from one cathode are deflected when they pass near the other4 ,experiments bearing on this subject have been made by ,crookes and ,wiedemann and ,ebert4 ,the phenomena may be described by saying that the repulsion of the rays from a cathode ,a by a cathode ,b is only appreciable when the rays from ,a pass through the ,crookes dark space round ,b4 ,this is what we should expect if we remember that the electric field in the dark space is far stronger than in the rest of the discharge1 and that the gas in the other parts of the tube is rendered a conductor by the passage through it of the cathode rays1 and therefore incapable of transmitting electrostatic repulsion4 ,scattering of the ,negative ,electrodes4--,in addition to the cathode rays1 portions of metal start normally from the cathode and form a metallic deposit on the walls of the tube4 ,the amount of this deposit varies very much with the metal4 ,crookes 7,proc4 ,roy4 ,soc4 #ej1 p4 #hh7 found that the quantities of metal torn from electrodes of the same size1 in equal times1 by the same current1 are in the order ,pd1 ,au1 ,ag1 ,pb1 ,sn1 ,pt1 ,cu1 ,cd1 ,ni1 ,in1 ,fe4444 ,in air there is very little deposit from an ,al cathode1 but it is abundant in tubes filled with the monatomic gases1 mercury vapour1 argon or helium4 ,the scattering increases as the density of the gas diminishes4 ,the particles of metal are at low pressures deflected by a magnet1 though not nearly to the same extent as the cathode rays4 ,according to ,grandquist1 the loss of weight of the cathode in a given time is proportional to the square of the current2 it is therefore not1 like the loss of the cathode in ordinary electrolysis1 proportional to the quantity of current which passes through it4 ,illustration3 ,,fig4 #bf4 ,positive ,rays or ,canalstrahlen4--,goldstein 7,berl4 ,sitzungsb4 #ci1 p4 #fia7 found that with a perforated cathode certain rays occurred behind the cathode which were not appreciably deflected by a magnet2 these he called ,canalstrahlen1 but we shall1 for reasons which will appear later1 call them positive rays4 ,their appearance is well shown in fig4 #bf1 taken from a paper by ,wehnelt 7,wied4 ,ann4 #fg1 p4 #dba7 in which they are represented at ,b4 ,goldstein found that their colour depends on the gas in which they are formed1 being gold-colour in air and nitrogen1 rose-colour in hydrogen1 yellowish rose in oxygen1 and greenish gray in carbonic acid4 ,the colour of the luminosity due to positive rays is not in general the same as that due to anode rays2 the difference is exceptionally well marked in helium1 where the cathode ray luminosity is blue while that due to the positive rays is red4 ,the luminosity produced when the rays strike against solids is also quite distinct4 ,the cathode rays make the body emit a continuous spectrum1 while the spectrum produced by the positive rays often shows bright lines4 ,thus lithium chloride under cathode rays gives out a steely blue light and the spectrum is continuous1 while under the positive rays the salt gives out a brilliant red light and the spectrum shows the red helium line4 ,it is remarkable that the lines on the spectra of the alkali metals are much more easily produced when the positive rays fall on the oxide of the metal than when they fall on the metal itself4 ,thus when the positive rays fall on a pool of the liquid alloy of sodium and potassium the specks of oxide on the surface shine with a bright yellow light while the untarnished part of the surface is quite dark4 ,w4 ,wien 7,wied4 ,ann4 #fe1 p4 #dde7 measured the values of e_/m for the particles forming the positive rays4 ,other measurements have been made by ,ewers 7,wied4 ,ann4 #fi1 p4 #afg7 and ,j4 ,j4 ,thomson 7,phil4 ,mag4 #ac1 p4 #efa74 ,the differences between the values of e_/m for the cathode and positive rays are very remarkable4 ,for cathode rays whose velocity does not approach that of light1 e_/m is always equal to #a4g #ajh1 while for the positive rays the greatest value of this quantity yet observed is #ajd1 which is also the value of e_/m for the hydrogen ions in the electrolysis of dilute solutions4 ,in some experiments made by ,j4 ,j4 ,thomson 7,phil4 ,mag41 #ad1 p4 #cei7 it was found that when the pressure of the gas was not too low the bright spot produced by the impact of a pencil of these rays on a phosphorescent screen is deflected by electric and magnetic forces into a continuous band extending on both sides of the undeflected position4 ,the portion on one side is in general much fainter than that on the other4 ,the direction of this deflection shows that it is produced by particles charged with negative electricity1 while the brighter band is due to particles charged with positive electricity4 ,the negatively electrified particles which produce the band c4c are not corpuscles1 for from the electric and magnetic deflections we can find the value of e_/m4 ,as this proves to be equal to #ajd1 we see that the mass of the carrier of the negative charge is comparable with that of an atom1 and so very much greater than that of a corpuscle4 ,at very low pressures part of the phosphorescence disappears1 while the upper portion breaks up into two patches 7fig4 #bg74 ,for one of these the maximum value of e_/m is #ajd and for the other #e #aj4 ,at low pressures the appearance of the patches and the values of e_/m are the same whether the tube is filled originally with air1 hydrogen or helium4 ,in some of the experiments the tube was exhausted until the pressure was too low to allow the discharge to pass4 ,a very small quantity of the gas under investigation was then admitted into the tube1 just sufficient to allow the discharge to pass1 and the deflection of the phosphorescent patch measured4 ,the following gases were admitted into the tube1 air1 carbonic oxide1 oxygen1 hydrogen1 helium1 argon and neon1 but whatever the gas the appearance of the phosphorescence was the same2 in every case there were two patches1 for one of which e_/m #ajd and for the other e_/m #e #aj4 ,in helium at higher pressures another patch was observed1 for which e_/m #b4e #ajh4 ,the continuous band into which the phosphorescent spot is drawn out when the pressure is not exceedingly low1 which involves the existence of particles for which the mean value of e_/m varies from zero to #ajd1 can be explained as follows4 ,the rays on their way to the phosphorescent screen have to pass through gas which is ionized by the passage through it of the positive rays2 this gas will therefore contain free corpuscles4 ,the particles which constitute the rays start with a charge of positive electricity4 ,some of these particles in their journey through the gas attract a corpuscle whose negative charge neutralizes the positive charge on the particle4 ,the particles when in this neutral state may be ionized by collision and reacquire a positive charge1 or by attracting another particle may become negatively charged1 and this process may be repeated several times on their journey to the phosphorescent screen4 ,thus some of the particles1 instead of being positively charged for the whole of the time they are exposed to the electric and magnetic forces1 may be for a part of that time without a charge or even have a negative charge4 ,the deflection of a particle is proportional to the average value of its charge whilst under the influence of the deflecting forces4 ,thus if a particle is without a charge for a part of the time1 its deflection will be less than that of a particle which has retained its positive charge for the whole of its journey1 while the few particles which have a negative charge for a longer time than they have a positive will be deflected in the opposite direction to the main portion and will produce the tail 7fig4 #bg74 ,illustration3 ,fig4 #bg4 ,a similar explanation will apply to the positive rays discovered by ,villard 7,comptes rendus1 #adc1 p4 #fgd7 and ,j4 ,j4 ,thomson 7,phil4 ,mag4 #ac1 p4 #cei71 which travel in the opposite direction to the rays we have been considering1 i4e4 they travel away from the cathode and in the direction of the cathode's rays2 these rays are sometimes called retrograde rays4 ,these as far as has been observed have always the same maximum value of e_/m1 i4e4 #ajd1 and there are a considerable number of negative ones always mixed with them4 ,the maximum velocity of both the positive and retrograde rays is about #b #ajh cm4_/sec4 and varies very little with the potential difference between the electrodes in the tube in which they are produced 7,j4 ,j4 ,thomson1 ,phil4 ,mag41 ,dec4 #aiji74 ,the positive rays show1 when the pressure is not very low1 the line spectrum of the gas through which they pass4 ,an exceedingly valuable set of observations on this point have been made by ,stark and his pupils 7,physik4 ,zeit4 #f1 p4 #hib2 ,ann4 der ,phys4 #ba1 pp4 #dj1 #deg74 ,stark has shown that in many gases1 notably hydrogen1 the spectrum shows the ,doppler effect1 and he has been able to calculate in this way the velocity of the positive rays4 ,anode ,rays4--,gehrcke and ,reichenhein 7,ann4 der ,phys4 #be1 p4 #hfa7 have found that when the anode consists of a mixture of sodium and lithium chloride raised to a high temperature either by the discharge itself or by an independent heating circuit1 very conspicuous rays come from the anode when the pressure of the gas in the discharge tube is very low1 and a large coil is used to produce the discharge4 ,the determination of e_/m for these rays showed that they are positively charged atoms of sodium or lithium1 moving with very considerable velocity2 in some of ,gehrcke's experiments the maximum velocity was as great as #a4h #ajg cm4_/sec4 though the average was about #ajg cm4_/sec4 ,these velocities are less than those of the positive rays whose maximum velocity is about #b #ajh cm4_/sec4 7,j4 ,j4 ,t47 ,,footnotes3 #a ,the values for nickel and bismuth given in the table are much higher than later values obtained with pure electrolytic nickel and bismuth4 #b ,the value here given1 namely #ab4hhe1 for the electric mass-resistivity of liquid mercury as determined by ,matthiessen is now known to be too high by nearly #a4 ,the value at present accepted is #ab4ghi ohms per metre-gramme at #j ,c4 #c ,the value 7#afcj7 here given for hard-drawn copper is about higher than the value now adopted1 namely1 #afbf4 ,the difference is due to the fact that either ,jenkin or ,matthiessen did not employ precisely the value at present employed for the density of hard-drawn and annealed copper in calculating the volume-resistivities from the mass-resistivities4 #d ,matthiessen's value for nickel is much greater than that obtained in more recent researches4 7,see ,matthiessen and ,vogt1 ,phil4 ,trans41 #ahfc1 and ,j4 ,a4 ,fleming1 ,proc4 ,roy4 ,soc41 ,december #ahii47 #e ,matthiessen's value for mercury is nearly #a greater than the value adopted at present as the mean of the best results1 namely #id1jgj4 #f ,the samples of silver1 copper and nickel employed for these tests were prepared electrolytically by ,sir ,j4 ,w4 ,swan1 and were exceedingly pure and soft4 ,the value for volume-resistivity of nickel as given in the above table 7from experiments by ,j4 ,a4 ,fleming1 ,proc4 ,roy4 ,soc41 ,december #ahii7 is much less 7nearly #dj7 than the value given by ,matthiessen's researches4 #g ,the electrolytic bismuth here used was prepared by ,hartmann and ,braun1 and the resistivity taken by ,j4 ,a4 ,fleming4 ,the value is nearly #bj less than that given by ,matthiessen4 #h ,in #ahii a committee was formed of representatives from eight of the leading manufacturers of insulated copper cables with delegates from the ,post ,office and ,institution of ,electrical ,engineers1 to consider the question of the values to be assigned to the resistivity of hard-drawn and annealed copper4 ,the sittings of the committee were held in ,london1 the secretary being ,a4 ,h4 ,howard4 ,the values given in the above paragraphs are in accordance with the decision of this committee1 and its recommendations have been accepted by the ,general ,post ,office and the leading manufacturers of insulated copper wire and cables4 #i ,platinoid is an alloy introduced by ,martino1 said to be similar in composition to ,german silver1 but with a little tungsten added4 ,it varies a good deal in composition according to manufacture1 and the resistivity of different specimens is not identical4 ,its electric properties were first made known by ,j4 ,t4 ,bottomley1 in a paper read at the ,royal ,society1 ,may #e1 #ahhe4 #aj ,an equivalent gramme molecule is a weight in grammes equal numerically to the chemical equivalent of the salt4 ,for instance1 one equivalent gramme molecule of sodium chloride is a mass of #eh4e grammes4 ,na,cl #eh4e4 #aa ,f4 ,kohlrausch and ,l4 ,holborn1 ,das ,leitvermgen der ,elektrolyte 7,leipzig1 #ahih74 #ab ,it should be noticed that the velocities calculated in ,kohlrausch's theory and observed experimentally are the average velocities1 and involve both the factors mentioned above2 they include the time wasted by the ions in combination with each other1 and1 except at great dilution1 are less than the velocity with which the ions move when free from each other4