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 \MBRIDGE PHYSICAL SERIES. 
 
 CONDUCTION OF ELECTRICITY 
 THROUGH GASES 
 
 
1 
 
 EonDon: C. J. CLAY AND SONS, 
 
 CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, 
 
 AVE MARIA LANE. 
 
 AND 
 
 H. K. LEWIS, 
 136, GOWER STREET, W.C. 
 
 (Slaaaoto: 50, WELLINGTON STREET. 
 
 Ettpjig: F. A. BROCKHAUS. 
 
 #rfo Hork: THE MACMILLAN COMPANY. 
 
 Bombay anH Calcutta: MACMILLAN AND CO., LTD. 
 
 [All Rights reserved.] 
 
ONDUCTION OF ELECTEICITY 
 THROUGH GASES J 
 
 BY 
 
 J. J. THOMSON, D.Sc., LL.D., PH.D., F.R.S. 
 
 FELLOW OF TRINITY COLLEGE, CAMBRIDGE 
 CAVENDISH PROFESSOR OF EXPERIMENTAL PHYSICS, CAMBRIDGE 
 
 CAMBRIDGE : 
 
 AT THE UNIVERSITY PRESS. 
 1903 
 
Oc 711 
 
 ' T4- 
 
 Cambridge : 
 
 PRINTED BY J. AND C. F. CLAY, 
 AT THE UNIVERSITY PRESS. 
 
I 
 
 Si 
 
 if PREFACE. 
 
 T HAVE endeavoured in this work to develope the view that 
 - the conduction of electricity through gases is due to the 
 presence in the gas of small particles charged with electricity, 
 called ions, which under the influence of electric forces move 
 from one part of the gas to another. My object has been to 
 show how the various .phenomena exhibited when electricity 
 passes through gases can be coordinated by this conception 
 rather than to attempt to give a complete account of the very 
 numerous investigations which have been made on the electrical 
 properties of gases ; I have therefore confined myself for the 
 most part to those phenomena which furnish results sufficiently 
 precise to serve as a test of the truth of this theory. The book 
 contains the subject-matter of lectures given at the Cavendish 
 Laboratory where a good deal of attention has been paid to 
 the subject and where a considerable number of physicists are 
 working at it. 
 
 The study of the electrical properties of gases seems to offer 
 the most promising field for investigating the Nature of Electricity 
 and the Constitution of Matter, for thanks to the Kinetic Theory 
 of Gases our conceptions of the processes other than electrical 
 which occur in gases are much more vivid and definite than they 
 are for liquids or solids; in consequence of this the subject has 
 advanced very rapidly and I think it may now fairly be cla: ned 
 that our knowledge of and insight into the processes going on 
 when electricity passes through a gas is greater than it is in 
 the case either of solids or liquid. The possession of a charge 
 by the ions increases so much the ease with which they can be 
 traced and their properties studied that as the reader will see 
 we know far more about the ion than we do about the uncharged 
 molecule. 
 
vi PREFACE. 
 
 L 
 
 With the discovery and study of Cathode rays, Rb'ntgen rays 
 and Radio-activity a new era has begun in Physics, in which the 
 electrical -properties of gases have played and will play a most 
 important part ; the bearing of these discoveries on the problems 
 of the Constitution of Matter and the Nature of Electricity is in 
 most intimate connection with the view we take of the processes 
 which go on when electricity passes through a gas. I have 
 endeavoured to show that the view taken in this volume is 
 supported by a large amount of direct evidence and that it 
 affords a direct and simple 'explanation of the electrical properties 
 of gases. 
 
 The pressure of my other duties has caused this book to be 
 a considerable time in passing through the press, and some 
 important investigations have been published since the sheets 
 relating to the subjects investigated were struck off. I have 
 given a short account of these in a few Supplementary Notes. 
 
 My thanks are due to Mr C. T, R. Wilson, F.R.S., for the 
 'assistance he has given me by reading the proofs and I am 
 indebted to Mr Hayles of the Cavendish Laboratory for the 
 preparation of the diagrams. 
 
 J. J. THOMSON. 
 
 CAVENDISH LABORATORY, CAMBRIDGE. 
 August, 1903. 
 
TABLE OF CONTENTS. 
 
 CHAP. PAOB 
 
 I. Electrical Conductivity of Gases in a normal state . C 1 
 
 II. Properties of a Gas when in the conducting state . . 8 
 
 III. Mathematical Theory of the Conduction of Electricity through 
 
 a Gas containing Ions . 64 
 
 IV. Effect produced by a Magnetic Field on the Motion of the 
 
 Ions . . . . . . .';*. . 79 
 
 V. --Determination of the Ratio of the Charge to the Mass of 
 
 an Ion 91 
 
 VI. Determination of the Charge carried by the Negative Ion . 121 
 
 VII. On some Physical Properties of Gaseous Ions . . . 133 
 
 VIII. lonisation by Incandescent Solids ,\ T^V. . 155 
 
 IX. lonisation in Gases from Flames . -^^\ \, . . . 193 
 
 X. lonisation by Light. Photo-Electric Effects . . .211 
 XL lonisation by Rontgen Rays. . . . \. . . 244 
 XII. Becquerel Rays . \ . * .,.'.''. \ . . 274 
 
 l/XIIL Spark^Discharge c^/ \ . .'. . ,, . . . 346 
 
 XIV. The_Electric Arc . . * ,, \ . . 416 
 
 v XV. Discjarge through Gases at Low Pressures . ^ . ' . . 432 
 
 XVI. Theory of the Discharge through Vacuum Tubes . . .479 
 
 XVII. Qailiode Rays '. . 493 
 
 XVIII. Rontgen Rays . 523 
 
 XIX. Properties of Moving Electrified Bodies .... 530 
 
 SUPPLEMENTARY NOTES .545 
 
 INDEX 555 
 
CHAPTER I. 
 
 ELECTRICAL CONDUCTIVITY OF GASES IN A NORMAL STATE. 
 
 1. A GAS in the normal state conducts electricity to a slight, 
 but only to a very slight, extent, however smallythe electric force 
 acting on the gas may be. So small however is the conductivity 
 of a gas when in this state, and so difficult is it to eliminate 
 spurious effects, that there have been several changes of opinion 
 among physicists as to the cause of the leakage of electricity which 
 undoubtedly occurs when a charged body is surrounded by gas. It 
 was thought at first that this leakage took place through the gas ; 
 later, as the result of further experiments, it was attributed to 
 defective insulation of the rods or threads used to support the 
 body, and to the dust present in the gas ; quite recently however 
 it has been shown that there is a true leak through the gas 
 which is not due to the dust or moisture the gas may happen 
 to contain. 
 
 2. The escape of electricity from an insulated charged body 
 has attracted the attention of many physicists. Coulomb*, whose 
 experiments were published in 1785, from his investigations on 
 the loss of electricity from a charged body suspended by insulat- 
 ing strings, came to the conclusion that after allowing for the 
 leakage along the strings there was a balance over, which he 
 attributed to a leakage through the air. He explained this leakage 
 by supposing that the molecules of air when they come into con- 
 tact with a charged body receive a charge of electricity of the 
 same sign as that on the body and are then repelled from it 
 carrying off some of the charge. We shall see later on that this 
 explanation is not tenable. 
 
 * Coulomb Memoires de VAcademie des Sciences, 1785, p. 612. 
 
 1 
 
2 ELECTRICAL CONDUCTIVITY [2 
 
 Matteucci* experimenting on the same subject in 1850 also 
 came to the conclusion that there was a leakage of electricity 
 through the gas ; he was the first to prove that the rate at which 
 this leak takes place is less when the pressure of the gas is low 
 than when it is high. He found also that the rate of leak was 
 the same in air, carbonic acid and hydrogen. On the other hand 
 Warburg f found that the rate of leak through hydrogen was only 
 about half of that through air and carbonic acid, he agreed with 
 Matteucci with regard to the equality of the rate of leak through 
 the other two gases arid could detect no difference between the 
 leaks through dry and moist air ; he confirmed Matteucci's obser- 
 vations on the effect of pressure on the rate of leak. Warburg 
 seemed inclined to suspect that the leak was due to dust in the 
 gases. The belief in dust being the carrier of the electricity was 
 strengthened by an experiment made by Hittorf J in which a small 
 carefully insulated gold leaf electroscope was placed in a glass 
 vessel filled with filtered gas ; the electroscope was found to have 
 retained a charge even after the lapse of four days. We know 
 now from recent experiments that the smallness of the leak 
 observed in this case was due to the smallness of the vessel 
 in which the charged body was placed rather than to the absence 
 of dust. 
 
 Further experiments on this subject were made by Nahrwold 
 and by Narr|| who showed that the rate of leak from a charged 
 hollow sphere was not increased when the temperature of the 
 sphere was raised by filling it with hot water. BoysH made an 
 experiment which showed very clearly, that whatever the cause of 
 the leak might be, it was not wholly due to want of insulation in 
 the supports of the charged body; in this experiment he attached 
 the gold leaves of an electroscope first to a short and thick quartz 
 rod and then to a long and thin one, and found that the rate of 
 leak of electricity from the gold leaves was the same in the two 
 cases; if the leak had been along the supports it would have 
 
 * Matteucci, Annales de Chimie et de Physique, xxviii. p. 390, 1850. 
 t Warburg, Pogg. Ann. cxlv. p. 578, 1872. 
 Hittorf, Wied. Ann. vii. p. 595, 1879. 
 Nahrwold, Wied. Ann. v. p. 460, 1878 ; xxxi. p. 448, 1887. 
 || Narr, Wied. Ann. v. p. 145, 1878; viii. p. 266, 1879; xi. p. 155, 1880; xvi.. 
 p. 558, 1882; xxii. p. 550, 1884; xliv. p. 133, 1892. 
 IT Boys, Phil. Mag. xxviii. p. 14, 1889. 
 
OF GASES IN A NORMAL STATE. 
 
 a 
 
 been much greater in the first case than in the second. Boys 
 also confirmed Warburg's observation that the rate of leak was 
 the same in dry and moist air. 
 
 3. The subject of the electric conduction through air is 
 evidently of considerable importance in relation to Meteorology 
 and Atmospheric Electricity. Experiments especially bearing on 
 this point, were made by Linss* on the loss of electricity from 
 charged bodies placed in the open air; he found tbe^vas an 
 appreciable loss of charge which control experiments *|pc<l was 
 not due to leakage along the supports of the charged body. 
 
 An extensive series of open air measurements were made by 
 Elster and Geitelf in many different localities and in different 
 states of the weather. They found that the rate of leak varied 
 from time to time and from place to place, that it was very 
 smaller in mist or fog than when the weather was bright 
 and clear, that it was greater at high altitudes than at low ones, 
 and that on the tops of mountains the rate of escape of negative 
 electricity was much greater than that of positive. This is doubt- 
 less due to the negative charge on the earth's surface, a mountain 
 top being analogous to a sharp point on a conductor and thus a 
 place where the earth's electric force is much greater than it is on 
 the plains, where they found the rate of leak to be the same 
 for plus and minus charges. These points are brought out by the 
 results of the observations given in Tables I. and II. Table I. 
 gives the results of experiments made at Wolfenbiittel at different 
 times. Table II. contains observations at different places. 
 
 TABLE I. 
 
 Weather 
 
 Bate of leak 
 for + charge 
 
 Bate of leak 
 for - charge 
 
 Fog, wind S.E , 
 
 277 
 
 2-64 
 
 Clear, air very transparent 
 
 8-58 
 
 9-82 
 
 Fine rain, mist ... 
 
 318 
 
 3-02 
 
 Sky half overcast, air very transparent... 
 
 13-67 
 
 13-83 
 
 * Linss, MeteoroL Zeitschr. iv. p. 352, 1887; Elektrotechn. Zeitschr. i. 11, 
 p. 506, 1890. 
 
 t Elster and Geitel, Drudes Ann. ii. p. 425, 1900. 
 
 12 
 
ELECTRICAL CONDUCTIVITY 
 
 [4 
 
 TABLE II. 
 
 Place and altitude 
 
 Weather 
 
 Kate of leak 
 + charge 
 
 Rate of leak 
 - charge 
 
 Brocken, 1140m. 
 
 Sunshine, hazy 
 
 6-67 
 
 10'28 
 
 Weissbad . 800 m. 
 
 Sunshine, air clear 
 
 9-66 
 
 9-52 
 
 Santisgipfel, ... 2500m. 
 Gornergrat, 3140 m. 
 Zermatt Valley, 1620 m. 
 Wolfenbuttel, ... 80 m. 
 
 Sunshine, air very clear 
 Sunshine, air very clear 
 Sunshine 
 No clouds, air clear 
 
 8-95 
 3-28 
 21-02 
 8-45 
 
 35-04 
 31-26 
 
 20-78 
 9-20 
 
 4. Further experiments on the rates of leak from a charged 
 body placed in a closed vessel filled with air were made almost 
 simultaneously by Geitel* and by Wilson f. The apparatus used 
 by Wilson for this purpose is represented in Fig. 1. Since the 
 
 Fig. 1. 
 
 quantity of electricity which escapes from the charged body is 
 very small it is necessary that the capacity of the instrument used 
 to measure it should be small ; this condition makes it advisable 
 to use a small gold leaf electroscope rather than a quadrant 
 electrometer. To prevent the leakage from the supports vitiating 
 the experiments the brass strip which carries the gold leaf is 
 attached to and insulated from a metal rod A by a piece of 
 
 * Geitel, Physikalische Zeitschr. ii. p. 116, 1900. 
 
 t Wilson, Proc. Camb. Phil. Soc. xi. p. 32, 1900 ; Proc. Roy. Soc. Ixviii. p. 151, 
 1901. 
 
4] OF GASES IN A NORMAL STATE. 5 
 
 sulphur B, A being insulated by a plug of sulphur from the vessel 
 containing the gas under examination, and connected with a 
 condenser C formed of parallel plates of metal imbedded in a 
 block of sulphur. The brass strip and gold leaf are initially 
 charged to the same potential as the rod by making momentary 
 contact between the rod and the strip ; the rod being connected 
 with a large capacity remains at almost constant potential, and 
 thus if there is any leakage of electricity along the sulphur 
 supporting the brass strip and gold leaf, it will tend to keep them 
 charged and not to discharge them. The position of the gold leaf 
 was read by means of a microscope provided with an eye-piece 
 micrometer scale. The brass strip and gold leaf were used as the 
 charged body and the rate at which the image of the gold leaf 
 moved across the micrometer scale was a measure of the rate of 
 leak through the gas. The following results were obtained by 
 both Geitel and Wilson the rate of escape of electricity in a 
 closed vessel is much smaller than in the open and the larger the 
 vessel the greater is the rate of leak. The rate of leak does not 
 increase in proportion to the difference of potential between the 
 gold leaves and the walls of the vessel ; the rate soon reaches 
 a limit*' beyond which it does not increase however much the 
 potential difference is increased (provided of course that this is 
 not great enough to cause sparks to pass). 
 
 It follows from Wilson's experiments 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 space 
 whose volume is V cubic centimetres is about 10~ 8 V electrostatic 
 units. Rutherford and Allen* working in Montreal obtained 
 results in close agreement with this. 
 
 As the result of a series of experiments made at pressures 
 ranging from 43 to 743 millimetres of mercury Wilson came to 
 the conclusion that the maximum rate of leak is very approximately 
 proportional to the pressure, thus at low pressures the rate of leak 
 is exceedingly small : this result is illustrated in a striking way by 
 an observation of Crookesf that a pair of gold leaves could retain 
 an electric charge for months in a very high vacuum. The rate of 
 leak is about the same in the dark as it is in the light, it is thus 
 
 * Rutherford and Allen, Physikalische Zeitschr. Hi. p. 225, 1902. 
 t Crookes, Proc. Roy. Soc. xxviii. p. 347, 1879. 
 
6 ELECTRICAL CONDUCTIVITY [5 
 
 not due to light, and that it can be caused by some invisible form 
 of radiation is rendered improbable by the observation of Wilson 
 that the rate of leak in a closed vessel is the same when the vessel 
 is inside a railway tunnel as when it is outside ; in the former case 
 any radiation reaching the gas from outside must have travelled 
 through many feet of solid rock. Wilson* has recently investigated 
 the greatest rates of leak through different gases and has obtained 
 the following results. 
 
 Relative rate of leak 
 Gas Relative rate of leak Specific gravity 
 
 air 1-00 I'OO 
 
 Ho -184 2'7 
 
 C0 2 1-69 1-10 
 
 S0 2 2-64 1-21 
 
 CHC1 3 4-7 1-09 
 
 5. Geitel (loc. cit.) made the very interesting observation that 
 the rate of leak in a closed vessel increases, after the refilling of 
 the vessel with fresh air, for some days, when it reaches a constant 
 value at which it remains for an indefinitely long time. The most 
 obvious explanation of this result is that it is due to the settling 
 down of the dust, as Elster and Geitel (loc. cit) have shown that 
 the presence of dust, fog, or mist diminishes the rate of leak. This 
 explanation is however rendered doubtful by some later experi- 
 ments f made by the same physicists, in which they found that 
 the period required for the gas to attain its maximum conduc- 
 tivity was not appreciably diminished by filtering the dust out of 
 the air by sending it through water, or by extracting the moisture 
 from the gas : thus if the increase in the rate of leak is due to the 
 settling down of some foreign matter from the gas, this matter 
 must be something which can not be got rid of by filtering the 
 gas through water traps or plugs of glass-wool : we shall find later 
 on when we study the diselectrification of ga,ses that there are 
 cases in which foreign matter present in gases is not removed by 
 such treatment, and the case of the discharge of negative elec- 
 tricity from a point (vide infra) shows that under certain con- 
 ditions the admixture of a very small amount of foreign matter to 
 a gas produces a great diminution in the rate of escape of electri- 
 city through it. ft 
 
 * Wilson, Proc. Roy. Soc. Ixix. p. 277, 1901. 
 
 t Elster and Geitel, Physikalische Zeitschr. ii. p. 560, 1901. 
 
6] OF GASES IN ,A NORMAL STATE. 7 
 
 6. Another aspect of this phenomenon is the very interesting 
 fact discovered by Elster and Geitel* that the rate of leak in 
 caves, and cellars where the air is stagnant and only renewed 
 slowly, is very much greater than in the open air : thus in some 
 experiments they made in a cave the Baumannshohle in the Harz 
 Mountains they found that in the cave the electricity escaped at 
 seven times the rate it did in the air outside even when this was 
 clear and free from mist. They found too that in a cellar whose 
 windows had been shut for eight days the rate of leak was very 
 considerably greater than it was in the air outside. These experi- 
 ments suggest that gas having abnormally great conductivity 
 slowly diffuses from the walls surrounding the gas, and that this 
 diffusion goes on so slowly that when fresh gas is introduced it 
 takes a considerable time for the gas from the walls to again 
 diffuse through the volume. The reader should compare with 
 this phenomenon the results described in the Chapter on Induced 
 Radioactivity. 
 
 The experiments we have described show that the rate of 
 leak of electricity through gas in a normal state is influenced by 
 a great variety of circumstances, such as the pressure of the gas, 
 the volume of gas in the electric field, and the amount of dust or 
 fog held in suspension by it; all these effects receive a ready 
 explanation on the view to which we are led by the study of the 
 effects shown on a larger scale by gases whose conductivity has 
 been increased by artificial means, and we shall return to the 
 subject of the leak through normal air after the study of gases 
 whose conductivity has been abnormally increased. We may 
 however at once point out that the increase of the rate of leak 
 with the size of the vessel containing the charged body shows that 
 the conduction is not due, as Coulomb thought, to particles of gas 
 originally uncharged striking against the charged body and 
 receiving a charge which they deliver up to the sides of the vessel ; 
 if this were the method by which the electricity escaped the rate 
 of leak would not increase with the size of the vessel. 
 
 * Elster and Geitel, Physikalische Zeitschr. ii. p. 560, 1901. 
 
CHAPTER II. 
 
 PROPERTIES OF A GAS WHEN IN THE CONDUCTING STATE. 
 
 7. THE electrical conductivity of gases in the normal state is 
 so small that as we have seen the proof of its existence requires 
 very careful and elaborate experiments. Gases may however in 
 various ways be put into a state in which they conduct electricity 
 with so much facility that the detection and investigation of this 
 property becomes a comparatively easy matter ; as the study of 
 the properties of a gas when in this state is of the highest 
 importance from the light which it throws on the general phe- 
 nomena of electric discharge through gases we shall find it useful 
 to discuss the subject at some considerable length. 
 
 8. There are many ways in which gases may be made to 
 possess considerable conductivity or, as we shall express it, be put 
 into the conducting state. They are for instance put into this 
 state when their temperature is raised above a certain point ; again, 
 gases drawn from the neighbourhood of flames or electric arcs or 
 which have recently been in contact with glowing metals or carbon, 
 or have diffused from a space through which an electric discharge 
 is passing or has recently passed, are in this state. A gas is put 
 into the conducting state when Rontgen, Lenard or Cathode rays 
 pass through it, the same effect is produced by the rays from 
 uranium, thorium, or the radioactive substances, polonium, radium, 
 actinium, obtained from pitch-blende by Curie, Curie and Bemont 
 and Debierne respectively, and also as Lenard has recently shown 
 by a very easily absorbed kind of ultra-violet light. E. Wiede- 
 mann has shown that electric sparks give out rays, called by him 
 Entladungstrahlen, which produce the same effect. Air which has 
 passed over phosphorus or which has bubbled through water 
 is also in this state and remains so for some time after it has 
 
9] PROPERTIES OF A GAS WHEN IN THE CONDUCTING STATE. 9 
 
 left the phosphorus or water. We shall have later on to discuss 
 the action of each of these agents in detail, but we shall begin by 
 studying some of the general properties possessed by a gas when 
 in this state, the experimental methods by which these properties 
 may be investigated, and a theory of this state by which they may 
 be explained. 
 
 9. A gas when in the conducting state possesses characteristic 
 properties. In the first place it retains its conductivity for some 
 little time after the agent which made it a conductor has ceased 
 to act ; its conductivity however always diminishes, in some cases 
 very rapidly, after the agent is removed, and finally it disappears. 
 The duration of the conductivity may be shown very simply by 
 having a charged electroscope screened off from the direct action 
 of Rontgen rays, the electrostatic field due to the electroscope 
 being screened off from the region exposed to the rays by covering 
 the electroscope with a cage made of wire gauze with a very large 
 mesh ; if the air is still the electroscope will retain its charge even 
 when the rays are in action, but if we blow some of the air 
 traversed by the rays towards the electroscope the latter will 
 begin to lose its charge, showing that the air has retained its con- 
 ductivity for the time taken by it to travel to the electroscope 
 from the place where it was exposed to the rays. A somewhat more 
 elaborate form of this experiment, which enables us to prove several 
 other interesting properties of the conducting gas, is to place the 
 electroscope in a glass vessel A in which there are two tubes, one 
 leading to a water-pump while the end of the other is in the region 
 traversed by the Rontgen rays. The tube used to produce the rays 
 
 c 
 
 Fig. 2. 
 
 is placed in a box covered with lead with the exception of a 
 window at B to let the rays through : this shields the electroscope 
 
10 PROPERTIES OF (^GASjJ [10 
 
 from the direct action of the rays : if the water-pump be worked 
 slowly so as to make a slow current of air pass from the region 
 traversed by the rays into the vessel A the electroscope will 
 gradually lose its charge whether this be positive or negative : if 
 the pump be stopped and the current of air ceases, the discharge 
 of the electroscope will cease. 
 
 The conducting gas loses its conductivity if it is sucked through 
 a plug of glass-wool or made to bubble through water*. This can 
 readily be proved by inserting in the tube B a plug of glass-wool 
 or a water-trap and working the water-pump a little harder so as 
 to make the rate of flow of air through the tube the same as in 
 the previous experiment ; it will now be found that the electroscope 
 will retain its charge, the conductivity has thus been taken out of 
 the gas by filtering it through glass-wool or water. The con- 
 ductivity is very much more easily removed from gases made 
 conducting by the various rays, Rontgen, Lenard, Cathode, &c., 
 than from the conducting gases derived from flames and arcs ; the 
 latter as we shall see require a great deal of filtering to remove 
 their conductivity. If we replace the tube B by a metal tube of 
 fine bore we shall find that the gas loses its conductivity by passing 
 through it, and the finer the bore the more rapidly does the con- 
 ductivity disappear. The conductivity may also be removed from 
 the gas by making it traverse a strong electric field so that a 
 current of electricity passes through itf. To show this, replace 
 the glass tube C by a metal tube of fairly wide bore and fix along 
 the axis of this tube an insulated metal wire; if there is no 
 potential difference between the wire and the tube, then the 
 electroscope in A will leak when a current of air is sucked through 
 the apparatus ; if however a considerable difference of potential is 
 established between the wire and the tube, so that a current of 
 electricity passes through the gas during its passage to A, the 
 leak of the electroscope will cease, showing that the conductivity 
 of the gas has been removed by the electric field. 
 
 10. The removal of the conductivity by filtering through 
 glass-wool or water and by transmission through narrow metal 
 tubes, shows that the conductivity is due to something mixed 
 
 * J. J. Thomson and E. Rutherford, Phil. Mag. xlii. p. 392, 1896. 
 t Ibid. 
 
11] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 11 
 
 with the gas, this something being removed from the gas in the 
 one case by filtration in the other by diffusion to the walls of the 
 tube. Further the removal of the conductivity by the electric 
 field shows that this something is charged with electricity and 
 moves under the action of the field ; since the gas when in the 
 conducting state shows as a whole no charge of electricity, the 
 charges removed must be both positive and negative. We are 
 thus led to the conclusion that the conductivity of the gas is due 
 to its having mixed with it electrified particles, some of these 
 particles having charges of positive electricity others of negative. 
 We shall call these electrified particles ions, and the process by 
 which a gas is made into a conductor the ionisation of the gas. 
 We shall show later on how the masses and charges of the ions 
 may be determined, when it will appear that the ions in a gas are 
 not identical with those met with in the electrolysis of solutions. 
 
 11. The passage of a current of electricity through a conducting 
 gas does not follow Ohm's law unless the electromotive force acting 
 on the gas is small. We may investigate the relation between the 
 current and potential difference by taking two parallel metal 
 plates A and B (Fig. 3) immersed in a gas, the gas between the 
 
 it hi 
 
 forth 
 
 Fig. 3. 
 
 plates being exposed to the action of some ionising agent such as 
 Rontgen rays or the radiation from a radioactive substance. One 
 of the plates A is connected with one of the pairs of quadrants of 
 an electrometer, the other pair of quadrants being put to earth. 
 The other plate B is connected with one of the terminals of a 
 
12 
 
 PROPERTIES OF A GAS 
 
 [11 
 
 battery of several storage cells, the other terminal of the battery 
 being connected with the earth ; initially the two pairs of quad- 
 rants of the electrometer are connected together, then the con- 
 nection between the quadrants is broken and as a current of 
 electricity is passing across the air space between A and B, the 
 plate B gets charged up and the needle of the electrometer is 
 deflected ; the rate of deflection of the electrometer measures the 
 current passing through the gas. By making a series of obser- 
 vations of this kind we can get the means of drawing a curve such 
 that the ordinates represent the current through the gas and the 
 abscissae the potential difference between the plates : such a curve 
 is represented in Fig. 4*. We see that when the difference of 
 
 Fig. 4. 
 
 potential is small the curve is a straight line, in this stage the 
 conduction obeys Ohm's law ; the current however soon begins to 
 increase more slowly than the potential difference and we reach a 
 stage where there is no appreciable increase of current when the 
 potential difference is increased : in this stage the current is said 
 to be saturated. When the potential difference is increased to 
 such an extent that the electric field is strong enough to ionise 
 the gas, another stage is reached in which the current increases 
 very rapidly with the potential difference; curves showing this 
 effect have been obtained by von Schweidlerf and by TownsendJ, 
 one of these is shown in Fig. 5. The potential gradient required 
 
 * J. J. Thomson, Nature, April 23, 1896. 
 
 t von Schweidler, Wien. Bericht, cviii. p. 273, 1899. 
 
 t J. S. Townsend, Phil. Mag. vi. 1, p. 198, 1901. 
 
12, 13] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 13 
 
 to reach this stage depends upon the pressure of the gas, it is 
 directly proportional to the pressure ; for air at atmospheric pressure 
 
 60 
 50 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 30 
 
 fo 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 s 
 
 
 
 
 x; 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 90 1X0 *00 H 
 
 V0 
 
 Fig. 5. 
 
 it is about 30,000 volts per centimetre, so that in air at a pressure 
 of one millimetre a potential gradient of about 40 volts per 
 centimetre would be sufficient to reach this stage. 
 
 12. The saturation current between two parallel plates of 
 given area depends upon the amount of ionisation between the 
 plates ; if the ionisation takes place throughout the whole volume 
 of gas between the plates, then the greater the distance between 
 the plates the greater is the saturation current, so that if we use 
 constant potential differences large enough to produce saturation, 
 the greater the distance between the plates the larger is the 
 current. Thus the N behaviour of the conducting gas is very 
 different from that of a metallic or liquid electrolytic conductor, 
 for if such conductors were substituted for the gas the greater 
 the distance between the plates the smaller would be the current. 
 Under very small potential differences however the three classes 
 of conductors would behave in the same way. 
 
 13. The peculiarities shown by the conduction through gases 
 are very easily explained on the assumption that the conduction is 
 due to ions mixed with the gas. Let us for example take the case 
 of saturation. Suppose that in the gas between the plates the 
 ionising agent produces in one second q positive and q negative ions 
 and let e be the magnitude of the electric charge on au ion, then 
 if an electric current i passes between the plates i/e positive ions 
 are driven against the negative electrode, and the same number 
 of negative ions are driven against the positive electrode in one 
 
14 PROPERTIES OF A GAS [14 
 
 second ; thus in each second i/e positive and negative ions are 
 taken out of the gas by the current. When the gas is in a steady 
 state the number of ions taken out of it in a given time cannot 
 be greater than the number of ions produced in it in the same 
 time, hence i/e cannot be greater than q, and thus i cannot be 
 greater than qe: qe is thus the value of the saturation current. 
 If the ions are produced uniformly throughout the gas, and if q Q 
 is the number of ions produced in one second in unit volume, then 
 since the volume of gas between the plates is equal to Al, where 
 A is the area of one of the plates and I the distance between the 
 plates, q the number of ions produced in the gas in one second is 
 equal to q<)Al; hence the saturation current is equal to q<>Ale, and 
 is thus proportional to the distance between the plates. This 
 relation between the saturation current and the distance between 
 the plates has been verified by measurements of the saturation 
 currents through gases exposed to Rontgeri rays*. 
 
 14. Even when there is no current of electricity passing 
 through the gas and removing some or all of the ions, the number 
 of ions present in the gas does not increase indefinitely with the 
 time which has elapsed since the gas was first exposed to the 
 ionising agent ; the number of ions in the gas and therefore its con- 
 ductivity acquire after a time steady values beyond which they do 
 not increase however long the ionising agent may act. This is 
 due to the recombinations that take place between the positive 
 and negative ions ; these ions moving about in the gas sometimes 
 come into collision with each other and in a certain fraction of 
 such cases of collision the positive and negative ions will remain 
 together after the collision, and form an electrically neutral system 
 the constituents of which have ceased to be free ions. The collisions 
 will thus cause the ions to disappear, and the steady state of a gas 
 which is not carrying an electric current will be reached when the 
 number of ions which disappear in one second as the result of the 
 collisions is equal to the number produced in the same time by 
 the ionising agent. Starting from this principle it is very easy to 
 investigate the relation between the number of free ions when 
 the gas is in a steady state, the strength of the ionising agent, 
 the rate at which the ions increase on the first exposure to the 
 
 * J. J. Thomson and E. Rutherford, Phil. Mag. v. 42, p. 392, 1896. 
 
14] WHEN IN THE CONDUCTING STATE. 15 
 
 ionising agent and' the rate at which they die away when the 
 ionising agent is cut off. 
 
 For let q be the number of ions (positive or negative) produced 
 in one cubic centimetre of the gas per second by the ionising 
 agent; n lt n^ the number of free positive and negative ions 
 respectively per cubic centimetre of the gas. The number of 
 collisions per second between positive and negative ions is propor- 
 tional to rij^. If a certain fraction of the collisions result in the 
 formation of a neutral system the number of ions which disappear 
 per second in a cubic centimetre will be equal to aw^, where a is 
 a quantity which is independent of ^ and ?? 2 ; hence we have 
 
 dn 
 
 Thus TC! ?i 2 is constant, so that if the gas is uncharged to 
 begin with n^ is always equal to n 2 . Putting n-^ = n 2 = n the 
 preceding equation becomes 
 
 *- ' ........................... < 2 >< 
 
 the solution of which is, if k 2 = q/a, 
 
 n the value of n when the gas is in a steady state is obtained 
 by putting t equal to infinity in equation (3) and is given by the 
 equation 
 
 4 
 
 n k = 
 
 We see from equation (3) that the gas will not approximate 
 to a steady state until t is large compared with l/2&a, that is 
 with l/2w a or 1/2 V^a. W T e may thus take 1/2 V^a as the 
 measure of the time taken by the gas to reach the steady state 
 under exposure to the ionising agent ; as this time varies inversely 
 as V^ we see that when the ionisation is feeble it may take a very 
 considerable time for the gas to reach the steady state. 
 
 Thus at some distance, say a metre, from an ordinary Rontgen 
 bulb it may require an exposure of a minute or two to bring the 
 gas into a steady state. 
 
16 PROPERTIES OF A GAS [15 
 
 We may use equation (2) to determine the rate at which the 
 number of ions diminishes when the ionising agent is removed, 
 putting q = in that equation we have 
 
 *--* < 4 >- 
 
 hence n = - - - (5 ), 
 
 1 + n^at 
 
 where n is the value of n when t = 0. Thus the number of ions 
 falls to one-half its initial value in the time l/w a. We may 
 regard equation (4) as expressing the fact that a free ion lasts for 
 a time which on the average is equal to l/<m. 
 
 15. Equation (4) has been verified by Rutherford for gases 
 exposed to Roritgen rays* and to the radiation from uranium f, 
 by M c ClungJ for gases exposed to Rontgen rays, and by 
 M c Clelland for the case of gases drawn from the neighbourhood 
 of flames and arcs. Two methods have been employed for this 
 purpose. In one method air exposed to rays at one end of a long 
 tube is slowly sucked through the tube, and the saturation currents 
 measured at different parts along the tube. These currents are 
 proportional to the value of n at the place of observation, and 
 knowing the velocity of the air and the distance of the place of 
 observation from the end of the tube, we know the time which 
 has elapsed since the gas was ionised ; we can thus find the values 
 of n corresponding to a series of values of t ; values determined in 
 this way were found by Rutherford to agree well with those given 
 by equation (5). This method can only be used when a large 
 quantity of gas is available. Another method also used by 
 Rutherford can be employed even for gases of which only small 
 quantities can be procured. In this method gas confined in a 
 vessel is exposed to the action of an ionising agent such as the 
 Rontgen rays. Inside the vessel are two parallel metal plates 
 A and B between which the ionisation is to be measured, (in some 
 of Rutherford's experiments one of these plates was replaced by 
 the case of the vessel which was made a conductor by lining it 
 
 * Rutherford, Phil. Mag. v. 44, p. 422, 1897. 
 t Rutherford, Phil. Mag. v. 47, p. 109, 1899. 
 t M c Clung, Phil. Mag. vi. 3, p. 283, 1902. 
 McClelland, Phil. Mag. v. 46, p. 29, 1898. 
 
15] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 17 
 
 with wire gauze, the other plate was replaced by an insulated 
 wire running down the middle of the vessel). One of these 
 plates A can be connected with an electrometer, the other jB with 
 one terminal of a large storage battery the other terminal of 
 which is kept to earth. A pendulum interrupter is arranged so 
 'that as a heavy pendulum swings it strikes against levers, and by 
 this means makes or breaks various connections. While the 
 vessel is under the influence of the rays, A and B are connected 
 together and to earth, then A is disconnected from both earth and 
 electrometer and left insulated, and B is disconnected from the 
 earth ; the pendulum is then let go : as it falls it first breaks the 
 current going through the primary of the induction coil used to 
 excite the rays, it thus stops the ionisation, then after an interval 
 t (which can easily be varied) it strikes against another lever 
 which has the effect of connecting B with the high potential pole 
 of the battery, thus producing a strong electric field between the 
 plates A and B: this field, if B is charged positively, drives in a 
 very small fraction of a second all the positive ions which exist 
 between A and B against A, so that A receives a positive charge 
 proportional to n ; the pendulum in its swing then goes on to dis- 
 connect B from the battery and connects it to earth. The plate 
 A is now connected with the electrometer the needle of which is 
 deflected by an amount proportional to the charge on the plate A, 
 i.e. to n. By adjusting the apparatus so as to alter the time 
 which elapses between cutting off the rays and connecting B with 
 the battery we find a series of corresponding values of n and t\ 
 these were found by Rutherford to fit in well with the relation 
 indicated by equation (5). The following table shows the rate at 
 which the ionisation dies away in a special case, the rate of course 
 depends upon the intensity of the ionisation, the figures may 
 however serve to give an idea of the order of magnitude of the 
 rate of decay in air under strong Rontgen radiation. 
 
 Time in seconds after 
 
 Deflection of 
 
 stoppage of rays 
 
 Electrometer 
 
 004 
 
 184 
 
 08 
 
 183 
 
 45 
 
 106 
 
 2 
 
 37 
 
 4 
 
 19 
 
18 
 
 PROPERTIES OF A GAS 
 
 [16 
 
 Thus after 4 seconds there was still a very appreciable amount 
 of ionisation -in the gas. The duration is still more marked in the 
 following example when the radiation was much weaker. The 
 electrometer was not equally sensitive in the two series of 
 experiments. 
 
 Time 
 
 Deflection 
 
 004 
 
 174 
 
 45 
 
 139 
 
 2- 
 
 107 
 
 4 
 
 54 
 
 8 
 
 30 
 
 16 
 
 16 
 
 Thus after 16 seconds in this case the gas retained more than 
 10 per cent, of its ionisation. 
 
 Rutherford measured the rate of decay in various gases 
 exposed to Rontgen rays of as nearly as possible the same 
 intensity. The results are shown in the following table, the first 
 column contains the name of the gas, the second T the time 
 taken for the ionisation to sink to one-half of its original value, 
 we have seen that T= l/ft a= l/V<?a; the third column contains 
 relative values of g, and the fourth column the relative values 
 of a calculated from the values of T and q. 
 
 Gas 
 
 T 
 
 q 
 
 a 
 
 Hydrogen 
 
 65 
 
 5 
 
 4-8 
 
 Air 
 
 3 
 
 1 
 
 11 
 
 Hydrochloric acid gas 
 Carbonic acid gas 
 Sulphur dioxide 
 Chlorine 
 
 35 
 
 51 
 45 
 
 18 
 
 11 
 1-2 
 
 4 
 18 
 
 75 
 3-3 
 
 1-25 
 
 2 
 
 
 
 
 
 16. Rutherford showed that the value of T was very much 
 diminished when any dust was present in the gas, the dust did 
 not however affect the saturation current. Thus for example when 
 chlorine was first admitted to the testing vessel the value of Twas 
 19 seconds, after standing for an hour T rose to about *3 seconds 
 
17] WHEN IN THE CONDUCTING STATE. 19 
 
 although there was no change in the saturation current. Again 
 for air which had been standing overnight T was about 1 second, 
 when a little dusty air was blown into the vessel T fell to '15 
 seconds, rising to about '5 seconds in about 10 minutes ; it took 
 several hours for T to rise to its original value. Again T was 
 found to be increased by filtering the gas through cotton-wool. 
 The effect produced by dust is easily explained, as the dust 
 particles are in all probability very large compared with the ions, 
 thus if a positive ion strikes against a dust particle and sticks to it, 
 it forms a large system which is much more likely to be struck by 
 a negative ion and neutralised than if the positive ion had re- 
 mained free ; in this way the presence of dust will facilitate the 
 recombination of the ions. The presence of dust in Rutherford's 
 experiments probably explains the discrepancy between his results 
 and Townsend's*, who used dust-free gases and determined a by 
 the first of the methods described, care being taken that the tubes 
 through which the ionised gases were sucked were so large that 
 the loss of ions from diffusion to the sides of the tube could be 
 neglected in comparison with those lost by recombination. 
 Townsend found that for air, oxygen, carbonic acid, and hydrogen 
 a had the values, 34200, 33800, 35000, and 30200, where 
 is the charge on the ion in electrostatic units. We shall see that 
 is about 3'5 x 10~ 10 so that a for air, oxygen, and carbonic acid is 
 about 1-2 x lO" 6 while for hydrogen it is about 15 per cent. less. 
 In Rutherford's experiments the value of a for air was about 
 three times that for carbonic acid but it is probable that the gases 
 in this case were not really dust-free. 
 
 17. A series of careful measurements of a under different 
 conditions would give us valuable information as to the nature of 
 the ions; from some preliminary experiments made by Dr Nabl at 
 the Cavendish Laboratory it would seem that a is but little if at 
 all affected by changes in pressure. Some recent experiments by 
 ,M c Clungf have shown that a is independent of the pressure, the 
 pressures investigated varying from 125 to 3 atmospheres. The 
 values found for a are for air and carbonic acid 3384 x and for 
 hydrogen 2938 x ; no experiments seem to have yet been made 
 on the variation of a with temperature. 
 
 * Townsend, Phil. Trans. A. 193, p. 129, 1900. 
 f M c Clung, Phil. Mag. vi. 3, p. 283, 1902. 
 
 22 
 
20 PROPERTIES OF A GAS [18 
 
 Diffusion of Ions. 
 
 18. In addition to the loss of ions arising from the recombina- 
 tion of the positive and negative ions there will be a further 
 loss due to the diffusion of ions to the sides of the vessel. 
 Thus suppose the ionised gas is contained in a metal vessel, then 
 when the ions come in contact with the sides of the vessel their 
 charges are neutralised by the opposite charge induced on the 
 metal and they thus cease to act like ions ; the layer of gas next 
 the sides of the vessel is thus denuded of ions, which exist in finite 
 numbers in the gas in the interior ; a gradient in the concentration 
 is thus established and the ions diffuse from the interior to the 
 boundary. The problem is closely analogous to that of the absorp- 
 tion of water vapour in a vessel whose sides are wet with sulphuric 
 acid. We shall begin by considering the theory of a very simple 
 case, that of ionised gas contained between two parallel metal 
 plates at right angles to the axis of x. Let n be the number of 
 positive ions per cubic centimetre, q the number of ions pro- 
 duced by the ionising agent per second in a cubic centimetre 
 of the gas, D the coefficient of diffusion of the positive ions 
 through the gas, m the number of negative ions per cubic centi- 
 metre, then we see that in consequence of diffusion the rate 
 of increase in the number of positive ions per cubic centimetre 
 
 d?n 
 is equal to D -^ :. assuming that the surfaces of equal density of 
 
 the ions are planes at right angles to the axis of x. Thus taking 
 recombination and external ionisation into account as well as 
 diffusion we have 
 
 dn ^ d?n 
 
 and when things are in a steady state, 
 
 Let us consider the special case when the plates are so near 
 together that the loss of ions from diffusion far exceeds that from 
 recombination, then we have 
 
18] WHEN IN THE CONDUCTING STATE. 21 
 
 If we take the plane midway between the metal plates as 
 the plane x = 0, and if 11 is the distance between the plates, then 
 the conditions to be satisfied by n are n = Q when x=l; the 
 solution of equation (1) with these conditions is 
 
 .(2). 
 
 The total number of free positive ions between the plates is 
 equal to 
 
 I ndx, 
 J -i 
 
 and this by equation (2) is equal to 
 
 We see from this result how we can measure D. For, if we 
 cut off the rays and apply a strong electric field between the 
 plates, we shall drive all the positive ions against the plate at the 
 lower potential, so that this plate will receive a charge of 
 
 electricity equal to - ^ I 3 e, where e is the charge on an ion ; if 
 
 O JL/ 
 
 this plate is connected with an electrometer we can measure its 
 charge, which will be proportional to the deflection ^ of the 
 electrometer. If the rays are kept on and the field is intense 
 enough to produce the saturation current, the charge received by 
 the plate in one second is equal to 2qle, hence if 2 is the deflec- 
 tion of the electrometer in one second in this case, we see that 
 
 an equation which enables us to determine D. 
 
 We have in this investigation neglected the effect of recom- 
 bination; it is necessary to verify that the plates are sufficiently 
 close together to make this justifiable. An easy way of doing thib 
 is as follows : the total number of ions on the hypothesis that the 
 only source of loss of ions is recombination is equal to 21 vq/a, 
 (see p. 15); the number on the assumption that the loss is 
 
 entirely due to diffusion is as we have just seen ^ -^ I 9 , hence 
 
 if |f> is small compared with *l\ the loss of ions from 
 
 o D 
 
22 
 
 PROPERTIES OF A GAS 
 
 [19 
 
 diffusion will be large compared with the loss by recombination, 
 and we shall be justified in neglecting the latter. 
 
 19. The coefficients of diffusion of the ions in air, oxygen, 
 hydrogen and carbonic acid gas have been determined by Town- 
 send* by a different method; ionised air being sucked through 
 very narrow tubes and the loss of ions suffered in passing 
 through a known length of tubing determined. The theory of the 
 method is as follows : ionised gas is sent through a metal tube the 
 axis of which is taken as the axis of z, the gas moving parallel to 
 z and being free from the action of any ionising agent in its course 
 through the tube. Consider the state of things in a small volume 
 ABCDEFGH: this volume loses ions by diffusion, and gains 
 them by the gas entering the volume through the face A BCD 
 
 JT 
 
 Fig. 6. 
 
 being richer in ions than that leaving it through the face 
 EFGH, when the gas is in a steady state the rates of loss and 
 gain of ions must be equal. If n is the number of ions per cubic 
 centimetre, D the coefficient of diffusion of the ions through the 
 gas, the rate of loss of ions from diffusion is equal to 
 
 n d?n d?n 
 
 If v is the velocity of the gas, the rate of gain of ions from the 
 second cause is equal to 
 
 d 
 
 or, since v does not depend upon z, to 
 
 dn 
 
 * Townsend, Phil. Trans. A. 193, p. 129, 1900. 
 
19] WHEN IN THE CONDUCTING STATE. 23 
 
 Hence equating the loss and the gain we get 
 n . d 2 n . d 2 n\ dn 
 
 In the experiments the term D~ was very small compared 
 with v-^; -^ being of the order 1/20, v of the order 100 and 
 
 D about "03 so that vn was about 70,000 times D - . Neglecting 
 
 d?n 
 D ^ and taking the case of a cylindrical tube of radius a sym- 
 
 metrical about the axis 
 
 d?n dnd*n I dn 
 
 where r is the distance of a point from the axis of the tube. Now 
 
 2F 
 
 v = - (a 2 r 2 ), where F?ra 2 is the volume of gas passing per 
 
 CL 
 
 second through each cross-section of the tube ; substituting these 
 values in equation (1) and neglecting d 2 n/dz z we get 
 
 The conditions to be satisfied by n are that n = when r = a 
 for all values of z, and that if the ionised gas enters the tube at 
 z 0, n n a constant, when z = 0, for all values of r. 
 
 To solve this equation put n = <f>e~ 2F where < depends only 
 upon r and 6 is a constant to be subsequently determined ; substi- 
 tuting this value of n in equation (2) we get 
 
 Put = 1 + B^ + Bft + Bj* + ..., 
 
 and we get from (3) 
 
 thus the first three terms in are 
 
24 
 
 PROPERTIES OF A GAS 
 
 [19 
 
 We have to choose such values of 6 that (f> when r = a, let 
 these values be O lt 2 ... and let </>!, <f> 2 be the values of </> when 
 these values of 6 are substituted in equation (4) ; then we may 
 write 
 
 To find the values of d, C 2 , C 3 ... we have the condition n = n 
 a constant when z 0. Hence 
 
 Now from the differential equation (3) we can easily prove the 
 following relations" 
 
 I <t>n<}>m (& 2 r*)rdr = Q when n and m are different . . .(7), 
 J o 
 
 Multiplying both sides of equation (6) by cf> n (a 2 r 2 ) r and 
 integrating from r = to r = a we obtain -by the aid of equations 
 (7), (8) and (9) 
 
 Cw= ~"71i 
 
 n dQ n 
 hence 
 
 = -K O ) i^V-.c 2F + ^ ^-n^e-'TF" + ...I .(10). 
 
 The number of ions which pass across the section of the tube 
 when s = is 7i 7ra 2 F, the quantity which pass across a section of 
 the tube at a distance z from the origin is equal to 
 
 /, 
 
 a 2F 
 ^ 
 
 this by equations (7), (9) and (10) is equal to 
 
 4<7rVn \ 1 
 a Jtfj 2 
 
 dr 
 
 2F 
 
19] WHEN IN THE CONDUCTING STATE. 25 
 
 The two smallest roots of the equation </> = were found by 
 Townsend to be 1 a 4 =7'313 and 6> 2 a 4 = 44'56, corresponding to 
 these roots we have 
 
 Hence substituting these values we find that the ratio of the 
 number of ions which pass a cross- section of the tube at a distance 
 z from the origin to the number which pass through the tube at 
 the origin is equal to 
 
 7'313J>z 
 
 4 {-1952e ** v + -0243e 
 
 If d is the saturation current through the gas after leaving a 
 tube of length l lt c 2 that after leaving a tube of length / 2 , then 
 since the saturation currents are proportional to the numbers of 
 ions given to the gas per second, we have 
 
 d -19526 
 
 c 
 
 1952e 
 
 Now d/c 2 can be determined by experiment, and hence from 
 equation (11) the value of D can be determined. The method 
 used by Townsend to solve this equation was a graphical one; 
 
 7'313_D 
 
 putting y = d/c 2 , x = 9 zv 1 , the curve representing the relation 
 
 (11) between y and x was drawn by calculating a number of cor- 
 responding values : when this curve had been obtained the value 
 of 7*313D^/2a 2 F corresponding to any value of d/Cg obtained by 
 experiment could be found, and hence D determined as I, a and V 
 are known. 
 
 The apparatus used to measure the value of d/Ca is represented 
 in Fig. 7. A is a brass tube 50 cm. long, 3'2 cm. in diameter, 
 provided with an aluminium window W through which the 
 Rontgeri rays which ionise the gas pass. C is another brass tube 
 17 cm. long fitting accurately into A and able to slide along it. 
 E is an electrode which is connected to a metal rod F passing 
 through an ebonite plug. A series of fine wires were soldered 
 parallel to one another and 2 mm. apart across the end of the 
 
PROPERTIES OF A GAS 
 
 [19 
 
 tube C. The gas entered the apparatus through the glass tube G 
 and then before reaching the electrode passed through the tubes T. 
 
 ojuu^- 
 
 G vm / 
 
 K%%T^N 
 
 Fig. 7. 
 
 These were twelve tubes 10 cm. long and *3 cm. in diameter, 
 arranged at equal intervals and all at the same distance 
 from the axis of the tube A ; they were soldered into holes 
 bored into two brass discs a and /3 which fitted so closely into A 
 that gas could not pass between the disc and the tube. Another 
 set of twelve tubes only 1 cm. long and '3 cm. in diameter were fused 
 into another disc 7. The tube A was insulated by the two ebonite 
 rings R, R'. The potential of the tube was raised to 80 volts by 
 connecting it with one of the terminals of a battery of small storage 
 cells, the other terminal of which was connected with the earth. 
 The electrode E was connected with one pair of quadrants of an 
 electrometer, the other pair of quadrants being kept to earth. 
 A uniform and measurable stream of gas was supplied by a 
 gasometer, this gas was ionised by the Rontgen rays as it 
 passed through the tube, some of the ions were lost by diffusion to 
 the sides, all the positive ones which escaped were driven against 
 the electrode E\ thus the charge on the electrometer measured 
 the number of positive ions which got through the tubes. By 
 charging the tube A up negatively, the negative ions could be 
 driven against the electrode, and the number of those which get 
 
19] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 27 
 
 through the tubes determined. After a series of measurements 
 had been made with the long tubes, these were replaced by the 
 short ones, and a similar series of measurements gone through. 
 These measurements, as was explained in the preceding theory, 
 give us the data for calculating the coefficient of diffusion of the 
 ions. For gases other than air, a somewhat different form of 
 apparatus was used, fora description of which we must refer to the 
 original paper. 
 
 The loss of ions even in the narrow tubes is not entirely due 
 to diffusion to the sides of the tube, a part, though only a small 
 part, of the loss will be due to the recombination of the ions. To 
 estimate how much was due to this effect, the small tubes Twere 
 removed and the deflection of the electrometer observed when the 
 tube C was placed at different distances from the place where the 
 gas is ionised ; in a wide tube such as A the loss from diffusion to 
 the sides is negligible, and the smaller deflection of the electro- 
 meter when the electrode E is moved away from the place of 
 ionisation is due to the loss of ions by recombination. By making 
 measurements at different distances and knowing the velocity of 
 the gas we can measure in this way the amount of recombination 
 taking place in a given time and hence determine the value of a, 
 the constant of recombination. It was in this way that the values 
 of a given on page 19 were determined. Knowing a it is easy to 
 calculate the loss of ions from recombination in their passage 
 through the narrow tubes, and then to apply a correction to the 
 observations so as to get the loss due to diffusion alone. 
 
 The following tables give the velocities of the coefficients of 
 diffusion on the C.G.s. system of units as deduced by Townsend 
 from his observations. 
 
 TABLE I. COEFFICIENTS OF DIFFUSION IN DRY GASES. 
 
 Gas 
 
 D for + ions 
 
 D for - ions 
 
 Mean value 
 ofD 
 
 Ratio of D for 
 - to D for 
 + ions 
 
 Air 
 
 028 
 
 043 
 
 0347 
 
 1-54 
 
 Oxygen 
 
 025 
 
 0396 
 
 0323 
 
 1-58 
 
 Carbonic acid 
 Hydrogen . . 
 
 023 
 123 
 
 026 
 190 
 
 0245 
 156 
 
 1-13 
 1-54 
 
 
 
 
 
 
28 
 
 PROPERTIES OF A GAS 
 
 [19 
 
 TABLE II. COEFFICIENTS OF DIFFUSION IN MOIST GASES. 
 
 Gas 
 
 D for + ions 
 
 D for - ions 
 
 Mean value 
 of D 
 
 Eatio of D for 
 - to + ions 
 
 Air 
 
 032 
 
 035 
 
 0335 
 
 1-09 
 
 Oxygen 
 
 0288 
 
 0358 
 
 0323 
 
 1-24 
 
 Carbonic acid 
 
 0245 
 
 0255 
 
 025 
 
 1-04 
 
 Hydrogen . 
 
 128 
 
 142 
 
 135 
 
 I'll 
 
 
 
 
 
 
 We see from these tables that the coefficient of diffusion for 
 the negative ions is greater than that for the positive, the difference 
 being much more marked in dry than in damp gases. The superior 
 mobility of the negative ions was first observed by Zeleny* who 
 measured by a method which we shall shortly describe the velocity 
 of the ions when placed in an electric field, and found that the 
 negative ions moved faster than the positive ones. The more 
 rapid diffusion of the negative ions explains why in certain cases 
 ionised gas, originally electrically neutral, acquires a charge of 
 positive electricity. Thus, for example, if such a gas is blown 
 through metal tubes, the gas emerging from the tubes will be 
 positively electrified, as in the passage through the tubes it has 
 lost more negative than positive ions. Zeleny (loc. cit.) has shown 
 that this effect does not occur with carbonic acid gas in which the 
 velocities of the two ions are very nearly equal. Some experi- 
 ments made by Rutherfordf seem to show that in addition to the 
 effect produced by diffusion, there is a specific effect due to the 
 metal, as he found that the excess of positive over negative ions 
 was greater when the ionised gas passed through zinc tubes than 
 when it passed through copper. The difference in the rate of 
 diffusion of the positive and negative ions causes a certain amount 
 of electrical separation to take place when a gas is ionised ; as the 
 negative ions diffuse more rapidly than the positive ones, the 
 region where ionisation takes place will have an excess of positive 
 ions and be positively electrified, while in consequence of the 
 diffusion of the negative ions the surrounding regions will have an 
 excess of these ions and will therefore be negatively electrified. 
 
 * Zeleny, Phil. Mag. v. 46, p. 120, 1898. 
 
 t Kutherford, Phil. Mag. v. 43, p. 241, 1897. 
 
19] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 29 
 
 The results given in Tables I. and II. show that the excess of 
 the velocity of diffusion of the negative ions over that of the 
 positive is much greater when the gas is dry than when it is 
 moist ; the effect of moisture on the velocity of diffusion is very 
 remarkable, the results quoted in the table show that with the 
 exception of ions in carbonic acid (where there is but little differ- 
 ence between the velocities of diffusion of positive or negative ions 
 in either wet or dry gas) the effect of moisture is to produce a 
 very considerable diminution in the rate of diffusion of the negative 
 ions, while on the other hand it tends to increase the rate of dif- 
 fusion of the positive ions, though the change produced in the 
 positive ions is not in general as great as that produced in the 
 negative. We shall see later on that water vapour condenses 
 more readily on negative ions than on positive ones, so that it is 
 probable that the negative ions in a damp atmosphere get loaded 
 with moisture and so are retarded in their movements through the 
 surrounding gas. 
 
 The preceding experiments relate to ions produced by the 
 Rontgen rays. Townsend* subsequently applied the same method 
 to the determination of the coefficients of diffusion of ions pro- 
 duced by radio-active substances, by ultra-violet light and by 
 discharges from electrified needle points ; the results of these 
 experiments are shown in the following table. 
 
 COEFFICIENTS OF DIFFUSION OF IONS PRODUCED IN AIR BY 
 DIFFERENT METHODS. 
 
 Method 
 
 Dry Air 
 
 Moist Air 
 
 + ions 
 
 - ions 
 
 + ions 
 
 - ions 
 
 Rontgen rays 
 
 028 
 032 
 
 0247 
 0216 
 
 043 
 043 
 043 
 037 
 032 
 
 032 
 036 
 
 028 
 027 
 
 035 
 041 
 037 
 039 
 037 
 
 Radio-active substances ... 
 Ultra-violet light 
 
 Point Discharge 
 
 
 From these numbers we conclude that the ions produced by 
 Rontgen rays, by radio-active substances and by ultra-violet light 
 
 * Townsend, Phil. Trans. A. 195, p. 259, 1900. 
 
30 
 
 PROPERTIES OF A GAS 
 
 [20 
 
 are identical, a conclusion which we shall find confirmed by several 
 other courses of reasoning. 
 
 Townsend* also investigated the coefficients of diffusion of ions 
 produced by radio-active substances at a series of pressures ranging 
 from 772 millimetres of mercury to 200 mm. and found that within 
 this range the coefficient of diffusion was inversely proportional to 
 the pressure ; the Kinetic Theory of Gases shows that this would 
 be true in a system where the diffusing systems do not change 
 character with the pressure ; as this result holds for ions we con- 
 clude that down to a pressure of at least 200 mm. the ions do not 
 change. We shall see that at very low pressures the negative ions 
 are very much smaller than at these high pressures. 
 
 20. It is of interest to compare the rates of diffusion of ions 
 through a gas with those of the molecules of one gas through 
 another. In the following table taken from Winkelmann's Hand- 
 buck der Physik, vol. i. pp. 645, 647, the coefficients of diffusion 
 into each other for hydrogen, air, carbonic acid, and carbonic oxide, 
 and for some vapours are given; it appears from the table that 
 the gases diffuse very much more quickly than the ions, but that 
 there are vapours whose coefficients of diffusion are of the same 
 order as those of the ions. 
 
 Gas 
 
 D 
 
 cm. 2 /sec. 
 
 Gas 
 
 D 
 
 cm. 2 /sec. 
 
 Gas 
 
 D 
 
 cm. 2 /sec. 
 
 CO C0 2 
 
 13142 
 
 CO 2 
 
 18717 
 
 ether CO 2 
 
 0552 
 
 air C0 2 
 2 -C0 2 
 
 13433 
 13569 
 
 H 2 -0 2 
 H 2 air 
 
 66550 
 63405 
 
 isobutylic ) TT 
 amide ) 2 
 
 1724 
 
 H 2 C0 2 
 
 53409 
 
 i ether H 2 
 
 296 
 
 air 
 
 0426 
 
 air O 2 
 
 17778 
 
 ether air 
 
 0775 
 
 
 0305 
 
 
 
 | 
 
 
 
 
 The most probable explanation of the slow diffusion of the 
 ions seems to be that the charged ion forms a nucleus round 
 which the molecules of the gas condense, just as dust collects round 
 a charged body, thus producing a complex system which diffuses 
 slowly : this explanation is supported by the fact discovered by 
 M c Clelland'f p that the coefficients of diffusion of the ions in the 
 flame gases depend very much on the temperature of the flame 
 
 * Townsend, Phil. Trans. A. 195, p. 259, 1900. 
 
 f M c Clelland, Camb. Phil. Soc. Proc. x. p. 241, 1899. 
 
21] WHEN IN THE CONDUCTING STATE. 31 
 
 and the distance of the ions from it ; a comparatively small 
 lowering of temperature producing a great diminution in the rate 
 of diffusion of the ions, as if precipitation had occurred upon 
 them. The view is also supported by the ability of the ions to 
 act as nuclei for the precipitation of water vapour. It must be 
 remembered also that an ion differs from an ordinary molecule in 
 being charged with electricity and thus being surrounded by a 
 strong electric field. 
 
 Rutherford* has recently shown that the vapour of alcohol or 
 ether, like that of water, produces a great diminution in the 
 mobility of the negative ion. 
 
 Velocity of the Ions in an Electric Field. 
 
 21. The coefficient of diffusion of the ions through a gas is 
 directly proportional to the speed with which the ions travel 
 through the gas under the action of an electric field of given 
 strength. The connection between this speed and the coefficient 
 of diffusion can be established as follows. From the definition of 
 the coefficient of diffusion D it follows that if n is the number of 
 ions per cubic centimetre, the number of ions which in unit 
 time cross unit area of a plane at right angles to x is equal to 
 
 D -j- . We may thus regard the ions as moving parallel to the 
 
 axis of x with the average velocity D-j. The ions being in 
 
 the gaseous state will produce a partial pressure p which when 
 the temperature is constant is proportional to the number of ions, 
 we see therefore that the average velocity of the ions parallel 
 
 to x is equal to -D-f. Now dp Idas is the force acting parallel 
 p dx 
 
 to the axis of x on unit volume of the gas, we may thus interpret 
 the preceding expression as meaning that when the force acting 
 parallel to the axis of x on the ions in unit volume is unity, the 
 ions move parallel to the axis of x with a mean velocity of transla- 
 tion equal to Djp. Suppose now that the ions are placed in an 
 electric field when the electric intensity parallel to the axis of x 
 is equal to X, then the force on the ions in unit volume is equal 
 
 * Eutherford, Phil. Mag. vi. 2. p. 210, 1901. 
 
32 PROPERTIES OF A GAS [22 
 
 to Xen, hence if u is the average velocity of translation of the 
 ions parallel to the axis of x 
 
 u = Xen . 
 P 
 
 Now n/p is the same for all gases at the same temperature, 
 hence if N is the number of molecules of air in a c.c. at this 
 temperature and at the atmospheric pressure II, since n/p N/Tl, 
 we have 
 
 or u the velocity of the ions in a field of unit intensity is given 
 by the equation 
 
 r\Ne 
 
 m-D^-. 
 
 Thus u is directly proportional to D, so that a knowledge of 
 one of these quantities enables us at once to calculate the other. 
 
 22. Measurements of the velocity of the ions under an 
 electric field were made some time before those of the coefficients 
 of diffusion. The earliest systematic measurements of the velocity 
 of the ions in an electric field were made in the Cavendish 
 Laboratory in 1897 by Rutherford*. Two different methods were 
 used in these experiments. The first method is as follows : 
 suppose that the current is passing through ionised gas between 
 two parallel plates A and B ; then if there are n positive ions and 
 n negative ions in each cubic centimetre of the gas and u lf u 2 are 
 respectively the velocities of the positive and negative ions, the 
 current i passing through each unit area of cross-section between 
 the plates is given by the equation 
 
 i = n (H! + u 2 ) e, 
 
 where e is the charge on an ion. Now i can easily be measured if 
 one of the plates A is connected to one pair of quadrants of an 
 electrometer, the other pair of which is connected to earth, and 
 if the other plate B is connected to one terminal of a battery of 
 known electromotive force, the other terminal of which is to 
 earth. For if the quadrants are at first connected together and 
 then disconnected, i will be the charge communicated in one 
 second to the plate connected with the electrometer. 
 
 * Rutherford, Phil. Mag. v. 44, p. 422, 1897. 
 
22] WHEN IN THE CONDUCTING STATE. 33 
 
 The value of ne can be determined in the following way; 
 after the gas has been exposed to the ionising agent, say 
 Rontgen rays, sufficiently long for it to get into a steady 
 state, the rays are suddenly cut off, and simultaneously with 
 the extinction of the rays a large electromotive force is suddenly 
 switched on between the plates; then if B is the positive plate all 
 the positive ions between the plates are driven against the plate 
 A before they have time to recombine with the negative ions, and 
 thus A receives a positive charge equal to that on the whole of 
 the positive ions between the plates, i.e. each unit area of A 
 receives a charge of positive electricity equal to nle, where / is the 
 distance between the plates. This charge can be measured by the 
 electrometer, let it equal q ; then since i = n (u^ + u 2 ) e, we have 
 
 i _ M! + u 2 
 
 q~ I 1} ' 
 
 a relation which enables us to determine u^ + U z . Now let E be 
 the potential difference between the plates when the current is i. 
 Then u^ + u 2 is the sum of the velocities of the ions when the 
 electric intensity is Ejl ; hence, since as we shall see the velocity 
 of an ion is proportional to the electric intensity, the sum of the 
 velocities of the positive and negative ions when the electric 
 intensity is unity is (u^ + u 2 ) l/E, or I 2 i/Eq. For this method to 
 give accurate results, the ionisation and the electric field must be 
 uniform between the plates ; this condition requires, as the investi- 
 gation in Chapter III. shows, that the current should be so small 
 that the conduction is in the stage represented by the first 
 part of the curve, Fig. 4, when the curve is straight and the 
 current is proportional to the electric intensity. Again, when the 
 ionisation is produced by Rontgen rays or the rays from a radio- 
 active substance, the rays should be arranged so that they pass 
 tangentially between the plates and do not strike against them ; 
 the reason for this precaution is that when the rays strike against 
 a metallic surface, there is an abnormally great ionisation of the 
 gas close to the surface of the plates and the ionisation between 
 the plates is not uniform. 
 
 The values for the sum of the velocities of the positive and 
 negative ions under a potential gradient of one volt per centimetre 
 obtained by Rutherford by this method are given in the following 
 table. 
 T. G. 
 
34 
 
 PROPERTIES OF A GAS 
 
 [23 
 
 Gas 
 
 Sum of velocities 
 of + and - ions 
 
 Gas 
 
 Sum of velocities 
 of + and - ions 
 
 Hydrogen 
 
 10 cm. /sec. 
 
 Carbonic acid 
 
 2*15 crn./sec. 
 
 
 2 *8 cm. /sec. 
 
 Sulphur dioxide ... 
 
 *99 cm. /sec. 
 
 Nitrogen 
 
 3 '2 cm. /sec. 
 
 Chlorine 
 
 2 cm. /sec. 
 
 Air 
 
 3 '2 cm. /sec. 
 
 Hydrochloric acid 
 
 2*55 cm./sec. 
 
 
 
 
 
 In these experiments the gases were not specially dried. 
 
 23. The method in this form can only be used when there is 
 a considerable volume of gas between the plates and when the 
 ionisation is large, in other cases the deflection of the electrometer 
 obtained when the large electromotive force is applied between the 
 plates is so small that accurate determinations of q are not possible; 
 thus if the distance between the plates is 3'2 cm. we see from 
 equation (1) that the deflection of the electrometer, when the 
 large electromotive force is applied, is only that produced in one 
 second by the steady leak caused by a potential difference of 8*2 
 volts between the plates ; this with a fairly sensitive electrometer 
 and not very weak ionisation, would often not exceed 2 or 3 scale 
 divisions, while the percentage error with such small deflections 
 would be very large. I have used a modification of this method 
 
 Earth 
 
 Earth 
 
 Electrometer 
 
 Earth 
 
 Fig. 8. 
 
 which is not subject to these disadvantages. The arrangement 
 is represented diagrammatically in Fig. 8. C is the plate con- 
 
23] WHEN IN THE CONDUCTING STATE. 
 
 35 
 
 nected with the electrometer, it is provided with a guard ring so 
 as to avoid difficulties connected with irregularities in the electric 
 field: this plate is placed between two parallel plates A and B 
 and the whole region between A and B is exposed to the ionising 
 agent. The plates are adjusted so that the rate of leak to the 
 plate G, when A is charged to a potential V and B connected 
 with earth, is the same as that to G, when B is charged to the 
 potential V and A is connected with earth. 
 
 A is connected to a point E in a high resistance GH which is 
 traversed by the current from the voltaic cell F, H is connected 
 with earth, and by moving the point of attachment E the plate A 
 can be raised to any potential from zero up to the electromotive 
 force of the battery ; if G is the positive pole of the battery 
 positive electricity will flow into the plate C (this plate is initially 
 connected with earth). B is connected with the earth through a 
 large resistance ft, the point 8 is touched at regular intervals by 
 a rotating brush which connects it for a very short time with the 
 negative terminal of a large battery of small storage cells the 
 other terminal of which is to earth. The contact lasts long 
 enough for the electric field to drive all the negative ions between 
 B and C on to the plate C, but not long enough for any appre- 
 ciable quantity of fresh ions to be produced while the field is on. 
 The plate C is thus receiving positive ions from one side and 
 negative from the other, and by moving the point E about we can 
 make the positive charge balance the negative so that there is no 
 deflection of the electrometer. When this is the case we can 
 easily prove by the same reasoning as before that K I 4- v lt the sum 
 of the velocities of the positive and negative ions when the 
 potential difference between the plates A and C is equal to that 
 between E and H, is equal to ml where I is the distance between 
 the plates B and (7, and m is the number of contacts per second 
 made by the rotating brush with S. As in this case the experi- 
 ment may be made to last while a large number of contacts occur, 
 the method is much more sensitive than when only one contact is 
 made. 
 
 To prevent the potential of G changing appreciably in the 
 interval between the contacts, C is connected with one of the 
 plates of a parallel plate condenser of large capacity. When the 
 final test is made as to whether C has or has not received a charge 
 
 32 
 
PROPERTIES OF A GAS 
 
 [24 
 
 the plates of the condenser are pulled apart so as to diminish its 
 capacity and thus increase the deflection of the electrometer due 
 to any charge that might be on the plate C. Care must be taken 
 to allow sufficient time to elapse between successive contacts at S 
 to permit of the gas getting into a steady state before the next 
 contact is made. When the ionisation is very weak it may 
 require an interval of several seconds for this condition to be 
 fulfilled. 
 
 24. Another method used by Rutherford* is represented in 
 Fig. 9. Two large metal plates A and B were placed parallel to 
 
 
 " 
 
 Earth 
 
 
 Lever 
 
 M 
 
 .// 
 
 r To Battery 
 A of cells 
 
 F!// 
 
 -- 
 
 j 
 
 Fig. 9. 
 
 one another and 16 cms. apart on the insulating blocks C and D. 
 The Rontgen rays were arranged so as to pass through only one 
 half of the gas included between the plates, thus no direct radia- 
 tion reached the air to the left of the line EF which is half-way 
 between the plates. The plate A was connected with one terminal of 
 a battery of a large number of small storage cells giving a potential 
 difference of 220 volts, the other terminal of the battery being con- 
 nected with the earth. The plate B was connected through a contact 
 lever LM, mounted on an insulating block, to one pair of quadrants 
 of an electrometer, the other pair being connected with the earth, 
 
 * Rutherford, Phil. Mag. v. 44, p. 422, 1897. 
 
25] WHEN IN THE CONDUCTING STATE. 37 
 
 A pendulum interrupter was arranged so as first to make the current 
 in the primary of the induction coil used to produce the rays, 
 then after a known interval to break the electrometer circuit by 
 knocking away the lever LM, and then to break the battery circuit 
 shortly afterwards. N is a condenser connected to the electrometer 
 to increase its capacity. With this arrangement the ions have to 
 travel over a distance of 8 cm. before they reach the plate B, and 
 the object of the experiment was to find the time occupied by the 
 rays in passing over this distance. It was found that there was 
 only a very small deflection of the electrometer when the interval 
 between putting on the rays and breaking the electrometer circuit 
 was less than '36 sec., but when the interval exceeded this value 
 the deflection of the electrometer increased rapidly. Thus '36 sec. 
 was taken as the time required for the ions to pass over a distance 
 of 8 cm. under a potential gradient of 220/16 volts per centimetre. 
 This corresponds to a velocity T6 cm./sec. for the gradient of a 
 volt per centimetre, and no difference was detected between the 
 velocities of the positive and negative ions. This makes the sum 
 of the velocities of the positive and negative ions in air under a 
 potential gradient of a volt a centimetre equal to 3'2 cm./sec. 
 which is exactly the velocity found by Rutherford using the first 
 method. 
 
 25. The difference between the velocities of the positive and 
 negative ions was discovered by Zeleny*, who has made very 
 valuable determinations of the velocities of the ions in an electric 
 field. The method by which he discovered the difference of the 
 velocities was by finding the electric force required to force an ion 
 against a stream of gas moving with a known velocity parallel 
 to the lines of electric force. Thus suppose A and B, Fig. 10, 
 represent two parallel plates made of wire gauze and that between 
 these plates we have a stratum of ionised gas, let the gas be 
 moving through the plates from A to B with the velocity V, and let 
 the potential gradient between the plates be n volts per centimetre, 
 B being the positive plate. Then if the velocity of the positive ion 
 under a potential gradient of 1 volt per centimetre be u, the velo- 
 city of the positive ion in the direction from B to A is nu V and 
 this is proportional to the number of ions giving up their charges 
 
 * Zeleny, Phil. Mag. v. 46, p. 120, 1898. 
 
38 
 
 PROPERTIES OF A GAS 
 
 [25 
 
 to A in unit time. Suppose now that we make B the negative 
 plate, then if the potential gradient between the plates is ri volts 
 
 d 
 
 u 
 
 B 
 
 Fig. 10. 
 
 per centimetre and the velocity of the negative ion under a 
 potential gradient of 1 volt per centimetre is v, the velocity of 
 the negative ion from B to A is n'v V, and this is proportional 
 to the number of negative ions giving up their charges to A 
 in unit time. If we adjust the potential gradients so that the 
 rate at which A receives a positive charge when B is positive is 
 equal to the rate at which it receives a negative charge when B is 
 negative, we have 
 
 nu Vn'v V, 
 
 or 
 
 Thus from the measurement of the potential gradients we can 
 determine the ratio u : v. 
 
 The apparatus used by Zeleny for carrying out this method is 
 shown in Fig. 11. P and Q are brass plates 9 centimetres square. 
 They are bored through their centres and to the openings thus 
 made the tubes R and $ are attached, the space between the 
 plates being covered in so as to form a closed box ; K is a piece of 
 wire gauze completely filling the opening in the plate Q ; T is an 
 
25] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 39 
 
 insulated piece of wire gauze nearly but not quite filling the open- 
 ing in the plate P and connected with one pair of quadrants of an 
 
 Earfh 
 
 Fig. 11. 
 
 electrometer E. 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 .P; this plug has also the effect of making the velocity of 
 flow of the gas uniform across the section of the tube. The 
 Rontgen rays to ionise the gas were produced by a bulb at 0, the 
 bulb and coil being, in a lead-covered box fitted with an aluminium 
 window through which the rays passed. Q is connected with one 
 pole of a battery of cells and P and the other pole of the battery 
 connected with earth. When the rays are entering PQ and the 
 ions are travelling in opposite directions in the box the charges 
 they give to P, Q and K are conducted to earth, while those they 
 give to T gradually change its potential at an approximately 
 uniform rate, as long as this potential is small compared with that 
 of Q. When the distribution of free charges in the gas has 
 assumed a steady state all the changes in the potential of T are 
 due to the charges given up by the ions striking against it. 
 
 The nature of the readings obtained with this apparatus are 
 indicated by the curves shown in Fig. 12 where the ordinates 
 represent the deflection of the electrometer in a given time and 
 the abscissse the potential difference in volts between the plates 
 P and Q. Curve I. is for the case when the negative ions, Curve 
 II. when the positive ions, are driven against the plate. It will 
 be seen that after a point about B the curves are for some distance 
 
40 
 
 PROPERTIES OF A GAS 
 
 [25 
 
 straight lines, but that there is a curved portion to the left of B, in- 
 dicating that some ions are delivered up to the gauze under smaller 
 
 20 30 40 50 60 70 80 90 
 
 voltages than we should expect. This may possibly be explained 
 by irregularities in the air blast, the deflections corresponding to 
 the part of the curve about A arriving in the lulls of the blast. One 
 way of treating the observations would be to produce the straight 
 portion of the curves until they cut the horizontal axis ; in the 
 figure this would happen for Curve I. at about 50 volts and for 
 Curve II. at about 60 ; we might then take 50 volts as the 
 potential difference between the plates which would give to the 
 negative ions a velocity equal to that of the blast, while 60 volts 
 would be required to give the same velocity to the positive ions, 
 so that under fields of equal strength the velocity of the negative 
 ion would be to that of the positive as 6 to 5. The method actually 
 adopted was different ; the curves were regarded as merely a 
 preliminary part of the experiment indicating about the values of 
 the potential differences to employ in the final observations. Thus 
 from the curves in Fig. 12 it is clear that to get the same deflec- 
 tion with the positive ions, as is got with the negative ions for a 
 potential difference of 60 volts, would require a potential difference 
 of between 72 and 74 volts; a careful series of measurements with 
 differences of potential between these values .is taken and the true 
 
26] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 41 
 
 value of the potential difference found by interpolation. When 
 this value, suppose for example 73'2, had been found, the ratio 
 of the velocities of the negative to the positive ions was taken 
 as 73-2 : 60. 
 
 The potential gradient between the plates was found to be not 
 quite uniform owing to the accumulation of ions between the 
 plates. The actual potential gradient was measured and a correc- 
 tion applied for the want of uniformity, this correction amounted to 
 about 2 per cent. The results obtained by Zeleny are given in 
 the following table. 
 
 RATIO OF VELOCITIES OF IONS. 
 
 Gas 
 
 Velocity of negative ion 
 
 
 Velocity of positive ion 
 
 Air 
 
 1'24 
 
 Oxygen 
 
 1-24 
 
 Nitrogen 
 
 1-23 
 
 Hydrogen ; 
 
 1-14 
 
 Coal gas 
 
 1-15 
 
 Carbon dioxide 
 
 1-00 
 
 Ammonia 
 
 1-045 
 
 Acetylene 
 
 0-985 
 
 Nitrogen monoxide . . . 
 
 1-105 
 
 Thus acetylene is the only gas in which the velocity of the 
 negative ion is less than that of the positive and here the differ- 
 ence is so small that it is within the limits of error of the experi- 
 ment. The gases in this experiment were not specially dried; 
 we have seen that moisture has a great effect in reducing the 
 velocity of the negative ion. 
 
 26. In some later experiments Zeleny* has determined the 
 absolute values of the velocity of both the positive and negative 
 ions. The method he employed was a blast method, though in 
 these experiments the blast was at right angles to the lines of 
 electric force instead of along them. A method similar to the 
 one just described was tried for a considerable time (it is evident 
 that if we know the velocity of the blast and the points where 
 
 * Zeleny, Phil. Trans. A. 195, p. 193, 1900. 
 
42 
 
 PROPERTIES OF A GAS 
 
 [26 
 
 the straight portions of the Curves I. and II. cut the horizontal 
 axis we can deduce the velocity of both the positive and negative 
 ions), but it had to be abandoned owing to the disturbance in the 
 distribution of the velocity of the blast caused by the wire gauze 
 which in this method has to be used for the electrodes. 
 
 The theory of the method finally used is as follows. A stream 
 of gas flows between two concentric metal cylinders which are 
 kept at different potentials, the gas at one place is traversed by 
 a beam of Rontgen rays at right angles to the axis of the cylinder ; 
 the ions thus produced are carried by the stream of gas parallel 
 to the axis of the cylinder, while a velocity at right angles to this 
 axis is imparted to them by the electric field. Let CO ', Fig. 18, 
 represent a section of the outer cylinder, DB that of the inner one, 
 
 Fig. 13. 
 
 dbmn the beam of Rontgen rays ionising the gas. If CC' is at 
 a higher potential than DB, then a positive ion starting from 
 d will move along a curved path between the cylinders, finally 
 reaching the inner cylinder at a point K whose horizontal distance 
 from d is one of the quantities measured in these experiments. 
 This distance, X, can easily be expressed in terms of the velocity of 
 the ion under unit electric force. For let b and a be respectively 
 the radii of the outer and inner cylinders, A the potential difference 
 between the cylinders, then the radial electric force R at a distance 
 r from the common axis of the cylinders is given by the equation 
 
 R = A 
 
 ~rlog e (6/a) ; 
 
26] WHEN IN THE CONDUCTING STATE. 43 
 
 thus if v is the velocity of the ion under unit electric force, then 
 on the assumption that the velocity is proportional to the electric 
 force we have, if V is the radial velocity of the ion at a distance 
 r from the axis of the cylinders, 
 
 V== Av 
 
 r log, (b/a) ' 
 
 If u is the velocity of the gas parallel to the axis of the cylinders 
 which we shall take as the axis of x, then the differential equation 
 to the path of the ion is 
 
 dx _ u 
 dr V 
 
 _ log e (b/a) ur 
 Av 
 
 hence X the horizontal distance from d at which the ion strikes 
 the inner cylinder is given by the equation 
 
 rb 
 
 Now 2?r urdr is the volume of gas which passes in unit time 
 
 J a 
 
 between the cylinders. We shall denote this quantity, which is 
 easily measured, by Q, then we have 
 
 log.(6/a) 
 ~ 
 
 
 Thus if we know X we can easily determine v. The time T 
 taken by the ion to pass from one cylinder to the other is given 
 by the equation 
 
 These equations apply to ions starting from the inner surface 
 of the outer cylinder. In practice the production of ions is not 
 
44 PROPERTIES OF A GAS [26 
 
 confined to the surface of the cylinder but extends throughout 
 a layer db reaching from one cylinder to the other. The ions 
 which start from a point in db, nearer to the surface of the inner 
 cylinder than d, will evidently not be carried so far down the tube 
 by the stream as an ion starting from d. Thus the preceding 
 equations give us the position of the furthest point down the inner 
 cylinder which is reached by the ions. In order to determine this 
 point the inner cylinder is divided at K into two parts insulated 
 from each other, the part D to the left being connected with the 
 earth, while the part B to the right is connected with one pair of 
 quadrants of an electrometer. If a constant stream of gas is sent 
 between the cylinders, then when the potential of CC' is above 
 a certain value, all the ions from the volume dd which move 
 inwards will reach DB to the left of K and will not affect the 
 electrometer. By gradually diminishing the potential of CC' we 
 reach a value such that the ions starting from the outer edge of 
 d reach DB just to the left of K\ when this stage is reached the 
 electrometer begins to be deflected. If then in equation (1) we 
 put for A the difference of potential corresponding to this stage, 
 and for X the horizontal distance of K from d, we shall be able 
 to deduce the value of v. 
 
 Corrections. In consequence of the diffusion of the ions, all 
 the ions starting from d will not follow exactly the line dK, and some 
 of the ions will be found to the right of the line. The consequence 
 of this is that the electrometer will begin to be deflected even when 
 the potential difference A is theoretically sufficient to bring all 
 the ions to the left of K\ thus the observed potential difference 
 when the deflections begin is slightly too large, and therefore the 
 values of v determined by equation (1) are a little too small. 
 Similar effects to those due to diffusion will be produced by the 
 mutual repulsion of the ions. It is evident that the magnitude of 
 these effects will depend upon the time it takes the ion to travel 
 between the cylinders ; if this time were zero, neither diffusion 
 nor repulsion would have time to produce any effect, thus the 
 longer the time taken by the ions to travel between the cylinders, 
 the smaller would be the value of v as determined by this method. 
 The time T, as we see from equation (2), depends upon the velocity 
 of the air blast and the strength of the field ; by altering these 
 quantities it is possible to determine the values of v for a con- 
 
26] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 45 
 
 siderable range of values of T \ the values so found decrease as was 
 to be expected slightly as T increases, the relation between v and 
 T being found by experiment to be a linear one. Curves in which 
 the ordinates were the ionic velocities and the abscissae the time 
 T were drawn, and the curve (which was found to be a straight 
 line) prolonged until it cut the line T = 0; the corresponding value 
 of v was taken as the ionic velocity. An example of such curves 
 is given in Fig. 14, the o's and xs are the points determined by 
 
 Fig. u. 
 
 actual experiments. The points at which the lines intersect 
 the line T=0 give 1/48 cm./sec. for the velocity of the negative 
 ion and 1/34 for the velocity of the positive, when the potential 
 gradient is one volt per cm. 
 
 Smaller corrections have to be applied for the disturbance in 
 the electric field produced by the presence of an excess of ions of 
 one sign over those of the other in different parts of the field. It 
 was proved by direct experiment that the effects due to surface 
 ionisation were not appreciable. 
 
 The apparatus used to carry out this method is represented in 
 section in Fig. 15. A A' was the outer cylinder; it had an internal 
 diameter of 5'1 cm. and a total length of 142 cm. The parts to the 
 right of V and to the left of V were made of brass tubing ; the 
 part between W was aluminium tubing of the same diameter; 
 this piece was inserted so as to permit the Rontgen rays to pass 
 through. The tubes were fastened together by airtight joints and 
 placed on insulating supports. 
 
 The inner cylinder BB' was an aluminium tube ; in one set of 
 experiments it was 1 cm. in diameter, in another it was 2'8 cm. ; 
 
46 
 
 PROPERTIES OF A GAS 
 
 [26 
 
 the ends of this tube were closed by conical pieces. The tube 
 was divided at C and the two portions separated by '5 mm. and 
 
 Fig. 15. 
 
 insulated by ebonite plugs. The tube was supported by the 
 ebonite rod Q and by the stiff brass wires Y and Y' which passed 
 through ebonite plugs in the outer cylinder, and served to connect 
 B' with the earth, and B with one pair of quadrants of the electro- 
 meter. The electrometer was a very sensitive one giving a 
 deflection of 500 scale divisions for a potential difference of one 
 volt. The narrow vertical beam of rays was adjusted and kept 
 definite by the slits in the lead plates 8, HH' and LL'. A con- 
 stant and measurable supply of gas was sent through the tube by 
 a gasometer. Experiments were made with gases carefully dried 
 and with gases saturated with water vapour. Two series of ex- 
 periments were made, one with an inner tube 1 cm. in diameter, 
 the other with an inner tube 2*8 cm. in diameter ; the results 
 obtained in the one series agreed very well with those obtained in 
 the other. 
 
 The values of the ionic velocities obtained by this method are 
 given in the following table; they have been reduced to the 
 uniform pressure of 760 mm. of mercury on the assumption (see 
 p. 30) that the ionic velocity under a given potential gradient is 
 inversely proportional to the pressure. 
 
27] 
 
 WHEN IN THE CONDUCTING STATE. 
 IONIC VELOCITIES. 
 
 47 
 
 Gas 
 
 Velocities in 
 under a potei 
 of one vo 
 
 Positive ions 
 
 cm. per sec. 
 itial gradient 
 t per cm. 
 
 Negative ions 
 
 Ratio of 
 velocities of 
 negative and 
 positive ions 
 
 Tempera- 
 ture 
 degrees 
 centigrade 
 
 Air dry 
 
 1-36 
 1-37 
 1-36 
 1-29 
 76 
 82 
 6-70 
 5-30 
 
 1-87 
 1-51 
 1-80 
 1-52 
 81 
 75 
 7-95 
 5-60 
 
 1-375 
 1*10 
 
 1-32 
 1-18 
 1-07 
 915 
 1-19 
 1-05 
 
 13'5 
 14 
 17 
 16 
 17-5 
 17 
 20 
 20 
 
 Air moist 
 
 Oxygen dry 
 
 Oxygen moist 
 
 Carbonic acid dry . . . 
 Carbonic acid moist 
 Hydrogen dry .... 
 
 Hydrogen moist ... 
 
 The intensity of ionisation was altered by causing the Rontgen 
 rays to pass through aluminium plates of different thicknesses, the 
 ionic velocities were found to be independent of the intensity of 
 the rays. 
 
 The results obtained by Zeleny agree well with those obtained 
 for the sum of the velocities obtained by Rutherford (see page 
 34) for air, oxygen, and hydrogen, allowing for the uncertainty 
 as to the amount of moisture in the gases used by Rutherford ; 
 for carbonic acid however there is considerable discrepancy, as 
 2*15 cm. /sec., the value of the sum of the velocities obtained by 
 Rutherford, is nearly 40 per cent, greater than the value 1'57 
 obtained by Zeleny, and as Zeleny found that this sum was the 
 same whether the gases were dry or moist the discrepancy cannot 
 be explained as due to the excess or defect of moisture in Ruther- 
 ford's gases. 
 
 Method of determining the velocity by measuring the number 
 of ions sent by a radial electric field to the sides of a tube of 
 given length when traversed by a current of gas. 
 
 27. The principle of this method which has been used by Ruther- 
 ford* to measure the velocities of the ions produced by uranium 
 radiation is as follows. Suppose that ionised air is blown through 
 a tube along the axis of which there is a wire charged positively, 
 
 * Eutherford, Phil Mag. v. 47, p. 109, 1899. 
 
48 PROPERTIES OF A GAS [27 
 
 the electric field around the wire will drag the negative ions into 
 the wire and thus rob the gas of a certain proportion of these ions ; 
 the number of these ions thus abstracted from the gas will depend 
 upon the relation between the velocity of an ion in the electric 
 field and the velocity of the air blast ; if the ionic velocity were 
 infinitely greater than the velocity of the blast, all the ions would 
 be abstracted, while if the velocity of the blast were infinitely 
 greater than the ionic velocity, they would all escape. 
 
 We see from equation (2), page 43, that t, the time taken 
 by an ion to reach the wire, is given by the expression 
 
 r 2 -a 2 , 6 
 t = jA^ lo &a ........................ (1) ' 
 
 where r is the distance from the axis of the tube of the point from 
 which the ion starts, b the internal radius of the tube, a the ex- 
 ternal radius of the wire, A the difference of potential between the 
 wire and the tube (the wire being at the higher potential), and u 2 
 the velocity of the negative ion under unit electric force. If in 
 equation (1) we put t equal to the time taken by the air blast to 
 pass from one end of the tube to the other, we see that all the ions 
 whose distance from the axis of the tube is less than the value of 
 r given by equation (1) will be dragged into the wire; hence if p is 
 the ratio of the number of ions dragged from the gas to the whole 
 number of ions, we have, assuming that the ions are uniformly dis- 
 tributed over the cross-section of the tube, 
 
 
 ........................... 
 
 The arrangement used by Rutherford is represented in Fig. 16. 
 
 A paper tube coated with uranium oxide was fitted into a 
 metal tube T 4 cm. in diameter. A blast of air from a gasometer 
 after passing through a plug of cotton- wool C to remove the dust 
 passed through a long metal tube AB connected with the earth ; 
 into this tube cylindrical electrodes A and B were fastened by 
 insulating supports so as to be coaxial with the tube. The elec- 
 trode A was charged up by a battery, and the electrode B was 
 connected with one pair of quadrants of an electrometer. If B 
 
28] WHEN IN THE CONDUCTING STATE. 49 
 
 were charged initially to a potential of the same sign as A 
 (suppose positive) large enough to saturate the gas, then the rate 
 
 Earth 
 Fig. 16. 
 
 of leak of the electrometer when the air blast was passing would 
 measure the number of negative ions which escaped being dragged 
 into the electrode A ; by comparing the rate of leak when the 
 electrode A is not charged with the rate when it is charged to a 
 known potential, we can determine the value of p in equation (2). 
 Rutherford did not use this arrangement to measure directly the 
 velocity of the ions produced by the uranium radiation, but proved 
 by means of it that the velocities of these ions were the same as 
 those of the ions produced by Rontgen rays. For this purpose, 
 after measurements of p had been made with the uranium cylinder 
 in place, this cylinder was removed and replaced by an aluminium 
 one exposed to Rontgen rays, the strength of these rays being 
 adjusted so that the amounts of ionisation in the two cases 
 were approximately equal ; measurements of p were then made 
 with the Rontgen rays on and were found to be identical with 
 those obtained when the ionisation was produced by uranium 
 radiation, thus proving that the ionic velocities are the same in 
 the two cases. 
 
 28. A method which is the same in principle as this was 
 first used by M c Clelland to measure the velocities of the ions 
 produced by flames*, and by arcs and incandescent wiresf: tht 
 results of these experiments showed that the velocity of the ions 
 diminishes very greatly when they get into the cooler parts of the 
 flame, suggesting that there is a rapid condensation round the 
 ions of some of the products of combustion of the flame. The 
 
 * McClelland, Phil. Mag. v. 46, p. 29, 1898. 
 
 t M c Clelland, Proc. Camb. Phil. Soc. x. p. 241, 1899. 
 
 T. G. * 
 
50 
 
 PROPERTIES OF A GAS 
 
 [29 
 
 diminution of velocity is clearly shown in the following table given 
 by M c Clelland. 
 
 Distance of point where 
 velocity was measured 
 from the flame 
 
 Temperature at this point 
 
 Velocity of ion under 
 a force of one volt 
 per centimetre 
 
 5'5 cm. 
 10 cm. 
 14'5 cm. 
 
 230 C. 
 160 C. 
 105 C. 
 
 23 cm. /sec. 
 21 cm. /sec. 
 04 cm./sec. 
 
 These velocities are all of them small compared with the velo- 
 cities of the ions produced by Rontgen rays or by radio-active 
 substances. In the case of the ions from flames as in other cases 
 the negative ions move faster than the positive. M c Clelland 
 applied the same method to the determination of the velocities 
 of the ions produced by arcs or incandescent wires ; he found in 
 these cases the same variability in the velocity as he had pre- 
 viously observed in the ions from flames ; in the case of the arcs 
 and wires, however, he found that the hotter the flame or wire the 
 smaller the velocity of the ion. We shall return to the considera- 
 tion of these phenomena when we discuss the electrical properties 
 of flames and arcs. 
 
 Determination of the ionic velocities by means of an alternating 
 
 electric field. 
 
 29. This method, which however can only be applied when 
 we have the ionisation confined to a thin layer of gas, and when 
 moreover all the ions are of one sign, is a very convenient and 
 accurate one. It was used by Rutherford* to determine the 
 velocity of the negative ions which are produced close to a 
 metallic plate when that plate is illuminated by ultra-violet light. 
 The principle of the method is as follows. AB (Fig. 17) is a, 
 horizontal plate made of well polished zinc, it is carefully insulated, 
 and can be moved vertically up and down by means of a screw ; 
 it is connected with one pair of quadrants of an electrometer,, 
 whose other quadrants are connected with the earth. CD is a 
 base plate with a hole EF cut in it ; this hole is covered in with 
 
 * Rutherford, Proc. Camb. Phil. Soc. ix. p. 401, 1898. 
 
29] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 fine wire gauze, ultra-violet light is sent through this gauze and 
 falls on the plate AB. CD is connected with an alternating 
 
 current dynamo or any other means of producing an alternating 
 difference of potential proportional to a simple harmonic func- 
 tion of the time ; the other pole of this instrument is put to 
 earth. Suppose now that at any instant the potential of CD is 
 higher than that of AB, the negative ions at AB will be attracted 
 towards CD, and will continue to move towards it as long as the 
 potential of CD is higher than that of AB. If however the 
 potential difference between CD and AB changes sign before the 
 negative ions reach CD these ions will be driven back to AB, sc 
 that this plate will not lose any negative charge. AB will thus 
 not begin to lose negative electricity until the distance between 
 the plates AB and CD is less than the distance passed over by 
 the negative ion during the time the potential of CD is greater 
 than that of AB. The method consists in altering the distance 
 between the plates until AB just begins to lose a negative charge, 
 then if we know this distance and the frequency and maximum 
 
 42 
 
52 
 
 PROPERTIES OF A GAS 
 
 [29 
 
 value of the potential difference we can deduce the ionic velocity 
 of the negative ion. For let the potential difference between 
 CD and AB at the time t be equal to a sinpt, then if d is equal 
 to the distance between these plates, the electric force is equal to 
 (a/d) sin pt, and if u is the velocity of the ion under unit electric 
 force, the velocity of the negative ion in this field will be 
 
 u (ajd) sin pt ; 
 
 hence if x is the distance of the ion from the plate AB at the 
 time t we have 
 
 dx 
 
 or 
 
 ua 
 
 ua 
 
 if x = when t = 0. 
 
 Thus the greatest distance the ion can get from the plate AB 
 is equal to 2ua/pd. If the distance between the plates is gradually 
 reduced, the plate AB will begin to lose a negative charge when 
 
 2ua vd 2 
 
 d = , , or u ~- . 
 pd 2a 
 
 Hence if we measure p, a and d we can determine u. 
 
 In this way Rutherford found for the velocities under a 
 potential gradient of 1 volt per cm. of the negative ion produced 
 by the incidence of ultra-violet light on a zinc plate, the following 
 values, for dry gases. 
 
 Gas 
 
 Ionic velocity 
 
 Air 
 
 1 "4 cm /sec 
 
 Hydrogen 
 Carbonic acid... 
 
 3*9 cm./sec. 
 
 78 cm./sec. 
 
 These values differ but little from those obtained for Rontgen 
 rays. 
 
 Rutherford found that the velocity of the ions was independent 
 of the metal of which the plate AB was made : and he proved by 
 this method that the velocity of the ions under a constant 
 
30] WHEN IN THE CONDUCTING STATE. 53 
 
 potential gradient varies inversely as the pressure, at any rate 
 down to pressures of 34 mm. of mercury which was the lowest 
 pressure at which he worked. 
 
 Chattock' 8 method of measuring the velocities of ions produced by 
 tlie disdiarye of electricity from a sharp point. 
 
 30. The preceding methods would be very inconvenient in 
 the case when the electric field is as strong and the velocities of 
 the ions therefore as great as they are when electricity is dis- 
 charging from a pointed conductor. For this case, in which the 
 ions at some little distance from the point are all of one sign, 
 Chattock* has devised a very ingenious method by means of which 
 he has been able to measure the velocities of these ions. The 
 principle of the method is as follows. Let P represent a vertical 
 needle discharging electricity from its point into the surrounding 
 air ; consider the force acting on the ions included between two 
 horizontal planes A and B, Fig. 18. If Z is the vertical corn- 
 
 Fig. 18. 
 
 ponent of the electric intensity, p the density of the electrification; 
 the resultant force F on the ions included between A and B is 
 vertical and equal to 
 
 InZpdxdydz. 
 
 If the velocity of the ion under unit electric force is u, then 
 w the vertical velocity of the ion is equal to uZ. If all the ions 
 
 * Chattock, Phil. Mag. v. 48, p. 401, 1899; Chattock, Walker and Dixon, Phil. 
 Mag. vi. 1, p. 79, 1901. 
 
54 PROPERTIES OF A GAS [30 
 
 are of one sign so that u is the same for all the ions, we have, 
 since Z w/u, 
 
 F = - \\\wpdxdydz. 
 
 Since the ions are all of one sign I \pwdxdy is the quantity of 
 
 electricity streaming across a horizontal plane in unit time ; this is 
 the same for all horizontal planes, and is equal to i where i is the 
 current of electricity flowing from the needle point, hence we have 
 
 where Z B Z A is the vertical distance between the planes A and B. 
 This force F must be balanced by the difference of the gaseous 
 pressures over A and B, hence if p B and p A denote respectively 
 the total pressures over the planes A and B we have 
 
 and hence u = B ~ A .. . . (1). 
 
 PB-PA 
 
 Thus, by the measurement of these pressures and of the 
 current flowing from the point (the latter measurement is easily 
 made by inserting a galvanometer in series with the needle point), 
 we can deduce the value of u. 
 
 The apparatus used by Chattock to carry out this method is 
 represented in Fig. 19. The discharging needle is supported in a 
 
 (Zero of 2) 
 
 Fig. 19. 
 
 narrow sliding glass tube drawn out at the end B ; it discharges to 
 a ring A made of smooth metal ; the needle and ring are enclosed 
 in a wide glass tube E, the ends of which are connected by tubes 
 T! and T 2 with the ends of a U tube pressure gauge containing 
 
30] WHEN IN THE CONDUCTING STATE. 55 
 
 water ; the ring A can be moved along the tube by means of a 
 screw. In this apparatus, since there is no current to the left of 
 the ring or to the right of the point, if we put Z B - Z A equal to the 
 distance of the point from the ring, and if o> is the difference 
 of pressure in dynes per sq. cm. measured by the pressure gauge, 
 A the area of cross-section of the tube, then 
 
 where p' is the part of the pressure which is borne by the ring. 
 We have, by equation (1), 
 
 It was assumed that when the point was a considerable .distance 
 from the ring p' became independent of z ; on this supposition we 
 have, if Aw, kz are corresponding changes in w and z t 
 
 and it was from this relation that u was calculated. Chattock 
 found for the velocities of the negative and positive ions in air 
 under a potential gradient of a volt per cm. the values 1'8 cm./see. 
 and T38 cm./sec., which agree well with those found for the ions 
 produced by Rontgen rays, and we conclude that the ions in the 
 two cases are the same. In the second paper Chattock extends 
 the method to hydrogen, oxygen, and carbonic acid as well as air, 
 and again finds close agreement between the velocities of the ions 
 produced by the point discharge and those produced by radio- 
 active substances. He points out that while the determination of 
 the ionic velocities of the positive ions showed in all gases great 
 consistency, considerable variations which could not be attributed 
 to errors of experiment were found in the values of the velocities 
 of the negative ions. This was especially the case in hydrogen, 
 where the values of the ionic velocity of the negative ion varied 
 from 6*8 to 8*5 ; in the other gases the variation is not so marked. 
 Chattock ascribes this variation to the gases occluded by the 
 discharging point ; when this point is negative some of these 
 occluded gases are given off and help to carry the discharge, and 
 as the velocity of the hydrogen ions is very large compared with 
 that of other ions, it is urged that a small admixture of other and 
 more slowly moving ions might produce a considerable lowering 
 
56 
 
 PKOPERTIES OF A GAS 
 
 [31 
 
 of the average velocity. When the point is positive the occluded 
 gas is supposed either not to be given off, or, if given off, not 
 to take any part in carrying the discharge. This explanation is 
 consistent with other phenomena connected with the discharge of 
 electricity from metals ; we shall see that in the electric discharge 
 through gas at low pressures occluded gas is given off from the 
 cathode, and that the amount of gas so given off has very con- 
 siderable influence upon the phenomena. The values obtained by 
 Chattock for the velocities of the ions produced by the point 
 discharge are given in the following table, in which V + denotes 
 the velocity of the positive ion, F_ that of the negative, and V the 
 mean of these velocities. The gases were dry. 
 
 Gas 
 
 V+ 
 
 V_ 
 
 V 
 
 F_/F + 
 
 Hydrogen 
 
 5 '4 
 
 7-43 
 
 6-41 
 
 1-38 
 
 Carbonic acid ... 
 Air 
 
 0-83 
 1-32 
 
 0-925 
 1-80 
 
 0-88 
 1-55 
 
 I'll 
 
 1-36 
 
 Oxygen ., 
 
 1-30 
 
 1-85 
 
 1-57 
 
 1-42 
 
 
 
 
 
 
 Charges on the ions. 
 
 31. We saw on page 32 that the coefficient of diffusion D of 
 an ion through a gas was connected with the velocity u of the 
 same ion through the same gas under unit electric force by the 
 equation 
 
 u Ne 
 
 where N is the number of molecules in a c.c. of gas at a 
 pressure of II dynes per square cm. It is to be remembered 
 that this relation is obtained on the supposition that a number 
 of ions in a given volume produce the same pressure as the same 
 number of molecules of a perfect gas at the same temperature ; in 
 other words, that the ions behave like a perfect gas with respect to 
 pressure. As we have seen that the ions in a gas at atmospheric 
 pressure are probably aggregations of considerable complexity as 
 compared with the molecules of a perfect gas, we must regard this 
 assumption as only an approximation to the truth, and one which 
 would cease to be even that when the ions are as large as those which 
 occur in the colder parts of flames or near an incandescent wire. 
 
31] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 57 
 
 Taking the values of D given by Townsend and (1) the values 
 of u given by Eutherford, (2) those given by Zeleny, we get the 
 following values for Ne x lO" 10 , e being expressed in electrostatic 
 units. 
 
 From Rutherford's experiments on the mean velocities of the 
 ions in gases, and the mean of the coefficients of diffusion given by 
 Townsend we get 
 
 I. 
 
 Gas 
 
 Ne x 10- 10 
 
 Air 
 
 1-35 
 
 Oxygen 
 
 1-25 
 
 Carbonic acid... 
 Hydrogen 
 
 1-30 
 1-00 
 
 From Zeleny 's values for the velocities of the ions and Townsend's 
 for the coefficients of diffusion we get 
 
 II. 
 
 
 Moisl 
 
 ; Gas 
 
 Dry 
 
 Gas 
 
 Gas 
 
 Positive ions 
 
 Negative ions 
 
 Positive ions 
 
 Negative ions 
 
 Air 
 
 1-28 
 
 1-29 
 
 1-46 
 
 1-31 
 
 Oxygen 
 
 1-34 
 
 1-27 
 
 1-63 
 
 1-36 
 
 Carbonic acid 
 Hydrogen 
 
 1-01 
 1-24 
 
 87 
 1-18 
 
 99 
 1-63 
 
 93 
 1-25 
 
 
 
 
 
 
 Since one electromagnetic unit or 3 x 10 10 electrostatic units 
 of electricity when passing through acidulated water liberates 
 1*23 c.c. of hydrogen at the temperature of 15 C. and pressure of 
 760 mm. of mercury, and since in T23 c.c. of gas there are 2'46AT 
 atoms of hydrogen, we have, if E is the charge in electrostatic 
 units on the atom of hydrogen in the electrolysis of solutions, 
 2'4>6NE = 3 xlO 10 , 
 
 or 
 
 The mean of all the values of Ne in Tables I and II. is T24 x 10 10 . 
 
58 PROPERTIES OF A GAS [32 
 
 We conclude then (1) that the charges carried by the gaseous 
 ions are the same whether the ions are produced in air, oxygen, 
 hydrogen or carbonic acid, (2) that this charge is equal to the 
 charge carried by the hydrogen atom in the electrolysis of 
 solutions. 
 
 The proof of the equality of the charges on the ions in dif- 
 ferent gases was first obtained by the author by direct measure- 
 ments of the charges carried by the gaseous ions. Though the 
 variations in the value of Ne given in Tables I. and II. are greater 
 than we should have expected from the accuracy with which the 
 experiments were made, they are not sufficiently regular to enable 
 us to draw any conclusions ; thus for example in Table I. Ne for 
 carbonic acid is considerably greater than for hydrogen, while in 
 Table II. it is very much less. We must remember too that these 
 results have been obtained on the supposition that the complex 
 ions behave like a perfect gas ; if they behaved like complex 
 vapours the values obtained on this supposition would be some- 
 what too large. 
 
 Currents in the gas caused by the motion of ions through it. 
 
 32. Since the charged ions when in an electric field settle 
 down to a state of steady motion in which they have no accelera- 
 tion the force exerted by the field on the ions is transferred to the 
 gas. Thus when in any region there is an excess of the ions with 
 charges of one sign over those having the opposite sign there will 
 be a resultant force acting on the gas in this region which may 
 start currents in the gas. Thus to take the case of a current 
 passing through ionised gas between parallel metal plates, there 
 is, as we shall see in the next paragraph, an excess of positive ions 
 in the layer of gas near the negative plate and of negative ions in 
 the layer next the positive plate ; thus these layers will be acted 
 on by forces tending to make them move towards their respective 
 plates. If these plates were infinite these forces would be balanced 
 by an excess of pressure next the plate, but if the plates are finite 
 this excess of pressure will relieve itself by the gas moving round 
 to the back of the plate and a system of air currents will be 
 set up. 
 
32] 
 
 WHEN IN THE CONDUCTING STATE. 
 
 59 
 
 These currents have been observed by Zeleny* by means of 
 the apparatus represented in Fig. 20. A and B are the two 
 parallel metal plates, connected to the opposite poles of a battery 
 of storage cells. The plates are enclosed in a box of which the 
 
 Fig. 20. 
 
 sides P and P r are made of blocks of paraffin, while the other 
 two sides are glass to enable the observer to see what is going on 
 inside. The bottom of the box is made of wood, Rontgen rays 
 pass through this and ionise the gas between the plates. The 
 vessel R contains liquid ammonia, from which ammonia gas passes 
 through the tube S into the box. The tubes T and T' contain drops 
 of hydrochloric acid. The particles of ammonium chloride formed 
 at the lower ends of the tube, where the acid is in contact with 
 the ammonia, fall slowly, producing well-defined vertical whitish 
 streams a and b near the plates A and B. These streams are 
 vertical so long as the Rontgen rays and the electric field are not 
 on together. If, however, when the electric field is on, the gas is 
 exposed to the rays, the streams are deflected towards the plates 
 as indicated by the dotted lines in the figure. In order to show 
 that this was not due to any charge on the solid particles of 
 ammonium chloride the experiment was repeated with streams 
 of carbonic acid gas, the difference of refractive index between 
 this gas and air being sufficient to render the streams visible ; it 
 was found that these streams, like those of the ammonium chloride, 
 were deflected towards the plate. 
 
 * Zeleny, Proc. Camb. Phil. Soc. x. p. 14, 1898. 
 
60 
 
 PROPERTIES OF A GAS 
 
 [33 
 
 33. For convenience of reference we give a table containing 
 the results of the measurements of the ionic velocities made up 
 to 1902. The velocities are expressed in cms. per second and are 
 for a potential gradient of 1 volt per cm. F+, F_, denote respec- 
 tively the velocities of the positive and of the negative ions, V the 
 mean of these velocities. 
 
 VELOCITIES OF IONS. 
 Ions from Rontgen Rays. 
 
 Gas 
 
 v+ 
 
 V_ 
 
 V 
 
 Observer 
 
 r Air 
 
 
 
 1-6 
 
 Eutherford 
 
 \ Air dry 
 
 1-36 
 
 1-87 
 
 1-61 
 
 Zeleny 
 
 Air moist 
 
 1-37 
 
 1-51 
 
 1-44 
 
 Zeleny 
 
 ( Oxygen . 
 
 
 
 1-4 
 
 Rutherford 
 
 < Oxygen dry... 
 
 1-36 
 
 1-80 
 
 1-58 
 
 Zeleuy 
 
 ( Oxygen moist 
 
 1-29 
 
 1-52 
 
 1-405 
 
 Zeleny 
 
 ( Carbonic acid 
 
 
 
 1-07 
 
 Rutherford 
 
 < Carbonic acid dry 
 
 76 
 
 81 
 
 78 
 
 Zeleny 
 
 ( Carbonic acid moist . . . 
 ( Hyc^roo'en 
 
 82 
 
 75 
 
 78 
 5 
 
 Zeleny 
 Rutherford 
 
 < Hydrogen dry . 
 
 6'70 
 
 7-95 
 
 7-2 
 
 Zeleny 
 
 ( Hydrogen moist 
 Nitrogen 
 
 5-30 
 
 5-60 
 
 5-45 
 1-6 
 
 Zeleny 
 Rutherford 
 
 Sulphur dioxide 
 
 
 
 5 
 
 Rutherford 
 
 Hydrochloric acid 
 Chlorine ... 
 
 ... 
 
 ... 
 
 1-27 
 1-0 
 
 Rutherford 
 Rutherford 
 
 
 
 
 
 
 Ions from Ultra- Violet Light. 
 
 Ions from Flames. 
 Velocities varying from -04 to '23 
 
 Ions from point discharge. 
 
 Air 
 
 
 1-4 
 
 
 Rutherford 
 
 Hydrogen 
 
 
 3-9 
 
 
 Rutherford 
 
 Carbonic acid 
 
 
 78 
 
 
 Rutherford 
 
 
 
 
 
 
 M c Clelland 
 
 Hydrogen 
 
 5-4 
 
 7-43 
 
 6'41 
 
 Chattock 
 
 Carbonic acid 
 
 0-83 
 
 0-925 
 
 0-88 
 
 Chattock 
 
 Air 
 
 1-32 
 
 1-80 
 
 1-55 
 
 Chattock 
 
 Oxygen 
 
 1-30 
 
 1-85 
 
 1-57 
 
 Chattock 
 
 
 
 
 
 
34] WHEN IN THE CONDUCTING STATE. 61 
 
 Potential gradient between two parallel plates immersed in 
 an ionised gas and maintained at different potentials. 
 
 34. It was shown first by Zeleny*, and then independently by 
 Child f, that when electricity is passing between two plates im- 
 mersed in ionised gas, the potential gradient between the plates 
 is not uniform, but is greatest in the neighbourhood of the 
 electrodes. The difference of potential between one of the plates 
 and any point in the gas may be measured by having a water or 
 mercury dropper at the point ; the most convenient way, however, 
 is to place at the point a fine wire, which will ultimately assume 
 the potential of the point. When the wire is used it is necessary 
 however to take several precautions : in the first place, if the 
 number of ions in the gas is small, the wire will only take up the 
 potential very slowly, and it is important that the instrument 
 used for measuring the capacity of the wire should have very 
 small capacity. This circumstance often makes it desirable to 
 measure the potential of the wire by means of a small gold leaf 
 electroscope instead of a quadrant electrometer, which though 
 more sensitive to differences of potential has yet a very much 
 greater capacity. Another point to be remembered is that if a 
 wire is placed in a region where the ions are all of one sign, its 
 potential can only change one way. Thus if it is a region where 
 there are only positive ions, its potential can increase but cannot 
 decrease, and thus if the potential of the wire gets by some 
 accident too high, it cannot sink to its true value. 
 
 A characteristic curve for the distribution of potential between 
 the plates, due to Zeleny, is given in Fig. 21. It will be seen 
 that the gradient near the centre of the field is uniform, but that 
 near the plates the gradients get much steeper and that they are 
 steeper at the negative than at the positive plate. 
 
 d' 2 V 
 
 From the equation , = - 4-7T/5, where V is the potential at a 
 ax" 
 
 distance x from the plate and p the density of the electrification, 
 
 * Zeleny, Phil. Mag. v. 46, p. 120, 1898. 
 t Child, Wied. Ann. Ixv. p. 152, 1898. 
 
62 
 
 PROPERTIES OF A GAS 
 
 [34 
 
 we caD, if we know the distribution of potential, calculate the 
 density of the electrification at any point between the plates. 
 
 Drs 
 
 IPO ^ 
 
 tances 
 
 \. 
 
 \ 
 
 Fig. 21. 
 
 The density corresponding to the potential curve in Fig. 21 is 
 shown in Fig. 22. 
 
 /v, 
 
 gat/ 
 
 Plat 
 
 Po. 
 
 Pizte 
 
 jti ve 
 
 Fig. 22. 
 
 We see that next the positive plate there is an excess of 
 
34] WHEN IN THE CONDUCTING STATE. 63 
 
 * 
 
 negative electricity and an excess of positive near the negative 
 plate. With the small potential differences used in this experiment 
 the regions where there is an excess of one kind of electricity over 
 the other are in the immediate neighbourhood of the plates, the 
 density of the free electricity being exceeding small in the central 
 portion of the field. If a larger potential difference had been 
 applied to the plates, the regions of free electricity would have 
 expanded, and with very large potential differences these regions 
 would fill the whole of the space between the plates. In the 
 example given, the greatest density of the electrification is about 
 2 x 10~ 4 electrostatic units ; as the charge on an ion is about 
 3'5 x 10~ 10 such units the number of positive ions in a cubic centi- 
 metre would exceed that of negative by about 6 x 10 5 . Taking 
 the number of molecules in a cubic centimetre of the gas as 
 3'5 x 10 19 , the ratio of the excess of ions of one sign to the number 
 of molecules is only 1'6 x 10~ 14 . As most of the negative ions 
 would be driven away from the negative plate, this will approxi- 
 mately represent the ratio of the number of free ions to the 
 number of molecules, and from it we learn what a very small 
 amount of ionisation is sufficient to account for many of the 
 phenomena of the conduction of electricity through gases. 
 
CHAPTER III. 
 
 MATHEMATICAL THEORY OF THE CONDUCTION OF 
 ELECTRICITY THROUGH A GAS CONTAINING IONS. 
 
 35. WE shall now proceed to develop the theory of electric 
 conduction through an ionised gas on the basis that the velocities 
 of the ions are proportional to the electric force acting upon them. 
 We shall take the case of two infinite parallel metal plates main- 
 tained at different potentials and immersed in an ionised gas; the 
 lines of electric force are everywhere at right angles to the plates ; 
 they are thus always parallel to a line which we shall take as the 
 axis of x. 
 
 Let n lt ?i 2 be respectively the number of positive and negative 
 ions per unit volume at a place fixed by the coordinate x, let q 
 be the number of positive or negative ions produced in unit time 
 per unit volume at this point by the ionising agent; let X be 
 the electric intensity at this point, R 1} R 2 the velocities of the 
 positive and negative ions under unit electric intensity, so that 
 the velocities of these ions at this point are respectively R^X, 
 R 2 X ; let e be the charge on an ion. The volume density of the 
 electrification, supposed due entirely to the presence of the ions, 
 is (rij n 2 ) e ; hence we have 
 
 = 4?r O, - n 2 ) e (1). 
 
 If i is the current through unit area of the gas, and if we 
 neglect any motion of the ions except that caused by the electric 
 field, we have 
 
 i (2). 
 
35] MATHEMATICAL THEORY OF THE CONDUCTION, ETC. 65 
 
 From equations (1) and (2) we get 
 1 
 
 dX 
 
 If we measure the distribution of electric force between the 
 plates, we can from these equations, if we know R l and R 2 , deter- 
 mine H! and n 2 , or if in addition to the distribution of electric 
 force, we measure, by the methods previously given, n 1} n z at 
 various points in the field, we can use these equations to deter- 
 mine R l and R^, the velocities of the ions. 
 
 When the gas is in a steady state, the number of negative and 
 of positive ions in each unit of volume must remain constant with 
 respect to the time, thus the loss of these ions must be balanced 
 by the gains. Now ions are lost in consequence of the recom- 
 bination of the positive and negative ions : these ions will come 
 into collision with each other, and a certain fraction of the whole 
 number of collisions will result in the positive and negative ions 
 combining to form a single system which is electrically neutral 
 and which no longer acts as an ion ; the number of collisions in 
 unit volume in unit time is proportional to n^n^. We shall sup- 
 pose that the number of positive or negative ions which recombine 
 in unit volume in unit time is an^n* : this is the rate at which unit 
 volume is losing positive and negative ions in consequence of 
 recombination ; in consequence of ionisation it is gaining them at 
 the rate q, and in consequence of the motion of the ions it is losing 
 
 positive ions at the rate ^-(n-^R^) and negative ones at the rate 
 dec 
 
 -=- (n 2 R 2 X): hence when the gas is in a steady state we have 
 dx 
 
 -T- (n^X) = q an^ .................. (5), 
 
 (6). 
 
 If R 1 and R z are constant at all parts of the field, we have 
 from (1), (5) and (6) 
 
 T. G. 
 
66 MATHEMATICAL THEORY OF THE CONDUCTION OF [35 
 
 From this equation, if we measure the distribution of X 2 
 between the plates, we can determine whether ionisation or re- 
 combination is in excess at any point, for from (7) q cm-^n^ and 
 d*X*/dx 2 have the same sign, hence when ionisation is in excess of 
 recombination, i.e. when q cm-^n^ is positive, d 2 X 2 /dx 2 is positive 
 and the curve whose ordinate is X z is convex to the axis of x ; when 
 recombination is in excess of ionisation the curve for X 2 is concave 
 to the axis of x. 
 
 Substituting in equation (7) the values of n lt n 2 given by 
 equations (3) and (4) we get 
 
 d*X* /_!_ _l_ 
 
 ' 6 
 
 fir* ~ V7? 7? / P f>*X*(~R 
 
 {*& X^l *2/ \ V J\. \J-^i 
 
 x I i+ ^ ,- I U 
 
 I have not been able to get a general solution of this differential 
 equation except when q is constant and R^ = R 2 ; in that case put- 
 
 ting X 2 = y and ~ =p we get, writing R for either R : or R 2 , 
 dp 
 
 Integrating this we get 
 
 where C is a constant of integration. From this equation we can 
 find the ratio of X Q , the electric intensity midway between the 
 plates, to X 1} the electric intensity close to a plate. For when 
 ^ = jR 2 the distribution of electric force is symmetrical and mid- 
 way between the plates dXjdx and p = ; let us further assume 
 that we are dealing with a case like that in Fig. 22, where there is 
 no free electricity for some distance from the middle of the plate, so 
 that here d 2 X/dx 2 also vanishes ; hence from (9) and (10) we have 
 
 X--.J5L. 
 
 ' 
 
 (11). 
 
35] ELECTRICITY THROUGH A GAS CONTAINING IONS. 67 
 
 Now at the positive plate % = and at the negative plate 
 n 2 = ; hence at either plate n^n^ = 0, but 
 
 hence if X t is the value of X at either plate, we have 
 
 = CXf^ ....... . ............. (12). 
 
 SvreR 
 
 Hence by (11) and (12) 
 
 a 
 or writing /3 for SirRe/a. we get 
 
 We see from this equation that X /X 1 is never greater than 
 
 <3 
 
 unity since /S 1 ^ diminishes from unity to zero as ft increases 
 from ft = to jB = infinity. Since ft does not involve either q or i, 
 the ratio of the electric intensities does not depend upon either 
 the intensity of the ionisation or of the current between the plates. 
 For air at atmospheric pressure R = 480 (since unit electrostatic 
 force is 300 volts per centimetre), a is about 1*2 x 10~ 6 , (see page 
 19), and e = 3'5 x 10~ 10 ; substituting these values we find ft = 3'9 
 for air at atmospheric pressure. Since R is inversely proportional 
 to the pressure, /3 is inversely proportional to the pressure, and 
 thus is very large at the pressure of a few millimetres of mercury. 
 Putting /3 = 4 we find 
 
 "V 
 
 -^ = 4* = 2'51 approximately. 
 
 ^-0 
 
 At low pressures j3 is large, in this case Xi/Xo^/3* approx 1 '- 
 mately, and thus the ratio of X 1 to X Q varies inversely as the 
 square root of the pressure. 
 
 The experiments we have described on the distribution of 
 electric force between the plates show that when the current is 
 small, the regions where X differs appreciably from X are con- 
 fined to two layers near the plates, the distribution of X between 
 the plates being represented by a curve like that shown in Fig. 23. 
 
 52 
 
68 MATHEMATICAL THEORY OF THE CONDUCTION OF [36 
 
 We can very easily find an inferior limit to X the thickness of one 
 of these layers. For let P be a point on the boundary of the 
 
 Fig. 23. 
 
 layer next the electrode, then since X becomes constant at P, 
 there are as many positive as negative ions in this region and if 
 the velocities of the ions are the same, half the current must be 
 carried by the positive and half by the negative ions. Thus if i 
 is the current through unit area, and e the charge on an ion, i/2e 
 positive ions must cross unit area of a plane through P in unit 
 time ; and all these positive ions must be produced in the region 
 between P and the positive plate. But if X is the thickness of the 
 layer, the number of positive ions produced in unit time corre- 
 sponding to each unit area of the plate is q\, the number that 
 cross unit area at P cannot therefore be greater than q\, and 
 can only be as great when there is no recombination of the ions 
 between P and the positive plate, hence 
 
 or X > i/2eq ; thus i/2eq is an inferior limit to X. If / is the 
 maximum current, I the distance between the plates, I qle\ 
 hence i/2I is an inferior limit to \/l. 
 
 36. Though we cannot find a general solution of the equations 
 (1), (2), (5), (6) when J^ is not equal to R 2 , we see at once that 
 a particular solution of these equations is given by the relations 
 
 R 
 
 X-l- 
 
36] ELECTRICITY THROUGH A GAS CONTAINING IONS. 69 
 
 This solution corresponds to a constant value of the electric 
 force between the plates, and indicates that the proportion of the 
 current carried by the positive and negative ions respectively is 
 the same as the ratio of the velocities of these ions. This solution 
 though it may apply to the central portion of the field, cannot 
 however hold right up to the plates. For suppose P is a point 
 between the plates at which this solution applies. Then across 
 unit area at P, iRij(Ri + R*) e positive ions pass in unit time, and 
 these must come from the region between P and the positive 
 plate ; if the distance of P from this plate is X this region cannot 
 furnish more than qX positive ions in unit time, and can only do 
 this when there is no recombination ; hence the preceding solution 
 cannot hold at a distance from the positive plate less than 
 
 Similarly it cannot hold at a distance from the negative plate less 
 than 
 
 We shall assume that the preceding solution does hold at distances 
 from the plates greater than the preceding values: and further 
 that in the layers in which the solution does not hold there is no 
 recombination of the ions. 
 
 Let us consider the state of things at the positive plate between 
 x and x \ , where 
 
 Then, since in this region there is no recombination, equations (1), 
 
 (5), (6) become 
 
 dX 
 
 -=- = 4?r (??! - n 2 ), 
 
 ax 
 
 5 <*.*>-* 
 
 If q is constant we have 
 
70 MATHEMATICAL THEORY OF THE CONDUCTION OF [36 
 
 where the constant of integration has been chosen so as to make 
 7^ = when x=0: substituting these values for n l} n 2 in the 
 equation giving dXjdx we get 
 
 dX ( fl 1 
 
 v dX . ( (I l\ i } 
 
 X -T- = 4-Tre \qx (^ + ^ }- -^ [ , 
 dx I 1 \R l RJ eR 2 ] 
 
 or Z 2 = 87re L ^ 2 f^r + -^ ) - ^ [ +C (13), 
 
 where (7 is a constant which may be determined from the condition 
 that when x = Xj 
 
 from this we find 
 
 a. 
 
 RI 
 
 C is the value of X 2 when x= 0, i.e. at the positive plate; if we 
 call this value X lt and if X Q is the constant value of X between 
 the layers, we have 
 
 j. 4?n? Rl (Tt j p ^l i 
 
 +- - p-^ + ^jjf , 
 O. M 3 ) 
 
 thus JTj is always greater than X and the ratio XJXo does not 
 depend upon the amount of ionisation or the strength of the 
 current between the plates. 
 
 If X z is the value of X at the negative plate, we can prove in 
 a similar way that 
 
 Thus if 1^2, the velocity of the negative ion, is very large compared 
 with R ly the velocity of the positive ion, the value of X at the 
 negative plate is large compared with its value at the positive, 
 and the thickness of the layer in which X is variable, is greater at 
 the negative than it is at the positive plate. A curve representing 
 the distribution of electric intensity between the plates in this 
 case is represented in Fig. 24. 
 
 If we put 
 
 a 4>7re R l p 2 
 
 Pi = - p- (-#1 + -#2) : P 2 = - - -=- 
 
 CL jfl-2 OL l l 
 
V 
 
 36] ELECTRICITY THROUGH A GAS CONTAINING IONS. 71 
 
 we have 
 
 when & and /9 2 are large we have approximately 
 
 Fig. 24. 
 
 In the special case when the velocities of the positive and 
 negative ions are equal & = /3 2 and X^X^ (S-n-eR/a.)^, this agrees 
 when 13 is large with the result found by the independent investi- 
 gation of this case given on p. 67. 
 
 The fall of potential V l across the layer next the positive plate 
 whose thickness is Xj is equal to 
 
 l Xdx; 
 
 substituting the value of X given by equation (13) and integrat- 
 ing we find 
 
 + 
 
 log 
 
 Since 
 
 -r , and \! = 
 
 Thus the fall of potential across this layer is proportional to 
 the square of the current. 
 
72 MATHEMATICAL THEORY OF THE CONDUCTION OF [37 
 
 If F 2 is the change in potential in crossing the layer next the 
 negative electrode we find similarly 
 
 If /:?! and /3 2 are very large we have approximately 
 
 Substituting the values of ft lt /9 2 we find 
 
 or the falls of potential at the positive and negative plates are 
 proportional to the squares of the velocities of the positive and 
 negative ions. 
 
 Let us consider how the fall of potential varies with the 
 pressure of the gas : if p is the pressure, R l and R 2 are inversely 
 proportional to p, and q is directly proportional to p, hence we see 
 that for a given current V l and F 2 vary inversely as p. 
 
 37. The relation between the potential difference between the 
 plates and the current. 
 
 The fall of potential between the plates is made up of the fall 
 of potential at the layers which we have already calculated and 
 the fall of potential in the space between the layers where the 
 electric intensity is uniform and equal to X ; the breadth of this 
 space is I (Xj + X 2 ) where I is the distance between the plates, 
 and since Xj + X 2 is equal to i/qe the fall of potential in this space 
 is equal to 
 
 
 
 
 adding to this the values for the fall of potentials across the layers 
 we get, if V is the potential difference between the plates, 
 
38] ELECTRICITY THROUGH A GAS CONTAINING IONS. 73 
 
 
 This equation is of the form 
 
 V=Ai* + Bi, 
 
 thus the curve whose ordinate is i and abscissa V is a parabola. 
 This equation ceases to be an approximation to the truth when 
 the two layers touch, i.e. when \ + \ 2 = l or i = qel\ in this case 
 the current is the greatest that can be carried by the ionised gas. 
 The minimum value of the potential difference required to pro- 
 duce this current is got by putting i = qel in equation (15); we see 
 that the potential difference required to produce saturation is 
 proportional to the square of the distance between the plates and 
 to the square root of the intensity of ionisation. 
 
 38. The study of the distribution of electric intensity between 
 the plates when the maximum current is passing leads to an easy 
 way of finding the ratio of the velocities of the positive and nega- 
 tive ions, for as in this case there is no recombination, equations 
 (5) and (6), p. 65, give 
 
 R l n l X = qx .............................. (16), 
 
 R z n,X = q(l-x) ..................... (17), 
 
 where x is measured from the positive plate. At the point 
 between the plates where the force is a minimum 
 
 .. _ . f -. 
 
 - = = 4?r (ft! - n z ) e, 
 
 hence at this point 7^ = <rc 2 , so that if x is the distance of the po : nt 
 P where X is a minimum from the positive plate we have by 
 equations (16) and (17) 
 
 Ms I -a' 
 
 thus the ratio of the velocities of the positive and negative ions is 
 equal to the ratio of the distances of P from the positive and 
 negative plates, so that if we have determined P by measuring 
 
74 MATHEMATICAL THEORY OF THE CONDUCTION OF [39 
 
 the distribution of potential between the plates we can at once 
 deduce the ratio of the velocities. 
 
 39. Case when the ionisation is confined to a thin layer. 
 
 In the preceding investigation we have supposed that the 
 ionisation is uniformly distributed between the plates, there are 
 however many very important cases when the region in which the 
 ionisation takes place is a thin layer of gas, the rest of the space 
 between the plates being free from the action of the ionising 
 agent. We proceed now to the consideration of this case, begin- 
 ning with the one where the ionised layer is close to one of 
 the plates A. Let us suppose that A is the positive plate, then 
 all the ions in the space between the plates must have been 
 dragged by the action of the electric field from the layer, hence 
 these ions must be all positive, so that the current is carried 
 entirely by positive ions. Let there be n x of these ions per 
 cubic centimetre and let X be the electric force, i the current, 
 then using the same notation as before our equations are now 
 
 dX 
 
 ^ 
 
 dx 
 
 from these equations we get 
 
 XdX 
 
 dx 
 
 Z = + C... ...(18), 
 
 ^i 
 
 where C is the constant of integration; it is evidently the value of 
 X z close to the positive plate. 
 
 If V is the potential difference between the plates, and I their 
 distance apart, we have 
 
 To find an expression for C we must turn our attention to the 
 layer of ionised gas ; let us suppose that the current is small com- 
 pared with that required to saturate this layer, then the number 
 of free positive or negative ions in unit volume of the layer 
 = (qloty, if q as before measures the intensity of ionisation ; if 
 
39] ELECTRICITY THROUGH A GAS CONTAINING IONS. 75 
 
 there is no great change in the electric force as we pass from the 
 gas into the layer the sum of the velocities of the positive and 
 negative ions will be of the order (R l + R 2 ) C* and as i the current 
 equals the number of ions multiplied by the sum of the velocities 
 of the ions, e (Rj. + jR 2 ) C* (q/a)* will be of the same order as i ; 
 hence C is comparable with 
 
 Hence C will be small compared with 8iril/R l if 
 
 is a small quantity. 
 
 If 8 is the thickness of the ionised layer, / the saturation 
 current, 
 
 I = qe8; 
 
 thus the preceding quantity will be small if 
 
 1 i 8 R 9 1 . 
 
 - is small, 
 
 >2 
 
 where A (ft + 
 
 OL 
 
 If 8/1, i/I are small, then since /3 2 is greater and R 2 /(R l 4- R%) 
 less than unity, we see that the quantity under consideration will 
 be small. When this is the case we can, in equation (19), neglect 
 
 C in comparison with -^ , and the equation becomes 
 
 We see that in this case the current is proportional to the 
 square of the potential difference, and thus increases more rapidly 
 with the electromotive force than if it obeyed Ohm's law. We 
 shall see examples of this when we consider the passage of 
 electricity through metals immersed in hot gases. In this case by 
 far the greater part of the ionisation occurs in the layer next the 
 metal and, as Pringsheim* has shown, the current increases more 
 rapidly than the potential difference. The current is proportional 
 to R l the velocity of the ion which carries it; thus since the 
 
 * Pringsheim, Wied. Ann. 55, p. 507, 1895. 
 
76 MATHEMATICAL THEORY OF THE CONDUCTION OF [39 
 
 velocity of the negative ion is greater than that of the positive, 
 the current for the same difference of potential between the plates 
 is greater when the ionisation takes place next the negative plate 
 than when next the positive, in other words the current is greater 
 in one direction than in the opposite; this unipolar conductivity 
 as it is called is very marked indeed in conduction through hot 
 gases and flames containing salts. Rutherford* has observed it 
 when the ionisation was due to Rontgen or radium radiation. We 
 see from (20) that for a given potential difference the current 
 is independent of q, the intensity of ionisation ; the maximum 
 currents between the plates will of course depend upon the 
 intensity of the ionisation, but as long as the currents are only a 
 small fraction of the maximum corresponding to the smallest 
 ionisation, the currents will be independent of the amount of 
 ionisation next the plate ; we see too that the current does not 
 depend on the charge carried by the ion. 
 
 The current for a given difference of potential varies inversely 
 as the cube of the distance between the plates ; as the current 
 varies as the square of the potential difference, if we keep the 
 average electric intensity between the plates constant as the 
 distance diminishes the current will vary inversely as the distance 
 between the plates. 
 
 When the ionisation is confined to a layer next the plate A, we 
 can stop the flow of ions and therefore of electricity to the plate B 
 by interposing between the plates a third plate, and the passage 
 of electricity will be stopped just as effectually by a plate of 
 metal as by a non-conductor ; thus we get the somewhat para- 
 doxical effect of completely stopping a current between two 
 plates by interposing between them an excellent conductor of 
 electricity. An example of this effect will be considered when 
 we discuss the passage of electricity through very hot gases. 
 
 If the layer of ionised gas is situated between the plates at a 
 distance ^ from the positive and / 2 from the negative plate, then 
 if V is the potential difference between the plates, we can easily 
 prove by the same method as we have used when the layer was 
 next the plate that 
 
 * Eutherford, Phil. Mag. vi. 2, p. 210, 1901. 
 
39] ELECTRICITY THROUGH A GAS CONTAINING IONS. 77 
 
 where R^ and E 2 are respectively the velocities of the positive and 
 negative ions. We see that if ^ is not equal to E 2 the current 
 for the same potential difference will not, unless Z x = l. 2) be the 
 same in one direction as in the opposite. If the velocity of the 
 negative ion is greater than that of the positive, the current 
 will be greatest when its direction is such that the negative plate 
 is nearer to the ionised layer than the positive. From this we 
 conclude that want of symmetry in the distribution of ionisation 
 will give rise to unipolar conductivity. The distribution of electric 
 intensity when the ionised layer is between the plates is repre- 
 sented in Fig. 25. 
 
 The preceding results are only true when the electric intensity 
 close to the ionised layer is small compared with its value some 
 distance away, a result which we have shown will be the case 
 when the current is not approaching saturation, provided there is 
 not a great increase in the value of the electric intensity as we 
 pass from the inside of the layer to a point just outside. There are 
 cases, of which the best known is that of ultra-violet light falling 
 on a metal plate, where this condition is not fulfilled. If the 
 illuminated plate is made the negative one, a current of electricity 
 will pass from it to a neighbouring plate, but in this case the 
 electric field between the plates will be approximately unifo.m 
 and the preceding results do not apply. We may explain this as 
 follows: we shall see that a metal plate exposed to ultra-violet 
 light emits negative ions, and these ions like cathode rays ionise 
 the gas through which they pass. Consider an insulated piece of 
 metal in air, it cannot go on indefinitely losing negative electricity, 
 for observation proves that its potential does not go on increasing 
 indefinitely ; it must reach a stage in which it receives as much 
 
78 MATHEMATICAL THEORY OF THE CONDUCTION, ETC. [39 
 
 negative electricity from the air as it loses by the action of the light. 
 We can see how this can be brought about : suppose A is the surface 
 of the metal, next this we have a layer of ionised gas; the metal loses 
 negative electricity and gets a positive charge, while the negative 
 electricity accumulates and forms a layer at some little distance from 
 the plate. The layers of positive and negative electricity produce 
 
 A 
 
 Fig. 26. 
 
 an electric field which tends to drive the negative ions in the ion- 
 ised gas between them into the metal, the stronger this field the 
 more negative ions go to the metal ; the electrification in the layers 
 will accumulate until the strength of the field is such that as 
 many negative ions are driven by it from the gas into the metal 
 as the metal loses by the action of the light. In passing however 
 from the inside to the outside of the layer of ionised gas we have 
 to pass across a layer of electricity, this will produce a discon- 
 tinuity in the electric intensity equal to 4>7rcr, where cr is the 
 surface density of the electrification ; there may thus be a great 
 difference between the electric intensity inside the layer and that 
 just outside, so that the reasoning which we used to prove X in 
 equation (19) small compared with 87ril/R need not apply in 
 this case. 
 
CHAPTER IV. 
 
 EFFECT PKODUCED BY A MAGNETIC FIELD ON THE 
 MOTION OF THE IONS. 
 
 40. WHEN a charged ion is moving in a magnetic field it 
 experiences a mechanical force whose direction is at right angles 
 to the direction of motion of the ion, at right angles also to the 
 magnetic force and equal in magnitude to HeVsmB, where H is 
 the magnetic force, V the velocity of the ion, e its charge, and 6 
 the angle between H and V\ H and e are to be expressed in the 
 electromagnetic system of units. The relation between the direction 
 of this force F, V and H, for a positively charged ion, is shown in 
 Fig. 27. 
 
 Fig. 27. 
 
 Now suppose that we have an ion moving through a gas, the 
 viscosity of the gas causing the velocity of the ion to be propc - 
 tional to the force acting upon it. Then if X, Y, Z, are the 
 components of the electric intensity, a, /3, 7 those of the magnetic 
 force, u, v, w those of the velocity, the mechanical force exerted on 
 the ion by the magnetic field has for components 
 
 e (ftw rfo), e (yu aw), e (av /3u), 
 while the components of the mechanical force due to the electric 
 
80 EFFECT PRODUCED BY A MAGNETIC FIELD [40 
 
 field are Xe, Ye, Ze. Thus as the velocity of the ion is proportional 
 to the mechanical force acting upon it we have 
 
 u = R (X + fiw - ryv)\ 
 
 v = R(Y+ryu-aw)[ (1), 
 
 w = R (Z + OLV - fin)) 
 
 R is evidently the velocity of the ion under unit electric intensity 
 when there is no magnetic field. Solving equations (1) we find 
 
 RX + R* (yY-/3Z) + R*a(aX + /3F+ yZ) 
 
 u = 
 
 (a 2 + 2 + 7 2 ) 
 
 = \ 
 
 22 2 2 ' 
 
 R*({3X-aY) + R*y (aX + j3Y + yZ) 
 
 = 
 
 The first term in the numerator of these expressions represents 
 a velocity parallel and proportional to the electric force ; the 
 second term a velocity at right angles both to the electric and 
 magnetic forces and proportional to R 2 HFsm (f> ; where H, F, and 
 < represent respectively the magnetic and electric forces and the 
 angle between them ; the third term represents a velocity parallel 
 to the m'agnetic force and proportional to R s H 2 Fcos (/>. The 
 relative importance of these terms depends upon the value of RH, 
 if this quantity is small the first term is the most important and 
 the ion moves parallel to the electric force, if on the other hand 
 RH is large the last term is the most important and the ion 
 moves parallel to the magnetic force. Since R is the velocity of 
 the ion under unit electric force, and the unit force on the electro- 
 magnetic system is 10~ 8 of a volt per cm., the value of R for an ion 
 moving through air at atmospheric pressure would be 1*5 x 10~ 8 , 
 since the velocity of the ion under a volt per cm. is about 
 I'D cm./sec. Thus at atmospheric pressure it would not be feasible 
 to get a magnetic field strong enough to make RH large. As R 
 varies inversely as the pressure of a gas through a considerable 
 range of pressures it might at very low pressures be possible 
 to make RH large and thus make the ions travel along the lines 
 of magnetic force. 
 
 Let us take the case of an ion placed in a field in which both 
 the electric and magnetic forces are uniform ; let the electric force 
 
41] ON THE MOTION OF THE IONS. 81 
 
 be parallel to the axis of x and let the magnetic force be in the 
 plane of xz t then Y= 0, Z = 0, /3 = 0, and equations (2) become 
 
 U = 1 + R 2 (a 2 + 7 2 ) = RX a PP roximatel y> if- & ( 2 + 7 2 ) is small, 
 
 Thus the effect of the magnetic force is to give the ion a 
 velocity - Ryu, at right angles to both the electric and magnetic 
 forces and a velocity R*y (a 2 + 7 2 )* w in the plane of xz at right 
 angles to the magnetic force. 
 
 If both positive and negative ions are present and if R l is the 
 value of R for the positive and R 2 that for the negative ion, and if 
 u 1} v l} w^ u 2 , v 2 , w 2 are respectively the velocities of the positive 
 and negative ions, then if there are n positive and negative 
 ions per unit volume the current parallel to y will be equal to 
 ne fa v 2 ) or, substituting the values of ^ and v 2 , to 
 
 if I is the main current parallel to x ; thus if the velocities of the 
 positive and negative currents are unequal the magnetic field will 
 give rise to a side current proportional to the main one and the 
 direction of the current will be deflected through an angle whose 
 tangent is (R 2 RJ y. If we retain terms proportional to (Rff) 2 , 
 where H is the magnetic force, we see that there will be an 
 additional current proportional to (Rf + R 2 2 RA) y (a 2 + 7 2 )* / 
 in the plane of xz at right angles to the magnetic force. 
 
 When the electric field is not uniform but, like that due to 
 a charged particle, radiates from a point we can prove without 
 difficulty that an ion in a uniform magnetic field will describe 
 a spiral traced on a cone of revolution, the axis of the cone being 
 parallel to the magnetic force. 
 
 Motion of a free ion in a magnetic field. 
 
 41. If the ion instead of having to move through the molecules 
 
 of a gas is moving in a vacuum, the path it describes in a uniform 
 
 magnetic field is readily found. We shall first of all take the case 
 
 when no electric forces act upon the ion, then, since the only force 
 
 T. G. 6 
 
82 EFFECT PRODUCED BY A MAGNETIC FIELD [42 
 
 acting on the ion is that due to the magnetic field and this force 
 is always at right angles to the path of the ion, the velocity of the 
 ion will be constant ; again since the force is at right angles to 
 the magnetic force, there will be no acceleration parallel to this 
 force, thus when the magnetic field is uniform the component 
 of the velocity parallel to the magnetic force is constant. As 
 the resultant velocity is constant this implies that the direction 
 of motion of the ion makes a constant angle with the magnetic 
 force. If p is the radius of curvature of the path of the ion, m its 
 
 '777??^ 
 
 mass, v its velocity, the force along the normal is equal to , but 
 
 this force is equal to Hev sin 0, where H is the magnetic force and 
 the angle between v and H, e the charge on the ion, thus 
 
 TT - a 
 
 - = lievsin u, 
 P 
 
 mv 
 
 Thus as v and are constant the radius of curvature of the path 
 is constant, the path of the particle is therefore a helix wound on 
 a circular cylinder whose axis is parallel to the lines of magnetic 
 force, the radius of the cylinder is p sin 2 6 or mv sin OjeH*. If the 
 particle is projected at right angles to the lines of magnetic force, 
 the helix shrinks into a circle whose radius is mv/eH: as the path 
 in this case is a closed one the ion never travels more than a finite 
 distance from its point of projection. If the velocity of the ion has 
 a component parallel to the magnetic force, this component remains 
 constant and the ion goes on describing equal spaces parallel to 
 the magnetic force in equal times, while in a direction at right 
 angles to the magnetic force the velocity of the ion is sometimes 
 in one direction and sometimes in the opposite, so that the ion, 
 however long it moves, never travels more than a finite distance 
 from the line of force. We may thus express the general features 
 of the effect by saying that in the magnetic field the ions tend 
 to follow the lines of magnetic force. 
 
 42. The preceding investigation relates to the case when the 
 magnetic field is constant and the lines of magnetic force do not 
 change their direction; it is of interest to see whether the ions will 
 
 * G. G. Stokes, Proc. Roy. Soc. Mar. 30, 1876 ; Phil. Mag. v. 2, p. 359, 1876. 
 
42] . ON THE MOTION OF THE IONS. 83 
 
 continue to follow the lines of magnetic force when these change 
 their direction from point to point. We shall take the special case 
 when the lines of magnetic force are circles round the axis of z, the 
 field being that due to a current i flowing along this axis ; in this 
 case if a, (3, 7 are the components of magnetic force at a point 
 whose coordinates are #, y, z, 
 
 2iy 2ix 
 
 = > = -' 7= ' 
 
 and if m is the mass of the ion, e its electric charge, we have 
 d?x 2ix\ dz 
 
 d 2 y 
 
 From these equations we have 
 
 6HS)' + - 
 
 where Fis the velocity of projection of the ion; 
 
 Thus if p and are the polar coordinates in the plane xy, of 
 the ion, 
 
 where h is a constant ; 
 
 dz 2ei i , n 
 = - log p + C t 
 dt m 
 
 where C is a constant: thus the orbit of the ion in the plane of 
 xy is that of a particle of mass m acted on by a central attractive 
 
 force equal to (- - log p + 2ei G\ jp. 
 Since 
 
 we have . , 
 
 v^y p" 2 Vm e _ 2 
 
84 EFFECT PRODUCED BY A MAGNETIC FIELD [43 
 
 Since f -j. j is essentially positive, p will always lie between the 
 greatest and least roots of the equation 
 
 so that the ion will always remain at a finite distance from the 
 axis of z. 
 
 43. Let us consider some special cases. Let the ion be pro- 
 jected parallel to the lines of magnetic force from the point p = a : 
 then since dz/dt = when p = a,v?e have 
 
 dz _ Zei , p 
 dt~ m % a ' 
 
 and h = Fa, 
 
 fdp\ 2 T7 . 9 /., a 2 \ f2ei , p\ 2 
 hence - = F 2 ( 1 log " ; 
 
 \dtJ \ p 2 J \m 6 a/ ' 
 
 from this equation we see that p can never be less than a, and thus 
 the velocity parallel to the axis of z never changes sign : again p 
 never exceeds the value R } given by the equation 
 
 2ei R_, 
 JYI a 
 
 R = a satisfies this equation but there is another root greater 
 than a ; it is this root which is the maximum value of p. 
 
 Thus in the plane at right angles to the axis of z the ion 
 circulates in an orbit included between the circles p = a and p=R' y 
 and thus again the ion moves in the general direction of the lines 
 of magnetic force, although in this case there is a drift of the ions 
 parallel to the axis of symmetry of the magnetic field. If F is 
 small compared with 2ei/m t the solution of the equation (1) is 
 
 In this case the maximum velocity parallel to z is V.(V/eim) 
 and is thus small compared with F. Thus the smaller the 
 velocity of projection and the stronger the field the more nearly 
 does the path of the ion coincide with a line of magnetic force. 
 
45] ON THE MOTION OF THE IONS. 85 
 
 44. In the next case the ion is projected from p = a in 
 a direction parallel to z, in this case h = and the path of the 
 ion is in the plane through the axis of z and the point of pro- 
 jection; if V is the velocity of projection, then 
 
 dz 2ei , p Tr 
 = log + Y: 
 dt m 6 a 
 
 now dz/dt can never be greater numerically than V, hence if V 
 and 2ei/m are of the same sign p can never be greater than a. 
 
 The values between which p oscillates are a and ae eilm ; the 
 orbit is a closed one and its dimensions are very small if V is small 
 compared with ei/m. If Y and ei/m are of opposite signs then we 
 can show that p is never less than a and varies between a and 
 
 45. A third case we shall consider is when the particle is pro- 
 jected with velocity V parallel to p from p = a, in this case again 
 h = Q, but 
 
 dz 2ei , p 
 
 = log - . 
 dt m a 
 
 Since dz/dt can never be greater numerically than V we see 
 
 mV mV 
 
 that p must lie between the limits p = ae 2ei and p = ae 2et ; the 
 orbit is in the plane through the axis of z and the point of 
 projection. If the magnetic field is very strong and therefore 
 mV/Zei small, p is always very nearly equal to a, let it equal 
 a (1 -f f), our equations are then approximately 
 
 d*% _ _/2ef\ 2 jr 
 di? ~ ~ \m) a? ' 
 
 dz _ 2ei 
 dt m 
 the solution of which is 
 
 2t e 
 
 z = aA cos t. 
 a m 
 
 Since V= a ^ when *= 0, aA = V j.= ^ when H is the 
 magnetic force at the point of projection. Thus, as we might 
 
86 EFFECT PRODUCED BY A MAGNETIC FIELD [46 
 
 have expected, the path in this case is a circle whose radius aA is 
 equal to (F/J7)(m/e). 
 
 We see from the consideration of the variable field as well as 
 from that of the constant one that the ion will tend to follow the 
 lines of magnetic force, except in the very special case when the 
 circumstances of projection are such that the ion during its motion 
 always cuts the lines of magnetic force at right angles. 
 
 Motion of an ion under the joint action of electric and 
 magnetic forces. 
 
 46. We shall now investigate the motion of an ion when it 
 is acted on simultaneously by both electric and magnetic forces; 
 we shall take the case when both these forces are constant. Let 
 the axis of z be parallel to the direction of the magnetic force, 
 and the plane of xz parallel to the direction of the electric force. 
 Let H be the magnetic force, X, 0, Z the components of the 
 electric force, then if m is the mass of an ion, e its charge, and 
 x, y, z its coordinates the equations of motion are 
 
 From equation (3) we have 
 
 -JJl'-fiM ........................ (4), 
 
 where w is the velocity of projection parallel to z, the origin of 
 coordinates being supposed to be taken at the point of projection. 
 
 From equations (1) and (2) we have 
 j^ 
 
 y-c+ fT t + Acoscot + B sin cot ............ (5), 
 
 Jj. , 
 
 x a A sin cot + B cos cot ..................... (6), 
 
 where a, c, A and B are arbitrary constants and a) = He/m. 
 Writing equations (5) and (6) in the form 
 
 V 
 
 y c = ,j. cot + A' cos (cot a), 
 
 CO 1 
 
 x a = A' sin (cot a) ; 
 
46] ON THE MOTION OF THE IONS. 87 
 
 we see that the projection of the path of the ion on the plane 
 of xy is a trochoid, generated by a circle whose radius is X/coH 
 rolling on a line perpendicular to the electric force, the distance 
 of the tracing point from the centre of the rolling circle being A'. 
 Since the average value of the periodic terms tends to vanish 
 when the time over which the average extends is large compared 
 with l/o) we see, from equations (5) and (6), that the equations 
 
 x = a, 
 
 give the average positions of the ion, and that the average 
 velocity parallel to y is X/H while that parallel to x vanishes. 
 
 As the velocity parallel to z at the time t is t + w we see that 
 
 m 
 
 if Z is finite the velocity parallel to z will ultimately become 
 infinite compared with the components parallel to the other 
 axes, thus in this case the ions will ultimately move along the 
 lines of magnetic force ; we must remember however that this 
 reasoning only applies when the electric field has a finite com- 
 ponent in this direction. 
 
 If we determine the constants in (5) and (6) in terms of v , u , 
 the initial values of the components of the velocity of projection 
 of the ion parallel to the axes of y and x respectively, we have, 
 the origin being taken at the point of projection, 
 
 y = (1 -coscot) + Tft + [vo-^J-sin wt ......... (7), 
 
 co H \ rLJ co 
 
 CJ\. \ \. , ~ j\ . ^0 /O\ 
 
 rr fy 1 (1 COS ' + Sin 0> ............... (o). 
 n. ) co co 
 
 If JT=0, i.e. if the directions of the electric and magnetic 
 forces coincide, we have 
 
 thus the projection of the path of the ion on the plane of xy is 
 a circle and the path of the ion is a helix of gradually increasing 
 pitch with its axis parallel to the lines of magnetic force. 
 
88 EFFECT PRODUCED BY A MAGNETIC FIELD [47 
 
 If Z = 0, i.e. if the electric force is at right angles to the 
 magnetic, and if in addition u , V Q , W Q all vanish, we have 
 
 TT 
 
 y f (tot sin wt), 
 
 v 
 
 X rr (1 COS 0)t). 
 
 wii 
 
 This is the equation to a cycloid, the radius of the generating 
 circle being XjwH or Xm/eH 2 , the line on which it rolls is 
 perpendicular to the electric force. The greatest distance which 
 the particle can get from its point of projection measured in the 
 direction of the electric force is 2Xm/eH 2 , the average velocity 
 in this direction is zero while the average velocity parallel to y, 
 i.e. in the direction at right angles both to the electric and 
 magnetic forces, is finite and equal to X/H. If the ion were 
 projected with the velocity w parallel to the axis of z it would 
 retain this velocity unaltered and the average direction of motion 
 of the ion would be at right angles to the electric force and along 
 a line making an angle i^rr l XjwH with the direction of the 
 magnetic force. 
 
 47. If w = and v = X/H we have 
 
 y = v<>t, 
 
 Thus in this case the path of the ion in the plane of xy is the 
 same as if there were neither electric nor magnetic forces acting 
 upon it : the force Xe acting on the particle due to the electric 
 field is in this case just balanced by the force Hev due to the 
 magnetic field. 
 
 48. Returning to the general case represented by equations 
 (7) and (8) we easily deduce that the maximum velocity F parallel 
 to the plane of xy attained by the ion is given by the equation 
 
 F * + wf-.)T- 
 
 H ( \H )} 
 
 thus until u and V Q are comparable with X/H, the maximum 
 velocity attained is very approximately ZX/H and is independent 
 of the velocity of projection, and the charge and the mass of 
 the ion. 
 
49] ON THE MOTION OF THE IONS. 89 
 
 The maximum displacement f measured parallel to the direc- 
 tion of the electric force is given by the equation 
 
 ~ V 
 
 and thus until u and v become comparable with X/H the distance 
 travelled by the ion parallel to the lines of electric force will be 
 very approximately independent of the velocity of projection of 
 the ion. 
 
 It will be gathered from the preceding discussion that except 
 in the special case when the electric and magnetic forces are 
 at right angles to each other, the ions ultimately travel along 
 lines of magnetic force. 
 
 49. The case when the electric and magnetic forces are at 
 right angles to each other is however a very important one as it 
 includes the fields produced by electric waves. In these waves 
 the electric and magnetic forces are not constant but in the case 
 of a simple harmonic wave may be taken as proportional to cospt. 
 When the waves are all divergent the electric force is equal to 
 V times the magnetic force, where V is the velocity with which 
 the electric waves travel through the medium. Thus if the 
 direction of propagation of the wave is parallel to the axis of y 
 and if the magnetic force is parallel to the axis of z and equal to 
 #o cos 0, the electric force will be parallel to the axis of x and 
 
 equal to VB Q cos 6 where = p(t- ^j . The equations of motion 
 of a charged particle acted on by this electric wave are 
 
 d?y dx 
 
 From these equations we have, if dx/dt and 6 vanish simul 
 
 taneously, 
 
 dx e V . - 
 
 ra 
 
90 EFFECT OF MAGNETIC FIELD ON MOTION OF IONS. [49 
 
 The character of the motion of the ions will depend upon the value 
 of H e/pm ; if this quantity is large the average velocity of the 
 ions parallel to x will vanish while that parallel to y will be equal 
 to V: thus the wave will in this case carry the charged particles 
 along with it. When however H e/pm is a small quantity the 
 effect of the wave will be to superpose on the undisturbed motion 
 a small vibratory motion parallel to the electric force in the wave 
 and thus at right angles to its direction of propagation. 
 
CHAPTER V. 
 
 DETEKMINATION OF THE RATIO OF THE CHARGE TO 
 
 THE MASS OF AN ION. 
 
 50. THE value of e/m the charge on an ion divided by its 
 mass has been determined by the application of some of the 
 results discussed in the preceding chapter. The first case we 
 shall consider is that of the ions in the cathode rays. 
 
 In the chapter on cathode rays we shall give the evidence 
 which leads us to the conclusion that the cathode rays, i.e. the 
 streams which in a highly exhausted tube through which an electric 
 discharge is passing start from the cathode and produce a vivid 
 phosphorescence when' they strike against the glass of the tube, 
 consist of negatively electrified particles starting from the neigh- 
 bourhood of the cathode and moving with a very hign velocity 
 along straight lines. Assuming that this is the nature of the 
 cathode rays we shall show here how to determine the velocity 
 of the particles and the value of e/m. Suppose that we have a 
 highly exhausted tube of the pattern shown in Fig. 28. 
 
 Fig. 28. 
 
 In this tube C is the cathode, A the anode, B is a thick metal 
 disc connected with the earth, holes a millimetre or so in diameter 
 are bored through the middle of the disc and through the anode ; 
 some t qf the cathode^ rays starting from the neighbourhood of the 
 
92 DETERMINATION OF THE RATIO OF [50 
 
 cathode pass through these holes, thus in the part of the tube to ' 
 the right of the disc we have a pencil of negatively electrified 
 particles travelling along straight lines parallel to the line joining 
 the holes in the discs, the place where they strike the glass being 
 marked by a patch of bright phosphorescence p. Suppose now 
 that the tube is placed in a uniform magnetic field, the lines of 
 force being at right angles to the path of the ions, the paths of the 
 ions will now be circles, the radii of the circles being (see p. 82) 
 mv/eH, where m is the mass of the ion, e its charge, v its velocity, 
 and H the strength of the magnetic field. The place at which 
 these particles strike the tube will no longer be at p but at some 
 other point p' y the direction of pp being at right angles to the 
 magnetic force. Since op' is an arc of a circle of which op is a 
 tangent, we have 
 
 pp' (2R + pp') = op*, 
 where R is the radius of the circle ; hence 
 
 : ' **-$-* 
 
 or, since R = mv/eH, we have 
 
 - 9 mv _ op 2 , 
 
 If the magnetic field is not uniform we may proceed as follows. 
 Since p the radius of curvature at any point of the path of the 
 ion is given by the equation 
 
 p vm' 
 
 and since, when the path of the ion is fairly flat l/p is very 
 approximately equal to d z yjdx 2 where y and x are the coordinates 
 of the ion, x being measured along the undisturbed path, and y at 
 right angles to it. We have 
 
 ds? vm ' 
 so that 
 
 :; ...(i). 
 
 V 
 
 Hence if we measure pp and know the distribution of the 
 magnetic force H along the tube we can from this eolation 
 
50] THE CHARGE TO THE MASS OF AN ION. 93 
 
 determine the value of e/vm. This gives us a relation between v 
 and m/e. We can determine v in the following way : two parallel 
 metal plates D and E are placed in the tube, the plates being parallel 
 to the lines of magnetic force and parallel also to the undisturbed 
 path of the rays ; these plates are maintained at a known difference 
 of potential by connecting them to the terminals of a battery. Thus 
 we have an electric field between the plates the lines of force of 
 which are at right angles to the lines of magnetic force and to the 
 direction of motion of the ions ; this electrostatic force Y tends to 
 deflect the ions, the force acting on an ion being Ye the force due 
 to the magnetic field acts in the same straight line and is equal 
 to Hev. Adjust the sign of the difference of potential so that the 
 electric and magnetic forces tend to oppose each other, then keeping 
 one of the forces fixed, say the electric force, alter the value of the 
 other until the two forces just balance, this stage can be ascertained 
 by observing when the phosphorescent patch p' is restored to its 
 undisturbed position. When this stage is reached we have 
 
 Ye = Hev, 
 
 Y 
 or v = jj .............................. (2). 
 
 Thus by measuring Y/H we can determine the velocity of tne 
 ions composing the cathode rays. As we know e/vm from the 
 experiments on the magnetic deflection we can in this way deduce 
 the values of both e/m and v. Equation (2) depends upon the 
 assumption that both the magnetic and electric fields are uniform, 
 if this condition is not fulfilled we must proceed as follows. 
 Suppose that p" is the displaced position of p when the electric 
 field alone is acting on the rays, then we can prove without 
 difficulty that 
 
 hence if we know the distribution of the electric field and the 
 value of pp" we can by equation (3) find the value of e/v*m and 
 since by equation (2) we can determine e/vm we have the data 
 for determining both v and, e/m. 
 
 In order to apply this method it is necessary that the pressure 
 of the gas in the discharge tube in which the rays are produced 
 should be very low; the passage of cathode rays through a gas 
 
94 
 
 DETERMINATION OF THE RATIO OF 
 
 [50 
 
 makes it a conductor and thus as the rays are shielded from the 
 electrostatic field by the gas through which they move the electro- 
 static repulsion is hardly appreciable ; if, however, the pressure of 
 the gas is very low the conductivity of the gas is so small that 
 there is hardly any appreciable shielding effect and the deflection 
 produced by the electric field is easily observed. 
 
 Using this method the author in 1897* obtained the values for 
 v and e/m given in the following table : the first column contains 
 the name of the gas filling the tube : the different numbers given 
 under one gas relate to experiments made at different pressures. 
 
 Gas 
 
 V 
 
 mfe 
 
 Gas 
 
 V 
 
 mje 
 
 Air 
 
 2-8 x 10 9 
 
 1-3 xlO" 7 
 
 Air* ... 
 
 2-8 x 10 9 
 
 1-1 x 10~ 7 
 
 Air 
 
 2'8 x 10 9 
 
 1-1 x 10~ 7 
 
 Hydrogen 
 
 2-5 x 10 9 - 
 
 l-5xlO~ 7 
 
 Air 
 
 2-3 x 10 9 
 
 l-2xlO~ 7 
 
 Carbonic ) 
 
 
 
 Air* 
 
 3*6 x 10 9 
 
 l-3xlO~ 7 
 
 acid ( 
 
 2'2x 10 9 
 
 1'SxlO r 
 
 
 
 
 
 
 
 The mean of the'values of m/e is 1/3 x 10~ 7 or e/m = 77 x 10 6 . 
 We see too that within the limits of the errors of the experiments 
 the value of e/m is th same whether the tube be filled with air, 
 hydrogen or carbonic acid, so that it does not depend upon the 
 nature of the gas. This result was first obtained by the writer ( 
 by another method ; the pressure in the discharge tube was 
 adjusted so that the potential difference between the electrodes 
 in the discharge tube was the same for all the gases tried, photo- 
 graphs were taken of the rays when deflected by a constant 
 magnetic field and from these it was found that the deflected rays 
 occupied the same position whether the gas in the tube was 
 hydrogen, air, carbonic acid or methyl iodide ; these gases give a 
 wide range of densities as the density of methyl iodide is about 
 70 times that of hydrogen. The constancy of the value of e/m for 
 the ions which constitute the cathode rays is in striking contrast 
 to the variability of the corresponding quantity in the ions which 
 carry the current through liquid electrolytes. Experiments were 
 made on the effect of altering the metal of which the cathode was 
 made, the experiments marked with an asterisk in the preceding 
 
 * J. J. Thomson, Phil Mag. v. 44, p. 293, 1897. 
 
 t J. J. Thomson, Proc. Camb. Phil Soc. ix. p. 243, 1897. 
 
51] 
 
 THE CHARGE TO THE MASS OF AN ION. 
 
 95 
 
 table were made with platinum electrodes, all the others were 
 made with aluminium electrodes ; it will be seen that the values of 
 e/m are the same in the two cases. A further series of experiments 
 on this point has been made by H. A. Wilson* who used cathodes 
 made of aluminium, copper, iron, lead, platinum, silver, tin and 
 zinc and found the sanle value for e/m in all cases. 
 
 If we compare tjle value of e/m viz. 77 x 10 6 for the ions in the 
 cathode rays with/the value of the corresponding quantity for the 
 ions* which carry the current through liquid electrolytes we are 
 led to some very interesting conclusions ; the greatest value of e/m 
 in the case of liquid electrolysis is when the ion is the hydrogen 
 ion, in this case! e/m is about 10 4 . When we discuss the electric 
 charge carried w the ion in the cathode rays we shall find that 
 it is equal in magnitude to the charge carried by the hydrogen 
 ion, ki liquid electrolysis ; it follows then that the mass of the 
 hydrogen ion mus^ be 770 times that of the ion in the cathode 
 rays /hence the carrier of the negative electricity in these rays 
 must be very small compared with the mass of the hydrogen atom. 
 We shall return to this point when we have studied other pheno- 
 mena involving gaseous ions. 
 
 1 
 Ions in Lenard rays. 
 
 51, Lenard f has determined by the method just described the 
 velocity alodrthe value of e/Tft for tne Lenard rays; these are cathod 
 rays which have escaped from the discharge tube through a window 
 of very thin aluminium foil. In his experiments after escaping 
 from the discharge tube they entered a highly exhausted vessel 
 where they were deflected by electric and .magnetic fprces in the 
 way described in the preceding article ; e results of these 
 experiments are given in the following tabl 
 
 v cm./sec. 
 
 ^4 m 
 
 67 x 10 9 
 
 6-49 X 10 6 
 
 7 xlO 9 
 
 6-32 x 10 
 
 8-1 x 10 9 
 
 6-36 xlO 6 
 
 * H. A. Wilson, Proc. Camb. Phil. Soc. xi. p. 179, 1901. 
 f Lenard, Wied. Ann. xliv. p. 279, 1898. 
 
96 
 
 DETERMINATION OF THE RATIO OF 
 
 [51 
 
 The mean of the values of e/m is 6'39 x 10 6 which agrees well 
 with the value 7'7 x 10 6 found above. It will be noticed that the 
 velocities of the ions in this case are much greater than in the 
 preceding, taking the two sets together we have velocities of the 
 ions ranging from 2 - 2 x 10 to 81 x 10 9 cm./sec. without any indi- 
 cation of a change in the value of e/m. 
 
 Lenard* has also made some very interesting experiments on 
 the effect of an external electric field in accelerating or retarding 
 the motion of the ions. The apparatus used for this purpose is 
 shown in Fig. 29. 
 
 Q 
 
 Fig. 29. 
 
 The rays after coming through the window A pass through small 
 holes in two parallel circular metallic plates G^ and C 2 ; of these C^ 
 is always kept connected with the earth while (7 2 is charged 
 positively or negatively by means of an electrical machine ; after 
 leaving this condenser the rays pass between two plates M, used 
 for producing the electrostatic deflection, on to a screen $; the 
 dotted circle round M represents the coil used for producing the 
 magnetic deflection. The velocities of the ions were measured 
 (1) when the plates of the condenser C^ were at the same 
 potential, (2) when they were maintained at different potentials; it 
 was found that when .the plate (7 2 was negatively electrified the 
 velocity in case (2) was less than that in (1) while when the plate 
 (7 2 was positively electrified it was greater ; if v t is the velocity of 
 the ions in case (1), v 2 that in case (2), then assuming that the 
 
 9 
 
 * Lenard, Wied. Ann. xlv. p. 504, 1898. 
 
52] 
 
 THE CHARGE TO THE MASS OF AN ION. 
 
 97 
 
 whole change in the energy is due to the action of the electric 
 field we have 
 
 m(vJ-vS)=eV. (1), 
 
 where V is the potential difference between the plates, V being 
 taken positive when C 2 is at a higher potential than C l . The 
 results of Lenard's experiments are given in the following table, 
 the fourth column contains the value e/m calculated by equation 
 
 (i). 
 
 *>! (cm. /sec.) 
 
 v 2 (cm./sec.) 
 
 V (electromagnetic 
 units) 
 
 elm 
 
 7 xlO 10 
 
 35 x 10 l 
 
 -291x 10 10 
 
 6'2 x 10 6 
 
 68 x 10 10 
 
 34 x 10 10 
 
 -210xl0 10 f 
 
 8-1 xlO 6 
 
 62 * 10 10 
 
 89 x 10 10 
 
 + 291 xlO 10 / 
 
 6-9 xlO 6 
 
 77 x 10 10 
 
 47 x 10 10 
 
 - 291 x 10 10 
 
 6'4 xlO 6 
 
 79 xlO 10 
 
 1-0 x 10 10 
 
 .+291xl0 10 
 
 6-6 x 10 6 
 
 88 x 10 10 
 
 1-07 x 10 10 
 
 + 291xlO l 
 
 6-5 x 10 
 
 The constancy of the value of e/m is a strong confirmation of 
 the truth of the theory that the rays are charged particles in 
 rapid motion. 
 
 Method of determining the value of e/m and v by measuring 
 the energy carried by the cathode rays. 
 
 52. Many other methods have been employed to measure e/m. 
 One used by the writer* was to measure the energy carried by 
 the rays. To do this a narrow pencil of rays passed through a 
 small hole in a metal cylinder and fell upon a thermo-couple, the 
 couple was heated by the impact of the rays, and by measuring by 
 means of a galvanometer the rate at which the temperature of 
 the junction increased, the amount of heat communicated to the 
 junction in unit time was determined, let us call this amount ^; 
 then if we assume that all the energy possessed by the cathode 
 rays is converted into heat we have 
 
 Nm& = Q, 
 
 where N is the number of ions which enter the cylinder through 
 the hole in unit time, m is the mass and v the velocity of an ion. 
 
 * J. J. Thomson, Phil Mag. v. 44, p. 293, 1897. 
 
98 
 
 DETERMINATION OF THE RATIO OF 
 
 [52 
 
 If e is the charge of the ion, then in each unit of time Ne units 
 of negative electricity will enter the cylinder ; the rate at which 
 the negative charge increases can easily be measured if the 
 cylinder is insulated and connected with an electrometer, let E 
 be the rate of increase of the negative electricity inside the 
 cylinder, then we have 
 
 Eliminating N from these equations we get 
 
 1m . Q 
 
 v = 
 2 e V E' 
 
 If we observe the magnetic deflection produced by a known 
 magnetic field we determine mv/e, hence since we have just seen 
 
 how to determine mtf/e we can deduce the values of v and m/e. 
 f* 
 
 The results of experiments made in this way are shown below. 
 
 Gas 
 
 v 
 
 elm 
 
 Air 
 
 2'4 x 10 9 
 
 1-1 x 10 7 
 
 Air 
 
 3-2 x 10 9 
 
 l'4x 10 7 
 
 Hydrogen 
 
 2-5 x 10 9 
 
 1-0x10* 
 
 The mean of the values for e/m is 1-17 x 10 7 : this value is 
 considerably greater than the one previously found, the method 
 however is not so reliable as the preceding one as three measure- 
 ments have to be made, the magnetic deflection, the heating effect 
 and the rate of increase of the charge in the cylinder, instead of 
 two, the magnetic and the electric deflection; and it is not merely 
 that the measurements are more numerous, they are also more 
 difficult, as the measurement of the heating effect and the rate of 
 increase of the charge are much more complicated than that of 
 the electrostatic deflection. The conductivity given to the gas 
 by the passage through it of the cathode rays allows some of the 
 charge in the cylinder to leak away and thus tends to make the 
 observed value of E smaller than .the true one ; in the experi- 
 ments described above efforts were made to diminish this effect 
 as much as possible by connecting the cylinder to a condenser of 
 large capacity so that the negative charge on the ra should 
 
53] THE CHARGE TO THE MASS OF AN ION. 99 
 
 only produce a small change in the potential of the cylinder. We 
 may remark in passing that the charges of negative electricity 
 carried by the rays are very large, thus with quite a small hole 
 (about 1 mm. in radius) in the cylinder the potential of the 
 cylinder would change sometimes as such as 5 volts per second 
 when exposed to the rays, even though it was connected with 
 a condenser having a capacity about '15 microfarad. 
 
 Methods of determining v and e/m from the magnetic deflection 
 and potential difference between the electrodes of the discharge 
 tube. 
 
 53. These methods which were first used by Schuster* in 1890 
 are based on the following principles. If V is the potential differ- 
 ence between the terminals of the tube, then the work done on an 
 ion in passing from one end of the tube to the other is Ve, hence 
 the kinetic energy acquired by the ion can not be greater than 
 Ve, so that 
 
 mv 2 $ Ve. 
 
 From the observation of the effect of the magnet on the 
 discharge (Schuster measured the radii of the circles which are 
 the path of the ions in a strong magnetic field) we know the 
 value of mv/e, let us call this quantity q, then from the preceding 
 equation we have 
 
 a 2F 
 
 e/m * . 
 
 To find an inferior limit for e/m, Schuster took v equal to the 
 velocity of mean square of the atoms of the gas in the tube ; calling 
 this velocity U we have 
 
 e/mji . 
 
 Substituting the values of q and V found in his experiments 
 Schuster found for air 
 
 e/m $11 x 10 5 , 
 
 e/m { 10 3 . 
 
 If we assume that the charge on the nitrogen atom is three times 
 that on the atom of hydrogen in the electrolysis of liquids and if 
 
 * Schuster, Proc. Eoy. Soc. xlvii. p. 526. 
 
 72 
 
100 DETERMINATION OF THE RATIO OF [54 
 
 m is the mass of the nitrogen atom, then e/m is equal to 2 x 10 3 ; as 
 this is within the limits for e/m previously found, Schuster con- 
 cluded that the negatively electrified particles in the cathode rays 
 in a tube filled with nitrogen are atoms of nitrogen. We have 
 seen that more recent investigations have led to quite a different 
 conclusion. 
 
 54. Several determinations of the values of e/m and v have 
 been made on the assumption that the kinetic energy possessed by 
 the ion is equal to the energy that would be acquired by the ion 
 in falling through the potential difference V between tHe anode 
 and the cathode ; on this assumption we have 
 
 \mtf = Ve .... ....................... (1) 
 
 and if q or mv/e is determined by the magnetic deflection we have 
 
 m 
 
 Determinations of e/m on this principle have been made by 
 Kaufmann* and subsequently by Simon f. Kaufmann found by 
 this method that 
 
 - = l-86x!0 7 . 
 m 
 
 And Simon, who made a very large number of experiments in 
 which the potential difference between the cathode and anode 
 ranged from 4860 to 11840 volts, found that 
 
 - = T865 xlO 7 . 
 m 
 
 The value of e/m was found to be independent of the potential 
 difference. A Wimshurst machine was used to produce the 
 discharge as this maintains a very much more uniform potential 
 difference than an induction coil. 
 
 The values found for e/m by this method are larger than 
 those found by the methods previously described ; the method 
 is however open to objection, for it assumes that the kinetic 
 energy of the ion is equal to the work done on an ion starting 
 in the cathode itself and thus experiencing the maximum fall of 
 
 * Kaufmann, Wled. Ann. v. 61, p. 544; 62, p. 596, 1897; 65, p. 431, 1898. 
 t Simon, Wled. Ann. v. 69, p. 589, 1899. 
 
54] THE CHARGE TO THE MASS OF AN ION. 101 
 
 potential possible in the tube, and also that all the work done 
 by the electric field is spent in increasing the kinetic energy of 
 the ion while none of this energy is lost by the collisions of the 
 ion with the molecules of the gas through which it passes. Now 
 we have no right to assume without proof that the ion starts from 
 the cathode itself; we shall see that, at any rate when the 
 pressure is not very low, large numbers of ions are produced at 
 some little distance away from the cathode, and as the change of 
 potential in the neighbourhood of the cathode is very rapid such 
 ions would experience a notably smaller potential fall than those 
 starting from the cathode itself. Nor is the fact that the values 
 of ejm found by this method are independent of the potential 
 difference a conclusive proof that the ions under observation 
 started from the cathode. For suppose that the distance from 
 the cathode of the place from which the greater part of the ions 
 start is d, and that V(B is the potential gradient, then the fall of 
 potential experienced by these ions is V(l {3d) ; now /3 diminishes 
 as the pressure of the gases diminishes while d increases, so that 
 it is quite possible that /3d is independent of the pressure of the 
 gas (it would be so if for example were directly and d inversely 
 proportional to the pressure); in this case the fall of potential 
 experienced by the ions would always be a constant fraction of 
 the total fall of potential in the tube, so that the value of e/m 
 determined by equation (1) would always bear a constant ratio 
 to the true value. As the maximum potential difference used by 
 Simon was only about 1100 volts the pressure could not have 
 been very low in his experiments. When the pressure of the gas 
 is exceedingly small the number of collisions with the molecules 
 of a gas made by an ion in its journey down the tube may be 
 so greatly reduced that but few fresh ions are produced by the 
 collisions and in this case the greater number of the ions may come 
 from the electrode itself, but even in this case the use of equation 
 (1) is not legitimate, as part of the work may be spent in tearing 
 the ions out of the metal and only the remainder is available 
 for increasing the kinetic energy. 
 
 These considerations show that the use of equation (1) leads 
 to an over-estimate of the kinetic energy of the ion and therefore, 
 since e/m = mv 2 /eq\ the value of e/m calculated by this method 
 will tend to be too large. 
 
102 DETERMINATION OF THE RATIO OF [55 
 
 The method used by Lenard, and described on page 96, though 
 it depends upon the same equations is not open to these ob- 
 jections, as in this method the potential difference which enters 
 into the equations is applied to the ions after they have been 
 produced and started on their path, and in this case the increase 
 in the kinetic energy must equal the work done if we can neglect 
 the loss of kinetic energy of the ions produced by collisions with 
 the molecules of the gas ; this effect can be eliminated by working 
 at very low pressures and varying the length of path traversed 
 by the ion under the electric field. 
 
 55. In January, 1897, Wiechert* published a determination 
 of the values between which e/m must lie. The principles on 
 which this determination is based are as follows : by measuring 
 the magnetic deflection in a field of known strength we can 
 
 determine v ; to get a second relation between m/e and v, 
 e 
 
 Wiechert put 
 
 where V is the difference of potential between the electrodes in 
 the discharge tube and k an unknown quantity which cannot be 
 greater than unity. To get the maximum value of v, and there- 
 fore the maximum of e/m, k in equation (1) was put equal to unity 
 To get minimum values for v and e/m Wiechert assumed that 
 the kinetic energy of the ions in the cathode rays was greater 
 than that due to a fall through a potential difference equal to 
 the ' cathode fall of potential.' The cathode fall of potential is 
 the difference between the potential of the cathode and that of a 
 point on the outer boundary of that dark space in the discharge 
 which adjoins the cathode. Warburg has shown that this cathode 
 fall of potential is independent of the magnitude of the current 
 through the gas, of the pressure of the gas and, within certain 
 limitations, of the nature of the electrodes. As its value in air is 
 about 270 volts, Wiechert assumed that a minimum value for 
 kV was 200 volts. The grounds for this assumption do not seem 
 obvious ; a priori it would seem more probable that the minimum 
 value to take for kV should have been the potential difference, 
 
 * Wiechert, Sitzungsber. d. Physikal.-okonom. Gesellsch. zu Konigsberg, i. Pr. 38, 
 p. 1, 1897. 
 
56] THE CHARGE TO THE MASS OF AN ION. 103 
 
 not between the cathode and the outer boundary of this dark 
 space, but between this boundary and the place where the mag- 
 netic deflection of the rays was determined, for we know that the 
 rays are fully developed at this boundary, and it is by no means 
 so certain that at moderate pressures they all exist close to the 
 cathode. Using these assumptions, however, Wiechert found for 
 the maximum value of e/m the value 4 x 10 7 and for the minimum 
 value 4 x 10 6 . 
 
 56. Wiechert* has also determined by direct measurement 
 the velocity of the ions in the cathode rays, using a method first 
 applied by Des Coudresf for this purpose. The principle of the 
 method is as follows : suppose that A BCD, A'B'C'D' are two circuits 
 traversed by very rapidly alternating currents, such as those 
 produced by the discharge of a Leyden jar, let us suppose that 
 the currents in the two circuits are in the same phase, and that 
 these circuits are placed close to a tube along which cathode rays 
 are passing. The currents in the circuits will give rise to electric 
 and magnetic forces which will deflect the rays as they pass by 
 the circuits. If the velocity of the rays were infinite, then the 
 deflections produced by the two circuits on the rays would be 
 equal and in the same direction ; if however the rays take a finite 
 time to travel from one circuit to the other, and if the distance 
 between the circuits is adjusted so that this time is equal to 
 half the period of vibration of the current, then the deflection 
 produced by the first circuit will be equal and opposite to that 
 produced by the second ; or if the distance between the circuits 
 is such that the time taken by the rays to pass from one circuit 
 to the other is equal to one quarter of the period of the currents, 
 then when the effect produced by the circuit ABCD is a maximum 
 that produced by A'B'C'D' will be zero. 
 
 The arrangement used to apply these principles to determine 
 the velocity of the cathode rays is represented in Fig. 30 ; ABCD, 
 A'B'C'D' are the circuits carrying the currents produced by the 
 discharge of the jars, C is a concave cathode, B lt B z metal dia- 
 phragms perforated at the centre, G a screen covered with some 
 material which becomes phosphorescent when bombarded by the 
 
 * Wiechert, Wied. Ann., 69, p. 739, 1899. 
 
 t Des Coudves, Verhandl. d. physikal Gesellsch. zu Berlin, xiv. p. 86, 1895. 
 
104 
 
 
 DETERMINATION OF THE RATIO OF 
 
 [56 
 
 cathode rays. If is a horse-shoe magnet which deflects the rays 
 from the hole in the diaphragm B lt so that when no currents are 
 
 Fig. 30. 
 
 passing through ABCD, A'B'C'D' the cathode rays are stopped by 
 the diaphragm and the phosphorescent screen remains dark. When 
 a current passes through ABCD the pencil of cathode rays is de- 
 flected and swings backwards and forwards like a pendulum, if 
 during the swing the pencil strikes the hole in B some of the 
 rays will get through B and B 2 , and the screen G will be illumi- 
 nated. The brightness of the illumination will be greatest when 
 the hole in BI is just at the extremity of the swing caused by 
 the current in ABCD, for in this case the pencil is momentarily at 
 rest, and the time the pencil remains on the opening is therefore 
 a maximum. If there is no current in A'B'C'D' the position 
 of the phosphorescent spot on the screen will be on the line 
 joining the holes in the two diaphragms ; if a current in the same 
 phase as that through ABCD is passing through A'B'C'D', then 
 since the cathode rays that reach the diaphragm are displaced 
 upwards by the current in ABCD, they w r ill be similarly displaced 
 by that in A'B'C'D', and the phosphorescent patch will be above 
 the line joining the holes in the diaphragm, while if the current 
 in A'B'C'D' is in the opposite phase the patch will be displaced 
 
56] THE CHARGE TO THE MASS OF AN ION. 105 
 
 downwards, the direction of the displacement of the patch will 
 be reversed by reversing the poles of the magnet. If however 
 the phases of the currents in ABCD, A'B'G'D' differ by a quarter of 
 a period, then when the vertical displacement due to ABCD is 
 a maximum that due to A'B'G'D' will be zero, and the vertical 
 distribution of the light on the screen G will not be affected by 
 reversing the magnet M. We can ensure that the rays which 
 get through the opening in B l are those which are passing when 
 the vertical displacement due to the current in ABGD is greatest, 
 by gradually increasing the deflection of the rays by moving the 
 magnet M ; when we have got M into such a position that any 
 further increase in the deflection prevents any rays from reaching 
 the screen, we know that only those which suffer the maximum 
 deflection come under the action of A'B'G'D' ; if then we move 
 A B G'D into such a position that the vertical distribution of phos- 
 phorescence on the screen is not affected by reversing M, we 
 know that when the rays are passing A'B'G'D' the current in this 
 circuit differs in phase by a quarter period from the phase of the 
 current in ABGD when the rays were passing that circuit. If the 
 circuits ABGD, A'B'G'D' are arranged so that the currents in them 
 are simultaneously in the same phase, we know that the rays must 
 have taken a time equal to one quarter of a period of the currents 
 to pass from ABGD to A'B'G'D'. The period of the currents can 
 be determined by Lecher's method*, hence knowing the distance 
 between the circuits we can determine the velocity of the rays. 
 
 The arrangement used to carry out this method is represented 
 in Fig. 31. GG are two pairs of parallel plates, the upper pair 
 of plates are connected with the spark gap F, which is also con- 
 nected with the terminals of an induction coil, the lower pair of 
 plates are connected symmetrically with the circuits ABCD, 
 A'B'C'D. The cathode rays are produced by a system in electrical 
 connection with that producing the alternating currents. L and L 
 are two Leyden jars whose outer coatings are connected with the 
 extremities of the spark gap F, the inner coatings of the jars 
 are connected with the primary coil of a high tension transformer, 
 the secondary coil of which is connected with the anode and 
 cathode of the discharge tube. In order to prevent the rays 
 being scattered to the walls of the tube during their passage 
 
 * Lecher, Wied. Ann. 91, p. 850, 1890. 
 
106 
 
 DETERMINATION OF THE RATIO OF 
 
 [56 
 
 from one circuit to another a magnetising spiral was wound 
 round the tube producing a magnetic force parallel to the length 
 
 of the tube; this concentrated the rays along the axis of the tube 
 and made the observations easier. With this contrivance it was 
 found possible not merely to find a position of A'B'C'D', when the 
 currents differed by a quarter of a period, when the rays passed 
 through them, but to find the second position when they differed 
 by three-quarters of a period. 
 
 If X is the distance between the circuits when they differ by 
 a quarter period, L the wave-length of the electrical waves pass- 
 ing through these circuits, v the velocity of the rays, and V the 
 velocity of light, then 
 
 v_ \_ 
 V 
 
 Thus, in one experiment, L = 940 cm., X = 39, hence v is about 
 5 x 10 9 . The pressure was between | and J of a millimetre. 
 v being determined, we get e/m from the value of mv/e, which 
 is got by measuring the magnetic deflection of the rays. The 
 determination of v by this method is difficult and we cannot 
 expect a high degree of accuracy. As the result of his experi- 
 
57] THE CHARGE TO THE MASS OF AN ION. 107 
 
 ments, Wiechert came to the conclusion that the value of e/m 
 is between 1-55 x 10 7 and 1-01 x 10 7 . The most probable value 
 he gives as 1'26 x 10 7 . 
 
 Determination of e/m for the negative ions produced when ultra- 
 violet light falls on a metal plate, the gas through which the 
 ions pass being at a very low pressure. 
 
 57. The writer* determined the values of e/m for the negative 
 ions produced by the incidence of ultra-violet light on a metal plate 
 by the following method. It is proved on page 88 that when 
 an ion starts from rest from the plane x = 0, at the time t = 0, 
 and is acted on by a uniform electric field of strength X, parallel 
 to the axis of #, and by a uniform magnetic force H, parallel 
 to z, the position of the particle at the time t is given by the 
 equations 
 
 cos - 
 e a.* ( \m 
 
 m X ( e . / e TT \ 
 
 y=~ r/o I" Ht - sin Ht I 
 
 e /:/- (m \m / 
 
 where x and y are the coordinates of the ion. The path of the 
 ion is thus a cycloid, and the greatest distance the ion can get 
 from the plane x = is equal to 2mX/eH 2 . 
 
 Suppose now that we have a number of ions starting from 
 the plane x = 0, and moving towards the parallel plane x a, 
 supposed to be unlimited in extent, if a is less than 2mX/eH* 
 all the ions which start from x = will reach the plane xa, 
 while if a is greater than 2mX/eH 2 none of the ions will reach 
 this plane. If x = is a zinc plate illuminated by ultra-violet 
 light, and thus the seat of a supply of negative ions, and x = a 
 a metal plate connected with an electrometer, then when a 
 definite electric intensity is established between the plates, so 
 that the number of ions which leave the plate in unit time is 
 fixed, and if a is less than 2Xm/eH 2 , all the ions which start 
 from x = will reach the plane x = a. Thus the rate at which 
 the plate connected with the electrometer receives a negative 
 charge will be the same when there is a magnetic force acting 
 across the plate as when there is no such force. If however 
 
 * J. J. Thomson, Phil. Mag. v. 48, p. 547, 1899. 
 
108 -DETERMINATION OF THE RATIO OF [57 
 
 a is greater than 2Xm/eH 2 , then no ion which starts from x = 
 will reach the plane x = a, and this plate will not receive any 
 negative charge : so that in this case the magnetic field entirely 
 stops the supply of negative electricity to the plate connected 
 with the electrometer. Thus, on this theory, if the distance 
 between the plates is less than a certain value, the magnetic 
 force produces no effect on the rate at which the plate connected 
 with the electrometer receives a negative charge, while when the 
 distance is greater than this value the magnetic force entirely 
 stops the supply of negative electricity to the plate. The actual 
 phenomena are not so abrupt as this theory indicates. We find 
 in practice that when the plates are near together the magnetic 
 force produces only an exceedingly small effect, and this an 
 increase in the rate of charging of the plate. On increasing 
 the distance between the plates, we come to a stage where the 
 magnetic force produces a very great diminution in the rate of 
 charging; it does not. however, stop it abruptly, as there is 
 a considerable range in which the magnetic field diminishes but 
 does not entirely stop the supply of negative electricity to the 
 plate. At still greater distances the current to the plate under 
 the magnetic force is quite insignificant compared with the 
 current when there is no magnetic field. We should get this 
 gradual instead of abrupt decay of the current, if the ions, 
 instead of all starting from the plane x = 0, started from a layer 
 of finite thickness t ; in this case the first ions which failed to 
 reach the plate would be those which started from x 0, this 
 would occur when a = 2mX/eH z , some ions would however con- 
 tinue to reach the plate until a = t + 2mX/eH 2 . Thus if we 
 measure the distance between the plates when the magnetic 
 force first begins to retard the current, we can, if we know the 
 values of X and H, determine the value of e/m. The finite thick- 
 ness of the layer from which the ions start may be explained by 
 the use of a principle which we shall find of great importance 
 in many other phenomena connected with the discharge of elec- 
 tricity through gases : it is that when ions move through a gas 
 with a velocity exceeding a certain limit, the ions by their 
 collisions with the molecules of the gas through which they 
 move produce fresh ions. Thus when the negative ions w r hich 
 start from the metal surface acquire under the electric field 
 a certain velocity they will produce new ions, and thus the ion- 
 
58] 
 
 THE CHARGE TO THE MASS OF AN ION. 
 
 109 
 
 isation will not be confined to the metal plate but will extend 
 through a layer of finite thickness. 
 
 In using this method of determining e/m it is necessary to 
 have the gas between the plates at a very low pressure, so low 
 that the mean free path of the ion is at least comparable with 
 the distance between the plates ; if this is not the case the resist- 
 ance offered to the motions of the ions by the viscosity of the gas 
 prevents the preceding investigation from being applicable. 
 
 The mean value of e/m found in these experiments was 
 7 3 x 10 6 . It thus agrees very well with the value 7'6 x 10 6 found 
 for the same quantity for the carriers of the negative electricity in 
 the cathode rays : and proves that the carriers of electricity in the 
 two cases are the same, or, as we may express it, that a metal 
 plate emits cathode rays when illuminated by ultra-violet light. 
 
 58. Lenard* in 1900 also measured the value of e/m in the 
 case of the discharge of negative electricity through gas at 
 a very low pressure from a cathode illuminated by ultra-violet 
 light. The arrangement he used is represented in Fig. 32. A is 
 
 Fig. 32. 
 
 an aluminium plate on which the ultra-violet light shines : this 
 
 light comes from a spark between zinc electrodes and enters 
 
 the tube through the quartz window B. E is another metal 
 
 * Lenard, Drudes Annalen, ii. p. 359, 1900. 
 
110 
 
 DETERMINATION OF THE RATIO OF 
 
 [58 
 
 electrode perforated in the middle and connected with the earth, 
 it shields the right-hand part of the apparatus from the electro- 
 static action of the charged electrode A. D and C are electrodes 
 which can be connected with an electrometer. When A is charged 
 up a stream of negative electricity goes through the opening in 
 E, and striking against the plate D, charges up the electrometer 
 with negative electricity. If the electrometer be connected with C 
 instead of with D, it will not however receive any charge. We can 
 however give C a charge by deflecting the stream of negative 
 ions by a magnet until they strike against C. As we still further 
 increase the magnetic field the ions will be deflected by the field 
 past C, and the charge communicated to C will fall off rapidly. 
 The amount of negative electricity received by the electrodes D and 
 C respectively, as the magnetic force is increased, was in Lenard's 
 experiments represented by the curves in Fig. 33. The ordinates 
 are the charges received by the electrodes and the abscissae the 
 values of the magnetic force. s The curve to the left is for the 
 
 Fig. 33. 
 
 electrode D, that to the right for C. Since the negative ions are 
 not exposed to any electric field in the part of the tube to the 
 right of E their paths in this region under a constant magnetic 
 field will be circles whose radii are equal to mvfeH. Now C will 
 receive the maximum charge when the circle with this radius 
 passing through the middle of the hole in E, and having its 
 tangent at this point horizontal, passes also through the middle 
 of the electrode C. The radius R of this circle is fixed by the 
 relative positions of E and C. Hence, if we measure H when 
 C receives its maximum charge, we have 
 
 R = 
 
 mv 
 
 .(1). 
 
 The velocity is determined by the assumption that the work 
 
60] THE CHARGE TO THE MASS OF AN ION. Ill 
 
 done by the electric field, when the ion passes from A to E, is 
 spent in increasing the kinetic energy of the ion (we have already 
 considered on page 100 the objections which may be raised against 
 this assumption) : this leads to the equation 
 
 ^mv^ = Ve (2), 
 
 where V is the potential difference between A and E. From 
 equations (1) and (2) the values of e/m and v can be determined. 
 In this way Lenard found that e/m for the negative ions produced 
 by the action of ultra-violet light in a gas at a very low pressure 
 is equal to I'lo x 10 7 . 
 
 59. Value of e/m for the negative ions produced by an incan- 
 descent wire. 
 
 A metal wire when raised to a white heat in a gas at a very 
 low pressure gives out negative ions; the writer* has determined 
 the value of e/m for the negative ions given out by an incan- 
 descent carbon filament in hydrogen at a very low pressure. The 
 method used was the same as that used by him to determine the 
 value of e/m for the ions produced by the action of ultra-violet 
 light, and which has already been described on page 107. The 
 value of e/m found in this way was 8'7 x 10 6 , which agrees within 
 the errors of experiment with the values found for e/m for the 
 ions in the cathode rays, and for those produced by the action of 
 ultra-violet light. 
 
 60. Value of e/m for the negative ions emitted by radio-active 
 substances. 
 
 It has been shown by M. and Madame Curie f that the radio- 
 active substance radium -emits negative ions. The velocity of these 
 ions and the value of e/m have been determined by BecquerelJ:. 
 The method he employed was to measure the deflections of the 
 rays produced by an electrostatic and also by a magnetic field. 
 The experiments were made at atmospheric pressure, and the 
 resistance offered to the motion of the ions by the gas through 
 which they pass was neglected : this would not be justifiable in 
 
 * J. J. Thomson, Phil. Mag. v. 48, p. 547, 1899. 
 t M. et Mme. Curie, Comptes Rendus, t. 130, p. 647. 
 
 Becquerel, Rapports pre'sentts au Congrls International de Physique a Paris, 
 t. iii. p. 47, 1900. 
 
112 DETERMINATION OF THE RATIO OF [60 
 
 the case of the ions we have hitherto been considering, but as 
 the ions emitted by radium are very much more penetrating than 
 those we have hitherto considered, and are able to travel as far 
 through a gas at atmospheric pressure as other kinds of ion 
 travel through a gas at a very low pressure, we shall probably get 
 approximately the right values for e/m and v for the radium ions 
 even if we neglect the resistance of the gas. The radium was 
 placed below two parallel vertical metal plates, about 3*5 cm. wide 
 and 1 cm. apart ; above these metal plates was a horizontal photo- 
 graphic plate protected by a covering of black paper from the action 
 of light ; a thin slip of mica, symmetrically situated with respect to 
 the metal plates, was placed over the radium, this cast a shadow 
 on the photographic plate which when the metal plates were at 
 the same potential was at the middle of the field ; when a great 
 difference of potential, 10,200 volts, was maintained between the 
 plates the position of this shadow was displaced towards the 
 positive plate. Consider an ion passing between the plates, then 
 if I is the length of its path between the plates, F the electric 
 force acting upon it, the displacement of the ion parallel to the 
 lines of electric force when it leaves the region between the plates 
 
 is -x , and its direction of motion is displaced through an 
 2m v 2 
 
 Fe I 
 
 angle tan" 1 - , hence if h is the vertical distance of the photo- 
 m v 
 
 graphic plate above the upper edge of the parallel metal plate, 
 the point where the ion strikes the plate will be deflected through 
 a space 8 parallel to the line of electric force, where 8 is given 
 by the equation 
 
 . I Fe I 2 ,Fe I 
 
 o = - ~i + h -- 
 
 z 77i v 2 m v 2 
 
 = Fe I (I 
 m \ 
 
 The magnetic deflection was found in the following way : a 
 small quantity of radium was placed in a little lead saucer on 
 a photographic plate ; as none of the rays from the radium reach 
 the plate the latter is not affected ; if however a strong magnetic 
 field, with the lines of force parallel to the plate, acts on the 
 negative ions coming from the radium, these will be bent round 
 and will strike the plate, producing a photograph. 
 
60] THE CHARGE TO THE MASS OF AN ION. 113 
 
 To find the boundary of this photograph, let us take the 
 plane of the photographic plate as the plane of xy y the magnetic 
 force H being parallel to x ; the equations of motion of an ion are 
 
 d?x d*y . dz d 2 z _ dy 
 
 m d<* = ' m d? = He Tt> m M=- He dt> 
 
 the solutions of these equations are, if a) = He/m, and u, A, B 
 are constants, 
 
 x = ut, 
 
 y = A (1 cos cot) -f B sin wt, 
 
 z = A sin cot + B (cos wt 1). 
 If v and w are the values of dy/dt, dzjdt when t = 0, we have 
 
 y = (1 cos at) + sin cot, 
 
 z = sin wt H (cos &> 1 ) ; 
 
 w a) 
 
 when the ion strikes the plane we have 2 = 0, hence 
 
 w 
 tan -kwt = ~ . 
 
 v 
 
 Now if the ion is projected so as to make an angle 6 with 
 the direction of the magnetic force, and if the plane through the 
 direction of projection and the axis of x makes an angle < with 
 the plane of xz, we have, if V is the velocity of projection, 
 
 u = V cos 6, v = V sin 6 sin <, w = V sin 6 cos </>, 
 hence tan ^a>t = cot < 
 
 = tan - 
 
 thus (tit = 7T 2(f). 
 
 Substituting this value for t, we find, if f and 77 are the co- 
 ordinates of the point where the ion strikes the photographs 
 plate 
 
 V cos 6 
 
 0) 
 
 2Fsin0 cc 
 
 Thus, for the particles projected in a plane through the axis 
 of x, the locus of the points where they strike the plate will be 
 T. G. 8 
 
114 DETERMINATION OF THE RATIO OF [60 
 
 an ellipse whose semi-axes are - ^ and (^ ~ 9_) $ p or 
 
 &) GO 
 
 the particle projected in the plane of xz, the semi-axes of the 
 ellipse are 2V/to and TrV/w. An example of such an ellipse is 
 shown in Fig. .34 which is copied from a photograph by Becquerel. 
 
 Fig. 34. 
 
 By the measurement of the axes of the ellipse we can deter- 
 mine F/ct), i.e. Vm/eH. As the radium emits ions having velocities 
 extending over a considerable range, the impression on the plate 
 is not the arc of a single ellipse, but a band bounded by the 
 ellipses corresponding to the smallest and greatest velocities of 
 the ions. Becquerel took photographs when the ions from the 
 radium went (1) through the air at atmospheric pressure, and 
 (2) through air at very low pressure ; the photographs were found 
 to be identical, in fact one-half of the photograph represented 
 in Fig. 34 is produced by ions going through air at atmospheric 
 pressure, and the other half by ions going through air at a very 
 low pressure. The identity of the results in the two cases justifies 
 us in our neglect of the resistance of the air. 
 
 A simpler method than the electrostatic method used by 
 Becquerel to get a second relation between v and e/m, would be 
 to place the radium on a photographic plate in a little tube 
 so that all the ions start at right angles to the plate. A uniform 
 magnetic field acts parallel to the plate, and above the photo- 
 graphic plate and parallel to it is a metal plate which is connected 
 with an electric machine ; when this plate is charged with elec- 
 tricity there will be a strong electric field acting on the ion 
 parallel to its direction of projection and at right angles to the 
 magnetic force. If photographs are taken (1) with the plate 
 uncharged, (2) with the plate charged, the two photographs will 
 give us a simple method of finding v and e/m. For let us suppose 
 that all the ions have the same velocity V, the distance *2R of 
 
60] THE CHARGE TO THE MASS OF AN ION. 115 
 
 the image from the radium in the first photograph is given by 
 the equation 
 
 m V 
 
 -K = -pp . 
 
 e H 
 
 To find the distance of the image in the second photograph, 
 let us take the same axes as before, and let Z be the electric 
 force at right angles to the plate, then the equations of motion 
 of an ion are 
 
 d 2 z dy 
 
 m = Ze - H e -*- , 
 dt 2 dt 
 
 d* dz 
 
 The solution of these equations, when z, y, dy/dt vanish when 
 t = 0, is 
 
 Z ( smcot\ V 
 V = jf (t -- -+ (1 - cos cot), 
 H \ co ) co 
 
 Z V . 
 
 (1 cos tot) H sin cot, 
 
 ^ CO 
 
 where V is the velocity of projection of the ion. 
 
 When the ion strikes the photographic plate z 0, hence 
 
 *"*"* j/ir 
 
 Substituting this value of t iu the expression for y we find, if R l 
 is the distance from the radium of the point at which the ion 
 strikes the plate, 
 
 but 2 V/to = R, where R is the distance from the radium of the 
 point of return of the ion when the upper metal plate is not 
 charged, hence we have 
 
 R l R = jg. t, 
 
 R,-R V 
 t= - 
 
 y 
 hence since tan \ cot 
 
 82 
 
116 DETERMINATION OF THE RATIO OF [60 
 
 -R V V 
 
 we have tan 
 
 an equation by which we can determine the value of V/(Z/H) 
 When V is known, e/m can be determined from the value of R. 
 
 When Z/H is small compared with V an approximate solution 
 of equation (1) is 
 
 Becquerel did not use this method of determining V, but the 
 electrostatic method previously described; the latter method is 
 not however in many respects so convenient as the one just given. 
 
 As the result of his experiments Becquerel found for one set 
 of rays given out by the radium 
 
 v = l'Q xlO 10 , e/m = I<y, 
 
 thus the value of e/m is the same for these negatively charged 
 ions from radium as for the ions in the cathode and Lenard rays, 
 as well as for those produced by ultra-violet light or by in- 
 candescent metals. The velocity of the ions is much greater than 
 any we have met with in the case of ions arising in other ways, 
 amounting as it does to more than half the velocity of light ; 
 the ions chosen by Becquerel for this experiment were by no 
 means the fastest given out by the radium. Becquerel detected 
 the existence of others whose velocity was at least half as much 
 again as the velocity of those he measured. 
 
 It may be convenient to summarise in a table the results of 
 the measurements of e/m made by different observers, and with 
 ions produced in different ways. 
 
 It will be seen from the table that taking the same method 
 the values of e/m are practically the same whatever the source of 
 the ions. We have seen too that they do not depend upon the 
 gas or upon the nature of the electrodes ; thus in every case in 
 which negative electrification has been observed in gases at low 
 pressures, the value of e/m is a constant quantity and is very 
 large, approximately 1000 times larger than the largest value of 
 the corresponding quantity in the electrolysis of liquid solutions. 
 It is to be noted that these large values of e/m for gases only 
 occur when the pressure of the gas is very low, when in fact there 
 
61] 
 
 THE CHARGE TO THE MASS OF AN ION. 
 
 117 
 
 is very little gas for the ion to get entangled with; when the 
 pressure of the gas is high, the ion seems to act as a nucleus 
 
 TABLE OF VALUES OF elm. 
 
 Source of Ions 
 
 Observer 
 
 Date 
 
 Method of Determination 
 
 Value of elm 
 
 Cathode rays 
 
 J. J. Thomson 
 
 1897 
 
 Magnetic and electrostatic 
 deflection 
 
 7-7 x 10 
 
 " 
 
 J. J. Thomson 
 
 1897 
 
 Magnetic deflection and 
 heating effect 
 
 1-17 xlO 7 
 
 " 
 
 Kaufmann 
 
 1897-8 
 
 Magnetic deflection and 
 potential difference 
 
 l-86x!0 7 
 
 
 
 Simon 
 
 1899 
 
 Magnetic deflection and 
 potential difference 
 
 1-865 x 10 7 
 
 " 
 
 Wiechert 
 
 1899 
 
 Magnetic deflection and 
 velocity of ions 
 
 1-01 x 10 7 
 1-55 x 10 7 
 
 Lenard rays 
 
 Lenard 
 
 1898 
 
 Magnetic and electrostatic 
 deflection 
 
 6'39xl0 6 
 
 " 
 
 Lenard 
 
 1898 
 
 Magnetic deflection and 
 retardation in electric 
 field 
 
 6-8 x 106 
 
 Ultra-violet 
 light 
 
 J. J. Thomson 
 
 1899 
 
 Retardation of discharge 
 by magnetic field 
 
 7-6 x 10 6 
 
 >? 
 
 Lenard 
 
 1900 
 
 Magnetic deflection and 
 potential difference 
 
 1-15 x 10 7 
 
 [ncan descent 
 metals 
 
 J. J. Thomson 
 
 1899 
 
 Retardation of discharge 
 by magnetic field 
 
 8-7 x 10 8 
 
 Radium 
 
 Becquerel 
 
 1900 
 
 Magnetic and electrostatic 
 deflection 
 
 10 7 approxi- 
 mately 
 
 round which the molecules of the gas collect ; the ion thus gets 
 loaded up, and the ratio of e/m is very small compared with 
 its value at lower pressures. 
 
 61. Value of e/m for the positive ions. 
 
 The number of determinations of the value of e/m for the ions 
 which carry the positive charge is small compared with those 
 made for the corresponding quantity for the negative ions. The 
 first determination of the value of e/m for the positive ions was 
 made by W. Wien*. The positive ions he used were those which 
 occur in what are known as ' Canal -strahl en.' If an electric dis- 
 charge passes between an anode and a cathode perforated with 
 
 W. Wien, Wied. Ann. Ixv. p. 440, 1898. 
 
118 
 
 DETERMINATION OF THE RATIO OF 
 
 [61 
 
 a number of holes, then behind the cathode, i.e. on the side of 
 the cathode opposite to the anode, pencils of light are seen to 
 
 penetrate through the holes as in Fig. 35*, producing phosphor- 
 escence when they strike the glass. These rays have been shown 
 by Wien to consist of positively charged ions. He exposed a long 
 pencil of these rays coming through a perforated iron cathode to 
 both an electrostatic and a magnetic field, and measured the 
 corresponding deflections ; from these he deduced by the method 
 described on page 93, the values of e/m and v, and found 
 
 v = 3'6 x 10 7 cm./sec., while e/m 300. 
 
 The ' canal-strahlen ' or positive rays are only deflected with 
 great difficulty by the magnetic field, and it is necessary to use 
 very strong fields; this increases the difficulty of the investigation; 
 in Wien's experiments the strength of the field was 3250. It will 
 be seen from this result that the velocity of the positive ions is 
 very much smaller than that of any of the cathode rays hitherto 
 measured, while the value of e/m is of an entirely different order, 
 being only about 1/30000 of the value for the negative ion ; more- 
 over the value of e/m for the positive ions in the gas is of the same 
 order of magnitude as the value of e/m in the ordinary electrolysis 
 of solutions. Thus if m were the mass of the atom of iron, e the 
 charge carried by an atom of hydrogen, e/m is about 200, or since 
 iron is divalent the value of e/m for the iron in the electrolysis 
 of solutions is about 400. We have not however sufficient data 
 to enable us to determine whether the carriers of the positive 
 electricity in the 'canal-strahlen' are the atoms or molecules of 
 the metal of the cathode or of the gas in the tube. 
 
 * Wehnelt, Wied. Ann. Ixvii. p. 421, 1899. 
 
62] THE CHARGE TO THE MASS OF AN ION. 
 
 119 
 
 The energy in the particles forming the positive rays or canal- 
 strahlen is that which they would acquire by a fall through a 
 potential difference of about 16000 volts. As we know the charge 
 and the mass of the particles forming the positive rays, we can 
 compare the energy in the particles due to this difference of 
 potential with the mean energy possessed at any temperature by 
 the molecules of a gas, the mass of the molecules being the same 
 as that of the particles in the positive rays; doing so we find 
 that, even at the highest attainable temperature the energy of a 
 molecule in the gas would be quite insignificant in comparison 
 with that of a particle in the positive rays. 
 
 62. The writer has determined the value of e/m for the positive 
 ions by the method described on page 106 for the determination 
 of the value of e/m for the negative ions produced by the action 
 of ultra-violet light. The positive ions were produced by raising, 
 by means of an electric current, an iron wire to a red heat in an 
 atmosphere of oxygen, the pressure being very low. The wire 
 was parallel to a metal plate connected with an electrometer, the 
 distance of the wire from the plate was 4 mm. If the wire was 
 charged positively the plate and the electrometer received a posi- 
 tive charge, the current passing between the plate and the hot 
 wire being easily measured by the electrometer; if now the space 
 between the hot wire and the plate was placed in a very powerful 
 magnetic field, the lines of force being parallel to the plate, the 
 rate of leak from the wire to the plate was found to diminish if 
 the potential difference between the wire and the plate did not 
 exceed a certain value just as in the corresponding case of 
 the negative ions produced by ultra-violet light but while in the 
 latter case a comparatively feeble magnetic force is sufficient to 
 diminish the current, it requires a very powerful magnetic force 
 to produce the effect with the hot wire ; thus for example in my 
 experiments on the positive ions I used a magnetic field of 
 strength 12400 c.G.s. units, while in the experiments on the 
 negative ones a field of 100 was amply sufficient to produce very 
 appreciable effects. In the case of the hot wire I found' that 
 using a magnetic field of strength 12400 the rate of leak was 
 less when the magnetic field was on than when it was off, when 
 the potential difference between the plates was less than 50 volts ; 
 when it exceeded this value the rate of leak was the same 
 
120 DETERMINATION OF THE RATIO OF THE CHARGE, ETC. [62 
 
 whether the magnet was on or off. Thus when H = 12400 and 
 X = 50 x 10 8 /'4 the critical distance is '4 cm. Hence by the 
 results given on p. 106 we have 
 
 _ 2 x 50 x 10 8 m 
 
 ~-4 x(12400) 2 7' 
 
 or - = 400. 
 
 m 
 
 This is about the value for e/m for the ion of iron in electrolysis : 
 it does not however prove that the carriers of the positive elec- 
 tricity are the atoms of iron, for if m were the mass of a molecule 
 of oxygen and e the charge on a hydrogen ion in the electrolysis of 
 solutions e/m would be about 310, and the difficulties of the 
 experiment are so great that we cannot say that this result differs 
 from that actually found by more than the possible errors of the 
 experiment. 
 
 We see however that for the positive ions e/m is of the same 
 order as in ordinary electrolysis of solutions, while for negative 
 ions it is of an entirely different order. 
 
 The effect of the strongest magnetic fields I have been able to 
 use on the current when this is carried by positive ions is very 
 much less marked than the effect of comparatively weak fields on 
 the current when it is carried by negative ions. In the case of 
 the positive ions the magnetic force, even in the most favourable 
 circumstances, only diminishes the current, it does not entirely 
 stop it : this points to the conclusion that the carriers of the 
 positive charge are not all of one kind, but that sonle are much 
 heavier than others; thus in the case of the leak of positive 
 electricity from a hot platinum wire the study of the effect of the 
 magnetic field on the current leads us to the conclusion that 
 a part of the current is carried by molecules of oxygen and the 
 rest by molecules of platinum, or perhaps by aggregates of several 
 molecules. The proportion between the numbers of the different 
 kinds of carriers seems to vary very largely with the temperature 
 arid state of the surface of the platinum. 
 
CHAPTER VI. 
 
 DETERMINATION OF THE CHARGE CARRIED BY THE 
 NEGATIVE ION. 
 
 63. WE have seen that the value of e/m for the negative ions 
 in gases at a low pressure is about a thousand times the greatest 
 value of the ratio of the same quantities for ordinary electrolytes. 
 The question at once arises, is this due to a difference in the 
 masses of the ions, or to a difference in their electrical charges, or 
 to both these causes : to decide these points we must determine 
 the value of ra or e. The writer made in 1898* and 1899f 
 determinations of the value of e for the ions produced in one 
 case by Rontgen rays and in the other by ultra-violet light. 
 The method was based on the discovery made by C. T. R. WilsonJ 
 (see Chap. VII.) that gaseous ions, whether positive or negative, 
 act as nuclei for the condensation of clouds even in the absence of 
 dust ; and that if we have a mass of dust-free gas containing ions 
 in a closed vessel, and cool the gas by a sudden expansion, then 
 a cloud will be produced if the ratio of the volume of the 
 gas after expansion to the volume before is greater than 1*25. 
 An expansion of this amount is quite incapable of producing 
 more than very slight condensation in the gas if it does not 
 contain ions. The water condenses round the ions, and if these are 
 not too numerous each ion becomes the nucleus of a drop of water. 
 Thus by producing a sudden expansion in a gas containing ion 
 we can get a little drop of water round each ion ; these drops 
 are visible, and we can measure the rate at which they fall. 
 Sir George Stokes has shown that if v is the velocity with 
 which a drop of water falls through a gas, a the radius of the 
 
 * J. J. Thomson, Phil. Mag. v. 46, p. 528; 1898. 
 t J. J. Thomson, Phil. Mag. v. 48, p. 547, 1899. 
 C. T. K. Wilson, Phil. Trans., A, 1897, p. 265. 
 
1 20 
 
 J2J DETERMINATION OF THE CHARGE [63 
 
 drop, //, the coefficient of viscosity of the gas, and g the acceleration 
 due to gravity, then 
 
 -*?' 
 
 thus if we measure v we can determine a, and hence the volume 
 of each drop. If q is the mass of water deposited from each 
 cubic centimetre of the gas, n the number of the drops, we have 
 
 q = n^7ra s . 
 
 To find q we may proceed as follows: the gas after being cooled 
 by the very rapid expansion is supersaturated and moisture is 
 deposited on the ions, during the condensation of the water heat 
 is given out which warms the gas so that the temperature of the 
 gas rises above the lowest temperature reached during the ex- 
 pansion before condensation has taken place. Let t a be the lowest 
 temperature reached during the expansion, t the temperature 
 when the drops are fully formed, then if L is the latent heat of 
 evaporation of water, C the specific heat of the gas at constant 
 volume, M the mass of unit volume of the gas after expansion, 
 we have 
 
 Lq = CM(t- tj ........................ (1); 
 
 we neglect the heat required to raise the temperature of the water 
 in the gas in comparison with that required to raise the tempera- 
 ture of the gas itself. We have further 
 
 2 = Pi ~ P> 
 
 where p t is the density of the water vapour before condensation 
 begjfcns, and p the density at the temperature t Substituting this 
 value for q in equation (1), we get 
 
 - ...................... (2). 
 
 Since p is a known function of t this equation enables us to find 
 t when t 2 is known. 
 
 If x is the ratio of the final to the initial volume of the gas 
 and T the temperature in degrees centigrade of the gas before 
 expansion, then since the mass of 1 cubic centimetre of air at the 
 temperature C. and under a pressure of 760 millimetres of 
 mercury is '00129 grm., we have 
 
 00129 273 P_ 
 ~~ X 760' 
 
63] CARRIED BY THE NEGATIVE ION. 123 
 
 where P is the initial pressure of the gas expressed in millimetres 
 of mercury. 
 
 Again, Pl = p - , 
 
 . w 
 
 where p' is the density of water vapour at the temperature T before 
 expansion ; as the air was saturated with water vapour at this 
 temperature p can be obtained directly from the Tables of the 
 vapour pressure of water vapour. 
 
 The cooling caused by the adiabatic expansion is determined 
 by the equation 
 
 4- 7 1 
 
 For in such an expansion pv? is constant, where p is the pressure 
 and v the volume and y the ratio of the specific heat at constant 
 pressure to that at constant volume : but pv = RO, where 6 is the 
 absolute temperature and R a constant, hence we have during an 
 adiabatic expansion 
 
 vy~ l 6 = a constant ; 
 
 hence if v l d l , v z O z are the initial and final values of v and 0, 
 we have 
 
 or 
 
 Since 7=1-41 this is equivalent to equation (3). From (3) we 
 determine t%, and then since 
 
 C ='167, Z = 606, 
 equation (2) becomes 
 
 167 -00129 273 P ,. 
 
 As an example of how this equation is applied let us take 
 a case which occurred in one of the experiments. Here 
 
 ^=16, P = 760, ^=1-36. 
 To get 2 we have 
 
 log 27 ^ + 16 = -41 log 1-36 = log 1-134, 
 hence 273 + 1 2 = 254'8, or t 2 = - 18'2. 
 
124 DETERMINATION OF THE CHARGE [64 
 
 We find from the Tables that at 16 
 
 p' = -0000135, 
 hence equation (4) becomes 
 
 p = 99'3x 1 0~ 7 - 2-48 x!0- 7 (+ 18-2) (5). 
 
 To solve this equation we keep substituting various values for t 
 until we find one for which the corresponding value of p given by 
 (5) is the same as the value of the vapour pressure of water 
 at the temperature t. We find by this process of trial and 
 error that the solution of equation (5) is = 1'2, and the corre- 
 sponding value of p is 51 '5 x 10~ 7 . Substituting this value for p 
 we find q = 477 x 10~ 7 grms. 
 
 When we know q and a, n the number of drops is at once 
 determined by the equation 
 
 n = q/%7ra*. 
 
 In this way we can determine the number of ions per cubic 
 centimetre of gas. When we know the number of ions and also 
 the velocity of the ions under unit electric force, we can very easily 
 deduce the charge carried by an ion by measuring the current 
 carried by these ions across each unit of area under an electric 
 force E. For if n is the whole number of ions per c.c., positive as 
 well as negative, U the mean of the velocities of the positive and 
 negative ions under unit electric force, the current through unit 
 area is equal to 
 
 neEU, 
 
 where e is the charge on the ion ; the electric force E ought to be 
 so. small that the current is proportional to the electric force. 
 When this is not the case the number of ions is diminished by 
 the action of the electric field, and depends upon the magnitude 
 of the electric force. 
 
 We can easily measure the current through the ionised gas 
 and thus determine neEU, and as n, E, U are known we can 
 deduce the value of e. 
 
 64. This method was first applied by the author to determine 
 the charge on the ions produced by Rontgen rays. The method used 
 for making the cloud and measuring the expansions is the same as 
 that used by C. T. R. Wilson*: the apparatus for this and the 
 
 * C. T. K. Wilson, Proc. Camb. Phil. Soc. ix. p. 333, 1897. 
 
641 
 
 CARRIED BY THE NEGATIVE ION. 
 
 125 
 
 electrical part of the experiment is represented in Fig. 36. The 
 gas which is exposed to the rays is contained in the vessel A 
 
 this vessel is connected by the tube B with the vertical tube C, 
 the lower end of this tube is carefully ground so as to be in 
 a plane perpendicular to the axis of the tube, it is fastened 
 down to the india-rubber stopper D. Inside this tube there is 
 an inverted thin-walled test tube P with the lip removed and the 
 open end ground so as to be in a plane perpendicular to the axis 
 of the tube. The test tube slides freely up and down the larger 
 tube and acts as a piston. Its lower end is always below the 
 surface of the water which fills the lower part of the outer tube ; 
 a tube passing through the india-rubber stopper puts the inside of 
 the test tube in communication with the space E. This space is 
 in connection by the tube H with a large vessel F in which the 
 pressure is kept low by a water-pump. The end of the tube H is 
 ground flat and is closed fjy an india-rubber stopper which presses 
 
126 DETERMINATION OF THE CHARGE [64 
 
 against it, the stopper is fixed to a rod, and by pulling this rod 
 down smartly the pressure inside the test tube is lowered and the 
 test tube falls rapidly until it strikes against the india-rubber 
 stopper. The tube T, which can be closed by a stop-cock, admits 
 air into E and allows us to force the test tube back into its place 
 for another expansion. The tubes R and S are for the purposes 
 of regulating the amount of expansion. To do this the mercury 
 vessel R is raised or lowered when the test tube is in its lowest 
 position until the gauge G indicates that the pressure in A is the 
 desired amount below the atmospheric pressure. The stop-cock S 
 is then closed and air is admitted into the interior of the piston 
 by opening the stop-cock T. The piston then rises until the 
 pressure in A differs from atmospheric pressure only by the amount 
 required to support the weight of the piston ; this pressure is only 
 that due to a fraction of a millimetre of mercury. 
 
 If II is the barometric pressure, then P lt the pressure of the 
 air before expansion, is given by the equation 
 
 p,=n-Tr, 
 
 where TT is the maximum vapour pressure of water at the tempera- 
 ture of the experiment. The pressure of the air P 2 after the 
 expansion is given by 
 
 P*-Pi-p, 
 
 where p is the pressure due to the difference of level of the mercury 
 in the two arms of the gauge G. 
 
 Thus if v z is the final and Vi the initial volume of the gas 
 
 0! ~~ P 2 ~ II TT p' 
 
 The vessel in which the rate of fall of the fog and bhe con- 
 ductivity of the gas are tested is at A. It is a glass tube 
 36 millimetres in diameter covered with an aluminium plate ; to 
 avoid the abnormal ionisation which occurs when Rontgen rays 
 strike against a metal surface, the lower part of the aluminium 
 plate is coated with wet blotting-paper, and the electric current 
 passes from the blotting-paper to the horizontal surface of the 
 water beneath. The induction coil and the focus bulb for the 
 production of the Rontgen rays are placed in a large iron tank, 
 in the bottom of which a hole is cut and closed by an aluminium 
 
64] CARRIED BY THE NEGATIVE ION. 127 
 
 window. The vessel A is placed underneath this window and 
 the bulb giving out the rays some distance above it, so that the / 
 beam of rays escaping from the tank is not very divergent. 
 The intensity of the rays can be reduced to any required degree 
 by inserting leaves of tinfoil or sheets of aluminium between the 
 bulb and the vessel. 
 
 In these experiments it is necessary to work with very weak 
 rays, so that the number of ions is comparatively small ; when the 
 number of ions is large some of them seem to escape being caught 
 by the cloud produced by the expansion, for if a second expansion be 
 produced (the ionising agent being cut off) a considerable cloud will 
 be formed, and it may require several expansions before the gas is 
 restored to the state in which it existed previous to the exposure 
 to the ionising agent. The cause of these secondary clouds has 
 not yet been definitely settled, but it is possible that they may be 
 due, partly at any rate, to ions which have not been caught by the 
 first cloud, and if this were so the number of ions deduced from 
 the time of fall of the cloud would be too small ; it is therefore 
 advisable to work with such weak ionisation of the gas that the 
 first cloud clears away all the ions. 
 
 To find the current passing through the gas, the tank and the 
 aluminium plate on the top of the vessel A are connected with 
 one pair of quadrants of the electrometer, the other pair of 
 quadrants is connected with the water surface in the vessel A\ 
 this surface is charged up to a known potential by connecting 
 it with one of the terminals of a battery, the other terminal of 
 which is connected with the earth. After the surface has been 
 charged it is disconnected from the battery and the insulation 
 of the system tested by observing whether there is any leak 
 when the Rontgen rays are shut off; the insulation having been 
 found satisfactory, the rays are turned on and the charge begins 
 to leak from the electrometer; by measuring the rate of leak 
 the quantity of electricity which in one second passes through 
 the gas exposed to the rays can be determined. For suppose 
 that in a second the electrometer reading is altered by p scale 
 divisions, and that one scale division of the electrometer corre- 
 sponds to a potential difference V between the quadrants, and 
 that C is the capacity of the system consisting of the electrometer, 
 the water surface and the connecting wires, then the quantity of 
 
128 DETERMINATION OF THE CHARGE [65 
 
 electricity which passes in one second through the gas exposed 
 to the rays is pVC. If n is the total number of ions positive as 
 well as negative per cubic centimetre of the gas, u the mean of 
 the velocities of the positive and negative ions under a potential 
 gradient of a volt per centimetre, E the potential gradient in 
 volts per centimetre acting on the ionised gas, A the area of the 
 water surface, the current through the gas is equal to Aneu^E\ 
 but as this current is equal to pVC, we have 
 
 pVC = Aneu Q E, 
 
 an equation by means of which we can determine ne, and as from 
 the experiments on clouds we know the value of n we can at once 
 deduce the value of e. Proceeding in this way the author found 
 in 1898 that for the ions produced by Rontgen rays passing through 
 air, using electrostatic units, 
 
 e = 6*5 x 10- 10 gr> (cm.) 1 (sec.)" 1 . 
 
 A similar series of experiments on the ions produced by 
 Rontgen rays passing through hydrogen gave for e the charge 
 on the hydrogen ion the value 
 
 67 x 10- 10 (gr.)*(cm.)^(sec.)- 1 . 
 
 The difference between this and the value of the charge on the 
 ion in air is much less than the error of experiment, so that the 
 charges on the ions are the same in these gases. This was shortly 
 afterwards confirmed by the experiments made by Townsend on 
 the rates of diffusion of the ions ; an account of these experiments 
 has already been given on p. 26. 
 
 65. The author in 1901-2 repeated these experiments on the 
 charges carried by the ions, making some modifications in the 
 method. In the first place the ionisation was produced by the radia- 
 tion from radium instead of by the Rontgen rays ; this was done to 
 get a more uniform rate of ionisation than is possible with Rontgen 
 tubes, the irregularity of which gave a great deal of trouble in 
 the earlier investigation. Secondly, the electrometer used in the 
 new experiments was much more sensitive than the old one, the 
 new electrometer was of the Dolezalek type and gave a deflection 
 of 20000 scale divisions for a potential difference of one volt. 
 
 The measurements made by C. T. R. Wilson* (see Chap. VII.) 
 
 * C. T. E. Wilson, Phil. Trans, cxciii. p. 289. 
 
66] CARRIED BY THE NEGATIVE ION. 129 
 
 show that with expansions between T25 and T3 negative, and only 
 negative, ions act as nuclei for cloudy condensation, while with 
 expansions greater than 1*3 both negative and positive ions are 
 brought down by the cloud. It was feared that when the expan- 
 sions were sufficiently large to bring both sets of ions into play the 
 more active negative ions might have a tendency to monopolise 
 the aqueous vapour, and that therefore the whole of the positive 
 ions might not be brought down with the cloud. This fear was 
 found to be justified, for with the expansion apparatus used in the 
 earlier experiments it was found that with expansions greater than 
 1*3 the number of particles in the cloud formed in the ionised gas 
 was not, as it should have been if all the ions had been caught by 
 the cloud, twice as great as when the expansion was less than this 
 value. The apparatus was modified so as to make the rate of 
 expansion very much more rapid than in the earlier experiments ; 
 with the new apparatus the number of particles in the cloud when 
 the expansion was greater than T3 was twice as great as when the 
 expansion was less than this value ; this confirms the view that 
 with this apparatus all the ions are caught by the cloud. The 
 result of a number of determinations of e with the new apparatus, 
 using different samples of radium and different intensities of 
 radiation, was that 
 
 e = 3-4 x 10- 10 (gr.)* (cm.)^ (sec.)- 1 . 
 
 66. Having found the value of e, let us compare it with E the 
 charge carried by the hydrogen ion in the electrolysis of solutions. 
 If N is the number of molecules in a cubic centimetre of a gas 
 at a pressure of 760 mm. of mercury and at C., then we know 
 as the result of experiments on the liberation of hydrogen in 
 electrolysis (see p. 57) that 
 
 NE=I'22 x 10 10 . 
 
 In treatises on the Kinetic Theory of Gases (for example, 0. E. 
 Meyer, Die kinetische Theorie der Gase) it is shown how by the 
 aid of certain assumptions as to the nature and shape of the 
 molecules it is possible to find N. The values got in this way 
 vary considerably, the best determinations of N lying between 
 2-1 x 10 19 and 10 20 ; this would make E lie between 61 x 10' 10 and 
 1-29 x 10" 10 ; the value of e is well between these limits. Hence 
 we conclude that the charge carried by any gaseous ion is equal 
 
 T. G. 9 
 
130 DETERMINATION OF THE CHARGE [67 
 
 to the charge carried by the hydrogen ion in the electrolysis of 
 solutions. 
 
 This conclusion is also confirmed by the experiments of 
 Townsend already referred to. In these experiments the charges 
 on the ions in air, hydrogen and carbonic acid gas were directly 
 compared with E, and proved to be equal to it (see p. 58). 
 Starting with this result we can by direct experiment on gases 
 determine the value of E, and then by the aid of the equation 
 
 the number of molecules in a cubic centimetre of the gas, and 
 hence the mass of a molecule of the gas ; proceeding in this way 
 we avoid all those assumptions as to the shape and size of the 
 molecules of the gas, and the nature of the action which occurs 
 when two molecules come into collision, which have to be made 
 when the same quantities are determined by means of the Kinetic 
 Theory of Gases. The value we have found for E makes 
 
 A r =3'9 x 10 19 . 
 
 67. The determinations of e described above have been made 
 on ions produced by Rontgen or radium rays. The properties of 
 tthe ions in gases are the same, however, whether the ions are 
 produced by Rontgen, radium, Lenard, or cathode rays, or by the 
 agency of ultra-violet light. Evidence in support of this is 
 .afforded by the fact that as we have seen the velocity of the ions 
 in the electric field is the same in whichever of the above-men- 
 itioned ways they are produced. We shall see too (Chap. VII.) that 
 ithey behave in exactly the same way with respect to their power 
 of producing condensation of clouds. We have thus strong reasons 
 for thinking that the charge on the ion does not depend upon 
 'the kind of radiation used to liberate the ion. I have made some 
 direct experiments on this point, and have made measurements 
 of the charge on the negative ions produced by the incidence of 
 ultra-violet light on metals ; the method used was the same as in 
 the case of the ions produced^by Rontgen rays, and the result was 
 that within the limits of experimental error the charge on the 
 negative ion produced by the action of ultra-violet light was the 
 same as that on the ion produced by Rontgen rays*. 
 
 The case of the ions produced by ultra-violet light is in- 
 teresting, as it is the one in which both the values of e and of e/m 
 * J. J. Thomson, Phil. Mag. v. 48, p. 547, 1899. 
 
69] CARRIED BY THE NEGATIVE ION. 131 
 
 (when the pressure is low) have been measured when the ions 
 are produced by the same kind of radiation in the two experi- 
 ments. 
 
 68. As e is the' same as E the charge on the hydrogen ion, 
 while elm is about a thousand times E/M, where M is the mass 
 of the atom of hydrogen, it follows that ra is only about 1/1000 
 of M, so that the mass of the earner of the negative charge is 
 only 1/1000 of that of the atom of hydrogen. 
 
 69. Let us no.w sum up the results of the determinations of e 
 and of e/m which have been made for the ions produced in gases by 
 radiations of different kinds. We have seen that in all the cases 
 in which e has been determined it has been found equal to E, the 
 charge on a hydrogen ion in liquid electrolysis. The charge on the 
 gaseous ion does not, like that on the ions in liquids, depend on 
 the substance from which the ions are produced ; thus in the case 
 of the ions produced by Rontgen or analogous radiation, the 
 charge on an ion produced from oxygen is the same as that on 
 one produced from hydrogen, though in liquids the charge on an 
 oxygen ion is twice that on a hydrogen one. 
 
 Again, at very low pressures, when the negative ion can 
 escape getting entangled with the molecules of the gas by which 
 it is surrounded, the mass as well as the charge of the negative 
 ion is invariable and much smaller than the mass of the smallest 
 portion of ordinary matter, i.e. that of an atom of hydrogen, 
 recognised in the .Kinetic Theory of Gases. We shall call each 
 of these small negative ions a corpuscle, thus negative electri- 
 fication when the pressure of the gas is low so that there is only 
 a very small quantity of ordinary matter present, consists of an 
 assemblage of corpuscles. 
 
 On the other hand the positive ions are as far as we know 
 always associated with masses which are comparable with th 
 masses of the ordinary atoms of the gas in which they occur. 
 
 We are at once led by this result to a view of the nature of 
 electricity which in many respects closely resembles that of the 
 old ' One Fluid Theory of Electricity.' The ' electric fluid ' corre- 
 sponds to an assemblage of corpuscles, negative electrification 
 consisting of a collection of these corpuscles : the transference of 
 electrification from place to place being a movement of corpuscles 
 
 92- 
 
132 DETERMINATION OF THE CHARGE, ETC. [69 
 
 from the place where there is a gain of positive electrification to 
 the place where there is a gain of negative. Thus a positively 
 electrified body is one which has been deprived of some corpuscles. 
 These corpuscles may either remain free or get attached to mole- 
 cules of matter with which they come in contact ; thus positive 
 electrification is always associated with ordinary matter, while 
 negative electrification may or may not be, according as the 
 corpuscles are or are not attached to molecules of ordinary 
 matter. Thus in gas at very low pressures the corpuscles are 
 free, but in gases at higher pressures they get attached to the 
 molecules of the gas so that there is not much difference between 
 the effective masses of the positive and negative ions ; that this 
 is the case is indicated by the results of the experiments we have 
 described on the velocities of the positive and negative ions in 
 the electric field, for though the negative ion moves faster than 
 the positive, the difference is not great. We shall return to the 
 development of this corpuscular theory of electricity in a later 
 chapter. 
 
CHAPTER VII. 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 
 
 70. ONE of the most striking effects produced by ions is the 
 influence they exert on the condensation of clouds. One instance 
 of this is the discovery by R. von Helmholtz* of the effect 
 of an electric discharge on a high pressure steam jet. When 
 steam rushes out from a jet placed near a pointed electrode 
 connected with an electric machine or an induction coil, a re- 
 markable change in the appearance of the jet takes place when 
 electricity is escaping from the electrode. This can conveniently 
 be shown by throwing the shadow of the jet on a screen; when 
 there is no escape of electricity the jet is nearly transparent and 
 the shadow is very slight ; as soon however as electricity begins 
 to escape, the opacity of the jet increases to a remarkable extent, 
 the shadow becomes quite dark and distinct, and colours arising 
 from the diffraction of the light by the small drops of water 
 make their appearance, the jet sometimes presenting a very 
 beautiful appearance. For an account of the ways of arranging 
 the experiments so as to observe these colours to the best ad- 
 vantage and of a method by which the size of the drops of water 
 can be deduced from the colour phenomena, we must refer to a 
 paper by Barusf. This effect evidently shows that the electrifi- 
 cation makes the steam condense into water drops. 
 
 In a later paper by R. von Helmholtz and RicharzJ;, published 
 after the death of the former, the authors show that a steam jet 
 is affected by making or breaking the current through the primary 
 
 * R. v. Helmholtz, Wied. Ann. xxxii. p. 1, 1887 ; see also Bidwell, Phil. Mag. 
 v. 29, p. 158, 1890. 
 
 t Barus, American Journal of Meteorology, ix. p. 488, 1893. 
 R. v. Helmholtz and Richarz, Wied. Ann. xl. p. 161, 1890. 
 
134 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [70 
 
 of an induction coil, even when the terminals of the secondary 
 placed in the neighbourhood of the jet are separated by much 
 more than the sparking distance, and that the effects persist 
 even when the terminals are wrapped in moist filter-paper so 
 as to catch any metallic particles that might be given off from 
 them. 
 
 R. vori Helmholtz and Richarz (loc. cit) showed that the 
 steam jet was affected by gases from the neighbourhood of flames 
 whether these were luminous or not ; the very cool flames of 
 burning ether and alcohol are exceptions to this statement. 
 
 A platinum wire raised to a dull red heat affected the jet 
 when electrified, and if raised to a bright yellow heat affected 
 the jet even when unelectrified, except when the wire was sur- 
 rounded by hydrogen, in which case the unelectrified wire had 
 no effect. Coal gas passed through platinum gauze raised to 
 a dull red heat also influenced the jet. 
 
 The jet is also affected by the presence in its neighbourhood 
 of certain substances such as sulphuric acid, also by gases which 
 are dissociating or undergoing chemical changes in the air such 
 as N 2 O 4 or N0 2 , it is not affected by ozone or hydrogen peroxide. 
 If however ozone is destroyed by bubbling through such sub- 
 stances as solutions of potassium iodide or potassium perman- 
 ganate, the gas which emerges has the power of affecting the jet; 
 this gas has also the power of forming clouds when it comes 
 into contact with moist air, as was first shown by Meissner*; 
 experiments on this point have also been made by R. von Helm- 
 holtz and Richarz and by J. S. Townsendf. The action in this 
 case and in other cases of the effect of chemicals ie, as we shall 
 see, probably due to the formation of some substance which 
 dissolves in the drops of water arid lowers their vapour pressure ; 
 thus the drops in this case are not formed of pure water, but of 
 more or less dilute solutions. 
 
 Moist air drawn over phosphorus, sodium or potassium also 
 affects the jet. 
 
 Lenard and Wolff J also showed that the incidence of ultra- 
 
 * Meissner, Jahresber. f. Chemie, 1863, p. 126. 
 
 t J. S. Townsend, Proc. Camb. Phil, Soc. x. p. 52, 1898. 
 
 + Lenard and Wolff, Wied. Ann. xxxvii. p. 443, 1899. 
 
70] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 135 
 
 violet light on a zinc plate or on some fluorescent solutions in the 
 neighbourhood of a steam jet produced condensation in the jet; 
 a similar effect was produced by ultra-violet light passing through 
 quartz. Richarz* showed that the incidence of Rontgen rays 
 produced condensation in the jet. There was for some time con- 
 siderable difference of opinion as to the cause of this behaviour 
 of the steam jet ; the earliest researches on this subject came 
 at a time when the experiments of Aitkenf, of CoulierJ and of 
 Kiessling had drawn attention to the great effect produced by 
 dust on cloudy condensation. These physicists had shown that 
 the clouds produced by the lowering of temperature resulting 
 from a small adiabatic expansion of the damp dusty air of an 
 ordinary room entirely disappeared if the dust were filtered out 
 of the air : the drops in the cloud were shown to collect round 
 the particles of dust, the water drops were thus able to start with 
 a finite radius that of the dust particle and so had not to 
 pass through the stage when their radius was of molecular 
 dimensions, when, as Lord Kelvin has shown, the effect of surface 
 tension would lead to such intense evaporation as soon to cause 
 the disappearance of the drops. 
 
 The discovery of the effect of dust on the condensation of 
 water vapour produced a tendency to ascribe the formation of 
 clouds in all cases to dust and to dust alone ; in fact, to use the 
 indication of the steam jet as a measure of the dustiness of the 
 air; thus, for example, Lenard and Wolff ascribed the effect 
 which they found was produced by the incidence of ultra-violet 
 light on metals to metallic dust given off by the metal under 
 the influence of the light. On the other hand, R. von Helmholtz,. 
 and later Richarz, strongly maintained the view that many of the 
 effects they observed were not due to dust, but to ions, and] 
 they gave strong arguments and made some striking experi- 
 ments in support of this view ; as however this evidence ~s 
 somewhat indirect, and as the truth of their view has been 
 indisputably proved by the direct experiments recently made by 
 
 * Richarz, Wied. Ann. lix. p. 592, 1896. 
 
 t Aitken, Nature, xxiii. pp. 195, 384, 1880. Trans. Roy. Soc. Edin. 
 p. 337, 1881. 
 
 Coulier, Journal de Pharm. et de Chemie, xxii. p. 165, 1875. 
 Kiessling, Naturw. Verein Hamburg -Altona, viii. 1, 1884. 
 
136 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 
 
 [71 
 
 C. T. R. Wilson*, we shall proceed at once to a description of 
 his researches. 
 
 71. The method used by Wilson was to suddenly cool the 
 moist gas by an adiabatic expansion, so that the gas which was 
 saturated with water vapour before cooling became supersaturated 
 afterwards. One of the arrangements used by Wilsoo to produce 
 
 ToPump 
 
 Fig. 37. 
 
 the expansion is shown in Fig. 37 : the way in which the appa- 
 ratus works has already been explained (see p. 125). It is very 
 important in these experiments that the expansions which produce 
 the cloud should be as rapid as possible, for with slow expansions 
 
 * C. T. E. Wilson, Phil. Trans. 189, p. 265, 1897. 
 
72] 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 
 
 137 
 
 as soon as the supersaturation is sufficient for the first drops to 
 be formed, if these have time to grow before the expansion is 
 completed, they will rob the air of its moisture, and the super- 
 saturation will not rise much above the value required for the 
 formation of the first drops. To ensure this rapid expansion, 
 the piston P, Fig. 37, should be light and able to move freely 
 up and down, and the arrangement by which the difference of 
 pressure between the inside and outside of the cylinder is pro- 
 duced should work very rapidly. 
 
 72. Using an arrangement of this nature, Wilson found that 
 when dusty air filled the expansion chamber a very slight expan- 
 sion was sufficient to produce a dense fog; if this was allowed to 
 settle and the process repeated, the air by degrees got deprived of 
 the dust which was carried down by the fog; when the air became 
 dust-free no fogs were produced by small expansions. If we 
 take as the measure of the expansion the ratio of the final to 
 the initial volume of the gas, no cloud was produced in the dust- 
 free air until the expansion was equal to 1'25. When the ex- 
 pansion was between 1'25 and 1 P 38, a few drops made their ap- 
 pearance ; these drops were very much fewer in hydrogen than in 
 air. On increasing the expansion beyond 1'38 a much denser 
 cloud was produced in the dust-free gas, and the density of the 
 cloud now increased very rapidly with the expansion. Thus we 
 see that even when there is no dust, cloudy condensation can be 
 produced by sudden expansions if these exceed a certain limit. 
 This limit appears to be independent of the nature of the gas, 
 as is shown by the following table, which gives the ratio of the 
 
 
 Rain-like condensation Cloud-like condensation 
 
 Gas 
 
 Final /initial i Super- 
 volume saturation i 
 
 Final / initial 
 volume 
 
 Super- 
 saturation 
 
 Air . . 
 
 1-252 
 
 4-2 
 
 1-375 
 
 7-9 
 
 
 Oxygen 
 
 1-257 
 
 4-3 
 
 1-375 . 
 
 7-9 
 
 Nitrogen 
 
 1-262 
 
 4-4 
 
 1-375 
 
 7-9 
 
 Hydrogen 
 
 
 
 
 1-375 
 
 7-9 
 
 Carbonic acid 
 
 1-365 
 
 4-2 
 
 1-53 
 
 7-3 
 
 Chlorine 
 
 1-30 
 
 3-4 
 
 1-44 
 
 5-9 
 
 volumes required to produce the first or rain-like stage of con- 
 densation and the supersaturation, i.e. the ratio of the pressure 
 
138 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [73 
 
 of the aqueous vapour actually present when the condensation 
 begins to the saturation vapour pressure at that temperature : 
 the third and fourth columns give the corresponding quantities 
 for the second stage of the condensation, i.e. when the expansion 
 produces a dense cloud. 
 
 The rain-like condensation is absent in hydrogen. 
 
 73. The description given above relates to the behaviour of gas 
 in the normal state ; on exposing the gas to Rontgen rays, Wilson 
 found that as in the normal gas, there were no drops until the 
 expansion was equal to 1*25 ; on passing this limit however the 
 density of the cloud was very greatly increased by the rays, and 
 if these were strong the few drops which were all that were formed 
 when the rays were absent were replaced by a dense and almost 
 opaque cloud. The strength of the rays does not affect the expan- 
 sion required to produce the cloud; no matter how strong the rays 
 may be there is no cloud produced unless the expansion exceeds 
 T25 : the strength of the rays increases the number of drops in 
 the cloud, but does not affect the stage at which the cloud begins. 
 The effect of the rays in producing a cloud lasts some few seconds 
 after the rays have been cut off. Wilson* has shown that the 
 radiation from uranium and other radio-active substances pro- 
 duces the same effect as Rontgen rays, as does also ultra-violet 
 light when incident upon such a metal as zinc : the effects pro- 
 duced by ultra-violet light are however somewhafc complicated and 
 we shall have to return to them again. 
 
 74. That the effect produced by Rontgen and uranium rays is 
 due to the production of charged ions produced in the gas can be 
 shown directly by the following experiment. If the ions produced 
 by the Rontgen rays act as nuclei for the water drops, then since 
 these ions can be withdrawn from the gas by applying to it a 
 strong electric field, it follows that a cloud ought not to be formed 
 by the rays when the air which is expanded is exposed to a strong 
 electric field while the rays are passing through it. This was 
 found to be the case, and the experiment is a very striking one. 
 Two parallel plates were placed in the vessel containing the dust- 
 free air : these plates were about 5 cm. apart, and were large 
 enough to include the greater part of the air between themf. The 
 
 * C. T. E. Wilson, Phil. Tram. 192, p. 403, 1899. 
 t J. J. Thomson, Phil. Mag. v. 46, p. 528, 1898. 
 
76] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 139 
 
 plates could be connected with the terminals of a battery of small 
 storage cells giving a potential difference of about 400 volts. 
 Rontgen rays passed through the gas between the plates ; the gas 
 had previously been freed from dust. When the plates were dis- 
 connected from the battery a suitable expansion produced a dense 
 cloud ; when however the plates were connected with the battery 
 only a very light cloud was produced by the expansion, and this 
 cloud was almost as dense when the Rontgen rays did not pass 
 through the air as when they did. 
 
 75. When a dense cloud has been produced by Rontgen rays 
 by an expansion between 1-25 and 1'38, or by an expansion with- 
 out Rontgen rays greater than 1*38, then for some little time after 
 drops can be produced by expansions less than 1*25, and these are 
 not eliminated by the action of an electric field. A dense fog 
 apparently leaves behind it little drops of water, which, though 
 too minute to be visible, act in the same way as particles of 
 dust, producing cloudy condensation with very slight expansions. 
 Wilson* has also shown that when electricity is discharged from a 
 pointed electrode in the expansion chamber, cloudy condensation 
 is, as in the case of exposure to Rontgen rays, much increased for 
 expansions between 1'25 and 1*38. When the discharge was stopped 
 before the expansion took place, it was found that fogs could be 
 produced for 1 or 2 minutes after the cessation of the discharge ; 
 the expansion required to produce the fog diminished as the 
 interval after the cessation of the discharge increased, showing 
 that some of the nuclei produced had grown during this interval. 
 This effect is probably due to the formation of some chemical 
 compound during the discharge, perhaps nitric acid, which by dis- 
 solving in the drops lowers their vapour pressure. 
 
 76. Wilson (loc. cit.) showed that the passage of ultra-violet 
 light through a gas (as distinct from the effects produced when it 
 is incident on a metallic surface) produces very interesting effects 
 on the condensation of clouds. If the intensity of the light is 
 small, then no clouds are produced unless the expansion equals 
 that (1'25) required to produce clouds in gases exposed to Rontgen 
 rays. If however the ultra-violet light is very intense, clouds are 
 produced in air or in pure oxygen, but not in hydrogen, by very 
 
 * C. T. R. Wilson, Phil. Tram. 192, p. 403, 1899. 
 
140 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [77 
 
 much smaller expansions, and the expansion required decreases as 
 the time of exposure to the light increases ; thus the nuclei pro- 
 ducing the clouds grow under the influence of the light. If the 
 light is exceedingly strong, clouds are produced in air or oxygen 
 without any expansion at all; these clouds are. exceedingly fine 
 and may last for hours after the light is cut off. Wilson was even 
 able to produce these clouds in air standing over a 17/ solution of 
 caustic potash, and which therefore was not saturated with water 
 vapour; in this case the drops lasted for three hours after the 
 light was cut off, so that there could be very little evaporation 
 from the drops ; this, as Wilson points out, shows that the drops 
 cannot be pure water. These clouds are probably analogous to 
 those observed many years ago by Tyndall*, when ultra-violet 
 light passes through air containing the vapours of certain sub- 
 stances of which amyl-nitrite was the one which gave the most 
 striking effects. The effects can be explained by the formation 
 under the influence of the ultra-violet light of some substance 
 Wilson suggests that in his experiments it was H 2 2 which by 
 dissolving in the drops as they form lowers the equilibrium vapour 
 pressure, and thus enables the drops to grow under circumstances 
 which would make drops of pure water evaporate. This explana- 
 tion is supported by the fact that ultra-violet light does not pro- 
 duce these clouds in water vapour by itself or in hydrogen : and 
 also by the fact that, unlike the clouds due to Rontgen rays, these 
 clouds formed by ultra-violet light do not diminish in density when 
 a strong electric field is applied to the gas, showing that the nuclei 
 are either not charged or that if they are charged they are so 
 loaded with foreign molecules that they do not move perceptibly 
 in the electric field. 
 
 77. Buisson f, who examined this question with great care, could 
 not detect any conductivity in the air through which the ultra-violet 
 light passed. Lenardj has however shown recently that a certain 
 kind of ultra-violet light which is absorbed so quickly by the air 
 as to be extinguished within a space of a few centimetres when the 
 air is at atmospheric pressure, does produce electrical conductivity 
 
 * J. Tyndall, Phil. Trans. 160, p. 333, 1870. 
 
 f Buisson quoted by Perrin, Theses presentees a la Faculte des Sciences de Paris, 
 1897, p. 31. 
 
 J Lenard, Drude's Annalen, i. p. 486 ; iii. p. 298, 1900. 
 
78] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 141 
 
 'if 
 
 in the gas through which it passes, and that a charged conductor 
 placed in the neighbourhood of air traversed by these rays loses its 
 charge, and does so much more rapidly when the charge is positive 
 than when it is negative. Lenard determined the velocity of the 
 negative ions by a method analogous to that described on page 38 
 and found for this velocity through air at atmospheric pressure 
 3*13 cm./sec. under a potential gradient of a volt per cm.: this is 
 about twice the velocity of the ions produced by Rontgen rays: 
 on the other hand the velocity of the positive ions under the same 
 potential gradient was not more than "0015 cm./sec., which is only 
 about one thousandth part of the velocity of the positive ion pro- 
 duced by Rontgen rays. The greater mobility of the negative 
 ions explains why the leak from a positively charged body in the 
 neighbourhood of the ionised gas is so much more rapid than 
 that from a negatively charged one. We shall return to this point 
 in the chapter on the effect of ultra-violet light on gases. 
 
 78. The results obtained by Wilson and Lenard seem to point 
 to the conclusion that when gas is exposed to the action of ordinary 
 ultra-violet light, we have some chemical action taking place 
 which results in the formation of a product which by dissolving 
 in water lowers the vapour pressure over the drops and thus 
 facilitates their formation. Whenjthese drops are exposed to the 
 influence of ultra-violet light of the kind investigated by Lenard, 
 they lose, as so many other bodies do when illuminated by light 
 of this kind, negative electricity, and it is the negative ions 
 liberated in this way which produce the electrical conductivity 
 investigated by Lenard. The difference between the action of 
 ultra-violet light and Rontgen rays is that the former when very 
 intense can produce clouds with little or no expansion, while the 
 latter cannot ; this on the theory given above is due to ultra- 
 violet light being more efficient than Rontgen rays in promoting 
 chemical action ; there are many examples of this, e.g. the com 
 bination of hydrogen and chlorine. 
 
 The influence of minute traces of soluble substances in pro- 
 moting the formation of clouds has been shown in a very straight- 
 forward way in some experiments made by H. A. Wilson*. The 
 writerf has shown how drops, even if their existence is very 
 
 * H. A. Wilson, Phil. Mag. v. 45, p. 454, 1898. 
 
 t J. J. Thomson, Phil. Mag. v. 36, p. 313, 1893 ; B. A. Report, 1894. 
 
142 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [79 
 
 transient, would facilitate the progress of chemical combination 
 between the gases surrounding them, and how this action would 
 afford an explanation of the remarkable fact investigated by 
 Baker* and Pringsheimf, that the occurrence of some of the best 
 known cases of chemical combination between gases depends upon 
 the presence of moisture and does not take place in gases dried 
 with extreme care. 
 
 79. Nuclei from metals. C. T. R. Wilson J has shown that 
 certain metals produce nuclei which cause cloudy condensation 
 when the expansion exceeds T25, although the effects are much 
 more marked when the expansion is increased to 1'30. The amount 
 of this effect depends greatly upon the kind of metal used : amal- 
 gamated zinc gives comparatively dense clouds, polished zinc and 
 lead also show the effect well ; on the other hand polished copper 
 and tin produce no appreciable effect. The order of the metals 
 in respect to their power of producing nuclei for cloudy condensa- 
 tion is the same as their order in respect to their power of 
 affecting a photographic plate placed at a small distance from their 
 surface, a subject which has been studied by Russell and ColsonjL 
 The effect produced by the presence of a metal on clouds in 
 hydrogen is very slight. 
 
 Although the expansion required to produce cloudy condensa- 
 tion when metals are present is the same as when charged ions 
 are produced by Rontgen rays, the metal effect differs from the 
 Rontgeii ray effect inasmuch as it is not diminished by the appli- 
 cation of an intense electric field. It is possible however that in 
 still air the ionised gas is confined to a layer close to the surface 
 of the metal, and that the rush of gas caused by the sudden 
 expansion detaches the layer and scatters the ions throughout the 
 volume of the gas. If this be the case, then, since the ions are 
 only free during the short time the expansion is taking place, they 
 will not be appreciably affected by the electric field, which cannot 
 in the short time at its disposal sweep the ions from the gas. 
 The existence of such a layer of ionised gas next the metal is 
 
 * Baker, Phil. Tram. 179, p. 571, 1888. 
 
 t Pringsheim, Wied. Ann. xxxii. p. 384, 1887. 
 
 J C. T. R. Wilson, Phil. Trans. 192, p. 403, 1899. 
 
 Russell, Proc. Eoy. Soc. Ixi. p. 424, 1897 ; Ixiii. p. 102, 1898. 
 
 || Colson, Comptes Rendus, 123, p. 49, 1896. 
 
79] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 143 
 
 , 
 
 rendered very probable by the effects which are known to 
 accompany the splashing of drops of water, mercury and many 
 other liquids. Thus Lenard* showed that when drops of water 
 splashed against a metal plate, the drops of water became posi- 
 tively electrified while there was negative electrification in the 
 surrounding air. Air shaken up in a bottle containing mercury 
 becomes negatively electrified. Lord Kelvin f has shown that when 
 air is bubbled through water it comes off charged with negative 
 electricity. I have recently found that if the air is made to 
 bubble with great vigour through water, then when it leaves the 
 water it contains positive as well as negative ions, though the 
 latter are the more numerous ; air treated in this way was found to 
 discharge a body with a negative charge, though not so rapidly as 
 one with a positive one. As another illustration of electrification 
 produced by an agitation at the surface of water we may mention 
 that Holmgren | has shown that when two wet cloths are brought 
 together and then pulled suddenl^ apart electrification is pro- 
 duced, the positive electrification being on the cloth, the negative 
 in the air. He also found that when the area of a water surface 
 was changing rapidly, as for example when ripples were travelling 
 over the surface, electrification was produced, the positive elec- 
 tricity being on the water and the negative in the air. The writer 
 found that when the liquids were surrounded by pure hydrogen 
 instead of air, the electrification produced by splashing was 
 exceedingly small : Wilson, as has already been stated, found that 
 the effect produced by metals on cloudy condensation was exceed- 
 ingly small in hydrogen. These facts are sufficient to show that 
 a disturbance at the surface of a large number of substances is 
 accompanied by the spread of ions through the adjoining gas : 
 the most natural explanation of this fact is that there is on the 
 surface of these bodies a thin layer of ionised gas which can be 
 detached by mechanical agitation. It is important to notice that 
 if this layer of ionised gas were very close to the surface of the 
 metal, the ions in it would not be dispersed into the surrounding- 
 gas even though the metal were charged up so as to produce an 
 
 * Lenard, Wied. Ann. xlvi. p. 584, 1892. 
 t Lord Kelvin, Proc. Roy. Soc. Ivii. p. 335, 1894. 
 
 t Holmgren, Sur le Developpement de VelectriciiS au contact de I'air et de Veau. 
 Societe physiographique de Lond. 1894. 
 
 J. J. Thomson, Phil. Mag. v. 37, p. 341, 1894. 
 
144 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [80 
 
 electric field of very considerable strength. For suppose we have 
 a charge e at a point P at a distance r from a plane conducting 
 surface, then there will, in consequence of the electricity of 
 opposite sign induced on the plane, be a pull on the charge at P 
 towards the plane equal to e 2 /4r 2 ; if there is an external field of 
 strength F tending to make the charged body move away from 
 the plane, this will not be able to overcome the attraction towards 
 the plane unless Fe is greater than e 2 /4r 2 , or F greater than e/4r 2 . 
 Let us suppose e is equal to the charge on an ion, 3'4 x 10~ 10 in 
 electrostatic units, and that the strength of the electric field is 
 100 volts per centimetre which on the electrostatic system is 
 equal to J, then we see that the force on the ion in this strong 
 field will be towards the plate, i.e. the ion will not be driven into 
 the surrounding gas if r is less than 1'G x 10~ 5 ; we see from this 
 example that it must be exceedingly difficult to detach very thin 
 layers of ionised gases by electrical means. 
 
 80. The few nuclei that produce rain-like condensation with 
 expansions between 1*25 and 1*38 in gases not exposed to any 
 external ionising agent may possibly I think come from a layer of 
 gas torn off the water in the vessel by the disturbance caused by 
 the expansion. These nuclei, as Wilson has shown, are not removed 
 by an electric field, and yet they produce clouds with exactly the 
 same expansions as is required for the charged ions produced by 
 Rontgen rays. We have seen (see Chap. I.) that even in gases in 
 the normal state there is a small amount of conductivity, indicat- 
 ing the presence of a few free ions, and these alone would cause 
 the formation of a few drops, but if these were the nuclei mainly 
 responsible for the rain-like condensation they ought to be 
 removed by the electric field ; indeed it seems not impossible that 
 some of the nuclei which produce the electrical conductivity in 
 normal air may have diffused from the layers of ionised gas at the 
 surface of liquids or solids in contact with the gas. If, as Elster 
 and Geitel hold, the gradual increase in the rate of escape of the 
 electricity which occurs after fresh gas is brought into a closed 
 vessel is not due to the settling down of dust from the gas, then 
 this phenomenon is an additional argument in favour of the view 
 that layers of ionised gas next the surface of solids or liquids 
 exert a considerable influence on the condensation of clouds by 
 expansion. The effect could be easily explained as due to the slow 
 
81] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 145 
 
 diffusion of ionised gas from the walls of the vessel in which the 
 gas is contained. 
 
 Comparative efficiency of positive and negative ions in producing 
 condensation of clouds. 
 
 81. The writer* in 1893 made an experiment with a steam jet 
 which showed that negative electrification had a decidedly greater 
 effect in promoting condensation than positive. The following 
 arrangement was used. A vertical glass tube dipped into the steam 
 chamber, and to the top of this tube was fused a horizontal cross 
 piece, the steam issued from nozzles at the ends of the cross 
 piece ; into these nozzles pointed platinum wires were fused, and 
 these wires were connected with the terminals of a small induction 
 coil. When the coil was in action there was great condensation in 
 the two jets, but the jet at the nozzle connected with the negative 
 terminal of the coil was always denser than that connected with 
 the positive ; this was not due to any want of symmetry in the 
 tubes or differences in the nozzles, for on reversing the coil the 
 denser cloud passed from one nozzle to the other. No sparks 
 passed between the platinum electrodes, the strength of the coil 
 being only sufficient to give a non-luminous discharge from their 
 points. 
 
 Later in 1898f 1 observed indications of a similar effect when 
 clouds were produced by expansion, but the subject was first 
 systematically investigated by C. T. R. Wilson J in 1899. Wilson 
 investigated the amount of expansion required to make positive 
 and negative ions act as nuclei for the condensation of water 
 drops ; he used several methods, the arrangement of the apparatus 
 in one of these is shown in Fig. 38. The vessel in which the 
 clouds were observed was nearly spherical and about 5'8 cm. in 
 diameter. It was divided into two equal chambers by a brass 
 partition (about 1 mm. thick) in the equatorial plane ; the vessel 
 was cut in two and the edges of the two halves ground smooth, to 
 allow them to be easily cemented against the face of the partition. 
 The latter was circular and had a narrow strip of brass soldered 
 to each face extending all round the circumference excJfl*for a 
 
 * J. J. Thomson, Phil. Mag. v. 36, p. 313, 1893. 
 
 t J. J. Thomson, Phil. Mag. v. 46, p. 528, 1898. 
 
 C. T. R. Wilson, Phil. Tram. 193, p. 289, 1899. 
 
 T. G. 10 
 
146 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 
 
 [81 
 
 gap at the top. When the halves of the glass vessel were cemented 
 against these strips, a slit was left at the gap about 4 '5 cms. long 
 
 Fig. 38. 
 
 and 2'5 mm. wide on each side of the partition. This slit was 
 covered with a thin piece of aluminium cemented to the outer 
 surface of the glass and to the edge of the brass partition. A 
 thin layer of air in contact with each surface of the partition 
 could thus be exposed to Rontgen rays from a source vertically 
 over the dividing plate. Each half of the apparatus contained a 
 second brass plate parallel to the central plate and 1*8 cm. from 
 it. There was room between the sides of these plates and the 
 walls of the vessel for the air to escape when the expansion was 
 made. To keep the beam of Rontgen rays parallel to the surface 
 of the partition a lead screen with a slit 4 mm. wide was placed 
 about 2 cm. above the aluminium window of the glass vessel : 
 this screen was moved until when both plates were kept at the 
 same potential exactly equal fogs were obtained on the two sides. 
 The metal plates were covered with wet filter-paper to get rid 
 of any ions due to the metal. Suppose now that the middle 
 plate is earthed while the left-hand plate is at a lower and 
 the right-hand plate at a higher potential. Then it is evident 
 since the ionisation is confined to a layer close to the middle plate 
 thatflMfcler these circumstances the left half of the vessel will 
 contain positive ions and the right half negative ones. Wilson 
 found that with an expansion of T28 there was a dense fog in the 
 half containing the negative ions, and only a few drops in the 
 
81] 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 147 
 
 half containing the positive ones, and that this excess of con- 
 densation in the negative half continued until the expansion was 
 equal to 1'31, when little or no difference was to be seen in the 
 clouds in the two halves. Care was taken that the potential of 
 the positive plate should exceed that of the middle one by the 
 same amount as this exceeded the potential of the negative 
 plate. 
 
 The difference between the effects produced by positive and 
 negative ions is shown in the following table, where the time of 
 fall of the drops is used to measure the number of nuclei which 
 produce condensation ; if this number is small, then the water 
 drops formed round them will be large and will therefore fall 
 rapidly, while if the number of nuclei be large, since there is 
 only the same quantity of water to be distributed among them, 
 
 TIME TAKEN BY FOGS TO FALL, IN SECONDS. 
 
 Expansion 
 
 Left side 
 
 Right side 
 
 Ratio of times 
 negative /positive 
 
 1-28 
 
 positive 5 
 negative 15 
 
 negative 16 
 positive 3 
 
 5-Oj 
 
 1-30 
 
 negative 15 
 positive 5 
 negative 10 
 positive 2 
 
 positive 2 
 negative 15 
 positive 2 
 negative 10 
 
 5-0 f 
 
 5-oJ 
 
 1-31 
 
 positive 7 
 negative 14 
 
 negative 12 
 positive 7 
 
 "I 1-8 
 2-OJ 
 
 1-32 
 
 negative 8 
 positive 8 
 negative 14 
 positive 12 
 
 positive 5 
 negative 10 
 positive 8 
 negative 17 
 
 1-6 
 
 1-5 
 1-7 
 
 1-4 
 
 1-33 
 
 negative 12 
 positive 12 
 
 positive 10 
 negative 13 
 
 ;> 15 
 
 1-35 
 
 negative 10 
 positive 10 
 
 positive 10 
 negative 10 
 
 13 w . 
 
 the drops will be small and will fall slowly. In the experiments 
 referred to in the table there was a potential difference equal 
 
 102 
 
148 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [81 
 
 to that due to two Leclanche cells between the middle plate 
 and either of the outer ones. The words positive and negative 
 in the table indicate that the positive or negative ions respec- 
 tively were in excess in the region referred to. 
 
 The difference in the rates of fall of the drops with the 
 same expansions is due to irregularities in the action of the bulb 
 used to produce the Rontgen rays. The negative ions begin to 
 act as nuclei for foggy condensation when the expansion is about 
 1*25, corresponding to about a fourfold supersaturation, while we 
 see from the table that the positive ions do not begin to act 
 as nuclei until the expansion is equal to 1'31, corresponding to 
 about a sixfold supersaturation. Wilson has shown that all the 
 negative ions are caught when the expansion is equal to 1'28, 
 but that it is not until the expansion reaches 1*35 that all the 
 positive ions are caught. This is not due to the negative ions 
 having a larger electrical charge than the positive ; to show this, 
 take an expansion vessel such as that shown in Fig. 36 and ionise 
 the gas in it by Rontgen rays ; first produce a fog with an ex- 
 pansion of 1'28 (which only brings down the negative ions), and 
 determine the number of ions from the time of fall in the way 
 explained on page 124 ; then with the same intensity of radiation 
 produce a cloud. by an expansion of 1*35, which brings down both 
 the positive and negative ions, and again calculate the number 
 of ions ; we shall find it twice as great as in the .first case, thus 
 showing that the numbers of positive and negative ions are equal. 
 As the gas as a whole has no charge, the total charge on the 
 positive ions must be equal to that on the negative, hence as 
 there are as many positive ions as negative, the charge on a posi- 
 tive ion must be the same as that on a negative one. We shall 
 return to the origin of the greater efficiency of the negative 
 than of the positive ions when we discuss the theory of the 
 action of ions in promoting condensation. In the meantime we 
 may point out that this difference between the ions may have very 
 important bearings on the question of atmospheric electricity, for if 
 the ions were to differ in their power of condensing water around 
 them*hen we might get a cloud formed round one set of ions 
 and not round the other. The ions in the cloud* would fall under 
 gravity, and thus we might have separation of the positive and 
 the negative ions and the production of an electric field, the work 
 
82] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 149 
 
 required for the production of the field being done by gravity*. 
 An action of this kind would tend to make the charge in the air 
 positive, as more negative ions than positive would be carried 
 down by water drops: for a further consideration of this effect 
 we may refer the reader to the papers by Elster and Geitelf on 
 the ionic theory of atmospheric electricity. 
 
 82. Theory of the effect of ions on Condensation. The effect 
 of electrification on the evaporation of drops of water was in- 
 vestigated by the writer in Applications of Dynamics to Physics 
 and Chemistry, p. 165. The general tendency of this effect can 
 easily be seen from elementary principles : for if we have a drop of 
 water of radius a, carrying a charge e of electricity, its potential 
 energy is equal to \e~/Ka, where K is the specific inductive 
 capacity of the dielectric surrounding the drop. Now as the drop 
 evaporates the electricity remains behind, so that e does not 
 change while a diminishes, hence the potential energy due to 
 the electrification of the drop increases as the drop evaporates; 
 thus to make the drop evaporate when charged more work has 
 to be available than when it is uncharged, so that electrification 
 will diminish the tendency of the drop to evaporate, and the drop 
 will be in equilibrium when the vapour pressure of the water 
 vapour around it would not be sufficient to prevent the evaporation 
 of an uncharged drop. The surface tension of the water will, as 
 was shown by Lord Kelvin, produce the opposite effect ; for the 
 potential energy due to the surface tension is equal to 4>7ra?T, 
 where T is the surface tension; thus as the drop evaporates 
 the energy due to surface tension diminishes, so that the work 
 required to vaporise a given quantity of water is less than if 
 surface tension were absent, or, what is the same thing, as if the 
 surface were flat. Thus a curved drop will evaporate when a flat 
 one would be in equilibrium. 
 
 It is shown in Applications of Dynamics to Physics and 
 Chemistry, p. 165, that when &p, the change in the vapour pres- 
 sure due to the electrification and surface tension, is only a small 
 fraction of the original vapour pressure p, 
 gp == J L _f2T_ # \ 
 ~~ 
 
 __ _ 
 
 p RO \ a 87rKa*} a- - p ' 
 
 * J. J. Thomson, Phil. Mag. v. 46, p. 528, 1898. 
 
 t Elster and Geitel, Ptiysikalische Zeitschrift, i. p. 245, 1900. 
 
150 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [82 
 
 cr is the density of water, p that of the vapour, 6 the absolute 
 temperature, R the constant which occurs in the equation for 
 a ' perfect' gas, p = Rdp ; in the investigation this equation is 
 assumed to hold for the water vapour. When the change in the 
 pressure is not a small fraction of the equilibrium vapour pressure 
 for an infinitely large drop, then the investigation already alluded 
 to shows that the preceding equation has to be replaced by 
 
 Mlocr P 
 
 log* 4 
 
 where p and p are the equilibrium vapour pressure and density 
 for a drop of radius a, P and p' the corresponding quantities for 
 a drop of infinite radius. Since p' p is small compared with a-, 
 this equation becomes approximately 
 
 We see from this equation that if e is zero the equilibrium 
 vapour pressure p for a drop of finite size is always greater than P, 
 so that such a drop would evaporate unless the vapour around 
 it were supersaturated ; when however the drop is electrified this 
 is no longer the case, for we see from equation (1) that in this 
 case if the vapour is saturated, i.e. if the vapour pressure is P, the 
 drop will grow until its radius a is given by the equation 
 
 2T 
 
 a SirKa 4 
 
 = 0. 
 
 Thus if the drop were charged with the quantity of electricity 
 carried by a gaseous ion, i.e. 3'4 x 10~ 10 electrostatic units, and if 
 the surface tension of the small drop had the value 76, which is the 
 value for thick water films, then a would be equal to l/3'2 x 10 7 , 
 and thus each gaseous iou would be surrounded by a drop of 
 water of this radius; if we call this radius c, then equation (1) 
 may be written 
 
 R6c loge^ = 2Tx(l-x?) (2), 
 
 where x = cja. This equation enables us to find $he size of a drop 
 corresponding to any vapour pressure. 
 
 For water vapour at 10 C., RB is equal to T3 x 10 9 . Putting 
 
83] ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 151 
 
 for c the value previously found and T= 76, equation (2) becomes 
 approximately 
 
 (3). 
 
 From this equation we see that even in a space far from saturated 
 with water vapour, i.e. when p is only a fraction of P, drops will be 
 formed, and that the size of these drops diminishes only very slowly 
 as the quantity of water vapour in the surrounding air diminishes ; 
 thus, if we diminish the quantity of water vapour in the air to 
 I/e, i.e. 1/2*7 of that required to saturate it, we see from equation 
 (3) that the radius of the drops formed round the ions would only 
 be a little less than 10/11 of the radius of the drop formed in 
 saturated air : and that to reduce the drop to half the radius 
 corresponding to saturation, we should have to dry the air so 
 completely that p/P was only about 1/3 x 10 16 . We have seen that 
 there are always ions present in the air, hence there will always 
 be small drops of water present if there is any water vapour in the 
 air ; if, as has been suggested, these drops play a part in certain 
 cases of chemical combination, the preceding numerical example 
 will show the difficulty of getting the gas dry enough to produce 
 a substantial reduction in the volume of these charged drops. 
 
 83. Supersaturation required to make one of the charged drops 
 grow to a large size. As the radius of the drop increases from c 
 to an infinite size, x diminishes from unity to zero. Now the right- 
 hand side of equation (2) vanishes at each of these limits, but 
 between them it reaches a maximum value which occurs when 
 
 4-tf 3 = 1 or x - , when x(l a?) reaches the value '471 ; hence 
 I'oo 
 
 we see from equation (3) that for the drops to increase to a large 
 size \og e p/P must reach the value 1/7 approximately. Hence for 
 the drops to grow p/P must be about 5*3 : this, on the theory we 
 have given, is the amount of supersatu ration required to make 
 large drops grow round the ions. We have seen from Wilson's 
 experiment that it actually requires a four- fold supersaturation, 
 but as in the theory the saturated water vapour was assumed to 
 obey Boyle's law, and the surface tension was assumed to have 
 the value it has for thick films, neither of which assumptions 
 is likely to be true, the agreement between the theory and the 
 experiments is as close as could be expected. 
 
152 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [84 
 
 84. Wilson showed that even when there is no external ionisa- 
 tion a dense cloud, the nuclei of which are not charged, is produced 
 by an eight-fold supersaturation : we can by the aid of equation (1) 
 determine the radii of these nuclei, supposed spherical ; putting 
 in that equation e = 0, T= 76, R6 = 1'3 x 10 9 , and p/P = 8, we 
 find that a, the radius of the nucleus which produces this kind 
 of condensation, is equal to 1/1*9 x 10 7 . This nucleus is thus 
 slightly larger than the drop which collects round an ion, as we 
 found that the radius of this drop is l/3'l x 10 7 . With regard 
 to the nature of the nuclei which produce the cloud corresponding 
 to the eight- fold supersaturation, Wilson has proved that the 
 amount of supersaturation required to produce the cloud is the 
 same in air, oxygen, hydrogen, and carbonic acid; the size of 
 the nuclei is therefore the same in all these gases ; it is thus very 
 improbable that they consist of aggregations of the molecules of 
 the gas, it would seem most likely that they are minute drops 
 of water which are continually being formed from the saturated 
 vapour and then evaporating, but lasting sufficiently long to 
 enable them to be caught during the sudden expansion, and 
 to act as the nuclei round which the drops in the cloud condense. 
 These minute drops of water are not however all of the same 
 size, for after passing the expansion 1*38 the density of the cloud 
 increases very rapidly as the expansion increases, showing that 
 many more nuclei become efficient when the expansion increases. 
 This behaviour of the cloud indicates that there are little drops 
 of water of different sizes, the small ones being more numerous 
 than the larger ones, and that there is a fairly definite limit to 
 the size of the drop, the number of drops whose size exceeds 
 this limit being too small to produce an appreciable cloud. This 
 collection of drops of different sizes is what we might expect if 
 we regard the little drops as arising from coalescence of molecules 
 of water vapour, and the larger drops from the coalescence of the 
 smaller ones. 
 
 85. The fact that the drops are of different sizes indicates that 
 they are not in a state of equilibrium with regard to evaporation 
 and condensation, and the drops have probably a very ephemeral 
 existence. It may however be pointed out that on the view of 
 the relation between surface tension and the thickness of water 
 films, to which Reinold and Riicker were led by their experi- 
 
86] 
 
 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. 
 
 153 
 
 ments on very thin films, drops of pure water of a definite radius 
 might be in equilibrium with saturated water vapour even if they 
 were not charged. For according to these physicists the relation 
 between the surface tension and the thickness of the film is re- 
 presented by a curve of the type shown in Fig. 39, the ordinates 
 
 Thickness 
 
 Fig. 39. 
 
 representing the surface tension and the abscissae the thickness 
 of the film : this curve shows maxima and minima values for the 
 surface tension. 
 
 Now consider the case of a drop whose diameter is a little 
 greater than OM ; in this case as the radius of the drop increases 
 the surface tension diminishes ; the potential energy due to surface 
 tension is proportional to the product of the surface tension T 
 and the area of the surface 4?ra 2 ; hence if we can find a point 
 
 dT 2T 
 
 between Q and T where S (T . 4?ra 2 ) = or T = , any small 
 
 change in the size of the drop would not be accompanied by a 
 change in the potential energy due to surface tension. Thus 
 surface tension would not affect the conditions of equilibrium 
 between the liquid and the water vapour, so that if the volume 
 were saturated with equilibrium the drop would be in equi- 
 librium. 
 
 86. We have seen that water vapour condenses more easily 
 on a negative than on a positive ion, while the velocity of the 
 negative ion under a given electric field is greater than that of 
 the positive ion : the second result seems to indicate that the 
 size of the system, consisting of the negative ion and whatever may 
 be attached to it, is smaller than the system for the positive ion, 
 
154 ON SOME PHYSICAL PROPERTIES OF GASEOUS IONS. [86 
 
 while the first indicates that it is larger. We must remember, 
 however, that the velocity of an ion under an electric field is the 
 average velocity estimated for the life of an ion. Now we have 
 seen that the negative ion when first liberated is what we have 
 called a corpuscle, and its mass is exceedingly small compared 
 with that of the positive ion; thus at first the velocity of the 
 negative ion will be greater than that of the positive, but in 
 consequence of its greater mobility the negative ion is more 
 likely than the positive to attach itself to foreign bodies in its 
 neighbourhood, say to those minute drops of water which an 
 expansion greater than T38 brings into evidence ; thus though 
 the negative ion starts by being smaller than the positive, it may 
 before it recombines with a positive ion to form a neutral system 
 have become the centre of an aggregation greater than that 
 surrounding the positive ion. The efficiency of an ion as a 
 nucleus for condensation depends upon the maximum size of 
 the aggregation, while the velocity under the electric field depends 
 upon the average size ; the average size of a negative ion may 
 easily be less than that of a positive ion, since the negative is 
 so much smaller to begin with, while the greater mobility of the 
 negative is likely to make it in the end the centre of a larger 
 system than the positive. 
 
CHAPTER VIII. 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 87. WE shall now proceed to the study of some special cases of 
 ionisation, beginning with that due to incandescent metals. That 
 the air in the neighbourhood of red-hot metals is a conductor 
 of electricity has been known for nearly two centuries ; the earliest 
 observations seem to have been made by Du Fay* in 1725, by Du 
 Tourf in 1745, by Watsonj in 1746, by Priestley in 1767, and 
 by Cavallojl in 1785. Becquerellj in 1853 showed that air at 
 a white heat would allow electricity to pass through it even when 
 the potential difference was only a few volts. Blondlot** confirmed 
 and extended this result, and proved that air at a bright red heat 
 was unable to insulate under a difference of potential as low as 
 1/1000 of a volt ; he showed, too, that the conduction through 
 the hot gas was not in accordance with Ohm's law. Recent 
 researches have thrown so much light on the causes at work in the 
 ionisation of gases in contact with glowing solids, that it is un- 
 necessary to enter into these earlier investigations in greater 
 detail. Guthrieff seems to have been the first to call attention to 
 one very characteristic feature of ionisation by incandescent metals, 
 i.e. the want of symmetry between the effects of positive and nega- 
 tive electrification. He showed that a red-hot iron ball in air 
 could retain a charge of negative but not of positive electrification, 
 while a white-hot ball could not retain a charge of either positive 
 or negative electrification. 
 
 * Du Fay, Mem. de VAcad. 1733. 
 
 t Du Tour, Mem. de Mathematique et de Physique, xi. p. 246, 1755. 
 
 Watson, Phil. Trans, abridged, vol. x. p. 296. 
 
 Priestley, History of Electricity, p. 579. 
 
 || Cavallo, Treatise on Electricity, vol. i. p. 324. 
 
 H Becquerel, Annales de Chimie et de Physique, iii. 39, p. 355, 1853. 
 ** Blondlot, Comptes Rendus, xcii. p. 870, 1881 ; civ. p. 283, 1887. 
 ft Guthrie, Phil. Mag. iv. 46, p. 257, 1873. 
 
156 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 [88 
 
 88. The ionisation produced by incandescent metals was in- 
 vestigated systematically in great detail by Elster and Geitel*, 
 who used for this purpose the apparatus represented in Fig. 40. 
 
 Battery 
 
 To Electrometer 
 
 Battery 
 
 Fig. 40. 
 
 This is a glass vessel containing an insulated metal plate A, 
 which is connected with one pair of quadrants of an electrometer. 
 Underneath this plate there is a fine metallic wire, which can 
 be raised to incandescence by an electric current passing through 
 the leads C, D ; to prevent any disturbing effects arising from the 
 change produced by the current in the electric potential of the 
 wire, the middle point of the wire was connected with the earth. 
 Let us first take the case when the gas in the vessel is air or 
 oxygen at atmospheric pressure, then, as soon as the glow of 
 the hot wire begins to be visible, the metal plate receives a 
 positive charge ; this charge increases until the potential of the 
 plate reaches a value which varies very much with the dimensions 
 of the apparatus used : in Elster and Geitel's experiments it was of 
 the order of a few volts. This potential increases as the tempera- 
 ture of the wire increases, until the wire is at a yellow heat ; at 
 
 * Elster and Geitel, Wied. Ann. xvi. p. 193, 1882 ; xix. p. 588, 1883 ; xxii. p. 123, 
 1884; xxvi. p. 1, 1885; xxxi. p. 109, 1887; xxxvii. p. 315, 1889. Wien. Berich. xcvii. 
 p. 1175, 1889. 
 
89] IONISATION BY INCANDESCENT SOLIDS. 157 
 
 this stage the potential of the plate is a maximum. After passing 
 this stage the potential diminishes as the wire gets hotter and 
 hotter, until at a bright white heat the charge received by the 
 plate is very small. 
 
 The electrification on the plate is very much influenced by the 
 pressure of the gas. Starting at atmospheric pressure and gradually 
 exhausting the vessel, we find that at first the change of pressure 
 does not produce any great effect upon the potential of the plate A, 
 but when we approach very high exhaustions, such as those in 
 Crookes' tubes, the potential of the plate begins to diminish, until at 
 very low pressures it changes sign and may as the exhaustion pro- 
 ceeds reach a very large negative value. The pressure at which the 
 change in sign of the electrification of the plate takes place depends 
 upon the temperature of the wire, the higher the temperature the 
 higher the pressure at which the reversal of the electrification 
 occurs. Again, long-continued incandescence of the wire favours 
 the negative electrification of the plate ; the physical condition of 
 the platinum wire is changed by long-continued heating, and the 
 wire becomes brittle. The following experiment, due to Elster 
 and Geitel *, seems to indicate that the gases absorbed in the 
 platinum wire and which are gradually, bui; only very gradually, 
 expelled by long-continued heating, play a considerable part in 
 the electrical phenomena connected with the incandescence of 
 metals. They found that if the platinum wire was kept glowing 
 in a fairly good vacuum long enough for the metal plate to receive 
 a negative charge, the introduction of a very small quantity of 
 fresh gas reversed the sign of electrification on the metal plate, 
 and the pressure had to be reduced far below the original value for 
 the negative electrification to be recovered. 
 
 89. The effects are also complicated by the dust and vapour 
 given off by the glowing platinum, and which form a deposit on the 
 walls of the vessel. The production of this dust can very easily oe 
 shown by the study of clouds formed by the method described in 
 Chapter VII. If a fine platinum wire is fused into the expansion 
 apparatus, and the air rendered dust-free in the usual way, so that 
 no clouds are produced by an expansion less than 1*25, dense 
 clouds will be formed by comparatively small expansions after 
 a current has been sent through the wire strong enough to raise it 
 * Elster and Geitel, Wien. Berich. xcvii. p. 1175, 1889. 
 
158 IONISATION BY INCANDESCENT SOLIDS. [90 
 
 to incandescence* ; indeed it is not necessary to make the wire so 
 hot as to be luminous, an increase in the temperature of the 
 
 wire to 200 or 300 C. is sufficient to produce the cloud. 
 
 t 
 The sign of the electrification produced by glowing substances 
 
 is influenced by the nature of the substances and of the gas 
 surrounding them ; thus in hydrogen Elster and Geitelf showed 
 that the plate above the incandescent wire became negatively 
 electrified even when the hydrogen was at atmospheric pressure. 
 This electrification continually increased with the temperature. 
 To get the negative electrification, however, the wire must be at 
 least at a bright yellow heat ; at lower temperatures the electrifica- 
 tion is positive ; a clean copper wire, on the other hand, gives a 
 positive electrification in hydrogen, unless the pressure is very low. 
 
 Elster and Geitel showed that the sign of the electrification 
 in water vapour and the vapours of sulphur and phosphorus was 
 the same as in air ; they could detect no electrification in mercury 
 vapour. 
 
 90. The influence of the nature of the incandescent substance 
 is shown by the fact that with incandescent carbon filaments the 
 electrification on the metal plate is always negative. It is also 
 shown clearly by some experiments made by BranlyJ. Branly's 
 method was as follows : he hung up a charged insulated conductor 
 in the neighbourhood of the incandescent body ; he found that 
 when the latter was a piece of platinum at a dull red heat the 
 insulated conductor lost a negative but not a positive charge; when 
 the platinum was white hot the conductor was discharged whether 
 electrified positively or negatively. If the incandescent body was 
 an oxide and not a pure metal, at any rate if it was an oxide of 
 one of the metals tried by Branly, viz. lead, aluminium or bismuth, 
 then it would discharge a positively electrified body but not a 
 negatively electrified one, which is exactly opposite to the effect 
 produced by a pure metal at a dull red heat. 
 
 91. M c Clelland sucked the gases from the neighbourhood of 
 the incandescent wire and then investigated their properties. He 
 
 * K. v. Helmholtz, Wied. Ann. xxxii. p. 1, 1887. Lodge, Nature, xxxi. p. 267, 
 1884. 
 
 t Elster and Geitel, Wied. Ann. xxxi. p. 109, 1887. 
 
 t Branly, Comptes Eendus, cxiv. p. 1531, 1892. 
 
 M c Clelland, Proc. Camb. Phil. Soc. x. p. 241, 1900. * 
 
92] IONISATION BY INCANDESCENT SOLIDS. 159 
 
 found that as soon as the wire began to glow the gas would 
 discharge a negatively but not a positively electrified body; when 
 the temperature of the electrified body was increased by about 
 400 C., the gas began to discharge a positively electrified body, 
 though not so freely as it did a negatively electrified one ; when 
 the wire got to a bright yellow heat the gas discharged both 
 positive and negative electricity with equal facility. M c Clelland 
 investigated the laws of conduction of electricity through the gas 
 which had been in contact with the glowing wire; he found that it 
 showed all the characteristics of conduction through a gas contain- 
 ing ions ; thus the relation between the current and the electro- 
 motive force is represented by a curve like Fig. 5, the current 
 soon reaching saturation. M c Clelland also determined the velocity 
 in an electric field of the ions, produced by the incandescent metal. 
 He found that their velocity was small compared with that of the 
 ions produced by Rontgen rays, and that the hotter the wire the 
 smaller was the velocity of the ions. 
 
 92. The account we have already given of the effects observed 
 in the neighbourhood of an incandescent wire shows that the 
 electrification produced in this way is a very complicated pheno- 
 menon, and depends : 
 
 (1) On the temperature of the wire. 
 
 (2) On the pressure of the gas around the wire. 
 
 (3) On the nature of the gas. 
 
 (4) On the nature of the incandescent wire. 
 
 We shall simplify the investigation of the cause of this electrifi- 
 cation if we study a case in which as many as possible of these 
 effects are eliminated. Now (2) and (3) are eliminated if we work 
 with the highest attainable vacuum ; in this case the phenomena 
 are greatly simplified and exhibit points of remarkable interest. 
 To investigate them we may use a piece of apparatus like that 
 shown in Fig. 41. It consists of a straight piece of fine wire AB, 
 which can he heated to any desired temperature by an electric 
 current led hi through the leads CA, DB. Around this wire and 
 insulated from it is a metallic cylinder, shown in section in EF and 
 GH; this cylinder should be longer than, and coaxial with, the 
 wire. This system is sealed into a glass vessel connected with an 
 air pump and the pressure reduced as low as possible, say to 
 
160 IONISATION BY INCANDESCENT SOLIDS. [93 
 
 001 mm. of mercury. It is desirable to keep the wire red hot for 
 a very considerable time (I have found a week not too long), in 
 
 Fig. 41. 
 
 order to expel gases absorbed in the wire ; until these are got rid 
 of the behaviour of the wire is very irregular. The vessel should 
 be pumped from time to time while the wire is hot, to get 
 rid of the gases coming out of the wire; it will be necessary 
 to exhaust the vessel from time to time, even after these have 
 been expelled, as the heat coming from the wire seems to liberate 
 gas from the walls of the glass vessel and the metal cylinder. 
 Connect the hot wire to one terminal of a battery and the cylinder 
 to the other, and place in the circuit a sensitive galvanometer. If 
 now the wire be made red hot and connected with the negative 
 pole of the battery, an appreciable current will go through the 
 galvanometer ; if, however, the terminals are reversed so that the 
 hot wire is connected with the positive pole of the battery, the 
 current which passes is too small to be detected by the galvano- 
 meter ; thus there can be a current through the exhausted vessel 
 when the negative electricity goes from the hot wire to the cold 
 cylinder, but not an appreciable one when the positive electricity 
 would have to go from the wire to the cylinder ; the system can 
 thus transmit a current in only one direction. The current does 
 not obey Ohm's law: at first it increases with the electromotive 
 force, but it soon reaches a saturation value beyond which it does 
 not increase, even though the electromotive force is increased, 
 provided the increase is not sufficient to enable the field itself to 
 ionise the gas. In some experiments made by the author, about 
 10 volts was sufficient to produce the saturation current. 
 
 93. The saturation current increases very rapidly with the 
 temperature. This is well shown by the curve in Fig. 42, which 
 
93] 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 161 
 
 represents the results of the experiments made by O. W. Richard- 
 son*, in the Cavendish Laboratory, on the saturation current 
 between a hot platinum wire and a metal cylinder surrounding it 
 
 220 
 20O 
 180 
 160 
 140 
 I 20 
 
 J 100 
 
 
 
 
 SO 
 
 60 
 
 40 
 
 20 
 
 1010 SO 
 
 90 130 /70 2/0 
 Temperature Centigrade. 
 Fig. 42. 
 
 in a high vacuum. The temperatures were obtained by measuring 
 the resistance of the wire. Richardson found that the relation 
 between the saturation current / and the absolute temperature 
 6 could be expressed by an equation of the form 
 
 0. W. Richardson, Proc. Camb. Phil. Soc. xi. p. 286, 1902. 
 
 T. G. 
 
 11 
 
162 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 [94 
 
 for the curve in Fig. 42, 
 
 a = 1-51 x 10 26 , b = 4-93 x 10 4 . 
 
 In the case of this wire the current amounted to about 
 4 x 10~ 4 amperes at the temperature 1500 C., which represents 
 a rate of emission of negative electricity from the hot wire of above 
 one milliampere per square centimetre of surface. If the same 
 formula held up to the melting point of platinum, which we shall 
 take to be 2000 C., the rate of emission of negative electricity 
 from the glowing wire would be about 1/10 of an ampere per 
 square centimetre. 
 
 The rate of escape of negative electricity from glowing carbon 
 in some cases greatly exceeds that from glowing platinum. This 
 is no doubt chiefly owing to the fact that the carbon can be 
 raised to a much higher temperature than the platinum. 
 Richardson has obtained from carbon filaments in a good vacuum 
 currents of the order of an ampere per square centimetre of 
 surface. 
 
 94. This escape of negative electricity from glowing carbon in 
 high vacua is the cause of an effect observed in incandescent electric 
 lamps, known as the Edison effect, and which has been studied by 
 Preece* and in great detail by Flemingf. The 'Edison effect' 
 
 Fig. 43. 
 
 is as follows : Suppose that ABC represents the carbon filament 
 of an incandescent lamp, and that an insulated metal plate is 
 
 * Preece, Proc. Roy. Soc. xxxviii. p. 219, 1885. 
 
 t Fleming, Proc. Roy. Soc. xlvii. p. 118, 1890 ; Phil. Mag. xlii. p. 52, 1896. 
 
94] IONISATION BY INCANDESCENT SOLIDS. 163 
 
 inserted between the filaments ; then if the positive end A of the 
 filament is connected with a wireD leading from the metallic plate 
 and a galvanometer inserted between A and D, a considerable 
 current, amounting in some of Fleming's experiments to three or 
 four milliarnperes, passes through the galvanometer, the direction 
 of the current being from A to D through the galvanometer. If, 
 however, the metal plate is connected with the negative electrode 
 of the lamp and a galvanometer inserted in this circuit, the current 
 through the galvanometer is exceedingly small compared with that 
 observed in the preceding case. We see that this is what would 
 occur if there was a vigorous discharge of negative electricity from 
 the negative leg of the carbon filament, and no discharge or 
 a much smaller one from the positive leg ; this would tend to 
 make the potential of the metal plate differ but little from that of 
 the negative leg of the carbon loop, while the difference of 
 potential between the positive leg and the plate would be nearly 
 that between the electrodes of the lamp, and consequently the 
 current through a circuit connecting the positive electrode to the 
 metallic plate would be much greater than through one connecting 
 the negative electrode to the plate. 
 
 Fleming showed that when the negative leg of the carbon loop 
 was surrounded by a cylinder made either of metal or of an 
 insulating substance, the Edison effect disappeared almost entirely. 
 Fleming too found, as Elster and Geitel had previously shown by 
 a somewhat different method, that a current of electricity could 
 pass between an incandescent carbon filament arid a cold electrode, 
 if the direction of the current was such as to cause the negative 
 electricity to pass from the hot filament to the cold plate, and that 
 a current would not pass in the opposite direction. Elster and 
 Geitel showed, too, that a plate placed near an incandescent fila- 
 ment received even in very high vacua a charge of negative 
 electricity. The behaviour of the hot filament shows that it, like 
 the incandescent platinum wire, emits negative electrification. 
 That the emission from the carbon filament is much greater than 
 that from the platinum wire great as we have seen the latter to 
 be is shown by the fact that although, as Fleming (loc. cit) has 
 shown, the 'Edison effect' can be observed with an incandescent 
 platinum wire in place of the carbon filament, the effect with 
 platinum is exceedingly small compared with that with carbon, and 
 
 112 
 
164 IONISATION BY INCANDESCENT SOLIDS. [95 
 
 is only appreciable when the platinum is so hot that it is on the 
 point of melting. 
 
 95. There can thus be no doubt that from incandescent metals 
 and carbon there is a very rapid escape of negative electricity. The 
 question arises, What are the carriers of this electrification ? The 
 answer to this question seems at first sight obvious, for both the 
 carbon filament and the platinum wire volatilise, or at any rate 
 give off dust if not vapour at high temperatures. This is shown 
 by the familiar deposit of carbon on the glass of incandescent 
 lamps, and of platinum or platinum oxide on the walls of an 
 exhausted vessel in which a platinum wire has been glowing for 
 a long period. It seems natural, therefore, to regard the carriers 
 of the negative electricity as the molecules or atoms of carbon 
 or platinum vapour. We might, however, be led to suspect the 
 accuracy of this view when we observe the enormous quantities of 
 negative electricity which can be discharged by a small piece of 
 very thin wire ; quantities which are inconsistent with that law of 
 electrolysis which states that to carry a quantity of electricity E 
 we require a mass of a substance Ee, where e is the electrochemical 
 equivalent of the substance. 
 
 We can, however, determine by the method of Art. 51 the 
 ratio of the charge e to the mass m of the carriers of the 
 negative electricity from an incandescent wire. The results of 
 this determination, which are given in Art. 51, are conclusive, 
 for they show that the value of e/m for these carriers is the 
 same as its value for the carriers of the negative electricity in the 
 cathode rays, and in the discharge of negative electricity from 
 metals placed in a good vacuum and illuminated by ultra-violet 
 light. Thus the negative electricity from the hot wire is carried 
 by the same carriers as the cathode rays, i.e. by ' corpuscles,' those 
 small negatively electrified bodies of constant mass which in all 
 the cases yet investigated act as the carriers of negative electricity 
 in high vacua. 
 
 We thus are led to the conclusion that from an incandescent metal 
 or glowing -piece of carbon ' corpuscles ' are projected, and though we 
 have as yet no exact measurements for carbon, the rate of emission 
 must, by comparison with the known much smaller rate for plati- 
 num, amount in the case of a carbon filament at its highest point of 
 
95] IONISATION BY INCANDESCENT SOLIDS. 165 
 
 incandescence to a current equal to several amperes per square 
 centimetre of surface. This fact may have an important applica- 
 tion to some cosmical phenomena, since, according to the generally 
 received opinion, the photosphere of the sun contains large, 
 quantities of glowing carbon; this carbon will emit corpuscles 
 unless the sun by the loss of its corpuscles at an earlier stage 
 has acquired such a large charge of positive electricity that the 
 attraction of this is sufficient to prevent the negatively electrified 
 particles from getting right away from the sun ; yet even in this 
 case, if the temperature were from any cause to rise above its 
 average value, corpuscles would stream away from the sun into the 
 surrounding space. We may thus regard the sun, and probably 
 any luminous star, as a source of negatively electrified particles 
 which stream through the solar and stellar systems. Now when 
 corpuscles moving at a high speed pass through a gas they make 
 it luminous ; thus when the corpuscles from the sun meet the 
 upper regions of the earth's atmosphere they will produce 
 luminous effects. Arrhenius* has shown that we can explain in 
 a satisfactory manner many of the periodic variations in the 
 Aurora Borealis if we assume that it is caused by corpuscles 
 from the sun passing through the upper regions of the earth's 
 atmosphere. 
 
 The emission of corpuscles from incandescent metals and 
 carbon is readily explained by the view for which we find con- 
 firmation in many other phenomena that corpuscles are dis- 
 seminated through metals and carbon, not merely when these are 
 incandescent, but at all temperatures ; the corpuscles being so 
 small are able to move freely through the metal, and they may 
 thus be supposed to behave like a perfect gas contained in a 
 volume equal to that of the metal. The corpuscles a*e attracted 
 by the metal, so that to enable them to escape into the space 
 surrounding it they must have sufficient kinetic energy to carry 
 them through the layer at its surface, where its attraction 
 of the corpuscles is appreciable. If the average kinetic energy 
 of a corpuscle like that of the molecule of a gas is proportional 
 to the absolute temperature, then as the temperature increases, 
 more and more of the corpuscles will be able to escape from the 
 metal into the air outside. 
 
 * Arrhenius, Physikalische Zeitschrift, ii. pp. 81, 97, 1901. 
 
166 IONISATION BY INCANDESCENT SOLIDS. [96 
 
 Rate at which the corpuscles escape from the metal. 
 
 96. We can without much difficulty find an expression for 
 this quantity if we assume that the corpuscles in the rnetal behave 
 like a perfect gas. Let AB, CD represent two planes parallel to 
 the surface of the metal including between them the region in 
 which the metal exerts an appreciable force upon the corpuscle. 
 Let us take the axis of x at right angles to these planes, the posi- 
 tive direction of x being from the air to the metal ; then if p is 
 the pressure due to the corpuscles, n the number of corpuscles in 
 unit volume, X the force acting on a corpuscle, we have when 
 there is equilibrium 
 
 ; 
 
 but if the corpuscles behave like a perfect gas p = ftOn, where 6 is 
 the absolute temperature and ft a constant which is the same for 
 all gases ; substituting this value for p in equation (1), we get 
 
 integrating this equation from CD to AB, we get 
 
 , n w 
 
 lo *;Sr-jg3' 
 
 or ri=Ne~& ........................... (3), 
 
 where n' and N are respectively the numbers of corpuscles in unit 
 volume of the air and metal, and 
 
 w IXdx; 
 
 thus w is the work required to drag a corpuscle out of the metal. 
 
 Equation (3) gives the number of corpuscles in the air when 
 things have attained a steady state. To find the number of 
 corpuscles coming from the metal in unit time let us proceed 
 as follows : regard the steady state as the result of a dynamical 
 equilibrium between the corpuscles going from the metal to the 
 air and those going from the air to the metal. If ri is the 
 number of corpuscles in unit volume of the air, the number which 
 
96] IONISATION BY INCANDESCENT SOLIDS. 167 
 
 in one second strike against unit area of the metal is by the 
 Kinetic Theory of Gases equal to 
 
 00 
 
 2 udn, 
 o 
 
 dn being the number of corpuscles which have velocities between 
 u and u + du, and the summation is to be taken for all positive 
 values of u. Now if n' is the total number of corpuscles in unit 
 volume 
 
 where m is the mass of a corpuscle : hence 
 
 , /hm f 00 
 1 \ ~ ~ I 6 ~' 
 
 V 7T Jo 
 
 2 udn n f \ / - - I e- hmu *udu 
 1 
 
 c 
 
 where c is the velocity of mean square and is equal to a (0/m)l, 
 a being a constant which is the same for all gases : substituting 
 the value of n from equation (3) we find that the number of 
 corpuscles coming from the air and striking against unit area of 
 the metal in unit time is equal to 
 
 if we suppose that all the corpuscles which strike against the 
 metal enter it, this will be the number' of corpuscles entering 
 the metal, and therefore in the steady state the number leaving it ; 
 the number may be written in the form 
 
 this number multiplied by e will be the quantity of negative 
 electricity leaving unit area of the metal in unit time, and 
 therefore will be the saturation current from a hot wire at 
 the temperature 0, Richardson's measurements of the saturation 
 current at different temperatures ' agree well, as we have seen, 
 with a formula of this form.. F f rom the values of a and b deter- 
 mined by experiments on the escape of electricity from a hot wire 
 
168 IONISATION BY INCANDESCENT SOLIDS. [97 
 
 we can deduce the values of N and w. Richardson found that for 
 platinum 
 
 a = T5 x 10 26 and 6 = 4'93 x 10 4 ; 
 this gives 
 
 N= 1-3 x 10 21 and w = 8 x 10' 12 ergs. 
 
 The pressure due to the corpuscles in the metal would at atmo- 
 spheric temperature be between 30 and 40 atmospheres. 
 
 97. The emission of the negative corpuscles from heated sub- 
 stances is not, I think, confined to the solid state, but is a property 
 of the atom in whatever state of physical aggregation it may occur, 
 including the gaseous. The emission of the negative corpuscles 
 from the atoms is well shown in the case of sodium vapour ; if 
 a little sodium be placed in a tube from which all gas has as far 
 as possible been exhausted there will be in the dark no leak from 
 a charged conductor sealed in the tube, if however the tempera- 
 ture is raised to about 300 C. in the dark a considerable leakage 
 of electricity from the charged conductor will occur, whether the 
 charge be positive or negative ; the leak in the former case is 
 however greater than in the latter. It might be thought that 
 the leak is due to the corpuscles given out by the solid sodium in 
 the tube, these however would be negatively charged and could 
 not discharge a negatively charged conductor; nor is it due to 
 sodium condensed on the charged conductor itself, for there is no 
 leak on cooling down to the temperature of the room and ex- 
 posing the charged conductor when negatively electrified to light ; 
 if sodium had condensed on the charged metal the leak would 
 have been very perceptible. 
 
 The emission of the negatively electrified corpuscles from 
 sodium atoms is conspicuous as it occurs at an exceptionally low 
 temperature ; that this emission occurs in other cases although at 
 very much higher temperatures is, I think, shown by the con- 
 ductivity of very hot gases (or at any rate by that part of it which 
 is not due to ionisation occurring at the surface of glowing metals), 
 and especially by the very high velocity possessed by the negative 
 ions in the case of these gases ; the emission of negatively elec- 
 trified corpuscles from atoms at a very high temperature is thus 
 a property of a very large number of elements, possibly of all. 
 
 The emission of corpuscles from the atom must play a very 
 
98] IONISATION BY INCANDESCENT SOLIDS. 169 
 
 important part in the decomposition of the molecules of a com- 
 pound by heat, if the forces which bind the atoms together in 
 the molecule are mainly electrical in their origin. For imagine 
 a molecule consisting of two atoms, one, A, positively, the other, B, 
 negatively electrified, and suppose that the temperature is raised 
 until the point is reached when the negatively electrified atom 
 begins to discharge the negatively electrified corpuscles: when 
 this stage is reached B loses a corpuscle. Let us suppose that 
 under the electric field this corpuscle finds its way to the positively 
 electrified A neutralising its charge, so that momentarily A and B 
 are without charge, the attraction previously existing between 
 them is annulled and there is no longer anything to prevent their 
 drifting apart. It does not follow however that the molecule is 
 necessarily permanently split up, for A has now no positive charge 
 to prevent the negative corpuscles from escaping, and as it is the 
 electro-positive element in the compound it would under similar 
 conditions lose corpuscles more readily than B; thus A will soon 
 regain its positive charge. B being without charge cannot dis- 
 charge negative corpuscles as easily as it did previously when it 
 was negatively electrified, thus some time may elapse before B 
 emits a corpuscle, and in the interval it may get struck by a 
 negative corpuscle and thus acquire a negative charge, recombina- 
 tion might then occur between it and the positively charged A, 
 this combination being dissolved again by the process we have 
 already sketched. We should thus get to a state in which there 
 is statistical equilibrium, the number of recombinations in unit 
 time being equal to the number of atoms dissociated in that time : 
 the proportion of the free to the combined atoms will depend upon 
 the properties of each of the atoms ; the more easily A loses its 
 corpuscles by heating and the greater the difficulty of getting 
 the corpuscles out of B, the smaller will be the proportion of free 
 atoms. These considerations show that heat may produce dis- 
 sociation in other ways than the more commonly recognised one 
 of increasing the kinetic energy until the centrifugal force is great 
 enough to overpower the attraction. 
 
 98. We thus see that from an incandescent wire corpuscles are 
 projected at a rate sufficient to produce a very large rate of leak 
 when the pressure of the gas surrounding the wire is very low ; 
 at such pressures there is very little gas to hamper the motion of 
 
170 IONISATION BY INCANDESCENT SOLIDS. [99 
 
 the corpuscles, which consequently can move with very high 
 velocities ; as soon as a corpuscle emerges from the incandescent 
 surface it travels away from it towards the cylinder surrounding 
 the wire, and when the current between the wire and the cylinder 
 is saturated none of the corpuscles diffuse back again into the wire. 
 
 When however the pressure of the gas surrounding the wire 
 is considerable the corpuscles cannot travel so freely, they tend to 
 accumulate in the neighbourhood of the wire and some of them 
 diffuse back into it again. The density of the corpuscles in the 
 neighbourhood of the wire cannot exceed a definite value, given 
 by equation (3), p. 166 : just as in the case of the evaporation of 
 a liquid, the pressure of vapour in contact with the liquid cannot 
 exceed a definite value depending upon the temperature. 
 
 99. To drive through a gas at a considerable pressure currents 
 comparable with those easily obtainable in a vacuum would re- 
 quire the application of very large differences of potential. For 
 let us take the case of two parallel plates at right angles to the 
 axis of x, 1 cm. apart ; let the plate x = be the hot plate, X the 
 electric force at a point #, u the velocity of a corpuscle under 
 unit electric force ; then if the velocity of the corpuscle is pro- 
 portional to the electric force, the velocity at the point x will be 
 u X, and if n be the number of corpuscles per unit volume, e the 
 charge on a corpuscle, i the current through unit area, then 
 we have 
 
 i = u Xne, 
 
 dX 
 
 
 
 dx 
 
 , v dX 
 
 hence X = 
 
 * = x + f, 
 M 
 
 where X is the value of X at the surface of the plate. From this 
 equation it follows that if V is the potential difference between the 
 plate and a point x away from it, then 
 
 F> 
 
99] IONISATION BY INCANDESCENT SOLIDS. 171 
 
 From this expression we may calculate a lower limit to the 
 potential difference necessary to send a current of 1 milliampere 
 per square centimetre from a hot to a cold plate 1 cm. distant 
 when the gas is at atmospheric pressure ; in a high vacuum and 
 at a white heat such a current could be produced by a potential 
 difference of 100 volts or so. In order to get a lower limit for V 
 we shall give to u the greatest value which has been observed for 
 the negative ions at atmospheric pressure ; this is the value 
 obtained by H. A. Wilson in the case of flames at a temperature 
 of about 2000 C. and is equal to 1000 cm. /sec. for a potential 
 gradient of 1 volt per cm. If we use the electrostatic system 
 of units, the unit electric force is 300 volts per cm. ; hence 
 for the case quoted u = 3 x 10 5 cm./sec. : on the same system 
 of units 1 milliampere = 3 x 10 6 ; substituting these values of 
 i and u and putting a?=l, we find V> 11 electrostatic units or 
 3300 volts. 
 
 From these results we see that if the emission of corpuscles 
 was the only effect occurring at the surface of the wire we should 
 at high pressures get a small leak when the hot wire was charged 
 negatively, no leak when it was charged positively. There would 
 be no positive leak because the corpuscles are negatively elec- 
 trified, and a positive leak requires a supply of positive ions. 
 The negative corpuscles when moving with sufficient velocity 
 through a gas ionise it, and if the corpuscles coming from the wire 
 moved fast enough they would ionise the gas around the wire, and 
 thus produce a supply of positive as well as negative ions; the 
 velocity however possessed by at any rate an enormous majority of 
 the ions from the metal is far too small to produce this ionisation. 
 When the field is so intense that the corpuscles acquire sufficient 
 velocity to ionise the gas the current will increase rapidly with 
 the pressure. 
 
 The phenomena we have already described show that when gas 
 is present there must be other sources of ionisation besides the 
 corpuscles : for we have seen that beginning at a very dull red 
 heat there are positive ions around the wire, and these increase as 
 the temperature increases; negative ions do not however make 
 their appearance until about a bright yellow heat ; they increase 
 more rapidly with the temperature than the positive, until at very 
 high temperatures there are as many negative as positive ; indeed, 
 
172 IONISATION BY INCANDESCENT SOLIDS. [100 
 
 in the opinion of Koch*, the number of the negative ions at these 
 high temperatures exceeds that of the positive. There is evidently 
 some source of ionisation besides the emission of corpuscles and 
 one which begins at a much lower temperature. We proceed to 
 the consideration of some of the effects arising from it. 
 
 100. Incandescent wire surrounded by gas. We have first to 
 notice that the source of the ionisation is at the surface of the 
 incandescent metal, and does not extend to any considerable 
 distance in the gas. One proof of this is that the saturation 
 current between an incandescent metal plate and a parallel plate 
 is independent of the distance between the plates ; thus in some 
 experiments I made on this point I found that the saturation 
 current was the same when the plates were 3 mm. apart as when 
 they were 5 mm., the pressure was that due to about '25 mm. of 
 mercury ; thus even at this low pressure the source of ionisation 
 did not extend as much as 3 mm. from the hot plate, for if it 
 had done so the saturation current would have been less at the 
 smaller distance. 
 
 Another very striking proof of the same thing is afforded by 
 the experiments of H. A. Wilson f on the conductivity of flames 
 containing the vapours of metallic salts. If two pieces of platinum 
 foil are immersed in a flame so as to be heated to a red heat and 
 are connected with the terminals of a galvanic battery, a current 
 will pass through the flame from one of these electrodes to the 
 other. This current is very largely increased when volatile salts are 
 placed in the flame so as to introduce into it large quantities of 
 salt vapour. Wilson found that when this vapour was produced 
 by placing a small bead of the salt in the flame there was little 
 or no increase in the current when the bead was so placed that 
 the vapour did not come into contact with either electrode; when 
 the vapour came into contact with the positive electrode there 
 was a substantial increase and when it touched the negative 
 electrode a very large one. The increase in the current produced 
 by the vapour indicates an increase in the number of ions, and 
 the preceding results show that this increase does not take place 
 unless the metallic vapour comes into contact with the glowing 
 metal. 
 
 * Koch, Wied. Ann. xxxiii. p. 454, 1888. 
 
 f H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 
100] 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 173 
 
 Another proof that the ionisation is confined to the surface of 
 the hot metal is that the saturation current between the two 
 electrodes is independent of their distance apart. 
 
 We can by the following method* measure the conductivity of 
 a flame without introducing into it any 'metallic electrodes and 
 can thus directly determine the change if any produced in the case 
 by the admixture of salt vapours. A and B (Fig. 44) are two 
 
 Fig. 44. 
 
 Ley den jars the insides of which are connected with the terminals 
 of an induction coil or electric machine. The outside coatings of 
 these jars are connected by the circuit CDEF containing the two 
 loops D and E ; in one of these loops, E, a glass bulb containing 
 gas at a very low pressure is placed : when the coil or machine is 
 in action the jars are continually being charged and discharged ; 
 each time the jars are discharged alternating currents with, for 
 moderate sized jars, a frequency of some millions per second pass 
 through the wire CDEF', the currents flowing round the loop E 
 induce currents through the rarefied gas in the bulb, these currents 
 through the gas make it luminous, so that the discharge of the jar 
 is accompanied by a bright ring in the bulb in E. If conductors 
 of not too great conductivity are inserted in the loop I) it will 
 be found that the brightness of the ring in E is diminished, and 
 the higher the conductivity the greater the diminution; in this 
 way by observing the effects of different conductors when placed 
 in D we can get some idea of their conductivity. Now Wilson 
 found that the effect of the flame of a Bunsen burner passing 
 through D upon the ring discharge in E was quite appreciable, but 
 
 * J. J. Thomson, Proc. Camb. Phil. Soc. viii. p. 258, 1895. 
 
174- IONISATION BY INCANDESCENT SOLIDS. [100 
 
 that this effect was not perceptibly increased when salt vapours were 
 introduced into the flame though the current between electrodes 
 in the flame was increased several hundred times by the intro- 
 duction of the salt. 
 
 The effect of a conducting metallic plate in facilitating ionisa- 
 tion in its neighbourhood is very easily explained ; ionisation 
 involves the separation of a positive from a negative charge of 
 electricity ; if these charges are placed close to a metallic plate, 
 other charges will be induced in the plate which will almost annul 
 the attraction between the original charges; these therefore will 
 be much more easily separated than when they are far from con- 
 ductors and the attraction between them has its normal value. 
 The strong ionisation of salts in solvents having very large specific 
 inductive capacities is another aspect of the same phenomenon, 
 for a dielectric of high inductive capacity produces much the same 
 kind of effect on the attraction between electrical charges in its 
 neighbourhood as a conductor: it thus facilitates the separation 
 of the charges and therefore ionisation. Water, alcohol, and indeed 
 all ionising solvents have large specific inductive capacities. 
 
 If the ionisation is confined to the surface of the incandescent 
 metal, then the current between a hot electrode and a cold one 
 will be carried by ions of one sign, even though ions of both signs 
 are found at the surface of the metal. When the temperature is 
 so low that only ions of one sign are produced at the metal (as is 
 the case with platinum below a yellow heat), then all the ions 
 carrying the current must have come from the same electrode. 
 This explains an effect observed by the author many years ago*: 
 the current between two pieces of platinum foil immersed in a vessel 
 heated to a bright red heat was found to be completely stopped by 
 placing a cold metallic plate between the electrodes and the current 
 did not recommence until the middle plate was raised to' incan- 
 descence. This is evidently what would occur if there was a pro- 
 duction of positive ions at the two electrodes A and B and nowhere 
 else ; for suppose A is the positive electrode, then all the ions 
 which reach B have started from A ; if we place between A and B 
 a plate whether made of a conductor or insulator we stop all the 
 ions before they reach B and thus stop the current. The current 
 
 * J. J. Thomson, Phil. Mag. v. 29, p. 441, 1890. 
 
101] IONISATION BY INCANDESCENT SOLIDS. 175 
 
 will recommence when the plate gets hot enough to produce ions 
 at its surface. If ions of both signs are produced at each of the 
 hot plates the current will not be stopped by the middle plate but 
 will be greatly diminished. 
 
 101. Relation between the current and the potential difference. 
 Let us consider the case of two parallel plates at right angles to the 
 axis of a?, then if only one of the plates is incandescent, or if both 
 are incandescent but the temperature is so low that only positive 
 ions are produced at the surface of the plates, then the ions 
 carrying the current between the plates will be all of one sign and 
 we may apply the results of Art. 98. Hence if X is the electric 
 force, R the velocity of the ion under unit electric force, we have, 
 if i is the current, 
 
 _ 
 dx~ R' 
 
 hence if R is independent of x we have 
 
 if the current is small X vanishes at the hot plate, hence if the 
 equation to this plate is x 0, 
 
 if V is the difference of potential between the plates, d the dis- 
 tance apart, we have 
 
 or 
 
 .(1). 
 
 This equation has been tested by Rutherford*; we canno 4 - 
 however expect the theory to be in very close agreement with the 
 facts, for in deducing equation (1) we have made several assump- 
 tions which are not satisfied in practice; in the first place we 
 have assumed that R is independent of x, this will only be true 
 when the temperature is uniform between the plates, it will not 
 be true when one plate is hot and the other cold, for the velocity 
 
 * Rutherford, Physical Review, xiii. p. 321, 1901. 
 
176 ION1SATION BY INCANDESCENT SOLIDS. [101 
 
 of the ion depends upon the temperature. Thus H. A. Wilson* has 
 shown that in a flame at the temperature of about 2000 C. the 
 velocity of the negative ion under a potential gradient of 1 volt 
 per cm. is about 1000 cm. /sec., that of the positive ion under the 
 same gradient 62 cm. /sec.; in hot air at a temperature of about 
 1000 C. the velocity of the negative ion is only about 26 cm./sec., 
 that of the positive about 7*2 cm./sec. M c Clelland-f- found that the 
 ions from an incandescent wire when they got into the cold air at 
 some distance from the wire travelled with velocities as small as 
 '04 cm./sec.: and that the velocity diminished as the ions got further 
 from the wire and could be increased again by warming the ions ; 
 thus R varies rapidly with the temperature and therefore with x. 
 
 The increase of R with the temperature makes the current 
 increase rapidly with the temperature of the hot plate. We 
 see from equation (1) that the current for a constant small 
 difference of potential does not depend upon the amount of ioni- 
 sation near the plate j, so that the increase of ionisation at the 
 higher temperature would not explain the increase of current when 
 the wire gets hotter ; a satisfactory explanation of this increase is 
 however afforded by the increase of R with the temperature. 
 
 W T hen the temperature of the hot plate is high enough for 
 negative as well as positive ions to exist near the plate, the 
 leak between the hot plate and a cold one will be greater when 
 the hot plate is the negative electrode than when it is the positive : 
 for in the former case the current is carried by negative ions, in 
 the latter by positive, and equation (1) shows that with the same 
 potential difference the current is proportional to the velocity of 
 the ion by which it is carried. Now the velocity of the negative 
 ion is always greater than that of the positive, and the ratio of the 
 velocity of the negative to that of the positive increases rapidly 
 with the temperature; thus the experiments of H. A. Wilson on 
 the leak through gases mixed with the vapours of salt (I.e.} show 
 that this ratio at 2000 C. is about 17 while at 1000 C. it is only 
 about 3 '5. At ordinary temperatures for the case of ions drawn 
 
 * H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 
 f M c Clelland, Phil. Mag. v. 46, p. 29, 1899. 
 
 I It must be remembered that equation (1) only applies when the current is 
 small, so that X=0 when x = 0-, when the current approaches saturation it increases 
 rapidly with the amount of ionisation at the plate. 
 
102] 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 177 
 
 from the neighbourhood of the hot wire, M c Clelland's experiments 
 show that this ratio is only about 1'25. The great increase of 
 current produced by changing the sign of a very hot electrode 
 from + to is a very well marked phenomenon; one striking 
 example of it is furnished by an old experiment of Hittorf's *. In 
 this experiment a bead of salt was placed in a flame between 
 glowing electrodes : the increase in the current was much 
 greater when the bead was placed close to the negative electrode 
 than when it was placed near to the positive. These results, it 
 must be remembered, are only true when the currents are very 
 small compared with their saturation values; the saturation values 
 do not depend upon the velocities of the ions but only upon the 
 number of ions produced in unit time at the surface of the hot 
 metal. 
 
 The velocity of an ion under a constant electric force increases 
 as the pressure of the gas diminishes, hence we see from equation 
 (1) that the current when small will increase when the pressure 
 diminishes. 
 
 100 
 
 200 
 
 300 
 
 Fig. 45. 
 
 400 Cells 
 (=800 Volts) 
 
 102. A well-marked feature of the discharge from incandescent 
 metals is the very rapid increase of the current, when this is small, 
 
 * Hittorf, Fogg. Ann. Jubelband, p. 430, 1874. 
 
 T. G. 
 
 12 
 
178 IONISATION BY INCANDESCENT SOLIDS. [103 
 
 with the electromotive force, an increase much more rapid than 
 that given by Ohm's law. This has frequently been observed ; thus, 
 for example, Pringsheim * gives as an empirical formula for the 
 current i in terms of the potential difference V for the discharge 
 between two pointed electrodes in a hot gas 
 
 ._F+aF 2 
 ~1T~' 
 
 where a and w are constants. The rapid increase in the current is 
 well illustrated by the curve in Fig. 45 given by H. A. Wilson + 
 for the case of the current between a hot platinum wire and a hot 
 platinum tube outside it; in this curve the ordinates represent 
 the current and the abscissse the potential differences, the curve 
 for the case when the tube is negative illustrates too the ' satura- 
 tion ' of the current under high electromotive forces. This rapid 
 increase of the current is accounted for by equation (1), which 
 shows that the current is proportional to the square of the 
 potential difference. 
 
 103. The nature of the carriers of the electricity in the current 
 from a hot wire. The discharge of positive electricity from a wire 
 at a temperature between a red and yellow heat is not determined 
 solely by the nature and pressure of the gas and the temperature 
 of the wire, it is very largely influenced by the treatment to which 
 the wire has been subjected previous to the discharge. Thus if we 
 measure the leak between a hot wire and a cold metal cylinder 
 surrounding it, the gas being at a low pressure, we often find that 
 when the wire is first heated the leak is very large to begin with, 
 but slowly diminishes until after several hours' continuous heating 
 the current may have sunk to 1/20 of its original value : if when 
 it has fallen to this point fresh gas is introduced into the vessel 
 containing the hot wire and then after some time pumped out 
 until the pressure is the same as before the introduction of the 
 gas, the current is very greatly increased for a time ; it again 
 diminishes as the heating continues but can be revived by the 
 introduction of fresh gas. As this diminution occurs whether or 
 not the current is kept flowing between the hot wire and the sur- 
 rounding cylinder, it cannot be due to an effect analogous to the 
 
 * Pringsheim, Wied. Ann. Iv. p. 507, 1895. 
 
 t H. A. Wilson, Phil. Trans. A. 197, p. 415, 1901. 
 
103] IONISATION BY INCANDESCENT SOLIDS. 179 
 
 ordinary polarisation of electrolytes, although we shall see reasons 
 for thinking that such an effect does exist to some extent in 
 conduction through hot gases. 
 
 The facts just mentioned suggest that the gas absorbed by the 
 platinum and slowly given off when heated plays an important 
 part in the carriage of the electricity from the wire, and we can 
 easily understand how this gas, coining straight from the midst of 
 a good conductor, would be ionised and able to carry the current. 
 The emission of absorbed gas from the platinum is however, 
 according to Berliner*, closely connected with the disintegration 
 of the platinum wire which takes place when the wire is kept 
 glowing and which is made evident by a deposit of platinum or 
 platinum oxide on the walls of the tube and a diminution in the 
 weight of the hot wire : the carriers of the electricity might thus 
 be the dust or vapour of platinum escaping from the wire. This 
 disintegration of the platinum has been studied by Berliner*, 
 Elster and Geitel f, Nahrwold }, and Stewart : who have shown 
 
 (1) That the amount of disintegration produced in a given 
 time by the incandescence of a platinum wire diminishes after 
 prolonged heating. 
 
 (2) That the amount of this disintegration is very much in- 
 creased by the presence of oxygen. It is exceedingly small in 
 nitrogen and hydrogen ; indeed, some of the experiments suggest 
 that there would be no disintegration of a glowing platinum wire 
 in these gases if every trace of oxygen could be removed from 
 them. We may suppose that where oxygen is present slight 
 oxidation takes place, producing a weathering of the surface 
 which facilitates the disintegration of the metal. 
 
 The disintegration of the platinum can be easily shown by 
 the effect of the incandescence of the wire on the condensatio: 
 of clouds in the air in its neighbourhood. We owe this method 
 to Aitken||. One simple way of showing this effect is to have 
 a fine platinum wire fused in the expansion chamber in the cloud 
 
 * Berliner, Wied. Ann. xxxiii. p. 289, 1888; xxxv. p. 791, 1888. 
 
 t Elster and Geitel, Wied. Ann. xxxi. p. 109, 1887. 
 
 t Nahrwold, Wied. Ann. xxxi. p. 448, 1887; xxxv. p. 107, 1888. 
 
 Stewart, Phil. Mag. xlviii. p. 481, 1889. 
 
 || Aitken, Trans. Roy. Soc. Edin. xxx. p. 337. 
 
 122 
 
180 IONISATION BY INCANDESCENT SOLIDS. [104 
 
 apparatus (Fig. 37). If the air be made dust-free when the wire 
 is cold, then on sending a current through the wire so as to raise 
 it to a red heat and then letting it cool, a dense cloud is produced 
 by a very small expansion; as this expansion is much smaller than 
 that required to produce a cloud on ions, there must be particles 
 much larger than molecules in the neighbourhood of the wire. 
 Unless the wire is very carefully cleaned an increase of tem- 
 perature much less than that required to produce luminosity is 
 sufficient to produce a cloud. This depends apparently upon dirt 
 or moisture deposited on the wire, and Aitken's experiments 
 show that this effect disappears when the wire has been cleaned 
 by long-continued incandescence ; no amount of incandescence 
 seems however to destroy the cloud when the temperature of 
 the platinum wire is raised to that corresponding to a red heat. 
 Mr Owen, who has recently made experiments in the Cavendish 
 Laboratory on this point, finds that when the platinum wire is in 
 air or oxygen there is, even after long-continued incandescence of 
 the wire, always a cloud when the temperature of the wire is raised 
 to about 300 C. In pure hydrogen however the wire has to be 
 raised nearly to a red heat before this cloud is formed. 
 
 104. There is a close similarity between the laws of disintegra- 
 tion of the wire and those of the leak of positive electricity from it. 
 We have already alluded to the effect of long-continued heating 
 on the leak : the presence of oxygen has also a very marked effect. 
 This can be shown in a striking way by observing the pressure 
 at which a plate in the neighbourhood of the hot wire begins 
 to acquire a negative instead of a positive charge. If the wire 
 ^be not too hot, then at high pressures the plate will be charged 
 positively ; on exhausting the vessel a point will be reached where 
 the positive charge begins to decrease, then vanishes and finally 
 is replaced by a negative charge. This change in the sign of the 
 charge on the plate occurs at much higher pressures in hydrogen 
 and nitrogen than in oxygen, where this reversal is difficult to 
 obtain unless the wire be very hot. When the reversal of sign 
 has been obtained in hydrogen or nitrogen the addition of a 
 surprisingly small quantity of oxygen is sufficient to make the 
 charge on the plate positive again. It is possible that part of 
 the diminution in the positive leak produced by long-continued 
 heating at low pressures may be due to the burning up of the 
 
105] IONISATION BY INCANDESCENT SOLIDS. 181 
 
 oxygen, or when there is any grease present to the replacement 
 of oxygen by the vapours of hydrocarbons liberated by the con- 
 tinuous heating. The increase in the positive electrification 
 produced by oxygen is easily explained if there is any oxidation 
 of the metal at a red heat ; for in the oxide thus formed the 
 oxygen carries the negative, the metal the positive charge; thus 
 if the oxygen in the neighbourhood of the platinum wire got 
 ionised by the heat, the platinum by combining with the negative 
 but not with the positive oxygen ions would leave an excess of 
 positive ions in the neighbourhood. That chemical action has 
 a considerable effect on the electrification is confirmed by the 
 observation of Branly that the oxides of metals give off at a dull 
 red heat negative electricity, whereas metals give off positive ; in 
 the case of the oxides the chemical action which takes place is the 
 dissociation of the oxide into the metal and oxygen, the oxygen 
 ions carrying the negative charge and thus producing negative 
 electrification round the wire. A similar explanation applies to 
 the following result which I observed with the arc discharge ; 
 when the arc passed between terminals of bright copper there 
 was an excess of positive electricity in the gas round the ter- 
 minals ; if however the terminals were thickly coated with oxide 
 and placed in hydrogen the electrification in the gas was negative 
 until the oxide was reduced : when this had been accomplished 
 the electrification became positive. 
 
 105. A very small amount of chemical action is sufficient to 
 produce very intense electrification, so that it might be urged that 
 even in the best attainable vacuum there is sufficient gas to produce 
 the electrification ; that this positive electrification occurs in very 
 good vacua is certain ; in a vacuum so good that it was hardly 
 possible to get any discharge through it with an induction coil 
 giving an 8-iiich spark, I have got the positive electrification 
 from a red-hot platinum wire which had been kept glowing at 
 a much higher temperature 8 hours a day for a week. Stronger 
 evidence that the positive electrification is not due entirely to 
 chemical action on the wire is afforded by a determination of the 
 nature of the carriers of this charge ; if the charge arose from 
 chemical action we should expect the carriers to be the atoms 
 or molecules of the gas. The following experiments show that 
 although there are a few carriers of this character the majority 
 
182 IONISATION BY INCANDESCENT SOLIDS. [105 
 
 of them are much larger and are probably molecules, ,or even 
 larger masses, of platinum. The method used to determine the 
 mass of the carriers was the same as that used (see p. 106) to 
 determine the mass of the negative carriers at high temperatures, 
 inasmuch however as the mass of the positive carriers turns out 
 to be enormously greater than that of the negative ones, it is 
 necessary in dealing with the positive leak to employ very much 
 greater magnetic forces than those used in the previous ex- 
 periments, and this involves some modifications in the conditions 
 of the experiment. The arrangement used is shown in Fig. 46. 
 
 To Electrometer 
 
 Battery 
 
 Fig. 46. 
 
 A is an insulated metal plate placed in the middle of a brass 
 tube about 5 mm. in diameter; this plate is connected with a 
 quadrant electrometer. B is a piece of platinum foil parallel to 
 the plate and about 3 mm. from it ; this foil can be raised to 
 incandescence by an alternating electric current passing through 
 the leads C, D. The current was produced by making the circuit 
 connecting the leads loop round a transformer. By this method 
 the hot wire and its leads could be easily insulated i the hot wire 
 and the brass tube were connected with one terminal of a battery 
 of small storage cells, the other terminal of which was connected 
 with the earth. The current to the plate A from the hot wire was 
 measured by the deflection produced in the electrometer in a given 
 time; this deflection was measured for various potentials of the hot 
 wire, with the magnetic field both on and off ; the highest potential 
 at which a given magnetic field produces an appreciable diminu- 
 tion gives, as is explained in Art. 48, the means of determining 
 
105] IONISATION BY INCANDESCENT SOLIDS. 183 
 
 m/e the ratio of the mass of the carrier to its charge. In the 
 investigation of Art. 48 it was assumed that the electric force 
 was uniform in the region in which the ions were moving; in the 
 case of the hot wire there are so many ions all of one sign 
 carrying the current that they disturb the potential gradient 
 and make the force vary from point to point. We can easily 
 prove however that this inequality in the electric field will not 
 impair the validity of the method. If the field is not uniform 
 the paths of the ions will not be cycloids ; the ions however 
 whether the field is uniform or not, after receding a certain 
 distance d from their source, will be turned round by the mag- 
 netic force and begin to move back, thus they will never get 
 further than d away from the source. Now if the plate on which 
 the ions are received is at a distance greater than d from the hot 
 metal which is the source of the ions, the magnetic field will 
 produce a diminution in the current flowing into the plate, while 
 if the distance is less than d, the magnetic field will produce no 
 diminution in the leak. This critical distance d can be de- 
 termined by comparing the currents with the magnetic field on 
 and off: it is evidently the distance from the source at which 
 the velocity of the ion parallel to the electric force vanishes. 
 If x is the distance of an ion from the hot plate, X the electric 
 force acting on the ion, H the magnetic force supposed to be 
 uniform and parallel to the axis of z, then we have 
 d*x ~ TT dy 
 
 < 2 > 
 
 or m - = - Hex, 
 
 at 
 
 since -j- = 0, when x = ; substituting this value for -j- ; n 
 at ut 
 
 equation (1) we get 
 
 r/' 2 r TfV 2 
 
 LV W i 1~ & -TT- 
 
 m -jrt + - - x = A e. 
 ar m 
 
 Integrating with respect to x from a? = to x = d, we have since 
 (&e/<ft vanishes both when x = and when a? = d 
 
 - -- = e \ Xdx ; 
 m Jo 
 
184 IONISATION BY INCANDESCENT SOLIDS. [105 
 
 if V is the difference of potential between the plates V 
 
 Jo 
 
 hence \ d* = V 
 
 m 
 
 e 2V 
 = 
 
 and thus even when the field is not uniform e/m is given by the 
 same equation as in Art. 48. 
 
 In applying this method to the case of the leaking of positive 
 electricity from a hot wire we find that enormously greater mag- 
 netic forces are necessary to produce any diminution upon the leak 
 than were required to produce the same effect on the leak of 
 negative electricity from a hot wire (see p. 164): and even with 
 the greatest magnetic forces obtainable the effects of the magnetic 
 field upon the rate of leak are sometimes scarcely appreciable. 
 The effect of a magnetic field upon the positive leak like the 
 positive leak itself is irregular, even when the temperature of the 
 wire and the pressure of the gas are kept as constant as possible, 
 small changes in conditions which it is very difficult to control or 
 even to specify producing great changes in the leak and in the 
 effect of the magnetic field upon it. It is probable that these 
 changes correspond to a change in the nature of the carriers of 
 the electricity. In some cases the leak is not affected by the 
 magnetic field even of 19000 units. When, however, the discharge 
 is sensitive to the magnetic field the general nature of the effects 
 observed with the apparatus already described and with a field 
 of 19000 units is as follows, the pressure of the gas (air) being 
 about '007 mm. ; the numbers given are only approximate as the 
 irregular variations in the leak are so large as to make accurate 
 measurement impossible. When the potential difference between 
 the hot metal and the plate connected with the electrometer was 
 small, say 3 or 4 volts, the leak was very nearly stopped by the 
 magnetic field; with a potential difference of 10 volts the leak was 
 reduced by the magnetic field to about one-quarter of its original 
 value, the effect of the magnetic force upon the leak diminished as 
 the potential difference increased but was appreciable until this 
 reached about 120 volts. Thus in this case we see that while some 
 of the carriers can reach the plate under a difference of potential 
 of 10 volts, there are others which require a potential difference 
 
105] IONISATION BY INCANDESCENT SOLIDS. 185 
 
 of 120 volts to do so. If e 1 /m 1 be the ratio of the charge to the 
 mass of the first carrier, e 2 /m 2 that of the second, then putting 
 in equation (8) 
 
 H= 19000, d = -3 and F= 10 x 10 8 and 120 x 10 8 , we get 
 
 m 
 
 2 =720; 
 m 2 
 
 if e lt e* were the same as the charge on a hydrogen ion, then 77^ 
 and w 2 would be respectively about 170 and 14 times the mass of 
 the hydrogen atom; these are limiting values of e/m t there are also 
 intermediate values. These results indicate that the electricity is 
 carried both by atoms of the metal (in this case platinum) and of 
 the gas, the former predominating. The fact that in certain cases 
 the rate of leak is not affected by the magnetic force even when 
 the potential difference is reduced to one volt or less shows that in 
 these cases the carriers have much larger mass than the molecule 
 of platinum, they are probably platinum dust. 
 
 Rutherford* from experiments on the velocity of the ions 
 through air at atmospheric pressure also came to the conclusion 
 that carriers of very different kinds were at work in carrying the 
 positive electricity from a hot metal. 
 
 Though the effect of the magnetic field on the rate of leak 
 diminishes when the potential difference is increased and at one 
 stage disappears, yet on still further increasing the potential a 
 stage is reached where the magnetic force again produces a very 
 considerable diminution in the rate of leak. This stage is closely 
 connected with the way in which the rate of leak varies with 
 potential difference ; if we represent the rate of leak by the ordi- 
 nates, the potential difference by the abscissae of a point on a curve, 
 then as M c Clellandf has shown, the curve is of the type represented 
 in Fig. 47 showing three well-marked stages : in the first the 
 current increases rapidly with the potential difference, in the 
 second the current is saturated and is independent of the potential 
 difference, in the third stage the current again increases rapidly. 
 This increase is as we shall see due to the formation of fresh ions 
 by the motion through the gas of ions coming from the hot plate, 
 
 * Rutherford, Physical Review, xiii. p. 321, 1901. 
 t M c Clelland, Proc. Camb. Phil. Soc. xi. p. 296, 1902. 
 
186 
 
 ION1SATION BY INCANDESCENT SOLIDS. 
 
 [105 
 
 there are in this stage negative as well as positive ions between 
 the electrodes. It is in the third stage that the magnetic field 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _ -* 
 
 e " 
 
 ^ 
 
 
 
 
 
 y* 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 D 
 
 4 
 
 
 
 8 
 
 
 
 12 
 
 
 
 1C 
 
 
 
 Fig 
 
 2 
 
 . 47 
 
 DO 
 
 2< 
 
 10 
 
 2! 
 
 JO 
 
 32 
 
 
 
 36 
 
 again produces a diminution in the rate of leak, the explanation 
 of this is I think that the magnet stops the motion of the negative 
 ions which are now helping to carry the current and which as we 
 have seen are very much hampered by a magnetic field. 
 
 Elster and Geitel* found that the rate of positive leak was often, 
 indeed in their experiments generally, increased, not diminished, 
 by the magnetic field ; with the apparatus described and arranged 
 as on page 182, I only observed an increase in one case, i.e. 
 when the temperature was high and the potential difference small. 
 At a very high temperature negative as well as positive ions are 
 produced at the plate, these negative ions are projected with great 
 velocity so that even if the plate has a small positive charge the 
 negative ions coming from the plate will exceed the positive ones 
 and a conductor in the neighbourhood will receive a negative 
 charge. If the potential of the plate be raised until this conductor 
 gets a positive charge, then the application of a magnetic field will 
 often considerably increase the positive charge on the conductor ; 
 this increase is, however, due to the retardation of the stream of 
 negative ions and not to the acceleration of the positive ones. If 
 the metal tube in which the hot plate (Fig. 46) is contained is 
 not connected with the hot plate but with the earth, then a mag- 
 netic field will often increase the rate at which the plate acquires 
 a positive charge; this, however, is merely the diversion of positive 
 ions from the tube to the cold plate by the magnetic field. 
 * Elster and Geitel, Wied. Ann. xxxviii. p. 27, 1889. 
 
106] IONISATION BY INCANDESCENT SOLIDS. 187 
 
 106. We could determine the value of e/m for the carriers of 
 electricity by the following method, which is applicable when the 
 current is carried by ions of one sign and when the pressure of 
 the gas is so low that we can neglect the resistance of the gas to 
 the motion of the ions. Let us consider the case of a current 
 between two parallel plates, one of which is the hot plate or other 
 source of ions. Take the axis of x at right angles to the plate, let 
 F be the difference of potential between the hot plate and a point 
 whose coordinate is x, p the density of the electricity. Then 
 
 If v be the velocity of the ion at x, V Q its velocity when starting 
 from the plate, m its mass and e its charge, then 
 
 m(v 2 -v *) = Ve ..................... (2); 
 
 but since all the ions are of one sign, i the current through unit 
 area is equal to vp, hence from (1) and (2) 
 
 m ' * "~* ' ' 
 
 integrating this equation we have, if we write X for dVjdx, 
 
 =c 
 
 + 
 
 e ( m 
 
 hence if X is the value at the cold plate, X Q that at the hot, F the 
 potential difference between the plates, and C the constant of 
 integration, 
 
 we have X* X ( ? 
 
 if X' and X ' t i' and V are corresponding values in a second 
 experiment we have 
 
 Z /2 -Z /sl = 8 rV+-F'j'-^l ' 
 LI m ) J ' 
 
 hence if (Z 2 - X 2 )/87ri = (Z /2 - Z /2 )/87ri v = ' , 
 
 we have ^ f 2 + 2^ - f = F, 
 
 m mm 
 
 ^'t+2v -? = - 
 m* m* m 
 
 (4), 
 
188 IONISATION BY INCANDESCENT SOLIDS. [107 
 
 an equation by which we can determine e/m when we know 
 f , f ', V, and V. To determine f and f ' we require to know the 
 value of X at the two plates. This can be done as follows : as 
 the pressure is very low we can produce by independent electrodes 
 cathode rays in the vessel in which the leak is taking place; if we 
 arrange these electrodes so ns to allow a small pencil of these rays 
 to pass close to first one plate and then the other and measure 
 the electrostatic deflection of the rays, we can from this deflection 
 deduce the electric force and then by equation (4) the value of 
 e/m. 
 
 Effect of the Gas on the rate of leak. 
 
 107. We have seen that in the best vacua we can produce a 
 metal when first it begins to glow gives oflf positive electricity 
 and then at considerably higher temperatures negative electricity 
 as well, the rate of emission of negative electricity increasing more 
 rapidly with the temperature than that of the positive, so that at 
 very high temperatures the negative is greatly in excess of the 
 positive. Thus to make a metal emit positive electricity we have 
 to communicate a certain amount of energy to its surface, a larger 
 amount being required to make it give out negative electricity. 
 When the incandescent metal is surrounded by gas at an appre- 
 ciable pressure we find that the nature of the gas has a very 
 distinct effect upon the amount of leak. The author* has shown 
 that gases such as the vapours of iodine and bromine, chlorine, 
 hydriodic acid gas, hydrobromic acid gas, hydrochloric acid gas, 
 the vapours of potassium iodide, sal-ammoniac, sodium chloride, 
 potassium chloride, which are dissociated by heat conduct elec- 
 tricity on quite a different scale from those which like air, 
 hydrogen or nitrogen do not suffer any dissociation ; thus the 
 dissociable gases furnish a much larger supply of ions than the 
 others : even in these easily dissociable gases by far the greater 
 part of the dissociation occurs where the gas is in contact with the 
 glowing electrodes ; this is proved by the experiment described on 
 page 172. 
 
 The vapours of many metals conduct very well ; of the metals I 
 tried, sodium, potassium, thallium, cadmium, bismuth, lead, alumi- 
 
 * J. J. Thomson, Phil. Mag. v. 29, pp. 358, 441, 1890. 
 
108] IONISAT10N BY INCANDESCENT SOLIDS. 189 
 
 nium, magnesium, tin, zinc, silver and mercury ; sodium and 
 potassium had the highest conductivity ; while the conductivity 
 of the vapours of mercury, tin, thallium, did not seem any greater 
 than that of air ; so that the small conductivity actually observed 
 might have been due to the presence of air and not to the vapour 
 of the metal. 
 
 Application of the leak through hot gases to determine the 
 amount of work required to ionise a gas. 
 
 108. By measuring the current through a gas we can deter- 
 mine the number of ions in unit volume if we know the velocity 
 of the ions under a given electric field : for if R^ and R 2 are the 
 velocities under unit electric force of the positive and negative 
 ions respectively, n the number of ions (of either sign) per cubic 
 centimetre, L the current under the electric force X, then 
 
 If these ions come from the gas we may regard the molecules 
 of the gas as dissociating into positive and negative ions and these 
 recombining to form neutral molecules ; the problem of finding 
 the proportion between the number of ions and the number of 
 neutral molecules is the same as that of finding the proportion 
 between the atoms and molecules in a gas which is dissociating. 
 This problem has been solved and an expression found for the way 
 in which the number of free atoms depends upon the temperature 
 (see Willard Gibbs, Equilibrium of Heterogeneous Substances, 
 p. 239; Boltzmann, Wied. Ann. xxn. p. 39; J. J. Thomson, 
 Applications of Dynamics to Physics and Chemistry, p. 193). 
 When the number of free ions is small compared with the num- 
 ber of neutral molecules as it is in the case of the ionisation of a 
 gas by heat, then if n is the number of ions per unit volume 
 
 where p is the pressure of the neutral molecules, 6 the absolute 
 temperature, w the work required to ionise one gramme of the 
 molecules of the gas, R is the constant which occurs in the equa- 
 tion p = RpO for the neutral gas, p being the density of the gas, 
 < (0) is a function of which does not change rapidly with the 
 temperature, so that when the number of ions changes very rapidly 
 
190 IONISATION BY INCANDESCENT SOLIDS. [109 
 
 with the temperature as it does in the case of conduction through 
 
 _ 
 hot gases the variation in n is chiefly due to the factor e~Ro. 
 
 Hence if n 1} n z are the numbers of free ions at the temperatures 
 6 l and 2 respectively, we have approximately, regarding < (6) and 
 w as constant, 
 
 nS w ( 1 1 
 
 hence if we determine w a /Wi by measuring the current through 
 the hot gas we can find w. By this method H. A. Wilson* found 
 that for air it required about 2100 calories to ionise one gramme 
 of air. As the ionisation of a gas consists in the separation of 
 positive and negative charges it is natural to express the work 
 required to effect this process as due to the movement of the 
 charge on the ion through a certain difference of potential. If V 
 is this potential difference, e the charge on an ion, n the number 
 of molecules in a gramme of air, in the mass of a molecule, we have 
 
 neV = 2100 calories = 2100 x 4'2 x 10 7 ergs ; nm = 1 ; 
 
 hence - F= 2'1 x 4*2 x 10 10 ; 
 
 m 
 
 for hydrogen ej M 10 4 if M is the mass of an atom of hydrogen ; 
 hence if the charge on the ion is the same as that on hydrogen we 
 have for air elm = 10 4 /28, hence 
 
 F=2'5 x 10 8 = 2-o volts. 
 
 Thus the work done in ionising a molecule of air corresponds 
 to moving the charges through about 2 '5 volts. 
 
 The distribution of potential near Glowing Electrodes. 
 
 109. We shall confine ourselves to the case when the current 
 is passing between two parallel plane electrodes. If one of these 
 be hot and the other cold too cold to produce any ionisation 
 at its surface the current will be carried entirely by ions of 
 one sign, the electric force will therefore increase continuously 
 from the hot plate to the cold one, and (see Art. 101) the dis- 
 tribution of potential will be represented by a curve similar to 
 that in Fig. 48, the lower electrode being the hotter of the two. 
 Similar curves will represent the distribution of potential when 
 * H. A. Wilson, Phil. Trans. A. 197, p. 415, 1901. 
 
109] 
 
 IONISATION BY INCANDESCENT SOLIDS. 
 
 191 
 
 both plates are hot provided the temperature of the negative plate 
 is not high enough for negative as well as positive ions to be pro- 
 duced at the plate, for it is evident that in this case the current 
 has to be carried entirely by positive ions. When however both 
 
 2468 cms. 
 Fig. 48. 
 
 plates are hot enough to ionise the gas and the negative so hot 
 that negative as well as positive ions are produced, then when the 
 field is so strong that most of the positive ions are driven from the 
 positive plate and the negative ions from the negative plate, we 
 shall have an excess of positive ions at the negative plate, so that 
 in the region the potential curve will be concave, and of negative 
 ions at the positive, which will make the potential curve convex, 
 and the potential curve will be like the higher curve in Fig. 49, 
 
 3 cms. 
 
 the straight part in the middle showing that except close to the 
 plates there are approximately equal numbers of positive and 
 negative ions present. Curves similar to these for the distribution 
 of potential have been obtained by H. A. Wilson* and Marxf. 
 When the hot plates are made of different materials Pettinelli 
 
 * H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 f Marx, Drude's Ann. ii. p. 768, 1900. 
 
192 IONISATION BY INCANDESCENT SOLIDS. [109 
 
 and Marolli* have shown that the magnitude of the current 
 depends upon which metal is used as the cathode, thus with 
 electrodes of carbon and iron the current when the carbon was 
 cathode was three or four times greater than when the iron 
 was cathode : they state that the current is greatest where the 
 more porous substance is used as the cathode. These effects are 
 much more marked at high than at low temperatures; it is pro- 
 bable that they clo not commence until the temperature is high 
 enough to produce negative ions. 
 
 The difference in the velocities of the ions produces very 
 marked unipolar effects in the current, i.e. the current with the 
 same electromotive force is very much greater in one direction 
 than the opposite ; we can very easily see the reason for this, for 
 take the case where only one electrode is hot enough to ionise 
 the gas, then jwe see from equation (1), p. 195 that the current 
 is proportional! to the velocity under unit force of the ion carrying 
 the current. As the velocity of the negative ion is greater than 
 that of the positive, the current will be greater when it is carried 
 by the negative ions than when it is carried by the positive. It 
 must be remembered that the ratio of the velocities of the ions 
 produced by an incandescent metal depends very largely upon the 
 temperature. Thus M c Clellandf who measured it in air at the 
 ordinary temperature (the ions having been blown from the in- 
 candescent wire to the place of observation), found that the 
 velocity of the negative ions was only about 25 per cent, greater 
 than that of the positive, while H. A. WilsonJ who measured this 
 ratio at high temperatures for the ions produced when salts 
 were volatilised in flames or hot air, found that at 1000 C. 
 the velocity of the negative ion was for the salts of the alkali 
 metals 3*6 and for those of the alkali earths 7 times that of the posi- 
 tive. At 2000 C. the velocity of the negative ions was for the alkali 
 metals seventeen times that of the positive. The absolute values 
 were still more different, thus M c Clelland found for the velocity 
 under a potential gradient of a volt per cm. velocities ranging from 
 006 cm./sec. to '03 cm./sec., while Wilson at 1000 C. found 
 26 cm./sec. for the negative, and 7*2 cm./sec. for the positive ; at 
 2000 C. the values were respectively 1030 cm./sec. and 62 cm./sec. 
 
 * Pettinelli and Marolli, Atti delta Accad. del Lincei, v. p. 136, 1896. 
 t M'Clelland, Proc. Camb. Phil Soc. x. p. 241, 1899. 
 $ H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 
CHAPTER IX. 
 
 IONISATION IN GASES FROM FLAMES. 
 
 110. IT has been known for more than a century that gases 
 from flames are conductors of electricity : a well-known applica- 
 tion of this fact the discharge of electricity from the surface of 
 a non-conductor by passing a flame over it was used by Volta in 
 his experiments on Contact Electricity. We shall not attempt 
 to give any historical account of the earlier experiments on this 
 subject, because the conditions in these experiments were generally 
 such that the interpretation of the results obtained is always ex- 
 ceedingly difficult and often ambiguous : the reason of this is 
 very obvious to investigate the electrical conditions of the flame 
 wires are generally introduced, these become incandescent and so 
 at once add to the electrical phenomena in the flame the very 
 complicated effects we have been discussing in the last chapter. 
 
 The gases which come from the flame, even when they have 
 got some distance away from it and have been cooled by the 
 surrounding air, possess for some time considerable conductivity, 
 and will discharge an insulated conductor placed within their 
 reach. The conductivity can be entirely taken out of the gas by 
 making it pass through a strong electric field, this field abstracts 
 the ions from the gas, driving them against the electrodes so that 
 when the gas emerges from the field, although its chemical com- 
 position is unaltered its conducting power is gone. This result 
 shows too that no uncharged radio-active substances, such as 
 emanate from thorium and some other substances, are produced 
 in the flame, these would not be taken out by the field so that if 
 they existed the conductivity of the gas would not be destroyed 
 by the field. If not driven out of the gas by an electric field the 
 ions are fairly long lived. Thus in some experiments Giese 
 
 T. G. 13 
 
194 IONISATION IN GASES FROM FLAMES. [110 
 
 noticed that the gas retained appreciable conductivity 6 or 7 
 minutes after it had left the flame. The ions stick to any dust 
 there may be in the air and then move very slowly so that their 
 rate of recombination becomes exceedingly slow. M c Clelland* has 
 shown that the velocity of the ions under a given electric force 
 decreases very much as they recede from the flame ; thus close to 
 the flame the velocity under the force of a volt per centimetre 
 was "23 cm. /sec., while some distance away from it the velocity 
 was only '04 cm./sec. 
 
 In order that a conductor should be discharged by a flame it 
 is not necessary that it should be placed where the gases from 
 the flame would naturally strike it thus for example it will be 
 discharged if placed underneath a Bunsen flame. The explanation 
 of this is that the electric field due to the charged conductor 
 drags out of the flame and up to the conductor ions of opposite 
 sign to the charge. 
 
 This ionised gas is produced by flames of coal gas whether 
 luminous or not, by the oxy-hydrogen flame, by the alcohol flame 
 of a spirit lamp, by a flame of carbonic oxide ; it is not however 
 produced in very low temperature flames such as the pale lambent 
 flame of ether. Thus to produce the ionised gas high temperature 
 as well as chemical combination is required. That chemical com- 
 bination alone is insufficient to produce ionisation is shown by the 
 case of hydrogen and chlorine which do not conduct even when 
 combining under ultra-violet light f. BraunJ has shown that 
 in the explosive wave produced in the combination of certain 
 gases there is ionisation, but in this case there is also very high 
 temperature. 
 
 In the coal gas flame the part where the gas comes in contact 
 with the air and where there is most combustion is positively 
 electrified, while the interior of the flame is negatively elec- 
 trified, this accounts for the effect produced by holding a 
 negatively electrified body near the flame, the luminous part 
 turns to the negative body, and if this is near stretches out until 
 it comes into contact with it ; if the flame be placed between two 
 
 * M c Clelland, Phil. Mag. v. 46, p. 29, 1898. 
 
 f J. J. Thomson, Proc. Camb. Phil. Soc. xi. p. 90, 1901. 
 
 J Braun, Zeitschrift fur Physikalische Chemie, xiii. p. 155, 1894. 
 
110] 
 
 IONISATION IN GASES FROM FLAMES. 
 
 195 
 
 oppositely charged plates the bright outer portion of the flame 
 is attracted towards the negative plate while the inner portion 
 moves, but less markedly, towards the positive plate. This effect 
 is illustrated by Fig. 50 taken from a paper by Neureneuf*; in 
 
 Fig. 50. 
 
 some experiments made by Holtz f, one of which is figured in 
 Fig. 51, the flame was divided by the electric field between the 
 
 Fig. 51. 
 
 plates into two sheets ; the reader will find many other interesting 
 experiments on the effect of an electric field on the shape of 
 flames in the papers by Neureneuf and Holtz. It appears from 
 these results that in the bright portion of the flame where combus- 
 tion is taking place there is an excess of positive electricity, while 
 in the unburnt coal gas there is an excess of negative, a fact 
 discovered a long time ago by PouilletJ. If the hydrogen and 
 oxygen were ionised by the heat, then since negative ions of 
 oxygen combine with positive ions of hydrogen to form water, the 
 
 * Neureneuf, Annales de Chim. et de Phys. v. 2, p. 473, 1874. 
 
 t Holtz, Carl Repert. xvii. p. 269, 1881. 
 
 t Pouillet, Ann. de Chim. et de Phys. xxxv. p. 410, 1827. 
 
 132 
 
196 IONISATION IN GASES FROM FLAMES. [110 
 
 negative oxygen ions and the positive hydrogen ones would get 
 used up, and there would be an excess of positive electricity in 
 the oxygen and of negative in the hydrogen. It is possible too 
 that at a temperature corresponding to that of vivid incandescence 
 in a solid the molecules of a gas may like those of a solid give out 
 the negative corpuscles, on this account there would be a tendency 
 for the hotter parts of the flame to be positively the colder 
 negatively electrified. When as in luminous flames we have 
 small particles of solid carbon raised to the temperature of vivid 
 incandescence the electrical effects are complicated by those due 
 to incandescent solids which as we have seen in the last chapter 
 are very considerable. 
 
 When two wires connected together through a sensitive 
 galvanometer are placed in different parts of the flame currents 
 flow through the galvanometer; suppose one of the wires is 
 placed in the cool inner portion of the flame where there is an 
 excess of negative electricity, while the other wire is placed at 
 the outside of the flame where there is an excess of positive 
 electricity there will, neglecting any ionisation due to the wire, 
 be a current from the hot outer portion of the flame to the cool 
 inner portion through the galvanometer : the wire in the outer 
 portion will however certainly be raised to incandescence if its 
 temperature keeps so low that only positive Jons are produced at 
 its surface, then there will on this account be a current of 
 electricity from the hot to the cool part of the flame through the 
 flame and thus in the opposite direction to the previous current. 
 If however the wire got so hot that it emitted more negative 
 than positive ions the effect of the incandescence of the wires 
 would be to increase instead of diminishing the current due to the 
 flame itself. Thus we see that these currents will vary in a 
 complex way with the temperature. For an account of the 
 currents which can thus be tapped from a flame and for other 
 electrical properties of flames we must refer the reader to the 
 papers of Erman*, Hankelf, Hittorf J, Braun, Herwig||, and 
 
 * Erman, Gilbert. Ann. xi. p. 150, 1802 ; xxii. p. 14, 1806. 
 
 t Hankel, Pogg. Ann. Ixxxi. p. 213, 1850 ; cviii. p. 146, 1859. 
 
 J Hittorf, Pogg. Ann. cxxxvi. p. 197, 1869 ; Jubelbd. p. 430, 1874. 
 
 Braun, Pogg. Ann. cliv. p. 481, 1875. 
 
 || Herwig, Wied. Ann. i. p. 516, 1877. 
 
Ill] IONISATION IN GASES FROM FLAMES. 197 
 
 especially of Giese*, who was the first to suggest that the 
 conduction of electricity through flames and hot gases was due 
 to the motion of charged ions distributed through the gases : 
 there is a very complete account of these researches in Wiede- 
 mann's Elektricitdt, bd. IV. B, chap. 4. 
 
 Conductivity of Gases containing Salt Vapours. 
 
 111. When the vapours of salts are introduced into a flame 
 the conductivity between metallic terminals is very greatly in- 
 creased, and the electrical properties are simpler and more regular 
 than in pure flames ; the laws of the flow of electricity through 
 these salt-laden flames have been investigated by Arrheniusf 
 and H. A. Wilson J. The method devised by Arrhenius and 
 adopted by Wilson of introducing the salt into the flame was 
 as follows : a dilute solution of the salt was sprayed into ex- 
 ceedingly fine drops by a Gouy sprayer, the spray got well mixed 
 with the coal gas on its way to the burner, and in the flame the 
 water evaporated and the salt vaporised. The amount of salt 
 supplied to the flame in unit time was estimated by determining 
 the rate at which a bead of salt introduced into an equal and 
 similar flame so as to produce the same coloration as that pro- 
 duced by the spray in the original flame burnt away. The salts 
 used were chiefly the haloid and oxy-salts of the alkali metals 
 and earths. The conductivity due to the salt was determined by 
 subtracting from the current observed when the salt was in the 
 flame the current with the same electromotive force in the pure 
 flame. It was found that when the concentration of the solutions 
 is small, equivalent solutions of all salts of the same metal 
 impart the same conductivity to the flame. With large concen- 
 tration this is no longer the case, the oxy-salts giving greater 
 conductivity than the haloid salts. According to Arrhenius aU 
 the salts in the flame are converted into hydroxides, so that what- 
 ever salts are used, the metal in the flame always occurs in the 
 same salts. The relation between the current and the electro- 
 
 * Giese, Wied. Ann. xvii. pp. 1, 236, 519, 1882 ; xxxviii. p. 403, 1889. 
 f Arrhenius, Wied. Ann. xlii. p. 18, 1891. 
 H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 
 Equivalent solutions are those in which the weight of salt per litre is pro- 
 portional to the molecular weight of the salt. 
 
198 
 
 IONISATION IN GASES FROM FLAMES. 
 
 [in 
 
 motive force is represented by Fig. 5 2 taken from Wilson's paper: 
 we see that the curves resemble in many respects those given in 
 
 20 40 60 80 100 120 14O 160 ISO 200 CeJ S. 
 
 (200 cells = 360 volts) 
 Fig. 52. 
 
 Fig. 4, which represent this relation for the typical ionised gas. 
 There is one well marked difference, however, in the typical curve, 
 the straight part is horizontal, i.e. the current does not increase 
 at all with the electromotive force ; in the case of the salt vapour 
 the straight part is inclined at a finite angle to the horizontal, 
 indicating a slow but steady increase of the current with the 
 electromotive force. The cause of this difference between the 
 normal curves and the curve for the flame is I think that in the 
 latter case the ionisation takes place mainly at the surface of the 
 electrodes (for the proof of this see p. 172). We have thus two 
 sources of supply for the ions, so that to ' saturate ' the current 
 we must use up all the ions from both sources, i.e. all the negative 
 ions produced at the negative electrode, and all the positive ions 
 at the positive electrode must be sent into the gas and used to 
 carry the current. Now as we shall see the velocity of the 
 negative ions in flames containing salt vapours is very much 
 greater than that of the positive, so that the negative ions will 
 be much more easily detached from the negative electrode than 
 the slowly moving positive ions from the positive electrode : thus 
 we shall exhaust the supply of the negative ions long before we 
 do that of the positive. If all the current were carried by the 
 negative ions it would be saturated as soon as the supply of these 
 was exhausted ; in practice a small but appreciable fraction of the 
 current is. carried by the positive ions, so that after the supply of 
 negative ions is exhausted the current will go on slowly increasing 
 for a long range of- potential difference until finally, the supply of 
 
 ''Y?^-'- 
 
112] 
 
 IONISATION IN GASES FROM FLAMES. 
 
 199 
 
 positive ions is exhausted, and then and not till then the current 
 will become independent of the potential difference between the 
 electrodes. The difference between the field required to drive all 
 the ions from the negative and positive electrodes is well illus- 
 trated by an experiment of Wilson's, in which only one of the 
 electrodes was hot, the other was too cold to give rise to any 
 ionisation ; in this case when the hot electrode was negative the 
 current was saturated with a comparatively small potential differ- 
 ence, while it required an exceedingly large potential difference 
 to saturate the current when the hot electrode was positive. 
 
 Another proof in addition to those given on p. 172 that the 
 ionisation at the electrodes is greater than in the body of the gas 
 is afforded by experiments made with the electrodes at different 
 distances apart. If the greater part of the ionisation took place 
 in the body of the gas the saturation current would be proportional 
 to the distance between the electrodes. In the case of conduction 
 through flames containing vapours of salts Wilson has shown that 
 the saturation current is very approximately independent of the 
 distance between the electrodes. 
 
 112. The conductivity given to the flame by the salts of the 
 different alkali metals under the same condition as to temperature, 
 potential difference and concentration. The Caesium salts conduct 
 the best, and then follow in order the salts of Rubidium, 
 Potassium, Sodium, Lithium, and Hydrogen. The order of the 
 conductivities is thus the same as that of the atomic weights of 
 the metals, and the difference between the metals is very large, 
 as is shown by the following table given by H. A. Wilson : 
 
 
 Chlorides. 
 
 Nitrates. 
 
 Potential Difference 
 
 5-60 
 
 795 
 
 237 
 
 5-60 
 
 795 
 
 237 
 
 
 Current 
 
 Current 
 
 Caesium 
 
 123 
 
 60-5 
 
 22-2 
 
 303 
 
 115 
 
 36-6 
 
 Rubidium 
 
 41-4 
 
 26-4 
 
 11-3 
 
 213 
 
 82-4 
 
 25-9 
 
 Potassium 
 
 21-0 
 
 13-4 
 
 5-75 
 
 68-4 
 
 29-3 
 
 9-35 
 
 Sodium 
 
 3-49 
 
 2-45 
 
 1-15 
 
 3-88 
 
 2-67 
 
 1-32 
 
 Lithium 
 
 1-29 
 
 87 
 
 41 
 
 1-47 
 
 99 
 
 53 
 
 Hydrogen 
 
 75 
 
 ... 
 
 27 
 
 
 
 
 
200 IONISATION IN GASES FROM FLAMES. [113 
 
 On the Variation of Conductivity with the strength of the 
 
 Solution. 
 
 113. Arrhenius came to the conclusion that, using the same 
 salt, the conductivity was proportional to the square root of the 
 concentration, while H. A. Wilson considered that the application 
 of this simple law was restricted in the case of the oxy-salts to 
 extremely dilute solutions, and that although the range of its 
 application was more extended in the. case of the haloid salts, the 
 agreement was only approximate. If we refer to the general 
 theory of conduction through an ionised gas (see page 68) we find 
 that the conductivity when the current is far from saturation is 
 proportional to ql, where q is the number of ions produced per 
 second in a cubic centimetre of the gas. In the case of the salt 
 vapour q will be proportional to the number of molecules of salt 
 in a cubic centimetre of the gas, and will thus be proportional to 
 the strength of the solution. This result is derived from the 
 study of the case when ioriisation takes place throughout the 
 volume of the gas; it will however be applicable in its main 
 features to the case when the ionisation only takes place near the 
 surface of the electrodes, provided the thickness of the layers in 
 which the ionisation occurs is large compared with the average 
 distance between the molecules of the salt, and that the dis- 
 tribution of potential between the electrodes is not affected by 
 the concentration of the salt ; this second supposition is probably 
 not true. The above reasoning only applies to the case when the 
 current is far from the saturation value ; when it approaches this 
 value the current is proportional to q and not to q 12 ; thus we 
 should expect that in the case of currents through flames under 
 large electromotive forces Arrhenius' law would cease to be true, 
 and the current would be proportional to the concentration. In- 
 spection of the curves given in Fig. 53 taken from a paper by 
 Smithells, Dawson and Wilson* will show that the variations of 
 the current with the strength of the solution, even when the 
 current is well past the knee of the curve representing the relation 
 between current and potential difference, are much less than they 
 would be if they varied directly as the concentration; in fact, 
 even in this stage they are much more nearly proportional to the 
 square root than to the first power of the concentration. This 
 * Smithells, Dawson and Wilson, Phil. Trans. A. 193, p. 89, 1900. 
 
113] 
 
 IONISATION IN GASES FROM FLAMES. 
 
 201 
 
 effect is rather difficult to account for. May it be due to the 
 thickness of the layer through which the ionisation extends de- 
 pending to some extent on the concentration ? This would be 
 
 Fig. 53. 
 
 the case if the ionisation were produced by radiation or corpuscles 
 proceeding from the electrodes, the absorption of the radiation 
 being due in whole or in part to the work done in ionising the 
 salt ; for consider the extreme case where the absorption is wholly 
 due to the ionisation of the salt, then if the absorption were great 
 enough to stop the radiation from one electrode before it reached 
 the other, the amount of ionisation, and therefore the saturation 
 current, would be independent of the concentration ; with large 
 concentrations the ionisation would be confined to a thin layer 
 near the electrodes, with small concentrations this layer would be 
 thicker, but the total amount of ionisation would be the same 
 in the two cases. If the radiation was not completely absorbed 
 in the space between the electrodes the amount of ionisation 
 would increase with the concentration, but its rate of increase 
 would be slower than that of the concentration. Wilson has 
 shown (see p. 210) that at very high temperatures the saturation 
 current is proportional to the concentration. 
 
202 
 
 IONISATION IN GASES FROM FLAMES. 
 
 [114 
 
 Velocity of the Ions. 
 
 114. The velocity of the ions in flames containing salt vapours 
 has been determined by H. A. Wilson*, who used a method of 
 which the principle is as follows. Suppose that in a flame we 
 have two electrodes one vertically over the other, and that we 
 introduce a bead of salt just underneath the upper electrode, the 
 vapour from this bead will be carried along by the upward rush 
 of gases in the flame, and unless the ions in the salt vapour are 
 driven downwards by the electric field between the electrodes, 
 none of them will reach the lower electrode. If however the ions 
 from the salt do not reach the electrode the current between the 
 electrodes will be unaffected by the presence of the salt. Thus 
 when the potential difference between the electrodes is small the 
 current will not be increased by the introduction of the salt, but 
 as soon as the electric force between the electrodes is sufficient to 
 drive one of the ions against the blast in the flame, the current 
 will be increased by the bead of salt; This is illustrated by the 
 curve in Fig. 54 taken from Wilson's paper ; we see that when 
 
 50, 
 
 80 
 
 160 240 
 
 Fig. 54. 
 
 300 
 
 400 volts 
 
 the upper electrode was positive the current was not increased by 
 the bead until the potential difference between the electrodes was 
 about 100 volts, while for greater differences of potential the bead 
 produced a substantial increase in the current. Thus when there 
 was a difference of 100 volts between the electrodes, the smallest 
 electric force in the space traversed by the ion must be just 
 
 * H. A. Wilson, Phil. Trans. A. 192, p. 499, 1899. 
 
114] IONISATION IN GASES FROM FLAMES. 203 
 
 sufficient to give to the positive ion a downward velocity equal 
 to the upward velocity of the gas in the flame. Since the 
 electric field is not uniform between the electrodes (see p. 191), it 
 is necessary to measure the distribution of potential between the 
 electrodes in order to determine the minimum electric force ; 
 when this and the upward velocity of the gas in the flame are 
 known we can determine the velocity of the ions in a flame 
 under a given electric force. By this and similar methods Wilson 
 deduced the following values for the velocities of the ions under 
 an electric force of a volt per centimetre. 
 
 In a flame whose temperature was estimated to be about 
 2000 C., the velocity of the negative ion, whatever salts were put 
 in the flame, was about 1000 cm./sec. 
 
 The velocities of the positive ions of salts of Caesium, Rubidium, 
 Potassium, Sodium, and Lithium were all equal, and were about 
 62 cm./sec. 
 
 In a stream of hot air whose temperature was estimated at 
 1000C. the following results were obtained for the velocities 
 under a potential gradient of 1 volt per cm. 
 
 Negative ions ... ... ... ... ... 26 cm./sec. 
 
 Positive ions of salts of Li, Na, K, Rb, and Cs 7*2 cm./sec. 
 Positive ions of salts of Ba, Sr, and Ca ... 3'8 cm./sec. 
 
 The absolute numbers must be regarded as only approximately 
 true, the relative values are probably much more accurate. 
 
 The velocities are very much less at 1000 C. than they are 
 at 2000 C., but we notice that while the negative ion at the 
 lower temperature moves at only 1/40 of its pace at the higher, the 
 velocity of the positive ion is by the same fall in temperature only 
 reduced to about 1/8*5 of its value. 
 
 These determinations of the velocity throw some light on the 
 character of the ions ; for suppose e is the charge of electricity on 
 the ion, X the electric force acting upon it, the mechanical force 
 acting on the ion is equal to Xe ; if X is the mean free path of 
 the ion, v its velocity of translation, then the time between 
 two collisions is \/v t and in this time the force acting upon 
 it will give it a velocity in the direction of the force equal to 
 Xekjvm, where m is the mass of the ion; the average velocity 
 
204 IONISATION IN GASES FROM FLAMES. [114 
 
 parallel to X due to the electric force will therefore be 
 and this will be the velocity with which the ion will, under the 
 electric force, move through the gas. > The equal velocity of all 
 negative ions from whatever source they may be derived might 
 at first sight seem to indicate that as Arrhenius supposed all the 
 salts were converted to hydroxides in the flame, and that the 
 negative ion was in every case the radicle OH : let us calculate 
 what on this supposition would be the velocity of the negative 
 ion at a temperature of 2000 G. We do not know the free path 
 of OH through a mixture of coal-gas and air, but as the free path 
 of the molecule H 2 through hydrogen at C. and at atmospheric 
 pressure is 1*8 x 10~ 5 cm., and the free path ofO 2 through oxygen 
 under the same circumstances is T06 x 10~ 5 cm., we may as a 
 rough approximation take for the mean free path of OH through 
 the mixture the value 1'4 x 10~ 6 cm. at 0C.; aj 2000 C. X the 
 mean free path would be this value multiplied by 2273/273, i.e. 
 1'2 x 10~ 4 . To get the value of v we remember that mv 2 is the 
 same for all gases at the same temperature, while at different 
 temperatures it is proportional to the absolute temperature. 
 For O 2 at C. v = 4'25 x 10 4 cm./sec., hence for OH at C. 
 v = 5-6 x 10 4 cm./sec., and for OH at 2000 C. v = T6 x 10 5 : e/m 
 for OH is equal to I'l x 10 3 , hence substituting these values in the 
 expression Xe\/Zvm and putting X = 10 8 we find for the velocity 
 under the potential gradient of one volt per cm. 37 cm./sec.: the 
 actual velocity is as we have seen 1000 cm./sec.: hence we con- 
 clude that the radicle OH cannot be the carrier of the negative 
 charges. The great velocity of the negative ions at these high 
 temperatures points to the conclusion that the negative ions 
 start as corpuscles and gradually get loaded by molecules con- 
 densing round them ; at temperatures as high as 2000 the time 
 they exist as free corpuscles is an appreciable fraction of their life; 
 while they are free corpuscles they have an exceedingly large 
 velocity, so that though this is enormously reduced when they 
 become the nucleus of a cluster, their average velocity is very 
 considerable. At low temperatures condensation takes place 
 much sooner, so that the average velocity is lower. 
 
 The fact that under an electric field the velocities of the 
 positive ions of all the salts of the univalent metals are the same, 
 shows that these too become the nucleus of a group whose size only 
 
115] IONISATION IN GASES FROM FLAMES. 205 
 
 depends upon the charge on the positive ion ; since the velocities 
 of the positive ions for the divalent metals while equal among 
 themselves are less than those of the monovalent metals, we con- 
 clude that these divalent ions become the centres of clusters more 
 complex than those which collect round the monovalent ions. 
 
 Determinations of the velocities of the ions in flames have also 
 been made by Marx*, he finds for the velocity of the negative 
 ion the same value as Wilson, i.e. 1000 cm./sec. under a potential 
 gradient of a volt per centimetre, he gets however for the positive 
 ions under the same gradient considerably larger values than 
 Wilson, i.e. 200 cm./sec. instead of 62 cm./sec. A calculation 
 similar to that just given for the velocity of the radicle OH 
 shows that a velocity of 200 cm./sec. is of the same order as the 
 velocity at 2000 C. of an atom of hydrogen in an electric field. 
 
 \ 
 
 Transverse Electromotive Force produced by a magnetic field 
 acting on a flame carrying a current. 
 
 115. If an electric current is flowing through a flame parallel 
 to the direction x, and a magnetic force at right angles to this 
 direction, say parallel to the direction y, is applied to the flame, 
 a transverse electromotive force is produced which is at right 
 angles to both x and y. This electromotive force has been detected 
 and measured by Marx~f*. The general explanation of this effect, 
 which is analogous to the ' Hall ' effect in metals, is easy ; the 
 calculation of its magnitude except in a few special cases is how- 
 ever beset by difficulties. 
 
 As there is a current parallel to x flowing through the flame, 
 the average direction of the positive ions will be along, say, the 
 positive direction of x, that of the negative ions in the opposite 
 direction. Let V be the average velocity of the positive ions, 
 V that of the negative, if these are moving in a magnetic field 
 where the magnetic force H is parallel to y, they will be subject 
 to mechanical forces tending to move them in the same direction, 
 this direction being parallel to z, at right angles to both x and y. 
 The magnitudes of the mechanical forces acting on the positive 
 and negative ions are respectively HeV and HeV, where e is the 
 
 * Marx, Drude's Ann. ii. p. 768, 1900. 
 f Ibid. p. 798, 1900. 
 
206 IONISATION IN GASES FROM FLAMES. [115 
 
 charge on an ion. The displacement of the ions under these 
 forces will (if V is not equal to V) produce a current of electricity 
 through the flame parallel to z ; if however the ions cannot 
 escape in this direction the current will soon stop, as the accu- 
 mulation of ions will produce a back pressure and an electrostatic 
 field which will balance the effect of the mechanical forces arising 
 from the magnetic field. 
 
 We shall now proceed to deduce the equations which give the 
 disturbance produced by the magnetic field ; these equations are 
 not limited to the case of flames, but apply to all cases of the 
 conduction of electricity through a gas containing ions. 
 
 Let the direction of the primary current, i.e. the current before 
 the magnetic field is applied, be taken as the axis of x, let the 
 magnetic force act downwards at right angles to the plane of 
 the paper : then the force on the ions will be in the plane of 
 the paper and at right angles to the axis of x ; we shall take the 
 axis of z in this direction. 
 
 Let H be the intensity of the magnetic force, 
 
 X, Z the components of the electric force parallel to the 
 
 axes of x and z respectively, 
 u, v the velocities of the positive and negative ions under 
 
 unit electric force, 
 Pit Pz the pressures at any point due to the positive and 
 
 negative ions respectively, 
 ra, n the number of positive and negative ions per cubic 
 
 centimetre at any point. 
 
 We shall assume that these ions behave like a perfect gas, so 
 that P! = Rm, p 2 Rn, where R is a constant proportional to the 
 absolute temperature. 
 
 Let us consider first the positive ions, their velocity parallel 
 to the axis of x is Xu, hence the mechanical force on an ion 
 parallel to z due to the magnetic field is euXH, the force on the 
 ion due to the electric field is Ze, and the force on the ions in unit 
 volume due to the variation in the pressure at different points in 
 the field is dpi/dz, hence the total force parallel to z on the 
 positive ions in unit volume is equal to 
 
 - < & + 
 
115] IONISATION IN GASES FROM FLAMES. 207 
 
 and the number crossing in unit time one square centimetre of 
 surface at right angles to z is equal to 
 
 U ( dp l , TTTT rr^} 
 
 - - -f + me (uXH + Z)\, 
 
 similarly the flux parallel to x is equal to 
 
 or, if we neglect terms depending upon H z the term uZH may 
 be omitted and the flux parallel to x is then 
 
 u ( dp l v ) 
 
 - ] -f- + meX . 
 e { dx } 
 
 Similarly the flux of the negative ions parallel to z is equal to 
 
 and the flux parallel to x to 
 
 v f dp z rr 
 
 - j- neX 
 e \ dx 
 
 Let q be the number of ions produced in one cubic centimetre 
 of the gas in one second, anm the number of ions which recombine 
 in one second in unit volume ; then by the equation of continuity 
 we have when things are in a steady state, 
 
 u d f dp l / VTT n\ I u d f dp^ v \ 
 
 -j- 4 f- + me (uXH + Z) > H :- f- 4- meX ) = q 
 
 e dz { dz } e dx\ dx J 
 
 v d ( dp% / VTT r7\\ v d / dp 2 
 
 j- 4 ^ 4- ne (vJLii Z) > H ^ 7 
 
 e dz { dz } e dx\ ax 
 
 we have also, using electrostatic units, 
 
 dX dZ 
 
 -j- + -j- = 4<7re (m n), 
 dx dz 
 
 dX dZ 
 
 and =- = 0. 
 
 dz dx 
 
 Since p^ = Rm, p 2 = Rn, we have as many equations as there 
 are variables, p lf p 2 , m, n, X, Z. The solution will however depend 
 very greatly upon the boundary conditions; thus one solution 
 is = 0, p l and p u constant, and X independent of z and the 
 
208 IONISATION IN GASES FROM FLAMES. [115 
 
 same as when the magnetic force is zero : this, however, involves a 
 transverse flux of positive ions equal to mu 2 XH and of negative 
 ions equal to nv 2 XH, and is not consistent with a steady state 
 unless there is some means for this transverse stream to escape. 
 If there is no way of escape for the transverse streams of ions 
 the flux of the ions parallel to z must vanish at the boundaries of 
 the gas. Let us suppose that it vanishes throughout the gas, then 
 we have 
 
 Q .................. (1) ; 
 
 .................. (2). 
 
 Putting p l = Rm, p 2 Hn and (m n)e = p we get from (1) 
 and (2) 
 
 + n) ......... (3); 
 
 6 CLZ 
 
 and since, changing to electromagnetic units, 
 dp I (d*Z d*Z 
 
 7r -~ + 
 
 where V is the velocity of light ; (3) becomes 
 
 + n) ...... (4), 
 
 R /( 
 
 an equation to find Z. In the terms on the right-hand side, we 
 may put for X, m, n the values when H = 0, if we are content to 
 neglect terms in H 2 . 
 
 Since 7 2 = 9 x 10 20 , e = I'l x 1Q- 20 (in electromagnetic units), 
 Ji = 5 x 10 ~ 14 , for a gas at C., we see that (4) may be written 
 
 4 x 10~ 16 (-T-J + -r-g ) = eXH (mu - nv) + Ze(m+ n). 
 \ (Lx (JiiZ ) 
 
 If the sum of the partial pressures due to the positive and 
 negative ions were 1 atmosphere e (m + n) would be about '5, hence 
 we see that if the pressure of the ions is large compared with 
 10~ 15 atmospheres and if Z does not vary exceedingly rapidly 
 with x, a very approximate solution of (4) will be 
 
 z= XH(nv-mu) 
 
 m + n 
 
115] IONISATION IN GASES FROM FLAMES. 209 
 
 This may be written 
 
 e (m + ri) ' 
 
 where i n and i p are respectively the currents carried by the negative 
 and positive ions. 
 
 At a place where there is no free electricity m n\ in this 
 case (5) becomes 
 
 This is the formula usually employed, but we see from the 
 preceding work it is only applicable in a very special case. 
 
 When solutions of KC1 of various strengths were sprayed into 
 a flame Marx* found values of Z/XH varying from 10'18 x 10~ 
 for the pure flame to 3*7 x 10 ~ 6 when a saturated solution of 
 KC1 was sprayed into it, the sign of the result showing that 
 the velocity of the negative ion is greater than that of the 
 positive. If we apply the preceding formula we find, on the 
 supposition that the measurements were made in a part of the 
 flame where there was no free electricity, that the difference 
 between the velocities of the negative and positive ions under an 
 electric force of one volt per centimetre, i.e. 10 8 units, would vary 
 from 2036 cm. /sec. for the pure flame to 740 cm. /sec. for the 
 flame containing the concentrated solution ; the value 940 found 
 by H. A. Wilson by direct experiment is between these limits. 
 
 If the electric and magnetic forces are considerable there will, 
 when there is no escape for the transverse flow of ions, be very 
 considerable variations in the number of ions in the gas : for putting 
 2>! = Rm, p 2 = Rn, we get from equations (1) and (2), 
 
 R -j- log mn = eXH (u + v), 
 
 or mn 
 
 where C is a constant. To see what concentration this implies 
 let us take the case of air ionised by Rontgen rays, the pressure 
 being 1/1000 of an atmosphere, then since u + v at atmospheric 
 pressure is 3 x 10- 8 crn./sec., at the assumed pressure it will be 
 3 x 10- 5 , and if X is 10 volts a centimetre, i.e. 10 9 , and #=10 2 , 
 then since e/J? = 4 x 10~ 7 , we see 
 
 mn = C f 1 ' 2z ; 
 
 * Marx, Drude's Ann. ii. p. 798, 1900. 
 T. G. U 
 
210 IONISATJON IN GASES FROM FLAMES. [116 
 
 thus in the space of a centimetre parallel to z, run will about triple 
 in value : this variation in the number of ions will affect the 
 distribution of the current parallel to x, the current will be 
 greatest where there are most ions and will therefore no longer 
 be independent of z : this variation in the current may affect the 
 distribution of potential between the electrodes and thus introduce 
 fresh sources of disturbance into the problem. 
 
 In the case when there are only ions of one sign present, say 
 the negative, there is a very simple solution of the preceding equa- 
 tions, for we see that Z = eHXv, p 2 constant and X the same as 
 when there is no magnetic force satisfies these equations. 
 
 Maximum current that can be carried by the vapour of a salt. 
 
 116. H. A. Wilson* has made an exceedingly important set 
 of experiments on the maximum current that can be carried by a 
 given amount of salt vapour ; in these experiments the solution 
 containing the salt vapour was not sprayed into flame, but into 
 air heated by passing through a long platinum tube raised to 
 bright yellow heat by a furnace ; a smaller central tube was 
 placed along the axis of the outer tube and the current between 
 the inner and outer tubes measured. When solutions of the 
 strength I/ 10th normal were sprayed and the temperature of the 
 tubes raised and the potential difference increased, a stage was 
 reached when neither an increase in the temperature nor in the 
 potential difference produced any increase in the current. Wilson 
 measured this limiting current and found that it was equal to the 
 current which when passing through an aqueous solution of the 
 salt would electrolyse in one second the same quantity of salt as 
 was sprayed in that time into the hot air ; thus if the salt had 
 been supplied to water at the same rate as it was supplied to 
 the hot air the maximum current that could be sent through 
 the aqueous solution would be the same as that which could be 
 sent through the air; this was proved for the following salts of 
 the alkali metals: CsCl, CsCO 3 , Rbl, RbCl, Rb 2 CO s , KI, KBr, 
 KF, K.C03, Nal, NaBr, NaCl, Na 2 CO 3 , Lil, LiBr, LiCl, Li 2 C0 3 . 
 
 * H. A. Wilson, Phil. Mag. vi. 4, p. 207, 1902. 
 
CHAPTER X. 
 
 IONISATION BY LIGHT. PHOTO-ELECTRIC EFFECTS. 
 
 THE discovery by Hertz* in 1887 that the incidence of ultra- 
 violet light on a spark gap facilitated the passage of the spark, 
 led immediately to a series of investigations by Hallwachsf, 
 HoorJ, Righi and Stoletow|| on the effect of light, and especially 
 of ultra-violet light, on charged bodies. It was proved by these 
 investigations that a newly cleaned surface of zinc, if charged with 
 negative electricity, rapidly loses this charge however small it may 
 be when ultra-violet light falls upon the surface; while if the 
 surface is uncharged to begin with, it acquires a positive charge 
 when exposed to the light, the negative electrification going out 
 into the gas by which the metal is surrounded ; this positive 
 electrification can be much increased by directing a strong air- 
 blast against the surface. If however the zinc surface is positively 
 electrified it suffers no loss of charge when exposed to the light : 
 this result has been questioned, but a very careful examination 
 of the phenomenon by Elster and GeitellF has shown that the 
 loss observed under certain circumstances is due to the discharge 
 by the light reflected from the zinc surface of negative electrifica- 
 tion on neighbouring conductors induced by the positive charge, 
 the negative electricity under the influence of the electric field 
 moving up to the positively electrified surface. 
 
 * Hertz, Wied. Ann. xxxi. p. 983, 1887. 
 
 t Hallwachs, Wied. Ann. xxxiii. p. 301, 1888. 
 
 $ Hoor, Repertorium des Physik, xxv. p. 91, 1889. 
 
 Kighi, G. R. cvi. p. 1349 ; cvii. p. 559, 1888. 
 
 || Stoletow, C. R. cvi. .pp. 1149, 1593; cvii. p. 91; cviii. p. 1241; Physikalische 
 Revue, bd. i., 1892. 
 
 IT Elster and Geitel, Wied. Ann. xxxviii. pp. 40, 497, 1889; xli. p. 161, 1890; 
 xlii. p. 564, 1891; xliii. p. 225, 1892; lii. p. 433, 1894; Iv. p. 684, 1895. 
 
 142 
 
212 IONISATION BY LIGHT. [116 
 
 The ultra-violet light to produce these effects may be obtained 
 from an arc lamp, or by burning magnesium, or by sparking with 
 an induction coil between zinc or cadmium terminals, the light 
 from which is very rich in ultra-violet rays. Sunlight is not rich 
 in ultra-violet rays, as these have been absorbed by the atmosphere, 
 and it does not produce nearly so large an effect as the arc-light. 
 Elster and Geitel who have investigated with great success the 
 effects produced by light on electrified bodies have shown that 
 the more electropositive metals lose negative charges even when 
 exposed to ordinary daylight. They found that amalgams of 
 sodium or potassium enclosed in a glass vessel lose a negative 
 charge in the daylight, though the glass would stop any small 
 quantity of ultra-violet light that might be left in the light after 
 its passage through the atmosphere. When sodium or potassium 
 by themselves instead of their amalgams were used, or, what is more 
 convenient for many purposes, the liquid alloy formed by mixing 
 these metals in the proportion of their combining weights, they 
 found that the negative electricity was discharged by the light 
 from a petroleum lamp : while with the still more electropositive 
 metal rubidium the negative electricity could be discharged by 
 the light from a glass rod just heated to redness. They found, 
 however, that the eye was more sensitive to the radiation than 
 the rubidium, for no discharge could be detected until after the 
 radiation from the glass rod was visible. 
 
 Elster and Geitel arrange the metals in the following order 
 with respect to their power of discharging negative electricity : 
 
 Rubidium. 
 Potassium. 
 
 Alloy of Potassium and Sodium. 
 Sodium. 
 Lithium. 
 Magnesium. 
 Thallium. 
 Zinc. 
 
 For copper, platinum, lead, iron, cadmium, carbon, and mer- 
 cury the effects with ordinary light are too small to be measurable. 
 The order of the metals for this effect is the same as in Volta's 
 series for contact-electricity, the most electropositive metals 
 
117] PHOTO-ELECTRIC EFFECTS/ 213 
 
 giving the largest photo-electric effect. Many substances besides 
 metals discharge negative electricity under the action of ultra-] 
 violet light: lists of these substances will be found in papers by) 
 G. C. Schmidt* and O. Knoblauch f. Among the more active 
 photo-electric solids are, fluor-spar, the various coloured varieties 
 of which vary greatly in the degree to which they possess this 
 property ; the sulphides of antimony; lead, arsenic, manganese, 
 silver, and tin (the sulphates do not possess this property); 
 hydroxide of tin, iodide of lead, many aniline dyes in the solid 
 state. 
 
 Pure water is not photo-electric, and a thin film of water over - 
 the surface of a metal destroys the effect due to the metal. The 
 solutions of many substances are however very photo-electric, 
 especially solutions of fluorescent substances such as eosine, |^ 
 fuchsine, cyanine, hydrochinone, congo-red ; potassium nitrate and 
 formic acid also show this effect. Among well-known substances 
 which do not show this effect we may mention solutions of sulphate 
 of quinine, potassium permanganate and phenol. 
 
 Photo-electric properties of gases. 
 
 117. With gases the action of light may be expected to mani- 
 fest itself in a different way from that occurring in the case of solids 
 and liquids, we cannot expect to get a separation of electricity 
 of such a kind that one region of the gas becomes positively, 
 another negatively, electrified. If a molecule of a gas loses, 
 like a piece of metal, negative electricity when exposed to ultra- 
 violet light, then this molecule will behave like a positive ion, and 
 the negative corpuscle it has lost will attach itself to some other 
 molecule of the gas which will act like the negative ion ; thus if , 
 ultra-violet light produced on the molecules and atoms of a gas ) 
 the same effect as it does on a mass of metal we should expect J 
 this effect to show itself as ionisation of the gas. In the case of 
 sodium vapour, light produces a decided increase in the conduc- 
 tivity; it is not necessary that the light should be ultra-violet, the 
 light from a petroleum lamp is sufficient to produce well-marked 
 effects ; we have seen that sodium when in the solid state is 
 
 G. C. Schmidt, Wied. Ann. Ixiv. p. 708, 1898. 
 
 1 O. Knoblauch, Zeit. /. Physikalische Chemie, xxix. p. 527, 1899. 
 
214 IONISATION BY LIGHT. [117 
 
 peculiarly sensitive to the action of light. Experiments have been 
 made on other gases; thus Henry* who tried the effect of ultra- 
 violet light on iodine vapour, which absorbs a good deal of light, 
 could not detect any increase in conductivity when the gas was 
 illuminated : Buissonf was unable to detect any conductivity in air 
 through which ultra-violet light was passing : recently, however, 
 Lenard j has described an effect due to a very easily absorbed 
 kind of ultra-violet light produced when sparks from an induction 
 coil pass between aluminium terminals ; this light is so easily 
 absorbed by air that its effect becomes inappreciable after it has 
 passed through a few centimetres of air at atmospheric pressure. 
 Quartz is more transparent than air to this light ; coal-gas, is very 
 much less transparent than air, while hydrogen is more so. If 
 the aluminium terminals were placed behind a quartz window 
 in a metal plate, then a charged conductor placed on the far side 
 of the plate near to the gas illuminated by these rays was found 
 to lose its charge rapidly if positively electrified, very much more 
 slowly if negatively electrified. In order to avoid spurious effects 
 due to the light falling on metal surfaces in the neighbourhood 
 Lenard covered these with soap and water, which he found pre- 
 vented any discharge of electricity due to light falling on a metal 
 plate. The much greater loss experienced by the plate when the 
 charge was positive than when it was negative indicates that the 
 velocity of the negative ions is much greater than that of the 
 positive. Lenard measured by a method used by Zeleny and 
 described on p. 38, the velocities of the ions; he found that 
 under a potential gradient of a volt per centimetre the velocity 
 of the negative ions through air at atmospheric pressure is 3'13 
 cm. /sec. : this is considerably greater than (almost double) the 
 velocity found by Rutherford for the negative ions produced by 
 ordinary ultra-violet light incident on a metal plate : the velocity 
 of the positive ions was found by Lenard for a gradient of a volt 
 per centimetre to be only '0015 cm. /sec., that is only about 1/2000 
 of the velocity of the negative ions. The exceedingly small velocity 
 of these positive ions raises the question as to whether they are 
 not particles of dust or minute drops of impure water, rather than 
 
 ' * Henry, Proc. Camb. Phil. Soc. ix. p. 319, 1897. 
 
 f Buisson, quoted by Perrin, Ann. de Chimie et de Physique, vii. 11, p. 526, 
 1897. 
 
 J Lenard, Drude's Ann. i. p. 486 ; iii. p. 298, 1900. 
 
117] PHOTO-ELECTRIC EFFECTS. 215 
 
 gaseous ions. It is essential to show that they are not of this 
 nature if these experiments are to demonstrate the ionisation of the 
 air by the ultra-violet light, for the enormous discrepancy between 
 the velocities of the positive and negative ions is exactly what we 
 should expect if dust possessing photo-electric properties were 
 exposed to the influence of ultra-violet light; such particles would 
 emit negative electricity, while the positive electricity would 
 remain behind on the dust ; the comparatively large dust particles 
 would move very slowly in an electric field, while the negative 
 ions being free from dust might be expected to move with much 
 greater velocity. Lenard discusses this interpretation of his 
 results and rejects it for reasons which do not appear to us abso- 
 lutely convincing. He considers that the negative ions produced 
 by the action 'of ultra-violet light on air are essentially different 
 from those produced when the light falls on a metal, and that 
 while the latter are able to produce condensation in a steam jet, 
 the former are unable to do so. The evidence for this is as follows ; 
 though the gas under direct illumination by the ultra-violet light 
 produces vigorous condensation in a steam jet, yet if the negative 
 ions are pulled out of the illuminated gas by a positively charged 
 plate placed at some distance away no condensation of the jet takes 
 place in the region between the plate and the gas exposed to the 
 light, though the leak of positive electricity from the plate shows 
 that this region is being traversed by negative ions. To make 
 the experiment conclusive, however, we require to know the 
 sensitiveness of the steam jet, i.e., the minimum number of ions 
 per cubic centimetre it is capable of detecting, and also to be sure 
 that the number of negative ions in the neighbourhood of the jet 
 exceeds this minimum : now the second point is one that requires 
 very careful attention, for if the electric field in the neighbourhood 
 of the plate is intense the negative ions will be moving at a very 
 high speed and a very small number of ions in each cubic ceniii- 
 metre would be sufficient to produce a very appreciable leak ; in 
 fact if this leak is ' saturated ' we see that the density of the ions 
 will be inversely proportional to the strength of the field, so that 
 by increasing this strength sufficiently we could certainly stop the 
 condensation of the steam-jet. Thus this experiment does noti. 
 prove that the negative ions are incapable of acting as centres 
 of condensation : to make the proof valid we should require to 
 know that the number of ions in each unit volume was so large 
 
216 IONISATION BY LIGHT. [118 
 
 that condensation would take place if these ions had the property 
 of the normal negative ion. 
 
 118. C. T. R. Wilson* has studied the action of ultra-violet 
 light on gases from the point of view of the effect produced by the 
 light on the formation of clouds. His results with intense light 
 have already been described in Chapter VII., we shall only consider 
 here the effects he got with very feeble light, as the effects have a 
 direct bearing on the question of the ionisation of air by ultra- 
 violet light, though they do not touch the question as to the effects 
 produced by the extremely absorbable light studied by Lenard. 
 Wilson found that with very feeble ultra-violet light clouds were 
 produced by expansion when this exceeded a definite amount, just 
 as in the case of a gas ionised by Rontgen rays, and that the 
 amount of expansion required was just the same for the ultra- 
 violet light as for these rays : this at first sight looks as if the 
 ultra-violet light ionised the gas. Wilson, however, found that the 
 clouds produced by ultra-violet light differed from those produced 
 by Rontgen rays, inasmuch as the former were not affected by 
 strong electric fields, whereas the formation of the latter was 
 almost entirely prevented by such fields. If the clouds due to 
 ultra-violet light had been due to the ionisation of the gas the 
 ions would have been removed by the field and the clouds stopped. 
 At the same time the coincidence between the expansions required 
 for the formation of clouds under ultra-violet light and when ions 
 are present is so remarkable that it makes us very reluctant to 
 believe that the nuclei are different in the two cases ; it seems to 
 me tfyat an explanation which is in harmony with the facts is that 
 charged ions do form the nuclei of the drops formed by weak 
 ultra-violet light, but that these ions are produced during the 
 expansion of the gas and are not present when the gas is at rest; 
 these ions might arise in the following way : we have seen in 
 Chapter VII. that under the action of strong ultra-violet light visible 
 clouds are formed without expansion, these clouds being probably 
 due to the formation of hydrogen peroxide, which mixing with the 
 water lowers the vapour pressure; now when the light is very 
 feeble it seems probable that there may still be a formation of 
 drops of water which, however, in consequence of the very small 
 amount of hydrogen peroxide produced by the feeble light, never 
 
 * C. T. R. Wilson, Phil. Trans. 192 A, p. 403, 1899. 
 
119] PHOTO-ELECTRIC EFFECTS. 217 
 
 grow large enough to be visible. Thus we may regard the air 
 exposed to the ultra-violet light as full of exceedingly minute 
 drops of water ; when the expansions take place the air will rush 
 violently past the drops and we get a state of things which in 
 many respects is analogous to the bubbling of gas through water; 
 when, however, air bubbles through water there is as Lord Kelvin* 
 has shown negative electricity in the air and positive in the water; 
 thus when the air rushes past the water drops we should expect 
 the air to contain negative ions, the positive ions being on the 
 drops; the ions once formed would act as nuclei for clouds if the 
 expansion exceeded the value 1*25. If this view is correct, then 
 we should expect the number of ions produced by an expansion 
 greater than 1'25 to increase with the expansion, for in this case 
 the expansion has to produce the nuclei as well as deposit the 
 clouds, and the more vigorous the expansion the greater would be 
 the number of nuclei produced. 
 
 It is an important meteorological question as to whether direct 
 sunlight can produce a cloud in the atmosphere without expan- 
 sion. Wilson was not able to get a cloud in a closed vessel in 
 sunlight with less than the normal expansion T25. He points 
 out, however, that the conditions in the open air are more favour- 
 able to the production of clouds than those in a closed vessel, for in 
 a closed vessel the drops might diffuse to the sides before they had 
 time to grow to a visible size, while in the atmosphere this way of 
 escape would not be open to them. 
 
 Photo-electric effects involve an absorption of Light. 
 
 119. Stoletowf at an early stage in the history of this subject 
 called attention to the connection between the photo-electric 
 effects and the absorption of the ultra-violet light ; he pointed 
 out that water which does not give photo-electric effects does not 
 absorb many of the visible or ultra-violet rays, while solutions 
 such as those of methyl -green or violet, which are photo-electric, 
 show strong absorption. Hallwachs^:, who investigated the subject 
 in greater detail, showed that all the photo-electric liquids which 
 he tried showed strong absorption for the ultra-violet light, but 
 
 * Lord Kelvin, Proc. Roy. Soc. Ivii. p. 335, 1894. 
 t Stoletow, Physikalische Revue, bd. i. 1892. 
 J Hallwachs, Wied. Ann. xxxvii. p. 666, 1889. 
 
218 
 
 IONISATION BY LIGHT. 
 
 [119 
 
 that strong absorption was not always accompanied by photo- 
 
 ? electric effects ; thus for example the aqueous solution of fuchsine 
 
 / is photo-electric, while the alcoholic solution is not, and yet the 
 
 S alcoholic solution absorbs more ultra-violet light than the aqueous 
 
 > one. 
 
 The effects of increased absorption are shown in a very 
 beautiful way by the experiments of Elster and Geitel* on the leak 
 of negative electricity from surfaces of sodium, potassium, and 
 rubidium under different coloured lights. The experiments, the 
 results of which are shown in the following table, were made as 
 follows ; the rate of escape from the three metals when exposed to 
 the white light from a petroleum lamp was measured, these mea- 
 surements are given in the table under the heading ' white light.' 
 The light from this lamp was then sent through an ammoniacal 
 solution of copper oxide and the metals exposed to the blue light 
 thus obtained ; this solution was replaced by one of potassium 
 chromate to get yellow light, by one of potassium bichromate to get 
 orange light, and by a plate of deep red glass to get the red light. 
 
 Colour of Light 
 
 Rate of leak of negative electricity 
 
 Na 
 
 K 
 
 Rb 
 
 White 
 
 21-0 
 
 7'8 
 226 
 8-2 
 21-9 
 3'1 
 21-9 
 2 
 
 53-1 
 30-3 
 52-9 
 3-5 
 53-9 
 2-2 
 52-9 
 
 o-i 
 
 537-0 
 86-8 
 527-7 
 339-7 
 552-3 
 182-0 
 527-7 
 21-0 
 
 Blue 
 
 White 
 
 Yellow 
 
 White 
 
 Orange . 
 
 White 
 
 Red 
 
 
 Thus we see from this table that though for white and blue 
 lights potassium is much more photo-electric than sodium, it is 
 much less so for yellow and orange light, owing to the strong ab- 
 sorption of these rays by the sodium. The very great sensitiveness 
 of rubidium to light of long wave-length is another instance. 
 Thus while the ratios of the leaks for rubidium and potassium 
 under blue light were only 3 to 1, the ratio- for yellow light was 
 about 100 to 1. 
 
 * Elster and Geitel, Wied. Ann. lii. p. 433, 1894. 
 
120] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 219 
 
 Connection between the rate of leak and strength of Electric Field. 
 
 120. The first measurements on this subject were made by 
 Stoletow*, who used the following arrangement: the light from 
 an arc lamp passed through a hole in a metal screen, and after 
 passing through a perforated plate C fell upon a parallel metal 
 plate D ; these plates were connected together through a battery, 
 the negative pole of the battery being connected with D, the plate 
 illuminated by the light. The current passing between the plates 
 was measured by a very sensitive galvanometer. By means of this 
 
 E-5 10 15 20 25 3O 40 50 60 70 80 90 1OO 
 
 Fig. 55. 
 
 arrangement Stoletow measured the relation between the current 
 and the potential difference between the plates, making experi- 
 
 * Stoletow, Journal de Physique, ii. 9, p. 468, 1890. 
 
220 IONISATION BY LIGHT. [120 
 
 ments with the plates at distances apart varying from about 2*5 
 millimetres to 100 millimetres; the results of these experiments, in 
 which the gas between the plates was air at atmospheric pressure, 
 are represented by the curves of Fig. 55 ; the abscissae represent 
 the potential differences between the plates, the unit being 
 1*43 volts (the electromotive force of a Clark's cell); the ordinates 
 represent the current passing between the plates, the unit being 
 8'6 x 10~ u amperes; the symbol on the curve, for example x+ 25, 
 indicates that the distance between the plates was x 4- 25 milli- 
 metres, where x is a small distance, about 1*5 mm., that was not 
 very accurately determined; the diameter of the plates was 22 mm. 
 An inspection of the curves shows that when the distance between 
 the plates is small and the electromotive force large the current 
 increases much more slowly than the electromotive force ; it is, 
 however, evidently far from saturation ; while when the plates 
 were separated by distances greater than 25 mm. there was no 
 approach to saturation. The curves corresponding to the greater 
 distances between the plates show that under small electromotive 
 forces the current increases more rapidly than the potential differ- 
 ence. As far as the measurements represented in the figure go 
 i is approximately the same at all distances d, provided V/d is 
 the same, V being the potential difference, i.e., i is a function 
 of the mean value of the electric force between the plates ; this 
 law, as Stoletow showed in a later paper*, does not apply for any 
 great range of potential differences, at lower pressures especially 
 the departures from it are soon very apparent. 
 
 Since in this case the ions are all of one kind we may apply 
 the equation of Art. 99, i.e., 
 
 7* Y 2 _L 8?n ^ 
 
 X = X + ~IT> 
 
 where R is the velocity of the ion under unit electric force, 
 i the intensity of the current, X and X the values of the electric 
 force at the plate and at a point distant x from it. 
 
 To form an estimate of the variation in the electric field which 
 is produced by the presence of the negative ions between the 
 plates, let us take one of Stoletow's experiments in which under an 
 electric field of 150 volts per cm. the current was 3*3 x 10~~ n 
 
 * Stoletow, Journal de Physique, ii. 9, p. 469, 1890. 
 
120] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 221 
 
 amperes. The velocity of the negative ions produced by a field 
 of 1 volt per centimetre has been shown by Rutherford to be about 
 1'5 cm. /sec. Hence using electrostatic units, X and X being 
 the values of X at places a centimetre apart, putting i = 10" 1 , 
 ^ = 4'5xl0 2 , X+X =1, in the preceding equation, we get 
 X - X Q = 1/180 or a little less than 2 volts per cm., thus the 
 variation in the strength of the field is comparatively small. 
 Stoletow, who determined the intensity of the field between two 
 parallel plates one of which was illuminated by ultra-violet light, 
 was not able to detect any variation in the intensity. Schweidler*, 
 who investigated this point at a later period, found that the distri- 
 bution of potential between the plates when the ultra-violet light 
 was in action, was not quite uniform ; his results are shown in 
 Fig. 56, where the curved line represents the distribution of 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 i' 
 
 
 
 
 
 
 
 
 
 l\ 
 
 
 
 
 
 
 
 
 
 
 n 
 
 
 
 
 
 
 
 
 
 / 
 
 i 
 
 
 
 Ij 
 
 
 
 
 
 
 n 
 
 
 
 
 <; 
 
 
 
 
 
 
 l 
 
 
 
 
 ~5 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 / 
 
 1 
 
 
 
 
 
 
 
 
 
 } 
 
 / 
 
 
 
 
 
 
 
 
 / 
 
 1 
 
 
 
 
 
 
 
 
 
 l 
 
 I 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 
 
 
 ) 
 
 / 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 // 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 5 10 16 20 35 30 39 40 45 50 65 
 
 Fig. 56. 
 
 potential when the light was shining, the straight one when it 
 was not. The curvature of the potential curve in the light is all 
 in one direction, indicating the presence of an excess of negative 
 ions in every part of the region between the plates. The varia- 
 tion in the intensity of the field between the plates has also been 
 observed and measured by Buissonf and used by him to determine 
 the velocity of the negative ions ; he finds that under a potential 
 gradient of a volt per cm. this velocity is about 2'2 cm./sec. 
 
 * Schweidler, Wien. Ber. cvii. p. 881, 1898. 
 
 t Buisson, Comptes Rendus, cxxvii. p. 224, 1898. 
 
222 
 
 IONISATION BY LIGHT. 
 
 [120 
 
 Schweidler* has also made experiments on the relation between 
 the current and the strength of the electric field over a wider 
 range than in Stoletow's experiments : his results for air at atmo- 
 spheric pressure are shown by the curve (Fig. 57). It will .be 
 
 120 
 
 no 
 
 100 
 
 10 
 
 , 1000 2000 3000 4000 5000 
 Fig. 57. 
 
 noticed that when the strength of the field approaches the value 
 5730 volts, which is the strength required to spark across the 
 plates which were 3 mm. apart in the dark, there is a very great 
 increase in the current. 
 
 This rapid increase of the photo-electric effect in the neigh- 
 bourhood of the sparking potential was first observed by Kreusler^. 
 The relation between the leak from plates of iron, aluminium, 
 copper, zinc, silver and amalgamated copper, and the strength of 
 field are represented in the curves given in Fig. 58 : the abscissae? 
 measured from represent the difference between the electromotive 
 force applied and that required to produce discharge in the dark. 
 The increase in the leak is so great that it cannot be adequately 
 
 * Schweidler, Wien. Ber. cviii. p. 273, 1899. 
 t Kreusler, Drude's Ann. vi. p. 398, 1901. 
 
120] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 223 
 
 represented in a moderately sized figure, a better idea in the case 
 of the zinc plate can be derived from the following table given by 
 
 Fig. 58. 
 
 Kreusler. V is the potential difference and i the current, the 
 potential required to produce a spark was 4060. 
 
 V 
 
 i(l = 10- 10 
 Amp.) 
 
 V 
 
 i(l = 10- 10 
 Amp.) 
 
 V 
 
 i(l = 10- 10 
 Amp.) 
 
 4040 
 
 13639 
 
 3050 
 
 0-19 
 
 ; i 
 3300 0-36 
 
 3970 
 
 25-67 
 
 2540 
 
 0-09 
 
 3440 0-58 
 
 3780 
 
 5-88 
 
 1760 
 
 0-06 
 
 3640 1-36 
 
 3700 
 
 2-40 
 
 1170 
 
 0-05 
 
 3710 1-98 
 
 3590 
 
 1-39 
 
 1760 
 
 0-06 
 
 3760 3-88 
 
 3440 
 
 070 
 
 2530 
 
 0-08 
 
 3970 21-09 
 
 3300 
 
 0'40 
 
 3060 
 
 0-17 
 
 4040 80-51 
 
 These figures also show evidence of an effect often observed 
 when using ultra-violet light the decrease of sensibility with the 
 time ; thus of the two readings taken with the greatest potential 
 difference the later one was very appreciably less than the earlier 
 
224 
 
 IONISATION BY LIGHT. 
 
 [120 
 
 one. This ' fatigue ' of the plates is probably due to oxidation, it 
 does not take place in hydrogen nor at very low pressures, nor 
 when platinum is used instead of zinc. 
 
 The increase in the rate of leak when the electric field ap- 
 proaches a certain strength is also very evident when the gas is at 
 lower pressures. The etfect of altering the pressure of the gas was 
 first investigated by Stoletow*, and subsequently by Schweidler f 
 and Lenardj. Stoletow showed that as the pressure was dimi- 
 nished, starting from atmospheric pressure, the current slightly 
 increased, the change in the current being small compared with 
 that in the pressure ; on carrying the reduction of pressure still 
 further, a stage was reached (if the strength of the field was not 
 too small) when the current increased rapidly as the pressure 
 diminished, this went on until the current reached a maximum 
 value, after which it began to decline, but at the lowest obtainable 
 pressures it had a finite value which was independent of the 
 strength of the electric field. 
 
 100 
 
 80 
 
 60 
 
 40 
 
 20 
 
 . I =o83 mfm 
 
 cL 
 
 Fig. 59. 
 
 The variation of the current with the pressure when the 
 potential difference remains constant is exhibited in the curves 
 (copied from Stoletow's paper) shown in Fig. 59; the distance 
 
 * Stoletow, Journal de Physique, ii. 9, p. 468, 1890. 
 t v. Schweidler, Wien. Ber. cviii. p. 273, 1899. 
 Lenard, Drude's Ann. ii. p. 359, 1900. 
 
120] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 225 
 
 between the plates was '83 millimetres and the figures on the 
 curves indicate the potential difference expressed in terms of 
 Clark's cells (1 Clark's cell = 1-4 volts). 
 
 The values of the current at a series of pressures when the 
 distance between the plates was 371 mm. and the potential 
 difference about 90 volts are shown in the following table : 
 
 Pressure in 
 millimetres 
 
 Current 
 
 Pressure in 
 1 millimetres 
 
 Current 
 
 Pressure in 
 millimetres 
 
 Current 
 
 754 
 
 8-46 
 
 2-48 
 
 74-7 
 
 0105 
 
 65-8 
 
 152 
 
 13-6 
 
 1-01 
 
 105-8 
 
 0-0147 
 
 53-8 
 
 21 
 
 26-4 
 
 0-64 
 
 108-2 
 
 0-0047 
 
 50-7 
 
 8-8 
 
 32-2 
 
 0-52 
 
 102-4 
 
 0-0031 
 
 49-5 
 
 3-3 
 
 48-9 
 
 0-275 
 
 82-6 
 
 
 
 We see by an inspection of the curves in Fig. 59 that the 
 pressure at which the current is a maximum increases with the 
 electric force between the plates : Stoletow has shown that p m , 
 the pressure at which the current is a maximum, is proportional 
 to E/d, where d is the distance and E the potential difference 
 between the plates; this law may also be expressed by saying that if 
 X is the mean free path of a molecule at the pressure for maximum 
 current, when the electric force is X, then X\ is constant. The 
 curves in Fig. 59 show that at very low pressures the current 
 is independent of the strength of the electric field, i.e. is 
 saturated. This is also well shown by the following numbers taken 
 from Lenard's paper. V is the potential difference in volts and t 
 the current, the vacuum was the best obtainable, the pressure being 
 less than '002 mm. of mercury. 
 
 V 
 
 t 
 
 V 
 
 t 
 
 45000 
 
 24-5 x 10 ~ 10 Coulomb/sec. 
 
 500 
 
 23-4 x 10~ 10 Coulomb/sec. 
 
 25000 
 
 26-6 
 
 120 
 
 21-9 
 
 8900 
 
 22-5 
 
 14 
 
 19-9 
 
 4100 
 
 24-8 
 
 9 
 
 15-9 
 
 3110 
 
 24-5 , 
 
 1 
 
 7 
 
 1300 
 
 24-5 
 
 
 
 4 
 
 The critical pressure is of the same order of magnitude as the 
 pressure at which the electric field would be able to produce a 
 
 15 
 
 T. G. 
 
226 
 
 IONISATION BY LIGHT. 
 
 [120 
 
 discharge in the dark ; in this region of pressure Stoletow has 
 shown that the current does not depend merely upon the value of 
 E/d where E is the potential difference and d the distance between 
 the plates, for with a constant value of E/d the current at these 
 pressures increases rapidly with the distance between the plates. 
 
 V. Schweidler* has given curves representing the relation 
 between the current and the potential difference at several 
 pressures. Similar curves have lately been obtained by Varley at 
 the Cavendish Laboratory, some of these are reproduced in Figs. 
 60 and 61. The curves show three distinct stages ; the first when 
 
 & 
 
 ISO 
 
 160 
 
 > 
 
 If 12 
 
 CO H 
 
 S '[ 10 
 
 1 
 1=3 
 
 JE . 
 
 .S 60 
 
 8 40 
 
 I 
 
 20 
 
 llmm 
 
 33mm 
 
 20 40 60 80 100 120 140 16O 180 
 
 Potential to which Zinc is charged in cells. 
 1 cell = 2-1 volts (nearly). 
 
 Fig. 60. Variation of ultra-violet light leak from zinc surface with the pressure 
 for constant illumination. 
 
 The experiments were conducted in hydrogen. The distance between the 
 electrodes was 1 cm. 
 
 the electric force is weak, then the current increases rapidly with 
 the electric force, the rate of increase gradually dies away as the 
 
 * v. Schweidler, Wien. Ber. cviii. p. 273, 1899. 
 
120] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 227 
 
 electric force increases, and the second stage is reached when the 
 current only varies slowly, at some pressures hardly at all, with 
 the electric field ; with still larger electric forces a third stage is 
 
 ^ 20 
 
 1 
 
 'il 180 
 g^ 160 
 
 o 140 
 
 .2 
 
 OJ 
 
 a 
 
 120 
 
 100 
 
 | so 
 
 1 
 
 ~ 60 
 
 20 
 
 0.36 m m 
 
 0- 140mi 
 
 0-074 mm 
 
 044 m m 
 
 0- 021 m m 
 
 -0-013-m-m 
 
 0- 008 mm 
 
 20 40 60 80 100 120 140 160 180 
 
 Potential to which Zinc is charged in cells. 1 cell = 2-1 volts (nearly). 
 
 Fig. 61. Variation of ultra-violet light leak from zinc surface with the pressure, 
 when the latter is low, for constant illumination. 
 
 The experiments were conducted in air. The distance between the electrodes 
 was 4 mm. 
 
 reached when the current increases rapidly with the electric force 
 and also with the distance between the electrodes. 
 
 152 
 
228 IONISATION BY LIGHT. [121 
 
 Theoretical considerations relating to the connection between the 
 current and the strength of the electric field. 
 
 121. It will be convenient to confine our attention in the first 
 place to electric fields which are weak compared with those required 
 to produce discharge in the dark. The view we take of the action 
 of the ultra-violet light is that under the action of this light the 
 metal emits from each unit area in unit time a certain number 
 of corpuscles; that these soon, when gas surrounds the metal, 
 get attached to one or more molecules of the gas and form 
 negative ions. If there is no electric field to remove these ions 
 they will go on accumulating in front of the metal plate, and as 
 the number of the ions is greater at a little distance from the 
 plate than at the plate itself, there will be diffusion of the ions 
 from the place of greater to the place of less density, i.e. back into 
 the plate, and things will reach a steady state when the accumu- 
 lation of ions in front of the plate is so great that the number of 
 ions which diffuse back into the plate is equal to the number 
 shot from it by the ultra-violet light. If an electric field acts on 
 the gas some of the ions will move off through the gas, producing 
 a current of electricity ; the accumulation of ions will not be so 
 great as in the previous case, and equilibrium will be reached 
 when the number of ions shot off by the ultra-violet light is equal 
 to the number which diffuse back into the plate plus the number 
 which are carried away by the electric field. 
 
 To put these considerations in a symbolical form let us take 
 the case when the current is flowing between two parallel plates : 
 let / be the number of negative ions emitted * by unit area of the 
 illuminated surface in unit time, and <r the number of ions per c.c. 
 at any point between the plates, then if X is the electric force, it 
 the velocity acquired by a negative ion under unit electric force, 
 e the charge on an ion, and i the current flowing through unit 
 area, then Xuo-e i : we have seen that X is approximately con- 
 stant between the plates, hence as i is constant it follows that a- 
 will be approximately constant. This constant value of cr will 
 not however hold right up to the illuminated plate, we may 
 suppose that the density of the ions increases from zero to this 
 
 * These ions start as corpuscles but are soon converted into ions by adhesion to 
 the molecules of the gas surrounding them. 
 
121] PHOTO-ELECTRIC EFFECTS. 229 
 
 constant value in a small distance \ from the plate : thus at the 
 surface of the plate there will be a gradient in the density of the 
 ions of the order cr/X, and if D is the coefficient of diffusion of the 
 ions through the gas the number of negative ioas flowing back 
 into unit area of the plate in unit time is Da/\. The number of 
 ions carried away through the gas by the electric field in unit 
 time is i/e, hence we have when things have settled into a steady 
 state, 
 
 Da- i 
 
 but Xuae = i, hence we have 
 
 /=- 
 ( 
 
 e\XuI 
 
 
 this relation between i and X exhibits the chief features of the 
 earlier parts of the curves obtained by Schweidler and Stoletow : 
 when X is small the current is proportional to the electromotive 
 force, it soon however increases less rapidly than X, and when X 
 is very large approximates to the constant value le. 
 
 We have seen (p. 32) that u = De (n/p), where n is the number 
 of molecules in a cubic centimetre of gas at the pressure p : thus 
 u/D is the same for all gases: hence we see from (1) that any 
 alteration in the current produced by altering the gas thrpugh 
 which the current passes must be due to the alteration in X : so 
 that if this equation were rigorously true then under the same 
 potential difference, provided this were small, the currents through 
 different gases would be proportional to the values of X for these 
 gases. In this connection it is necessary to remember that the 
 diffusion of the ions back into the metal takes place through 
 a layer of gas in immediate proximity to the metal, and that D 
 refers to this layer, while the u which occurs in equation (1) 
 relates to the gas at a considerable distance away from the 
 plate ; if there were anything in the nature of a gaseous layer 
 adhering to the metal, then the gas through which the ions diffuse 
 might be different from the gas in the rest of the field, so that 
 we should not be justified in assuming that the ratio of D to 
 u was a constant independent of the nature of the gas. Again, 
 we have assumed that the only ions available for carrying the 
 
230 IONISATION BY LIGHT. [122 
 
 current are those which come out of the metal : now we shall see 
 directly that the motion of ions through a gas with a high velocity 
 ionises the gas, thus if the corpuscles are projected from the 
 metal with a velocity exceeding a certain critical value they will 
 ionise the molecules of the gas against which they strike, and thus 
 the total number of ions produced would exceed the number 
 projected from the metal by an amount depending upon the 
 nature of the gas. The observations hitherto made on different 
 gases are not sufficiently extensive to enable us to decide whether 
 or not an effect of this kind does exist*. Elster and Geitelf and 
 StoletowJ found that with the strength of electric field used by 
 them the rate of escape of electricity through carbonic acid gas 
 was much greater than that through air or oxygen. Breisig on 
 the contrary found that the rate was less through C0 2 than 
 through air: and that it was exceptionally large through the 
 vapours of ether and alcohol. The rate of leak varies so much 
 with the potential difference that a comparison of the rates of 
 leak for the different gases with only one value for the potential 
 difference is not satisfactory and gives little information. What 
 is really wanted is a comparison for the different gases of the 
 curves representing the relation between the current and the 
 potential difference. It would also be desirable to have these 
 curves drawn for ultra-violet light of different wave-lengths. 
 The different gases might also cause the currents to differ by 
 altering the surface of the metal either by combining with it or 
 by condensing on its surface. 
 
 122. We shall now go on to consider the sudden increase in 
 the current which occurs when the electric field approaches the 
 intensity required to produce a discharge in the dark. We can, 
 I think, explain this by means of some considerations first advanced 
 by the author || to explain the ionisation produced when a strong 
 electric field causes a discharge to pass through a gas. When 
 cathode or Lenard rays pass through a gas, the gas becomes a 
 
 * Since this was written Varley has made at the Cavendish Laboratory experi- 
 ments proving the existence of this secondary ionisation. 
 
 t Elster and Geitel, Wied. Ann. xli. p. 161, 1890. 
 
 J Stoletow, C. R. cvii. p. 91, 1888. 
 
 Breisig, Bonn. Diss. 1891 ; Wied. Beiblatter, xvii. p. 60. 
 
 || J. J, Thomson, Proc. Camb. Phil. Soc. Feb. 5, 1900; Phil. Mag. v. 50, 
 p. 278, 1900. 
 
122] PHOTO-ELECTRIC EFFECTS. 231 
 
 conductor, i.e. it is ionised ; hence we see that when very rapidly 
 moving ions pass through a gas and come into collision with its 
 molecules the gas is ionised : the energy required for the ionisation 
 coming from the kinetic energy of the rapidly moving ions. 
 Inasmuch as the ionisation of a molecule of a gas requires the 
 expenditure of a finite amount of work, a moving ion cannot 
 ionise a molecule against which it strikes unless its kinetic energy 
 exceeds a certain critical value, but when its energy does exceed 
 this value then a certain fraction of the number of collisions 
 between the ions and the molecule will result in ionisation. Now 
 when the ions are moving in an electric field, the kinetic energy 
 acquired by the ions will increase as the strength of the field 
 increases, and when the field is strong enough to make the kinetic 
 energy of the ions exceed the critical value, the ions by their 
 collisions will give rise to new ions, and thus there will be an 
 increase both in the number of ions and the current through the 
 gas: it is this increase which is so marked a feature of the 
 currents produced by ultra-violet light when the electric field is 
 strong. 
 
 If I is the mean free path of an ion, X the electric force, e the 
 charge on the ion, then the mean kinetic energy given to the ion 
 by the electric field is Xel ; when therefore Xel exceeds a certain 
 critical value, ionisation will take place in a certain fraction of the 
 collisions ; let us denote this fraction by f(Xel), f(x) being a 
 function of x which vanishes when x is less than a certain value. 
 If there are n ions per cubic centimetre, then the number 
 of collisions in unit time is equal to nv/l, where v is the average 
 velocity of translation ; hence the number of ions produced in 
 
 77?) 
 
 unit time per unit volume is -j-f(Xel). A certain number of 
 
 6 
 
 collisions may result either in the recombination of the ion, or 
 the attachment of the ion to the system against which it collides, 
 so that the ion ceases to be available for carrying the current ; let 
 a fraction /3 of the collisions result in the destruction of the ion as 
 an ionising agent, then the number of these ions which disappear 
 
 from a cubic centimetre of the gas in unit time is fi -j- *, hence the 
 
 * We have here neglected the loss of ions due to the recombination of positive 
 and negative ions in comparison with that due to the collision of the ions with the 
 molecules. 
 
232 IONISATION BY LIGHT. [122 
 
 excess of the ions produced over those which disappear is equal to 
 
 We have by the equation of continuity, if u is the average 
 velocity of translation parallel to the axis of x, 
 
 Now when the ions are moving so rapidly that they have 
 sufficient kinetic energy to act as ionising agents, their velocity 
 must be mainly due to the electric field, since when this field is 
 absent no ionisation is produced. Hence we have approximately 
 
 v u. 
 Hence when things are in a steady state we have by (2) 
 
 integrating we get 
 
 } 
 
 nu = Ce l 
 or if as a first approximation we regard X as constant we have 
 
 If the current has reached the saturation stage before ionisation 
 begins, then nu I when x = when x is measured from the 
 illuminated plate, hence 
 
 T 
 
 nu = Ie l 
 
 if d is the distance between the plates, then i the current is the 
 value of nue when x = d, thus 
 
 ........................... (3), 
 
 thus when this additional ionisation sets in, the current with a 
 constant value of X increases with the distance between the 
 plates ; this effect has been observed by Stoletow*. As long as the 
 ionisation is confined to that produced at the metal plate by the 
 ultra-violet light, the current is determined by the electric force, 
 i.e. i is a function of X and not of d ; when however the secondary 
 ionisation occurs i is a function of both X and d. 
 
 * Stoletow, Journal de Physique [2], ix. p. 468, 1890. 
 
122] PHOTO-ELECTRIC EFFECTS. 233 
 
 The point at which the secondary ionisation begins is when 
 Xel has a certain definite value ; as I the mean free path of an ion 
 is inversely proportional to the pressure, the value of X required 
 to start the secondary ionisation will be directly proportional to 
 the pressure; the curves given by v. Schweidler* for the relation 
 between the current and electromotive force at different pressures 
 show that his experiments are in fair agreement with this result, 
 he only gives approximate values for the pressures, and there 
 are hardly sufficient points determined on the curve to enable 
 us to determine with accuracy the points at which the secondary 
 ionisation commences ; but from an inspection of his curves 
 I should say that at a pressure of 750 mm. secondary ionisation 
 began when the difference of potential between his plates, whose 
 distance apart is given as between 3 5 mm., was equal to 
 4700 volts, at 130mm. to 1150 volts, and at 17mm. to about 
 140 volts. 
 
 It is evident that the current cannot go on continually in- 
 creasing as the pressure diminishes, for in the limit when the free 
 path gets comparable with the distance between the plates there 
 will be very few collisions, and therefore little if any secondary 
 ionisation ; in the limit when the pressure is indefinitely reduced, 
 the number of ions reaching the plate not exposed to the light 
 must equal the number leaving the illuminated plate, hence 
 with our previous notation the limiting current will be equal 
 to le. 
 
 The value of the free path at the pressure when the current 
 is a maximum is by equation (3) determined by finding the 
 value of I which makes {/ (Xel) /3}/l a maximum, this condition 
 gives /' (Xel) Xel f (Xel) /3, an equation to determine Xel ; 
 thus when the current is a maximum XI has a constant value, 
 this coincides with Stoletow's result that if p m is the pressure 
 at which the current is a maximum X/p m is constant. 
 
 We alluded before to the question as to whether secondary 
 ionisation was produced close to the surface of the metal by the 
 corpuscles shot out from the metal through the influence of the 
 ultra-violet light ; it would seem that this point might be deter- 
 mined by careful measurements of the current under a constant 
 
 * v. Schweidler, Wien. Ber. cvii. p. 273, 1899. 
 
234 IONISATION BY LIGHT. [123 
 
 electromotive force at different pressures, for if it was found that 
 the current before secondary ionisation began rose to a value 
 greater than that corresponding to an exceedingly low pressure, it 
 would prove that such secondary ionisation at the surface of the 
 metal did occur. In Stoletow's experiments at various pressures 
 the current before secondary ionisation took place did not exceed 
 the value at zero pressure, this point however is one that would 
 repay further examination*. 
 
 The Photo-electric Effect depends upon the orientation of the plane 
 of polarisation of the Light. 
 
 123. Elster and Geitel f made the very interesting discovery 
 that when the incident light is plane polarised, the photo-electric 
 effect, the intensity and angle of incidence being the same, is greater 
 when the light is polarised at right angles to the plane of incidence 
 than when it is polarised in that plane. On the Electro-magnetic 
 Theory of Light there is in light polarised at right angles to the plane 
 of incidence an electric force with a component normal to the re- 
 flecting surface, when the light is polarised in the plane of incidence 
 the electric force is parallel to this surface. The most convenient 
 way of investigating the effect of polarisation is to use a liquid 
 surface, as it is important that the reflecting surface should be 
 smooth, and to choose a liquid which is sensitive to ordinary light, 
 as it is then possible to use a Nicols prism to polarise the light : 
 the liquids used by Elster and Geitel were the liquid alloy of 
 sodium and potassium, and amalgams of rubidium and caesium, 
 these were placed in vessels from which the air was exhausted 
 and the rate of escape of negative electricity observed with light 
 incident on the surfaces at different angles. Some of the results 
 obtained in this way are given below, data were not given to 
 enable us to say to which stage of the curve connecting the rate 
 of escape of negative electricity with the electromotive force the 
 observations refer. 
 
 * See foot-note, p. 230. 
 
 t Elster and Geitel, Wied. Ann. lii. p. 433, 1894; Iv. p. 684, 1895; Ixi. p. 445, 
 1897. 
 
123] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 235 
 
 Rate of escape (t) of electricity from sodium potassium amal- 
 gam exposed to white light polarised at right angles to the plane of 
 incidence. 
 
 Angle of 
 incidence 
 
 t 
 
 Angle of 
 incidence 
 
 i 
 
 Angle of 
 incidence 
 
 i 
 
 o 
 
 
 
 2-8 
 
 o 
 
 30 
 
 17-4 
 
 60 
 
 28-7 
 
 10 
 
 5-2 
 
 40 
 
 23-4 
 
 70 
 
 23-8 
 
 20 
 
 11-2 
 
 50 
 
 27-0 
 
 80 
 
 11-0 
 
 Rate of escape (i) of electricity from the same cell exposed to 
 white light polarised in the plane of incidence. 
 
 Angle of 
 incidence 
 
 i 
 
 Angle of 
 incidence 
 
 i 
 
 Angle of 
 incidence 
 
 i 
 
 o 
 
 3 
 
 10 
 
 20 
 
 2-8 
 2-78 
 2-87 
 
 o 
 
 30 
 
 40 
 50 
 
 2-65 
 2-24 
 1-80 
 
 o 
 
 60 
 
 70 
 80 
 
 1-51 
 1-01 
 33 
 
 Thus, except at perpendicular incidence when the two are 
 necessarily equal, the leak caused by the light polarised in the 
 plane of incidence is very much smaller than that caused by light 
 polarised at right angles to this plane, and we see too that 
 whereas in the former case the current continually diminishes as 
 the angle of incidence increases, in the latter it increases with 
 the angle of incidence until the latter is about 60, after this the 
 current decreases. 
 
 Elster and Geitel have determined how the amount of light 
 absorbed by the metal varies with the angle of incidence for light 
 polarised in and at right angles to the plane of incidence. The 
 absorptions and the corresponding photo-electric currents are shown 
 in Fig. 62. Curves (1) and (2) represent the photo-electric 
 currents due to light polarised at right angles and in the plane of 
 incidence respectively, curves (3) and (4) the absorptions of the light 
 in these cases. It will be seen that in each case the current and 
 absorption increase and decrease together, but that a given amount 
 of absorbed light is very much more efficacious in producing dis- 
 charge when its plane of polarisation is at right angles to, than 
 
236 
 
 IONISATION BY LIGHT. 
 
 [123 
 
 when it is in, the plane of incidence. The connection between the 
 absorption and current is made clearer by the following considera- 
 tions given by Elster and Geitel. Suppose the intensity of the 
 incident light polarised at right angles to the plane of incidence 
 is unity, let the amount of light absorbed when the angle of 
 incidence is </> be a$, and a when <f> = 0, then when the angle of 
 incidence is <, the component of the electric force parallel to the 
 
 48 
 44 
 40 
 36 
 32 
 28 
 24 
 -20 
 16 
 12 
 
 e 
 
 4 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 24 
 22 
 
 20 
 18 
 13 
 14 
 12 
 10 
 8 
 6 
 4 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 - ' 
 
 -^. 
 
 -^^B 
 
 **> 
 
 N^ 
 
 
 
 
 
 
 
 
 
 3 
 
 .-- 
 
 -" 
 
 
 X 
 
 
 
 
 
 *** 
 
 \\ 
 
 
 
 
 -~- J 
 
 -r 
 
 i^_ 
 
 \ 
 
 4 
 
 
 
 ^ 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 ~ - 
 
 - _ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 v \ 
 
 \ 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 \\ 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 "v 
 
 
 
 \ 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^ 
 
 **^ 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 3 
 
 10 
 
 20 
 
 30 
 
 40 
 
 Fig. 
 
 5 
 62. 
 
 _o 
 
 60 7 
 
 _o 
 
 80 9( 
 
 surface is proportional to cos <, and the energy corresponding to 
 this component to cos 2 </> ; the amount of this energy absorbed will 
 be a cos 3 <f>, hence a^ a cos 8 </> will be the energy due to the 
 electric force at right angles to the surface absorbed by the metal. 
 Suppose /^ is the current when the angle of incidence is <f>, I 9 the 
 current when the angle of incidence is zero for unit intensity of 
 light, the intensity due to the electric force parallel to the surface 
 is cos 2 <, the current due to this is J cos 3 <f>, hence the current 
 arising from the component of the electric force perpendicular to 
 the surface may be taken to be /^ / cos 3 <. Now Elster and 
 Geitel have shown that a^ a cos 2 < and /^ 7 cos* $ are approxi- 
 mately proportional to each other ; this is shown by the two curves 
 in Fig. 63, which represent the variation of the two quantities 
 with the angle of incidence. The continuous line represents the 
 variation of the current, the dotted line that of the absorption. 
 
123] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 237 
 
 If we take the view that the photo-electric effect is due to 
 the emission of negatively electrified corpuscles from the metal, 
 we can explain the influence of the orientation of the planes of 
 polarisation as follows. We may suppose that the energy from 
 the light absorbed by the metal goes into some of the corpuscles, 
 giving them sufficient kinetic energy to escape from the metal, 
 just as they are able to do at a very high temperature. These 
 corpuscles have acquired from the ultra-violet light very much 
 
 40 
 
 24 
 
 12 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 80 
 
 Angle of incidence. 
 Fig. 63. 
 
 more kinetic energy than is possessed by a molecule of a gas at the 
 temperature of the metal ; thus every collision a corpuscle makes 
 with the molecules of the metal will result in a loss of kinetic 
 energy, so that if it is to escape from the metal it is important that 
 it should make as few collisions as possible before reaching the 
 surface, i.e. that it should move approximately at right angles to 
 the surface. When the light is polarised at right angles to the 
 plane of incidence there is a component of the electric force at 
 right angles to the surface which will direct some of the corpuscles 
 in this direction, when however the light is polarised in the plane 
 of incidence the electric force is parallel to the surface and tends 
 to make the corpuscles move parallel to the surface instead of 
 towards it ; thus the corpuscles have in order to escape to make 
 more collisions in this case than the former, and so are less likely 
 to reach the surface with sufficient energy to escape from it. 
 
238 IONISATION BY LIGHT. [124 
 
 Influence of Temperature on the Photo-electric Effect. 
 
 124. The influence of the temperature of the metal on the 
 photo-electric effect has been investigated by Hoor*, Stoletow f, 
 Elster and Geitel J, Righi, and Zeleny||. Hoor found that the 
 sensitiveness of a zinc plate to light diminished when the tem- 
 perature was raised from 18 to 55. Stoletow found on the other 
 hand that raising the temperature to 200 C. increased the sensi- 
 tiveness, Elster and Geitel that an alteration of temperature had 
 no effect on zinc. Righi found that the positive charge given by 
 light to a previously uncharged plate was greater when the plate 
 was hot than when it was cold : we must remember that a blast 
 of air blowing across the plate increases the positive charge so 
 that part of the effect observed by Righi may have been due to air 
 currents set up by the hot plate. In considering the interpre- 
 tation of these seemingly discrepant results we must remember 
 that the circumstances which affect the sensitiveness of the metal 
 to the light will depend very much upon the strength of the field. 
 Thus supposing we are dealing with a strong field and the gas 
 surrounding the metal is at an exceedingly low pressure, the 
 photo-electric current is saturated and measures the number of 
 corpuscles given off from the metal in unit time ; measurements of 
 the effect of temperature in this case would admit of a perfectly 
 definite interpretation, but when the gas is at a high pressure and 
 the strength of the field is weak, i.e. when we are working on the 
 earlier part of the curve connecting the current and the electro- 
 motive force, then the interpretation of the effect of temperature 
 is ambiguous, for the current at this stage depends not only upon 
 the rate of emission of the corpuscles, but also upon the velocity of 
 the ions through the gas. Now the increase in temperature may 
 alter the density of the gas, and hence the velocity of the ions 
 through it, and it would require further experiments to disentangle 
 this effect of the velocity of the ions from the effect on the rate 
 of emission of the corpuscles from the plate. The experiments 
 
 * Hoor, Wien. Berichte, xcvii. p. 719, 1888. Exner's Rep. xxv. p. 91, 1889. 
 
 t Stoletow, Comptes Rendus, cviii. p. 1241, 1889. 
 
 t Elster and Geitel, Wied. Ann. xlviii. p. 625, 1893. 
 
 Righi, Atti 1st. Yen. vii. Mem. 11. 
 
 il Zeleny, Physical Review, xii. p. 321, 1901. 
 
124] 
 
 PHOTO-ELECTRIC EFFECTS. 
 
 239 
 
 of Elster and Geitel on the effect of temperature on the current 
 from a potassium surface in a good vacuum are not open to this 
 objection, as the effect of the gas is eliminated, and in this case 
 they found an increase in the current of about 50 per cent, when 
 the temperature was increased from 20 to 50: from some experi- 
 ments made by the writer it appears that when the temperature 
 is raised considerably higher, say to 200, there is a very great 
 increase in the current from the alkali metals, and that these are 
 very much more sensitive to light at high temperatures than they 
 are at low. 
 
 Zeleny, who measured the current from platinum and iron 
 exposed to ultra-violet light and surrounded by air at atmospheric 
 
 Electrometer Deflection. 
 
 * 10 (0 
 80 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ' 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 ^ 
 
 7 
 
 
 
 
 
 
 
 
 S 
 
 \ 
 
 
 
 / 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 ^^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 100 200 300 400 500 8OO 7C 
 Temperature. 
 Fig. 64. 
 
 pressure, found that from platinum the current first decreased 
 as the temperature increased, reached a minimum, and then 
 increased with the temperature as far as the highest temperature 
 used. The results showed a curious hysteresis effect in the currents 
 obtained, when the metal was cooling they were greater than those 
 at the same temperature when the wire was getting hotter. These 
 
240 
 
 IONISATION BY LIGHT. 
 
 [124 
 
 results are indicated in the curves shown in Fig. 65, where (i) 
 represents the currents corresponding to continuously increasing 
 temperatures, (ii) those for continuously decreasing temperatures ; 
 (iii) those for increasing temperatures, and (iv) for decreasing 
 temperatures when the wire was cooled to the temperature of the 
 room between each observation. These observations show that 
 heating the wire produces some change in the surface, possibly in 
 the amount of gas condensed upon it or absorbed by the metal, 
 from which it only slowly recovers. With iron the minimum 
 current is not nearly so clearly marked as with platinum, nor is 
 there so great a difference between the curves for increasing as 
 
 300 
 
 200 
 
 H iOO 
 
 ^ 
 
 
 \ 
 
 500' 
 
 600 700* 
 
 100* 200' 300* 400' 
 
 Temperature. 
 Fig. 65. 
 
 those for decreasing temperature ; on the other hand the photo- 
 electric current increases more rapidly with the temperature for 
 iron than for platinum, the current at 700 C. being for iron about 
 40 times the current at 15 C., while for platinum the current at 
 700 C. was only about 2'5 times that at 15 C. 
 
 ^eleny also investigated whether, if the metal were raised to 
 a temperature just below that at which it would begin to give off 
 positive ions in the dark, it could be made to give off positive ions 
 by the incidence upon it of ultra-violet light; the positive ions 
 
125] PHOTO-ELECTRIC EFFECTS. 241 
 
 were however not produced at a lower temperature in the light 
 than in the dark. Nor when the metal was raised to the tem- 
 perature at which the positive ions were produced was the rate 
 of production increased by the incidence of ultra-violet light. 
 
 The experiments of Elster and Geitel and Zeleny seem to 
 establish the fact that the photo-electric effects of metals are 
 greater at a high temperature than at a low one. This is what we 
 should expect if we take the view that the photo-electric effect 
 is due to the acquisition by the corpuscles in the metal under the 
 action of the ultra-violet light of sufficient kinetic energy to enable 
 them to escape from the metal. The higher the temperature the 
 greater would be the initial kinetic energy possessed by the 
 corpuscles, and the smaller the increment required to enable them 
 to move fast enough to escape from the metal. 
 
 Nature of the ions produced by the action of ultra-violet light 
 
 on metals. 
 
 125. The experiments made by the author and Lenard (see 
 p. 107) show that in high vacua metals when illuminated with 
 ultra-violet light give out corpuscles, i.e. bodies whose mass is 
 only about y^- of that of the hydrogen atom; when however 
 the metal is surrounded by gas the corpuscles soon strike against 
 the molecules, get attached to them and have to drag them 
 along with them as they move under the action of the electric 
 field. The velocity of the negative ions through different gases 
 has been measured by Rutherford (see p. 52), who showed that 
 the velocity of the ion did not depend upon the nature of the 
 metal on which the light fell, but that it did depend on the nature 
 of the gas through which the ion had to travel, and that the 
 velocity through any gas of the negative ion produced by ultra- 
 violet light was very approximately the same as that of the ion 
 produced by Rontgen rays through the same gas. 
 
 The diminution of the photo-electric effect produced when the 
 pressure of the gas is low by a transverse magnetic field, which 
 was discovered by Elster and Geitel*, has already been discussed 
 on page 107. 
 
 Elster and Geitel, Wied. Ann. xli. p. 166, 1890. 
 
 T. G. 16 
 
242 IONISATION BY LIGHT. [126 
 
 The photo-electric effect does not persist after the light is cut 
 off. Stoletow*, who made a series of experiments on this point, 
 'could not obtain any evidence that there was any finite interval 
 between the incidence of the light and the attainment of the full 
 photo-electric effect, or between the eclipse of the light and the 
 total cessation of the effect, and he showed that the interval must 
 at any rate be less than y^ of a second. 
 
 126. Connection betiueen photo-electric effects and the fluorescence 
 and ionisation of solutions. G. C. Schmidt f made a series of 
 experiments on this subject, with the result that there was no 
 clear evidence of any intimate relation between photo-electric 
 effects, ionisation and fluorescence : for while in fuchsme there 
 seemed to be clear indications of a connection between ionisation 
 and photo-electric effects since aqueous solutions of fuchsine 
 are photo-electric, while solutions in alcohol and acetone are not, 
 and fuchsine is ionised in water and not in the other solvents the 
 results with eosine seemed decisive against this connection, as 
 the addition of neutral salts, such as potassium iodide or sodium 
 chloride, destroys the ionisation, while in aqueous solutions it has 
 no influence upon the photo-electric effects. Again, magdala 
 red fluoresces in alcohol, amyl-alcohol and acetone, the first two 
 solutions are photo-electric, the last is not. Salts which undergo 
 decomposition in the light such as the haloid salts of silver are 
 strongly photo-electric. 
 
 In the case of water a change in the physical state seems to 
 be accompanied by a change in the photo-electric properties, as 
 dry ice was found by BrillouinJ to be photo-electric, while water 
 in the liquid state is not. 
 
 The opinion has been advanced by Cantor and Knoblauch ||, 
 that the photo-electric effect depends upon oxidation, on the 
 ground that the substances, elementary and compound, which 
 exhibit this effect are those which combine with oxygen; it is 
 however, I think, necessary to distinguish between the poiver of 
 
 * Stoletow, Aktinoelektrische Untersuchungen, Physikalisch. Revue, i. p. 725, 
 1892. 
 
 f G. C. Schmidt, Wied. Ann. Ixiv. p. 708, 1898. 
 
 J Brillouin, Eel. Electr. xiii. p. 577, 1897. 
 
 Cantor, Wien. Sitzungsber. 102, p. 1188, 1893. 
 
 || Knoblauch, Ze.it. f. Physikalische Chemie, xxix. p. 527, 1899. 
 
126] PHOTO-ELECTRIC EFFECTS. 243 
 
 combining with oxygen and the act of combination. We should 
 expect the photo-electric substances to be oxidisable, as they lose 
 readily negative corpuscles, and thus get positively charged and 
 in a fit state to combine with an electro-negative substance like 
 oxygen ; there is no evidence however that the presence of oxygen 
 is necessary for the photo-electric effect, in fact the evidence the 
 other way seems quite conclusive, for substances like rubidium 
 and potassium enclosed in highly exhausted vessels seem to 
 retain their photo-electric power indefinitely, and any trace of 
 oxygen originally present would soon be absorbed by the metals. 
 
 162 
 
CHAPTER XI. 
 
 IONISATION BY RONTGEN RAYS. 
 
 127. WE shall in this chapter mainly confine our attention to 
 the ionising properties of the rays, leaving for future consideration 
 the manner of their production and a discussion of their nature ; 
 it will however be convenient to enumerate some of their most 
 important properties. Rontgen* found in 1895 that very remark- 
 able effects occurred in the neighbourhood of a highly exhausted 
 tube through which an electric discharge was passing ; the exhaus- 
 tion of the tube being so great that a vivid green phosphorescence 
 appeared on the glass. He found that a plate covered with a phos- 
 phorescent substance such as potassium-platino-cyanide became 
 luminous when placed near the tube, and that a thick plate of 
 metal cast a sharp shadow when placed between the tube and the 
 plate ; while light substances, such as thin aluminium, cardboard, 
 wood, cast but slight shadows, showing that the agent which 
 produced the phosphorescence on the plate could traverse with 
 considerable freedom bodies which are opaque to ordinary light. 
 As a general rule the greater the density of a substance the more 
 opaque it is to this agent ; thus the bones are much more opaque 
 to this effect than the flesh, so that if the hand is placed between 
 the discharge tube and the plate the outlines of the bones are 
 distinctly visible in the shadow cast on the screen, or if a purse con- 
 taining coins is placed between the tube and the plate the purse 
 itself casts but little shadow, while the coins cast a very dense 
 one. Rontgen showed that the agent, now called Rontgen rays, 
 producing the phosphorescence on the plate is propagated in 
 straight lines, and is not bent in passing from one medium to 
 
 * Bontgen, Wied. Ann. Ixiv. p. 1, 1898 (reprinted from the original paper in the 
 Sitzungsberichte der Witrzburger. Physik. Med. Gesellsch. 1895). 
 
127] IONISATION BY RONTGEN RAYS. 245 
 
 another ; there is thus no refraction of the rays. The rays affect a 
 photographic plate as well as a phosphorescent screen and shadow 
 photographs can readily be taken : the time of exposure depends 
 on the intensity of the rays, and this depends on the discharge 
 through the tube and on the substances traversed by the rays in 
 their passage to the plate ; the time of exposure required to 
 produce a photograph may vary from a few seconds to several 
 hours. The power of the rays to penetrate obstacles in their path 
 varies very much with the condition of the discharge tube from 
 which they originate ; when the pressure in this tube is not very 
 low, and the potential difference between its electrodes conse- 
 quently comparatively small, the rays have but little penetrating 
 power and are readily absorbed ; such rays are called ' soft rays.' 
 If the exhaustion of the tube is carried much further, so that the 
 potential difference between the electrodes is greatly increased, 
 the Rontgen rays have much greater penetrating power and are 
 called 'hard rays.' With a very highly exhausted bulb and a 
 large induction coil it is possible to get rays which will produce 
 appreciable effects after passing through sheets of brass or iron 
 several millimetres thick. The difference in penetrating power is 
 well shown by observing the changes which take place in the 
 shadow of a hand on a phosphorescent screen, as the pressure of 
 the gas in the discharge tube is gradually reduced. When first 
 the rays appear they are so 'soft' that they are stopped by the 
 flesh as well as the bones, so that the bones are very indistinctly 
 seen ; when the exhaustion proceeds further the rays get harder, 
 and are able to penetrate the flesh but not the bones. At this 
 stage the difference between the shadow of the flesh and the 
 bones is most distinct ; when the exhaustion proceeds further the 
 rays get so hard that they are able to penetrate the bones as well 
 as the flesh and the shadow again becomes indistinct. Not only 
 may the rays from different discharge tubes be different, but even 
 the same bulb may emit at the same time rays of different degrees 
 of hardness. The property by which it is most convenient to 
 identify a ray is its hardness, and this is conveniently measured 
 by the amount of absorption when it passes through a layer of 
 aluminium or tinfoil of given thickness. Now in some experi- 
 ments made by the writer and M c Clelland* on the absorption 
 
 * J. J. Thomson and M c Clelland, Proc. Camb. Phil. Soc. ix. p. 126, 1899. 
 
246 IONISATION BY RONTGEN RAYS. [128 
 
 produced when the rays passed through one layer of tinfoil after 
 another, it was found that the absorption produced by the first few 
 sheets of tinfoil traversed by the rays was much greater than 
 that due to the same number of sheets after the rays had already 
 travelled through several sheets of tinfoil. This shows that some 
 of the ray^ are readily absorbed by the tinfoil while others pass 
 through with much greater facility, thus the first few layers of 
 tinfoil would stop the first kind of rays while the remainder pass 
 through with comparatively little absorption. M c Clelland showed 
 that if he took plates of different metals, the thickness of the 
 plates being chosen so that they gave the same absorption for the 
 rays from one tube, they would not necessarily give the same 
 absorption for the rays from another. 
 
 The Rontgen rays when they pass through a gas make it a 
 conductor of electricity, they ionise the gas*: the number of ions 
 produced in one second in one cubic centimetre of the gas by rays 
 of given intensity depends upon the pressure of the gas, the 
 nature of the gas and its temperature. 
 
 128. Effect of Pressure. Perrinf has shown that the rate of 
 production of ions per cubic centimetre by rays of given intensity 
 is proportional to the pressure of the gas. He proved this by 
 showing that the saturation current through a given volume of 
 gas was proportional to the pressure : the current passed between 
 two large plates of metal, care being taken that the rays did not 
 fall upon the plates ; this precaution is necessary, because as we 
 shall see when the Rontgen rays fall upon metal secondary rays 
 are produced which ionise the gas, and complicate the effects ; in 
 addition to this precaution it is necessary to arrange the electric 
 field so that all the gas exposed to the rays or at least all of it 
 from which the ions can move to the electrodes is under the 
 influence of an electric field strong enough to produce saturation, 
 for unless saturation is reached throughout the whole of the gas 
 the current will depend upon the velocity of the ions under the 
 electric field as well as upon the number of ions produced ; as the 
 velocity of the ions increases as the pressure diminishes the 
 unsaturated current will diminish less rapidly with the density 
 
 * J. J. Thomson, Camb. Univ. Reporter, Feb. 4, 1896. Benoist and Harmozescu, 
 C. R. cxxii. p. 235, 1896. Righi, Ace. del Lincei (5), v. p. 143, 1896. 
 t Perrin, Annales de Chimie et de Physique [7], xi. p. 496, 1897. . 
 
129] 
 
 IONISAT1ON BY RONTGEN RAYS. 
 
 247 
 
 than the saturated one. In fact when the electric field is feeble 
 the current will increase as the pressure diminishes, for if n is 
 the number of positive or negative ions per cubic centimetre, q 
 the number of ions produced in one second in a cubic centimetre, 
 then (see p. 15) n (#/)*; the current under a small electric 
 force X is equal to ne X (u -4- v\ where e is the charge en an ion, 
 u and v the velocities of the positive and negative ions under unit 
 electric field. Now n is proportional to V^, and therefore to Vp 
 p being the pressure of the gas, since (see p. 19) a is independent 
 of p, while u and v are proportional to l/p ; the current under 
 small electric forces will vary as 1/Vp. 
 
 129. lonisation of Different Gases. When Rontgen rays of the 
 same intensity pass through different gases at the same pressure 
 the amount of ionisation depends greatly upon the composition of 
 the gas; the number of ions produced, measured by the satura- 
 tion current, is least in hydrogen, and for the gases hitherto tried 
 greatest in the vapour of methyl iodide : it is also exceedingly 
 large for mercury vapour: the relative values of q the number 
 of ions produced in one second in a cubic centimetre of the gas at 
 atmospheric pressure and temperature are given in the following 
 table. The number for air is taken as unity. 
 
 
 
 1 
 
 
 
 
 2 
 
 
 Gas 
 
 Perrin * 
 
 Ruther- 
 ford t 
 
 Thom- 
 son J 
 
 Gas 
 
 Perrin 
 
 Ruther- 
 ford 
 
 Thom- 
 son 
 
 H 2 
 
 026 
 
 5 
 
 33 
 
 C 2 N 2 
 
 
 
 1-05 
 
 N 2 
 
 . .. 
 
 9 
 
 89 
 
 C 2 H 2 
 
 
 
 ... 
 
 1 
 
 2 
 C0 2 
 CO" 
 
 1-34 
 
 12 
 1 2 
 
 1-1 
 1-4 
 
 86 
 
 HC 2 1 
 
 6* 
 
 8 
 
 6 
 4 
 11 
 
 6 
 6-4 
 
 8-9 
 
 NO 
 N 2 
 
 1-3 
 
 
 1-08 
 1-4?- 
 
 CL 
 NH 3 
 
 "1 ? 
 
 18 
 
 17'4 
 1? 
 
 We see that though the results of different observers are in 
 fair agreement for most gases, for hydrogen they are very dis- 
 cordant. We must remember that different observers used rays 
 of different degrees of hardness, and that it is probable that the 
 
 * Perrin, Annales de Physique et de Chimie [7], xi. p. 496, 1897. 
 
 t Rutherford, Phil. Mag. v. 43, p. 241, 1897. 
 
 J J. J. Thomson, Proc. Camb. Phil. Soc. x. p. 10, 1900. 
 
248 
 
 IONISATION BY KONTGEN RAYS. 
 
 [130 
 
 relative ionisation in two gases depends upon the kind of rays used 
 to ionise them. The gases in which the ionisation is large have 
 also large refractive indices, it does not however seem that a large 
 refractive index necessarily implies large ionisation ; for example, 
 the refractive index of acetylene C 2 H 2 as determined by Mascart 
 is very nearly the same as that of sulphuretted hydrogen H 2 S, yet 
 the ionisation in the H 2 S is about six times that in C 2 H 2 . The 
 ionisation by the Rontgen rays does not seem to be closely 
 connected with the density of the gas ; thus the density of H 2 S is 
 a little greater than that of O 2 and considerably less than that of 
 C0 2 , yet the ionisation in either of these gases is small compared 
 with that in H 2 S. In other cases of ionisation such as that due 
 to radiation from some radio-active substances, or to the passage of 
 cathode rays through a gas, we shall see that the ionisation is much 
 more closely connected with the density of the gas, being (except 
 in the case of hydrogen) directly proportional to the density. 
 
 130. The writer* pointed out that the measurements given 
 in the above table indicate that the ionisation of a gas is approxi- 
 mately an additive property, i.e. if 2 [A] is the value of q for a gas 
 A 2 , 2 [B] the value for a gas B 2 and so on, then the value of q for 
 a gas AiB m C n will be I [A] + m [B] + n [C]. Thus if we use the 
 numbers given in the third column of the preceding table for 
 H 2 , N 2 , O 2 , C0 2 , SO 2 , and C1 2 to determine the values of 2[H], 
 2 [N], etc., we find 
 
 = 165, [C]= '3, 
 
 -55, 
 
 if we use these numbers to calculate the ionisation in the other 
 gases in the table using the additive rule we get the following 
 results. 
 
 Gas 
 
 Ionisation 
 observed 
 
 Ionisation 
 calculated 
 
 Gas 
 
 Ionisation 
 observed 
 
 Ionisation 
 calculated 
 
 CO 
 
 86 
 
 85 
 
 Og-H^ 
 
 1 
 
 93 
 
 NO 
 N i 
 
 1-08 
 1-47 
 
 995 
 1-44 
 
 HC1 
 
 6 
 8-9 
 
 5-63 
 
 8-86 
 
 Cjft 
 
 1-05 
 
 1-49 
 
 NH 3 
 
 1 
 
 94 
 
 * Loc. cit. 
 
130] IONISATION BY RONTGEN RAYS. 249 
 
 Thus except in the case of C 2 N 2 the agreement is within the 
 limits of the errors of experiment. 
 
 Connection between the absorption of the rays by a gas and the 
 ionisation produced in a gas by the rays. The rays are absorbed 
 by gases through which they pass, the amount of this absorption 
 has been measured by Rutherford*, who used for this purpose the 
 apparatus represented in Fig. 66. Two large and similar conical 
 
 Fig. 66. 
 
 vessels ABC, A'B'C', much larger at the top than at the bottom, 
 were placed in such positions that the axis of each cone passed as 
 nearly as possible through the anode of the tube producing the 
 Rontgen rays. The upper parts of the vessels AB, A'B' were 
 made of lead, and were separated from the lower portions, which 
 were made of glass, by thin plates of ebonite, similar plates 
 covered the ends of the glass cylinders at C and C', so that the 
 vessels BC, B'C' were air-tight and could be exhausted when 
 required. The intensities of the rays after they had passed 
 through the glass cylinders were measured by determining the 
 saturation currents through the lead cylinders AB, A'B'. In- 
 sulated wires DE, D'E' were used as the electrodes, these were 
 connected with opposite pairs of quadrants of an electrometer, 
 both initially charged to the same potential. The outsides of 
 the vessels AB, A'B' were connected with the earth. The posi- 
 tion of the bulb giving the rays was adjusted so that when the 
 glass vessels BC, B'C' were filled with air at the same pressure 
 
 * Rutherford, Phil. Mag. v. 43, p. 241, 1897. 
 
250 
 
 IONISATION BY RONTGEN RAYS. 
 
 [1:30 
 
 the needle of the electrometer remained at rest when the rays 
 were passing through the vessel ; this showed that the potentials 
 of each pair of quadrants were falling at the same rate, and 
 therefore that the currents through the vessels AS, A'E' were 
 equal. If the gas were removed from one of the vessels BC, B'C' 
 or another gas introduced, the balance was disturbed, thus 
 showing the absorption of the rays by the gas in the vessel. 
 If we assume that the energy absorbed when the rays pass 
 through unit length of the gas is proportional to the energy of the 
 rays / and equal to X/, then the change 87 in the intensity when 
 the rays traversed a distance Bx is given by the equation 
 
 or 
 
 a/ =- 
 
 r_ T P -\x 
 
 J. J.Q 6 , 
 
 where / is the intensity of the rays when x = 0. Thus if / is the 
 length of path of the rays through the vessel BC, the ratio of the 
 intensity of the radiation in AB when BC is full of a gas whose 
 coefficient of absorption is X, to the intensity when BC is exhausted 
 is equal to e~ ZA , in this way X can be determined. Rutherford found 
 that for air X is about 10~ 3 , so that the rays lose about 1 per cent, 
 of their energy in passing through 10 cm. of air at atmospheric 
 pressure ; about 7 cm. of mercury vapour at atmospheric pressure 
 and at the temperature of boiling mercury reduced the intensity 
 of the rays to about . The values of X for different gases are 
 given in the following table. The third column of this table 
 contains the relative values of q the number of ions produced in 
 each volume in unit time by rays of equal intensity. 
 
 Gas 
 
 X 
 
 q 
 
 Gas 
 
 X 
 
 q 
 
 Hydrogen 
 Air . . 
 
 small 
 001 
 
 about 
 001 
 
 5 
 1 
 1-2 
 9 
 8 
 1-2 
 
 Sulphur dioxide 
 
 0025 
 0037 
 0065 
 0095 
 1 
 07 
 
 4 
 6 
 11 
 
 18 
 
 Sulphuretted hydrogen 
 Hydrochloric acid 
 Chlorine 
 
 Oxygen } 
 Nitrogen 1 
 Coal gas j 
 
 
 Carbon dioxideJ 
 
 Methyl iodide 
 
 
 These numbers show that good conductors under the rays are 
 good absorbers of the radiation : if the conductivity were pro- 
 portional to the radiation, i.e. if q/\ were constajtfe, then if the 
 
131] IONISATION BY RONTGEN RAYS. 251 
 
 whole of the radiation were absorbed by a gas the number of ions 
 produced would be independent of the nature of the gas. For 
 if 7 is the initial intensity of the rays the intensity after they 
 have passed through a distance x of the gas is I^-**, hence the 
 number of ions produced in unit time in the space dx is pro- 
 portional to qI 6~^ c , thus the total number of ions produced in the 
 gas in unit time is proportional to 
 
 and this is equal to qlj\ : thus if q/\ is the same for all gases the 
 total number of ions produced by rays of given intensity will be 
 the same. The numbers given above for q/\ show considerable 
 variations in the different gases : the discrepancies however chiefly 
 occur in the gases for which X is very small, and in which the 
 errors of experiment are necessarily large. 
 
 Rutherford and MClung* have recently made very careful 
 determinations of the values of X for carbonic acid and air; they 
 found the ratio for the two gases was 1*59, for the ratio of the 
 currents they found T43, but they consider the current through 
 the carbonic acid was not quite saturated. I found the ratio of 
 the currents through the two gases to be 1*53, which is very nearly 
 the ratio of the absorption. The value of X depends upon the 
 character of the rays, for hard rays it is very much smaller than 
 for soft ones, thus the value of X for air in Rutherford and 
 M l 'Clung's experiments was only about one-quarter of the value 
 in Rutherford's earlier experiments in which softer rays were used. 
 In the case of the radiation from uranium which is much more 
 easily absorbed than Rontgen rays Rutherford f has shown that 
 when all the radiation is absorbed by a gas, the total amount of 
 ionisation is approximately the same in all gases. 
 
 The absorption depends upon the pressure of the gas : usii,g 
 the vapour of methyl-iodide, Rutherford has shown that down to 
 a pressure of a quarter of an atmosphere the absorption is pro- 
 portional to the pressure. 
 
 131. BenoistJ concludes from experiments on the vapours of 
 bromine and iodine, of ethyl-bromide and methyl-iodide that the 
 
 * Rutherford and M c Clung, Phil. Tram. A, cxcvi. p. 25, 1901. 
 
 t Rutherford, Phil. Mag. v. 47, p. 109, 1899. 
 
 t Benoist, Journal de Physique [3], x. p. 653, 1901. 
 
252 IONISATION BY RONTGEN RAYS. [131 
 
 absorption produced by a given mass of a substance is indepen- 
 dent of its physical state; that, for example, the vapour of a 
 volatile liquid or solid absorbs the same amount of radiation when 
 in the gaseous state as when condensed into a solid or liquid. 
 
 Benoist introduces a quantity which he calls the coefficient of 
 transparency of the substance ; it is the weight in milligrammes 
 of a prism of the substance on a base one square centimetre 
 in area which produces the same absorption as a standard prism 
 of paraffin- wax 75 mm. long, when the rays travel along the 
 axes of the prisms. He has proved the very important law, that 
 if we have a mass M of a substance whose transparency is E made 
 up of masses M lt M 2 , M 3 ..., of substances whose coefficients of 
 transparency are E 1} E 2 , E s ..., then whether the substances are 
 mechanically mixed or in a state of chemical combination 
 
 M_M M M 
 
 E~E, + E, + E^ 
 
 I think the meaning of this law is made clearer by the intro- 
 duction of a quantity which we may call the molecular absorption 
 of the substance, i.e. the absorption produced by one molecule of 
 the substance, and which is connected with the Benoist coefficient 
 as follows : suppose that the mass of a molecule is m, and that in 
 Benoist's prisms there are N molecules, then Nm = c.E where c is 
 a constant ; by the definition of E these N molecules produce a 
 given amount of absorption ; hence if a is the absorption due to 
 one molecule Na = G where C is a constant ; hence we see that 
 
 m 
 
 where X does not depend on the nature of the substance. Let us 
 now express Benoist's law in terms of the absorption a. If there 
 are N! molecules of the first substance, JV 2 of the second, and so on 
 
 2 = N 2 m Z) M=Nm, 
 
 and -TT = N\a ; 
 
 & 
 
 thus equation (1) becomes 
 
 Na = N l a l + N 2 a 2 
 
 This is equivalent to the statement that the absorption of any 
 substance is equal to the sum of the absorptions of the individual 
 
131] 
 
 IONISATION BY RONTGEN RAYS. 
 
 253 
 
 molecules in that substance, the absorption due to any molecule 
 being independent of the nature of the chemical compound of 
 which it forms a part or its physical state. Benoist states that 
 the absorption does not depend upon the temperature. The 
 absorption of a body for the Rontgen rays is thus an additive 
 property. 
 
 35 
 
 30 
 
 25 
 
 20 
 
 15 
 
 10 
 
 \Na 
 
 60 
 
 70 
 
 50 
 
 50 
 
 100 150 
 
 Fig. 67. 
 
 200 
 
 10 30 
 
 There is a very close connection between the absorption of 
 an element and its molecular weight ; this is shown by the curve 
 in Fig. 67 (taken from Benoist's paper) in which the ordinates 
 
254 
 
 IONISATION BY HONTGEN RAYS. 
 
 [131 
 
 represent the equivalents of transparency of the elements, the 
 abscissae the molecular weight ; it will be seen that the curve 
 is quite a smooth one, in every case the transparency diminishes 
 as the molecular weight increases. From this it follows that the 
 molecular absorption increases with the molecular weight. Having 
 got the curve connecting the transparency with the molecular 
 weight, it is evident that we have the means of determining its 
 molecular weight by measuring its transparency to Rb'ntgen rays 
 when in a pure state or when combined with elements whose 
 transparency is known. Benoist has applied this method to 
 determine the molecular weight of indium. 
 
 From Benoist's results I have calculated the following relative 
 values of a for some of the elements which often occur in gaseous 
 compounds. 
 
 Substance 
 
 a 
 
 Substance 
 
 a 
 
 O 9 
 
 N 2 
 
 36 
 
 27 
 
 S 2 
 
 Clo 
 
 2-8 
 4 
 
 C, 
 
 17 
 
 Br 2 
 
 47 
 
 Knowing a for these gases we can calculate the absorptions of 
 the gases measured by Rutherford (see page 250), the results are 
 given in the following table : 
 
 Gas 
 
 a (Benoist) 
 
 X (Kutherford) 
 
 o 
 
 36 
 
 001 
 
 CO 
 
 45 
 
 001 
 
 S0 2 
 
 1-76 
 
 0025 
 
 H 2 S 
 
 1-4 
 
 0037 
 
 HC1 
 
 2 
 
 0065 
 
 C1 2 
 
 4 
 
 0095 
 
 a/X 
 
 360 
 450 
 700 
 378 
 301 
 420 
 
 In calculating the numbers in the second column I have 
 neglected the absorption due to the hydrogen in the compound, 
 as this is too small to be accurately determined. Benoist showed 
 that the relative values of a depended to some extent upon the 
 nature of the rays ; taking this into account Rutherford's results 
 are in fair accordance with Benoist's law except in the case 
 of S0 2 . 
 
132] IGNISATION BY RONTGEN RAYS. 255 
 
 The question arises whether the energy absorbed by the gas is 
 wholly accounted for by the work spent in ionising the gas or 
 whether part of the energy of the rays is directly transformed into 
 heat and energy in the gas without the intervention of ionisation : 
 if the ions are allowed to recombine, the work spent in ionisation 
 will ultimately appear as heat energy in the gas; this would 
 however not necessarily be the case if the ions were driven out of 
 the gas by a strong electric field. The evidence is, I think, in 
 favour of the view that the ionisation of the gas is only accountable 
 for a small part of the loss of energy. Rutherford and M c Clung* 
 have calculated the work necessary to ionise a molecule of the gas 
 on the assumption that all the loss of energy in the rays was due 
 to the ionisation of the gas ; on this hypothesis they found the 
 work necessary to ionise a molecule of air was equal to the work 
 done on the ionic charge when it fell through a potential difference 
 of about 175 volts, this is very much larger than the value of the 
 same quantity, about two volts, obtained by H. A. Wilson and 
 Townsend (see p. 190) by different considerations. Combining 
 these results we conclude that only about 1/80 of the energy of 
 the rays is expended in the ionisation of the gas, the rest being 
 converted into heat. 
 
 Variation of tlie ionisation of a gas iviih the temperature. 
 
 132. This was investigated in the case of air by Perrin-f who 
 showed that if the pressure of the gas was kept constant, then 
 between the temperatures 12 and + 145 C. the total ionisation 
 was independent of the temperature ; as the density of the gas 
 when the pressure is constant varies inversely as the absolute 
 temperature, and, as we have seen, the amount of ionisation is 
 proportional to the density, it follows that the amount of ionisa- 
 tion in a given mass of gas is directly proportional to the absolute 
 temperature. 
 
 It is very desirable that further experiments should be made 
 on the variation of the ionisation of different gases with the 
 temperature, as this variation has a direct bearing on the question 
 as to what is the condition of the molecules which are ionised 
 by the Rontgen rays. We must remember that it is only an 
 
 * Rutherford and M c Clung, Phil. Trans, cxcvi. p. 25, 1901. 
 
 t Perrin, Annales de Chimie et de Physique [7], xi. p. 496, 1897. 
 
256 IONISATION BY RONTGEN RAYS. [132 
 
 exceedingly small fraction of the molecules which are ionised by 
 the rays ; even when the ionisation is exceptionally large the pro- 
 portion of the number of free ions to the number of molecules of 
 the gas is less than 1 to 10 12 . Thus if all the molecules of the gas 
 are equally exposed to the rays, since the ionisation is confined to 
 an exceedingly small fraction of the number of molecules the 
 molecules which are ionised must be in some state very far 
 removed from the average condition of the molecules. One sup- 
 position which naturally suggests itself is that it is only those 
 molecules which possess an amount of kinetic energy exceeding 
 a certain value which get ionised by the rays : the following in- 
 vestigation however shows that in this case the ionisation ought 
 to vary much more rapidly with the temperature than is consistent 
 with Perrin's results. 
 
 For according to the Kinetic Theory of Gases the number of 
 molecules in a cubic centimetre which have velocities between 
 c and c + dc is equal to 
 
 VTT 
 
 where N is the whole number of molecules per unit volume, 6 
 the absolute temperature and m the mass of a molecule of the gas, 
 hence if n is the number of molecules which have velocities 
 greater than c, 
 
 . ,00 _m 
 
 n=-^N0-* e ' c*dc, 
 
 V 7T Jet 
 
 or putting c 2 = 0o> 2 , 
 
 4 f 
 
 n = -~N\ e-^tfdw; 
 VTT J , 
 V* 
 
 hence we have 
 
 dn_ 2 -* 
 M-fir* -&' 
 
 Now since the number of molecules ionised is an exceedingly 
 small fraction of n, if these are the molecules having a velocity 
 
 _mc? 
 
 greater than c 1} then e 9 must be very small, but when this is 
 the case dn/dd will increase very rapidly with 0; thus suppose 
 
 me? 
 
 for a moment that e is equal to 10~ 12 , then if we double 6 the 
 
132] IONISATION BY RONTGEN RAYS. 257 
 
 value of dn/dO at the higher temperature would be about 120,000 
 times its value at the lower, while according to Perrin's result the 
 temperature coefficient of the ionisation is constant : hence we 
 conclude that the few molecules that are ionised cannot owe their 
 ionisation to the possession of an abnormal amount of kinetic 
 energy; a similar objection would apply to the ionisation being 
 due to any property of the molecule whose frequency was given by 
 the Max well- Bolt zmann Law of Distribution. 
 
 Another view that at first sight appears as if it might explain 
 the small amount of ionisation is that this is not due to the direct 
 action of the Rontgen rays on the molecules, but that these rays 
 act on the free ions, which as the phenomenon of spontaneous 
 ionisation shows are always present in small numbers, even when 
 the gas is in its normal state ; the rays giving to these ions sufficient 
 kinetic energy to enable them to ionise the molecules of the gas 
 against which they strike. To express the results of this hypothesis 
 in an analytical form, let us suppose that the number of free positive 
 or negative ions per cubic centimetre is n, and that in consequence 
 of the kinetic energy given by the rays to an ion, each ion 
 produces o> other ions per second, let the number of ions which 
 recombine in one second be cm 2 , and let (3 be the number of ions 
 produced per second from the spontaneous ionisation of the gas, 
 then when things are in a steady state we have 
 
 o>?? +/3-cw 2 =0, 
 
 '8 a) 2 
 or n .-_ ._ + 
 
 -f+v- 
 
 'la. v a 
 
 Since the number of ions produced by the rays is large compared 
 with that V/3/a due to the spontaneous ionisation @/a must 
 be small compared with o> 2 /4a 2 , and we have approximately n = w/a, 
 thus we should have a definite value for the number of ions in i 
 cubic centimetre of the gas. This view however leads to a result 
 which is not in accordance with the results of observation, for the 
 saturation current for a cubic centimetre of the gas is proportional 
 to the number of ions produced in one second in a cubic centi- 
 metre of the gas, i.e. con. Now this number being proportional to n, 
 the number of free ions, should be less in a strong electric field 
 than in a weak one, for in a strong field the life of the ion is 
 shorter than it is in a weak one, as it is rapidly driven out of the 
 T. G. 17 
 
258 IONISATION BY RONTGEN KAYS. [133 
 
 gas against the electrodes ; hence if the view we are discussing 
 were the true one, the current through a gas when the electric 
 field is strong ought to diminish as the strength of the field 
 increases ; as this is not the case we conclude that the ionisation 
 cannot be produced in the way we have been considering. 
 
 Other possible explanations of the small number of molecules 
 dissociated by the rays are (1) that the rays are of such a kind 
 that only a small fraction of the molecules are exposed to the full 
 force of their influence : that if for example we consider a plane 
 at right angles to the direction of propagation of the rays the 
 energy is not distributed uniformly over this plane, but that the 
 distribution of energy has as it were a structure, although an 
 exceedingly fine one, places where the energy is large alternating 
 with places where it is small, like the mortar and bricks in a wall ; 
 thus if the places where the energy is intense enough to produce 
 ionisation of a molecule occupied but a small fraction of the area 
 of the plane at right angles to the rays, the rays would be able to 
 pass through a gas and yet only a small fraction of the molecules 
 would be exposed to their maximum influence, just as is the case 
 when a beam of cathode rays passes through the gas ; we shall 
 return to this point when we consider the nature of the Rontgen 
 rays. Another view which might be taken is that all the molecules 
 of a gas, even though this gas may be like hydrogen an element,, 
 are not of the same kind, and that mixed with the ordinary mole- 
 cules we have a few which are of such a kind as to be very easily 
 ionised, and that the number of molecules of this kind, which 
 are practically molecules of a different gas, is not given by 
 Maxwell's law of distribution. The idea that even a gas is not 
 uniform in composition, but contains, as it were mixed with it,. 
 small quantities of other gases not necessarily as impurities due 
 to its method of preparation but as an essential constituent of it 
 may appear at first stating so opposed to the ordinary facts of 
 chemistry as not to be worthy of discussion. We may however 
 point out that the quantities of such gases, if we may take the 
 ionisation as their measure, are so small as to be utterly beyond 
 the power of chemical analysis to detect, so that it cannot be 
 by chemical considerations that the truth or falsehood of this 
 hypothesis can be decided. 
 
 133. Secondary Rontgen radiation. When the Rontgen rays 
 pass through a substance they cause it to emit Rontgen rays 
 
13:3] 
 
 IONISATION BY RONTGEN RAYS. 
 
 259 
 
 called secondary rays which in many cases at any rate are different 
 in character from the rays primary rays which produced them. 
 These secondary rays are produced by solids, liquids and gases. 
 Perrin* observed that when the rays struck a metal plate, more 
 ionisation was produced than if rays of the same intensity passed 
 through the air without coming into contact with the plate. He 
 arranged two pairs of parallel plates so that the same volume of 
 gas was exposed to rays of the same intensity between each pair 
 of plates, in the one pair however the rays passed between the 
 plates without touching the metal, while in the second pair the 
 rays were incident normally on one of the plates ; he found that 
 the saturation current was always greater for the second pair of 
 plates than for the first, the excess depending on the metal struck 
 by the rays. If this plate were made of gold, zinc, lead or tin, 
 the difference was considerable, if it was made of aluminium it 
 was only small, while it was quite inappreciable if the plate were 
 wet with water, alcohol or petroleum. 
 
 Fig. 68. 
 
 Sagnacf has made some experiments which show very clearly 
 the existence of these secondary rays; the method he used is 
 shown in Fig. 68 a and j3 ; in the experiment represented in 
 
 * Perrin, Annales de Chimie et de Physique [7], xi. p. 496, 1897. 
 t Sagnac, ibid. [7], xxii. p. 493, 1901. 
 
 172 
 
260 
 
 IONISAT10N BY KONTGEN RAYS. 
 
 [134 
 
 Fig. 68 a the secondary rays were detected by their action on a 
 photographic plate, in that represented in Fig. 68 ft by their action 
 in discharging a gold-leaf electroscope. L is the bulb producing 
 the primary rays, EE a thick lead plate to screen off these rays 
 from the photographic plate or the electroscope, MM the plate 
 struck by the primary rays and emitting the secondary ones, ee in 
 Fig. 68 a the photographic plate ; the electroscope is covered with 
 a metal case connected with earth to screen off from the gas 
 exposed to the primary rays the electric field due to the charged 
 gold-leaves, the secondary rays entered this case through a thin 
 aluminium window. The electroscope was discharged and the 
 plate affected even when MM was made of comparatively light 
 and transparent substances, such as paraffin, ebonite, sulphur, or 
 aluminium, while a greater effect was produced by heavy sub- 
 stances. A small effect is produced even when the plate MM is 
 absent, this is due to the secondary rays emitted by the air ; the 
 secondary rays emitted by air were first observed by Rontgen* 
 who detected them by the luminosity they produced in a phos- 
 phorescent screen. 
 
 134. Sagnac (loc. cit.) showed that the secondary rays were not 
 diffusely reflected primary rays ; he did this by proving that the 
 secondary rays were much more easily absorbed than the primary 
 ones. The method he used for this purpose is shown in Fig. 69. 
 The primary rays from the bulb I passed through two openings 
 
 * Eontgen, Wied. Ann. Ixiv. p. 18, 1898. 
 
135] IONISATION BY RONTGEN RAYS. 261 
 
 ab, cd in the lead plates E 1 E 1 , E 2 E 2 , the secondary rays from the 
 plate LL passed through a hole in a lead plate E^E^, then through 
 a thin aluminium window into the electroscope G. A plate of 
 aluminium AA is placed first in the path of the primary rays and 
 the rate of leak observed, it is then removed from the path of the 
 primary rays and placed at A! A' in the path of the secondary 
 rays, and the rate of leak again observed ; the rate of leak in the 
 latter case is always less than that in the former, showing that the 
 secondary rays are more absorbed by the plate than the primary 
 ones. If t is the time taken by the gold-leaves to fall through a 
 certain angle when the plate is at AA, t f the time when the plate 
 is at A' A', then if c = (t' t)/t, c is called by Sagnac the coefficient 
 of transformation of the rays. This coefficient depends upon the 
 nature of the plate LL; it is much smaller when the plate is made 
 of light substances such as aluminium or paraffin than when it is 
 made of heavy ones such as gold or lead : this shows that the 
 secondary rays emitted by light substances, although not so 
 numerous, are more penetrating than those emitted by heavy ones. 
 Sagnac also showed that when the distance of the electroscope 
 from the plate LL was increased, a much greater diminution was 
 produced in the rate of leak when the plate LL was made of lead 
 than when it was made of zinc or copper, showing that a con- 
 siderable proportion of the secondary rays from lead were absorbed 
 by a few centimetres of air. 
 
 135. Some very interesting experiments on the secondary 
 rays were made by Townsend* who used the method represented 
 in Fig. 70. The bulb producing the rays and the induction coil 
 by which it was worked were placed inside a box covered with 
 lead, having one aperture at A through which the rays passed up 
 through a lead tube to prevent them from spreading out laterally. 
 C is a cylinder of wire-gauze containing an axial electrode 0. 
 The gauze was connected with one terminal of a battery of small 
 storage cells, the other terminal of which was put to earth, the 
 electrode G was connected with an insulated pair of quadrants of 
 an electrometer. The potential difference between the gauze and 
 the electrode G, 85 volts, was sufficient to produce the saturation 
 current. The substance emitting the secondary radiation was 
 placed at D and measurements were made (1) when the secondary 
 
 * J. S. Townsend, Proc. Camb. Phil. Soc. x. p. 217, 1899. 
 
262 
 
 IONISATION BY RONTGEN RAYS. 
 
 [135 
 
 radiation passed through nothing but air, (2) when it passed 
 through a plate of aluminium '25mm. thick. The results are 
 
 Fig. 70. 
 
 contained in the following table, the numbers being the deflection 
 of the electrometer in 10 seconds : 
 
 Radiator 
 (substance 
 placed at D) 
 
 Rays 
 passing 
 through 
 Air 
 
 Rays 
 passing 
 through 
 Al 
 
 Radiator 
 (substance 
 placed at D) 
 
 Rays 
 passing 
 through 
 Air 
 
 Rays 
 passing 
 through 
 Al 
 
 Air 
 
 2 
 
 1 
 
 Solid Paraffin 
 
 30 
 
 15-5 
 
 Aluminium . 
 
 6 
 
 3'5 
 
 Brass 
 
 66 
 
 2-5 
 
 Glass 
 
 7-5 
 
 3 
 
 Zinc 
 
 68 
 
 3 
 
 Lead . 
 
 24 
 
 6 
 
 
 70 
 
 2-5 
 
 
 
 
 
 
 
 This table shows very clearly the different kinds of radiation 
 given out by different substances, thus the radiation from brass, 
 zinc, and copper is almost completely stopped by the aluminium 
 while the radiation from other substances passes through it com- 
 paratively easily. The secondary radiation was found not to be 
 much affected by the state of the surface of the body, thus the 
 radiation from polished brass was only 2 or 3 per cent, greater 
 than from brass coated with oxide : if the brass was covered with 
 wet filter-paper the deflection of the electrometer was reduced 
 from 66 to 46. The secondary radiation is not merely a surface 
 effect, the radiation comes from a layer of the substance of appre- 
 ciable thickness. This was proved by covering a plate of aluminium 
 
135] 
 
 IONISATION BY RONTGEN RAYS. 
 
 263 
 
 with a thin layer of paraffin ; the radiation was reduced to about 
 one-sixth of the amount from a solid block of paraffin. With denser 
 substances such as lead the layer from which the secondary radia- 
 tion comes will be much thinner than for a light substance like 
 paraffin. In the first place the primary rays can only penetrate to 
 a very small depth below the surface, and in the second place the 
 secondary rays being so much more easily absorbed will only be 
 able to pass through a small fraction of the thickness penetrated 
 by the primary rays. Thus the thickness of the layer from which 
 the radiation comes will always be much less than the thickness 
 which can be penetrated by the primary rays. The arrangements 
 in the preceding experiments were such that the only radiation 
 which would affect the electrometer was that which had passed 
 through several centimetres of air. Townsend showed that in 
 addition to this there was also secondary radiation which was 
 absorbed by a layer of air a few millimetres thick. 
 
 The arrangement used for this purpose is shown in Fig. 71. 
 It was arranged to find the saturation-current between two 
 circular plates A and B, 4'8 cm. radius, for different distances 
 
 Fig. 71. 
 
 between the plates ; if there were no secondary radiation this 
 current would be proportional to these distances. 
 
 The primary rays passed through a hole M in a lead plate and 
 then through a hole N in another lead plate on which the lower 
 
264 
 
 IONISATION BY RONTGEN RAYS. 
 
 [135 
 
 plate BB, which was made of aluminium, rested. After passing 
 through N the primary rays passed through the air and fell on 
 the plate A A, whose distance from B could be adjusted by means 
 of a screw. A series of experiments were made with plates of 
 different materials at A, the plate B was an aluminium one 
 throughout the experiments ; the results of the experiments are 
 given in the following table : t is the distance between the plates 
 in millimetres, and the numbers in the other columns are propor- 
 tional to the saturation-currents in the various cases. The 
 composition of the upper plate is given in the first row in the 
 table. 
 
 t 
 
 Brass 
 
 Cu 
 
 Zn 
 
 Al 
 
 1 
 
 55 
 
 54-4 
 
 49 
 
 15 
 
 2 
 
 81 
 
 84 
 
 66 
 
 23-7 
 
 5 
 
 109-5 
 
 107-5 
 
 87 
 
 40-8 
 
 10 
 
 126 
 
 128 
 
 103 
 
 57 
 
 15 
 
 142 
 
 144 
 
 119 
 
 73 
 
 If there were no secondary radiation the 2, 3, 4 and 5 columns 
 should be identical, and the numbers proportional to the distance 
 between the plates. Let us take the case of brass, then when the 
 distance between the plates is 15 mm., the number of ions pro- 
 duced is proportional to 142; when the distance between the plates 
 is reduced to one millimetre, the number of ions is not reduced to 
 1/15 but to l/2'6 only, showing that there are relatively a great 
 many more ions in the millimetre of air next the brass plate than 
 there are in the layers of air at a considerable distance away from 
 it. We see from the table that the ionisation in the millimetre 
 of air nearest the metal is proportional to 55, in the next milli- 
 metre it is 26, the average in the next three millimetres is 9'5, 
 in the next five 3*5, and in the last five 3'2 : thus by far the greater 
 part of the secondary radiation is absorbed by a layer of air 2 milli- 
 metres thick, this part of the radiation would be all absorbed by 
 the air between the plate and the cylinder in the experiment 
 shown in Fig. 70, so that the numbers obtained by the use of 
 this instrument relate to a different class of rays from those 
 detected by the parallel plates. The curves in Fig. ?2, taken 
 from Townsend's paper, give a good idea of the rapidity with 
 
136] 
 
 IONISATION BY RONTGEN RAYS. 
 
 265 
 
 which the ionisation diminishes as the distance from the metal 
 surface increases ; the ordiriates in the curves are proportional to 
 the total amount of ionisation up to a distance from the plate 
 represented by the abscissae. If S is the ratio of the number of 
 ions produced by the easily absorbable secondary rays in the air to 
 the number of ions produced by the primary rays when they 
 traverse a layer of air 1 cm. thick, then Townsend found that for 
 
 ao 
 
 6Q 
 
 Fig. 72. 
 
 copper S = 2'o, for zinc S=l'84i, for aluminium $ = '4: these 
 numbers are considerably larger than those previously obtained 
 by Perrin, and this and the difference between these results 
 and those obtained by Sagnac indicate that the character of 
 the secondary radiation depends very largely upon that of the 
 primary. H. S. Allen* has compared the number of ions produced 
 by the secondary ionisation with those which would be produced 
 if the primary rays were entirely absorbed by the gas ; using brass 
 as the metal and sulphuretted hydrogen as the gas, he found that 
 the number of ions produced by the secondary radiation was about 
 1/2000 of the number which would have been produced if the 
 primary rays had been absorbed by the sulphuretted hydrogen. 
 
 136. The effect of the secondary ionisation has to be taken 
 into account in all investigations on the relation between the 
 ionisation and the pressure. Thus suppose we were investigating 
 the relation between the saturation-current and the pressure, the 
 
 H. S. Allen, Phil. Mag. vi. 3, p. 126, 1902. 
 
266 IONISATION BY RONTGEN RAYS. [137 
 
 current passing between two parallel plates, one of these being 
 exposed to the primary rays and giving out secondary radiation. 
 The secondary radiation is absorbed within a short distance from 
 the plate, and though when we diminish the pressure we increase 
 this distance the total amount of ionisation will not be affected 
 until the pressure gets so low that the secondary rays can travel 
 from one plate to the other. Thus if S is the secondary and P 
 the primary ionisation, the latter is proportional to the pressure p, 
 equal say to cap, then, until the pressure gets so low that the 
 secondary radiation extends from one plate to the other, the satu- 
 ration-current will be proportional to S + ap ; thus if the secondary 
 ionisation is large compared with the primary, there will be at first 
 very little change in the saturation-current due to a change in 
 pressure; when the pressure gets so low that the secondary 
 radiation is not nearly absorbed between the plates, then both 
 secondary ionisation and primary ionisation, and therefore the 
 saturation-current, will be proportional to the pressures. 
 
 137. A metal plate when struck by Rontgen rays emits, in 
 addition to the easily absorbed secondary radiation, negatively 
 electrified particles, or, as we may express it, the metal gives out 
 cathode as well as Rontgen rays. The cathode rays can be distin- 
 guished from the others by being deflected by a magnetic field, 
 and by carrying with them a charge of negative electricity so that 
 the metal plate from which they start would, if insulated, acquire 
 a charge of positive electricity. Dorn* has shown that rays which 
 can be deflected by a magnet are emitted by plates of lead and 
 platinum, and to a smaller extent by plates of copper and zinc 
 when exposed to Rontgen rays. The direction of the deflection 
 is the same as that of cathode rays coming from the metal. Curie 
 and Sagnac f have shown that the metal plate emits negative 
 electricity and acquires a positive charge; in order to demonstrate 
 this effect it is necessary to work in a good vacuum, as if the 
 plate is surrounded by air at an appreciable pressure, the con- 
 ductivity of the air due to the primary and secondary radiations is 
 so great that any charge on the plate leaks away before it can be 
 observed. One of the methods used by Curie and Sagnac to 
 demonstrate the charge on the plate is shown in Fig. 73. 
 
 * Dorn, Abhand. d. naturf. Ges. zu Halle, xxii. p. 39, 1900, Beiblatter, 24, p. 572. 
 t Curie and Sagnac, Journal de Physique, [4], i. p. 13, 1902. 
 
137] 
 
 IONISATION BY RONTGEN RAYS. 
 
 267 
 
 A thin piece of metal M is insulated and connected with one 
 pair of quadrants of an electrometer; M is enclosed in a metal 
 box ABCD which is connected with the earth, the lower face 
 of the box is pierced with windows closed with thin foil of the 
 same material as the box ; the bulb I which produces the rays is 
 enclosed in a box covered with lead. When the plate M and the 
 box ABCD are made of different metals, then at atmospheric 
 pressure the conductivity of the air is considerable, and the 
 arrangement acts like a galvanic battery, a potential difference 
 equal to the contact difference of potential being established 
 between M and the box; as we exhaust the air from the box this 
 
 meter 
 
 Fig. 73. 
 
 difference remains at first unaltered, but when a very good vacuum 
 is obtained the potential difference is greatly increased; thus when 
 the plate M is made of platinum and the box of aluminium, Curie 
 and Sagnac found that at atmospheric pressure M was positive to 
 the box by less than 1 volt, but at a high vacuum the potential of 
 M was greater than that of the box by about 30 volts. This 
 shows that the platinum emits more negative electricity than it 
 receives from the aluminium. If the plate M is aluminium, and 
 the box platinum, the plate acquired a negative charge. Curie 
 and Sagnac showed that the penetrating power of these negatively 
 charged rays was of the same order as that of the Lenard rays, 
 a piece of aluminium foil about '46 x 10~ 6 cm. thick reducing 
 the stream of negative electricity about 40 per cent.: from this we 
 
268 IONISATION BY RONTGEN RAYS. [138 
 
 may conclude that the velocity of the secondary rays is of the 
 same order as that of cathode rays in a highly exhausted tube, 
 say between 10 9 and 10 10 cm. /sec. Dorn* has measured the mag- 
 netic deflection of these rays and finds velocities varying from 
 1'8 x 10 9 to 8*5 x 10 9 cm./sec., the values depending upon that 
 assumed for e/m. 
 
 We may compare the effects produced when Rontgen rays fall 
 on a metal plate with those produced by the incidence of ultra- 
 violet light ; in both cases cathode rays are emitted by the metal. 
 The secondary Rontgen rays may be compared with the reflected 
 light or perhaps with greater accuracy with the phosphorescent 
 light given out by certain substances under the influence of 
 ultra-violet light, for which the reflected light is of the same 
 quality as the incident light ; the secondary Rontgen rays are not 
 of the same nature as the primary rays, part at least of the 
 secondary rays being much more easily absorbed than the 
 primary ones. 
 
 On account of the great absorption of the secondary and 
 cathode rays, the layer from which they come must be very 
 close to the surface : thus suppose AB is the face of a metal 
 plate on which Rontgen rays are incident, let the primary rays 
 penetrate to CD, then all the metal between AB and CD will be 
 emitting secondary and cathode rays, but it is only the secondary 
 rays which come from a thin layer ABEF which escape extinc- 
 tion before reaching the surface, and as the cathode rays are still 
 more easily absorbed it is only those from a still thinner layer 
 ABE'F' which emerge into the air. 
 
 138. Theory of the Secondary Radiation. The secondary 
 radiation is readily explained if we take the view, which we shall 
 discuss later, that the Rontgen rays consist of exceedingly thin 
 pulses of very intense electric and magnetic force. Let us suppose 
 that such a pulse is travelling through a medium containing ions 
 it is not necessary that the ions should be free : when the pulse 
 reaches a charged ion the ion will be acted on by a very intense 
 force and its motion accelerated. Now when the velocity of a 
 charged body is changing pulses of electric and magnetic force 
 proceed from the body, the magnitude of these forces being pro- 
 
 * Dorn, Lorentz Jubilee volume, p. 595, 1900. 
 
138] IONISATION BY RONTGEN RAYS. 269 
 
 portional to the acceleration of the body : thus while the primary 
 Rontgen pulse is passing over the ion and accelerating its motion, 
 the ion gives out a pulse of electric and magnetic force the 
 secondary Rontgen pulse the secondary pulse ceasing as soon 
 as the acceleration of the ion vanishes, i.e. as soon as the primary 
 pulse has passed over. It is easy to compare the energy in the 
 secondary pulse with that in the primary. For suppose the ion 
 is moving parallel to the axis of a?, let / be its acceleration, then 
 the ion emits a pulse of magnetic force such that when the 
 pulse reaches the point P, the magnitude of the force is equal to 
 fe sin 6 1 V. OP, V being the velocity of light, 6 the angle be- 
 tween OP and the axis of as, and e the charge on the ion in 
 electromagnetic units ; the direction of the force is at right angles 
 to OP and the axis of x ; this magnetic force is accompanied by 
 an electric force at right angles to OP in the plane containing OP 
 and the axis of x, and equal in magnitude to fe sin 6 /OP: hence by 
 Poynting's theorem the flow of energy is along OP, and since the 
 quantity of energy flowing across unit area in unit time is, when 
 as in this case the electric and magnetic forces are at right angles 
 to each other, equal to the product of the electric and magnetic 
 forces divided by 4-7T, the rate at which energy flows across unit 
 surface is equal to 
 
 47T 
 
 integrating this expression over the surface of a sphere with the 
 ion as centre, we see that the rate at which energy is leaving the 
 ion is equal to 
 
 1 &f* 
 
 3 V ' 
 and the total amount of energy emitted by the ion is equal to 
 
 i p 1 * r 
 I V //* 
 
 Now suppose that the electric force in the primary Rontgen 
 pulse is parallel to x and equal to X, then if in is the mass of the 
 
 ion /= ; substituting this expression for / we find that the 
 energy emitted by the ion is equal to 
 
270 IONISATION BY RONTGEN RAYS. [138 
 
 the integration extending over the time taken by the pulse to 
 pass over the ion ; if d is the thickness of the pulse and if X is 
 constant from the front to the back of it, then 
 
 V 
 
 and thus the total energy in the secondary radiation emitted by 
 the ion is equal to 
 
 l^X^d 
 
 3 ra 2 T 2 ' 
 if E is the energy per unit area of the pulse, then 
 
 -. 
 
 47T F 2 ' 
 
 thus the energy emitted by the ion is equal to 
 
 47T # 
 
 3 m* E > 
 
 and if there are N ions per unit volume the energy of the 
 secondary radiation per unit volume is 
 
 3 77? 
 
 Though each pulse of secondary radiation given out by an ion 
 is of the same thickness as the primary pulse, yet the properties 
 of the secondary radiation may be very different from those of the 
 primary, for each pulse of primary radiation causes each ion to 
 emit a pulse of secondary radiation, so that the single primary 
 pulse produces a great number of secondary pulses following each 
 other at intervals which depend upon the proximity of the ions in 
 the medium traversed by the primary waves ; the properties of 
 this train of pulses would depend upon X the average distance 
 between the ions : they would approximate to those of light of 
 wave-length X and might thus differ materially from those of the 
 primary rays. In fact on this point of view there is much the 
 same difference between the primary and secondary rays, as there 
 is between the sharp crack of lightning and the prolonged roll of 
 thunder. 
 
 We see from the preceding equations that in passing over 
 a distance dx, the primary pulse causes the ions to emit secondary 
 radiation whose energy is 
 
138] IONISATION BY RONTGEN RAYS. 271 
 
 if this were the only loss of energy experienced by the primary 
 rays, we should have 
 
 , 4-7T , 
 dE = Edx, 
 3 w 2 
 
 or E=Ce~ s * , 
 
 so that the opacity of the substance to the primary rays would be 
 measured by 
 
 47T 
 
 this is independent of d, the thickness of the pulse, and depends 
 merely upon the medium and not upon the kind of rays passing 
 through it : the very great difference between the penetrating 
 power of hard and soft rays shows that the energy spent in the 
 secondary radiation cannot be the chief cause of the absorption of 
 the primary rays. Another source of loss of energy is the energy 
 given to the ions and retained by them : the energy of the 
 secondary rays is energy radiated from the ions, but in addition to 
 this energy the ions under the action of the rays retain an amount 
 of energy which is large compared with the energy they give out 
 as radiant energy. To calculate the energy acquired by the ions 
 from the primary Rontgen radiation, we regard that radiation as 
 consisting of a succession of pulses. In some of these the electric 
 force is in one direction, in others in the opposite, and we suppose 
 that there are as many pulses with the force in one direction as 
 there are with the force in the opposite. 
 
 Let us consider the effect produced on an ion when a pair of 
 pulses, one positive and the other negative, pass over it. Let 
 X, X be respectively the electric forces in the positive and 
 negative pulses, d the thickness of either pulse, D the distance 
 between the pulses; then the positive pulse gives to the ion a 
 velocity Xed/Vm, and the ion on the arrival of the second pulse 
 will have moved through a distance (Xed/Vm) (D/V) (if we 
 assume that the time interval between the arrival of the two 
 pulses at the ion is small compared with the free time of vibration 
 of the ion). The second pulse gives to the ion a momentum equal 
 and opposite to that given to it by the first pulse and thus reduces 
 it to rest : the joint action of the two pulses is thus to leave the 
 
272 IONISATION BY RONTGEN RAYS. [138 
 
 velocity of the ion unaltered, and to displace the ion through a 
 distance f given by the equation 
 
 t_Xe d jD 
 * ~ m F F ' 
 
 If we suppose that the ion was in equilibrium in the position 
 f = 0, and that when displaced from this position the force tending 
 to bring it back is //,, the work done in displacing the ion 
 through the distance f is i/^f 2 , thus the energy communicated by 
 the positive and negative pulses to the ion is 
 
 d 2 D 2 
 
 yz YZ ' 
 
 If E is the energy in the two pulses per unit area, we have 
 
 E = --~. 
 
 Thus the work done on the ion is equal to 
 
 e 2 dD 2 r 
 
 If n is the frequency of the free vibration of the ion, n z = p/m, so 
 that the work done on the ion is 
 
 a 
 
 -mi* - T -=- E 
 m F 2 
 
 e 2 dD z 
 
 where \ is the wave-length of the free vibration of the ion. Thus 
 the work done on the ions when the two pulses travel over a 
 distance Sx, is equal to 
 
 4-7T 3 - d.D*2^ EZx = hESa;, say, 
 Tit AT 
 
 where N is the number of ions giving out light of the wave-length 
 X in unit volume, hence we have 
 
 dE ---hE 
 
 J "~~ ti/JJ/f 
 
 dx 
 
 or E = E e~ hx ; 
 
 h is thus the coefficient of absorption of the medium for the 
 Rontgen rays : when we take into account the energy absorbed by 
 
138] 1ONISATION BY RONTGEN RAYS. 273 
 
 the ions and neglect that radiated by them, we see that h increases 
 with the thickness of each pulse and the distance between the 
 pulses, it thus depends upon the character of the primary rays ; 
 the broader the pulses the greater the absorption. Thus on this 
 view of the nature of the Rontgen rays the soft rays correspond to 
 broad pulses, the hard rays to narrow ones. 
 
 Sagnac, by allowing secondary rays to fall on metal, has ob- 
 tained tertiary rays, which are even more easily absorbed than the 
 secondary; he suggests that by a repetition of this process we 
 might ultimately get rays having the properties of ordinary 
 light. As yet however no Rontgen rays have been obtained which 
 show any trace of refraction when passing from one medium to 
 another. 
 
 T. G. 18 
 
CHAPTER XII. 
 
 BECQUEREL RAYS. 
 
 139. THE very marked phosphorescence produced in certain 
 substances by Rb'ntgen rays led to a series of investigations whose 
 object was to see whether phosphorescence was accompanied by 
 the emission of Rontgen rays: since Rontgen rays produced 
 phosphorescence the question naturally suggested itself, may not 
 phosphorescence be accompanied by Rontgen rays ? Early in 1896 
 Henry* showed that the phosphorescent substance sulphide of zinc, 
 after exposure to sunlight or magnesium light, acted photographi- 
 cally on a plate protected by black paper or by thin aluminium 
 foil. A little later Becquerelf found that if the double sulphate 
 of uranium and potassium was placed on a photographic plate 
 protected by light-proof paper and the system exposed to the 
 sun the plate was affected : he thought at first that this was due 
 to the phosphorescence emitted by the uranium while in the 
 light, he soon found however that exposure to the sunlight was 
 not necessary {,. and that the plate was equally affected in the 
 dark. To test whether this effect was due to a phosphorescence 
 which had persisted from some previous exposure of the uranium 
 salt to light he took a crystal of uranium nitrate and dissolved 
 it in water in the dark; he then, keeping it still in the dark, 
 allowed it to recrystallise, and tested its action on the photo- 
 graphic plate without ever exposing the crystal to light ; he found 
 that it acted strongly on the plate; he found also that the solu- 
 tion of uranium nitrate which is not phosphorescent is active. 
 On these, grounds Becquerel came to the conclusion that the 
 
 * Henry, Comptes Eendus, cxxii. p. 312, 1896. 
 t Becquerel, Comptes Rendus, cxxii. p. 420, 1896. 
 J Ibid. p. 501. 
 Ibid. pp. 691, 765. 
 
140] 
 
 BECQUEREL RAYS. 
 
 275 
 
 effect is not due to phosphorescence but is a property of the 
 metal itself. He found too that the salts of uranium as well as 
 the metal itself retained this radio-active property without sensible 
 diminution after being kept in the dark, some of them in lead 
 boxes, for more than a year. In addition to affecting a photo- 
 graphic plate protected by a covering opaque to ordinary light, 
 the radiation from uranium, like the Rontgen rays, makes the gas 
 through which it passes a conductor ; thus a charged electroscope 
 with a piece of uranium placed on the disc slowly loses its charge, 
 whether this be positive or negative. Becquerel at first thought 
 that the rays from uranium differed from the Rontgen rays in 
 being capable of refraction and polarisation ; subsequent investiga- 
 tions made by himself and others have shown however that this 
 is not the case. 
 
 140. Rutherford* made a very extensive series of experiments 
 on the radiation from uranium and its compounds, using the elec- 
 trical method of investigation, i.e. measuring the intensity of the 
 radiation by the ionisation produced by the rays. He made the 
 very interesting discovery that the radiation from uranium, like 
 the secondary Rontgen radiation, is a mixture of two types of 
 radiation, one type a being absorbed by a few millimetres of air 
 at atmospheric pressure, the other type ft having a penetrating 
 power comparable with the rays from a Rontgen tube of moderate 
 exhaustion. This fact is illustrated by the following table, which 
 shows the effect of successive layers of very thin aluminium foil 
 in cutting down the intensity of the radiation. 
 
 Thickness of aluminium foil, '0005 cm. 
 
 Number of layers of 
 Aluminium foil 
 
 Leak per minute in. 
 scale divisions 
 
 Proportion in which the 
 diminished by one layer 
 
 leak is 
 of foil 
 
 
 
 182 
 
 
 
 1 
 
 77 
 
 42 
 
 
 2 
 
 33 
 
 43 
 
 
 3 
 
 14-6 
 
 44 
 
 
 4 
 
 9-4 
 
 65 
 
 
 12 
 
 7 
 
 
 
 From these numbers we see that the first layer of aluminium 
 foil cuts down the intensity of the radiation to about one-half of 
 
 * Rutherford, Phil. Mag. v. 47, p. 109, 1899. 
 
 182 
 
276 BECQUEREL RAYS. [140 
 
 its original value, the second and third layers each diminish it in 
 much the same proportion, the fourth layer however produces 
 sensibly less effect, while the joint effect of the next eight layers 
 is small ; in fact to reduce the intensity of the radiation to one- 
 half the value it has after passing through four layers of foil 
 requires the interposition of one hundred additional layers. Thus 
 before the rays had been filtered by the foil, one layer of foil 
 produces as much absorption as one hundred layers after the 
 filtering has taken place. These results show that part of the 
 radiation emitted from the uranium is almost entirely absorbed 
 by about four layers of foil, while there is another part of very 
 much greater penetrating power which can pass through about 
 one hundred layers of foil before its intensity is reduced to one- 
 half. Rutherford calls the easily absorbable radiation the a 
 radiation, the other the /3 radiation. The penetrating power of 
 the /3 radiation is of the same order as that of Rontgen rays 
 emitted by an average bulb. Rutherford found that the absorption 
 by the different gases of the a type of radiation emitted by 
 uranium or any of its compounds was such that the intensity of 
 the radiation was reduced to one-half its value after passing 
 through 
 
 3 mm. of carbonic acid gas, 
 
 4' 3 mm. of air, 
 
 7 '5 mm. of coal gas, 
 
 16*3 mm. of hydrogen. 
 
 The pressure in all cases was that due to 760 mm. of mercury. 
 The penetrating power of the a radiation is thus intermediate 
 between that of ordinary primary and secondary Rontgen rays. 
 
 The absorption of the a rays was shown by Rutherford to be 
 proportional to the density of the gas. 
 
 Near a layer of uranium we have thus a region of very intense 
 ionisation extending over the few millimetres necessary to absorb 
 all the a rays, beyond this only the ft rays penetrate, and as these 
 have only small ionising power compared with the a rays there is 
 'in this region very much less ionisation than in the layers close to 
 the uranium. Thus if we have two parallel metal plates over one 
 of which a layer of uranium is spread, then if the distance 
 between the plates is greater than that required to absorb the a 
 radiation, the total amount of ionisation between the plates and 
 
140] 
 
 BECQUEREL RAYS. 
 
 277 
 
 therefore the value of the saturation current which can pass from 
 one plate to the other will not increase much as the distance 
 between the plates is increased, while as long as the distance 
 between the plates is less than that required to absorb the a 
 radiation the saturation current will be approximately propor- 
 tional to the distance between the plates ; this illustration will 
 suffice to show that the phenomena of electric conduction under 
 uranium radiation are somewhat intricate, they can however be 
 readily explained by the existence of the two types of radiation, 
 one very easily absorbed, the other much more penetrating. 
 
 Since the intensity of the ionisation is much greater close to 
 the plate covered with uranium than at some distance away, the 
 electric force near to the uranium will be less than the average 
 value between the plates ; this fall in the electric force at the 
 place where there is most ionisation makes it more difficult to 
 produce a saturation current than it would be if the ionisation 
 
 I 
 
 Cy 
 
 375 
 
 cms 
 
 40 
 
 80 
 
 160 
 
 200 
 
 Fig. 74. 
 
 were uniform between the plates ; this may account for the fact 
 discovered by Rutherford (I. c.) that even with large potential 
 differences between the plates the current shows an increase, 
 
278 
 
 BECQUEREL RAYS. 
 
 [141 
 
 though only a small one, when the potential difference is in- 
 creased. This is illustrated in the curves in Fig. 74 which 
 represent the relation between the potential difference and the 
 current under uranium radiation. 
 
 The proportion between the amounts of the ft and a radiations 
 emitted by a layer of a salt of uranium was found by Rutherford 
 (I. c.) to depend upon the thickness of the layer of salt, the thicker 
 the layer the larger the ratio of the ft to the a. radiation. This is 
 what we should expect if we regard the a and ft radiations as 
 independent of each other : for if the a radiation is stopped by a 
 thickness t-^ of the salt, while the ft radiation is not stopped until 
 the thickness is t 2 , the a radiation will not increase with the 
 thickness of the layer when this is greater than t l} while the ft 
 radiation will go on increasing until the thickness is equal to t 2 . 
 If one of the radiations was produced by the other, if for example 
 the ft radiation corresponded to primary Rontgen rays, the a to 
 the more absorbable secondary rays produced by the impact of the 
 primary ones with the uranium close to the surface, then we should 
 expect the proportion between the radiations to be independent of 
 the thickness of the layer. 
 
 141. lonisation in different gases. Since the a radiation is 
 absorbed by a few millimetres of most gases, the total amount of 
 ionisation produced on different gases when it is completely ab- 
 sorbed can be readily determined : the result of such a determina- 
 tion made by Rutherford (I. c.) is given in the following table. 
 
 Gas 
 
 Total lonisation 
 
 Gas 
 
 Total lonisation 
 
 Air 
 
 100 
 
 
 111 
 
 Hydrogen 
 
 95 
 
 Hydrochloric ) 
 
 
 Oxygen 
 
 106 
 
 acid gas j ' 
 
 102 
 
 Carbonic acid 
 
 96 
 
 Ammonia 
 
 101 
 
 
 
 
 
 The salt used to produce the rays was uranium oxide, and as 
 its radiating power was slightly affected by ammonia and hydro- 
 chloric acid the numbers for these gases must be regarded as only 
 approximately true. It will be seen that the numbers expressing 
 the total ionisation produced in the various gases when all the 
 radiation is absorbed are very nearly equal ; so nearly indeed that 
 
141] BECQUEREL RAYS. 279 
 
 we cannot say with certainty that the differences are not due 
 to experimental errors. The experiments thus point very dis- 
 tinctly to the conclusion that the absorption of a fixed quantity 
 of Becquerel rays gives rise to the same number of ions whatever 
 may be the nature of the gas ionised; we saw (p. 251) that Ruther- 
 ford's experiments on the absorption of Rontgen rays indicated 
 that a similar result was true for these rays. We may express 
 this result in the form that when all the rays whether Becquerel 
 or Rontgen are absorbed in a certain volume of gas, the maximum 
 quantity of electricity which can be forced through the gas 
 depends only upon the intensity of the rays and not upon either 
 the composition or pressure of the gas. This result is so in- 
 teresting that it is worth while discussing it a little more closely. 
 The energy absorbed may be spent (1) in ionising the gas, (2) in 
 raising the temperature of the gas. Suppose that the rays are 
 travelling parallel to the axis of x, let / be the intensity of the 
 rays at the distance x from the origin, 7 + S7 the intensity at 
 x + Sx ; SI is the energy absorbed in the layer S%. 
 
 Suppose that the number of ions produced is proportional to 
 the energy of the rays, and that the number produced in the layer 
 $x is equal to X7S#, let the work required to produce an ion be a, 
 then the energy absorbed in ionising the gas is aXl&x; let the 
 amount absorbed as heat * in the layer be ql&x, then we have 
 
 _ SI = (q + X) IBx or 1= Ce~ <2+ aA > * 
 where C is the value of 7 when x = 0. 
 
 The number of ions produced when the radiation is all absorbed 
 is equal to 
 
 r oo -so 
 
 \Idx = C\e~ 
 
 / 
 
 = 
 J 
 
 o 
 
 Rutherford's experiments show that as long as C is constant this 
 number is independent of the nature of the gas; this shows that 
 the production of each pair of positive and negative ions abstracts 
 from the energy of the rays an amount of energy which is inde- 
 pendent of the nature of the gas ionised : if all the energy 
 absorbed were spent in ionising the gas this result would imply 
 that the energy required to produce a given number of ions was 
 
 * If the ions are allowed to recombine all the energy will ultimately appear 
 as heat. 
 
280 BECQUEREL RAYS. [141 
 
 independent of the nature of the gas from which the ions are 
 obtained. The evidence seems however to be against the view 
 that the separation of ions from the molecules of the gas is the 
 only source by which the rays lose energy. Rutherford and 
 M c Clung* have measured the energy in Rontgen rays, and also 
 the total amount of ionisatioii these rays would produce if they 
 were completely absorbed by a gas. The energy in the rays was 
 measured by absorbing them in thin strips of platinum used in a 
 bolometer and determining the heating effect from the change in 
 resistance. Dornf had previously shown that appreciable thermal 
 effects were produced by the absorption of Rontgen rays in thin 
 sheets of metal, and had by this means measured the energy in 
 the rays. Measurements of this kind give us C, while the measure- 
 ment of the total number of ions gives us C\/(q + X), combining 
 the two we get (q + X)/X. Rutherford and M c Clung assumed 
 that the energy of the Rontgen rays was entirely spent in ionising 
 the gas, so that if the ions were prevented from recombining by 
 means of a strong electric field no heat was developed in the gas ; 
 on this supposition q = 0, so that (q + aX)/X is equal to a, the work 
 required to produce an ion. Making this supposition Rutherford 
 and M c Clung found that the work required to ionise a gas was 
 equivalent to the work done when each ion was moved through a 
 potential difference of about 95 volts, so that since the ions are 
 produced in pairs it would require a potential difference of at 
 least 190 volts to separate the ions. We saw however (p. 190) 
 that the experiments made by H. A. Wilson on the ionisation of 
 hot gases indicated that a much smaller difference of potential 
 about 2 volts is all that is required to ionise a gas, this conclusion 
 is confirmed by other lines of argument. If we take Wilson's 
 value for the work required to ionise a gas, we see that a is the 
 work done when the ionic charge is moved through the potential 
 difference of about 1 volt. Rutherford's and M c Clung's experi- 
 ments show that in the case of the Rontgen rays used by them 
 
 a + = 95a, 
 
 or 
 
 * Rutherford and M c Clung, Phil. Trans. A. cxcvi. p. 25, 1902. 
 t Dorn, Wied. Ann. Ixiii. p. 160, 1897. 
 
142] BECQUEREL RAYS. 281 
 
 Thus for each ion produced the mechanical equivalent of the 
 heat developed in the gas is about 94 times the work required to 
 separate the ion from the molecule. 
 
 Rutherford's experiments on the ionisation produced by the 
 complete absorption of the a radiation from uranium show that 
 if the number of ions produced is proportional to the energy in 
 the rays, then as long as the rays remain the same the liberation 
 of an ion always abstracts the same amount of energy from the 
 rays whatever may be the nature of the gas. This, since by far 
 the greater part of the absorption of energy is apparently due to 
 the heating of the gas, is a very remarkable result. We do not 
 know however whether or not the amount of energy absorbed 
 when an ion is produced depends upon the nature of the rays, 
 whether for example it is the same for Becquerel as for Rontgen 
 rays, for hard Rontgen rays as for soft. It is much to be desired 
 that experiments of the type of those made by Rutherford and 
 M c Clung should be made with as many kinds of rays as possible. 
 
 If we regard the Rontgen and Becquerel rays as pulses of 
 electric and magnetic force made up of Faraday tubes, we may 
 see why the amount of ionisation should not depend upon the 
 nature of the gas : for when a pair of ions is separated the ends 
 of one of the Faraday tubes in the pulse will now be on the ions, 
 one end on the positive, the other end on the negative ion ; this 
 Faraday tube gets anchored as it were by the ions, and is dragged 
 back from the pulse which passes on without it. Thus each pair 
 of ions means the abstraction of one Faraday tube from the pulse, 
 and when all the tubes are extracted, the number of ions produced 
 will be twice the number of Faraday tubes originally in the pulse 
 and independent of the nature of the gas. 
 
 142. The total amount of ionisation produced when the 
 a rays of uranium and its salts are completely absorbed has be n 
 determined by Monsieur and Madame Curie* and by Rutherford 
 and M c Clungf, it increases somewhat with the thickness of the 
 layer, as the following table given by the latter observers shows. 
 The amount of ionisation is expressed in terms of the saturation 
 current which is given in amperes per square centimetre of 
 surface. 
 
 * Curie, Rapports presentes au Congres de Physique a Paris, t. iii. p. 79, 1900. 
 t Rutherford and M'Clung, Phil. Trans. A. cxcvi. p. 25. 
 
282 BECQUEREL RAYS. [143 
 
 Surface of Uranium Oxide = 38 sq. cms. 
 
 Weight of Uranium Oxide spread 
 over this surface in grammes 
 
 138 
 365 
 718 
 1-33 
 3-63 
 
 Current in Amperes per 
 sq. cm. of surface 
 
 17 xlO- 13 
 3-2xlO~ 13 
 4 xlO' 13 
 4-4 xlO~ 13 
 4-7 xlO- 13 
 
 Taking the value given by Rutherford and M c Clung for the 
 energy .absorbed when each ion is produced, we find that when 
 the saturation current is 4*7 x 10~ 13 amperes per square centimetre 
 the energy emitted from a square centimetre is about 10~ n calories 
 per second, or at the rate of 1 calorie in about 3000 years. If we 
 take the radiation corresponding to the thinnest layer we find 
 that for each gramme in the layer it is about 1 calorie in 30 years. 
 
 Magnetic Deflection of the more penetrating Uranium Rays. 
 
 143. The fact that some of the rays given out by some radio- 
 active substances are deflected by a magnet was first discovered for 
 the radiation from radium, we shall give an account of these experi- 
 ments when we discuss the radiation from that body. Becquerel* 
 subsequently found that the /3 rays from uranium were deflected 
 by a magnet, the direction of the deflection being the same as 
 that of the cathode rays : so that for this arid other reasons we 
 conclude that the ft rays consist of negatively charged particles. 
 Assuming that the ratio of the mass to the charge for the ft rays 
 is the same as for the cathode rays, Becquerel from his determina- 
 tion of the magnetic deflection of these rays concluded that they 
 were moving with a velocity of 2 x 10 10 cm. per sec.: this velocity, 
 which is two-thirds of that of light, is considerably greater than 
 that of any cathode rays hitherto produced by electrical means. 
 
 The a rays from radium, have been shown by Rutherford ( to 
 carry a positive charge, and Becquerel { has shown that they are 
 deflected by a strong magnetic field in the direction corresponding 
 to a charge of this sign. 
 
 * Becquerel, Comptes Rendus, cxxx. p. 1583 ; cxxxi. p. 137, 1900. 
 
 t Rutherford, Phil. Mag. vi. 5, p. 177, 1903. 
 
 Becquerel, Comptes Rendus, cxxxvi. p. 431, 1903. 
 
144] BECQUEREL RAYS. 283 
 
 144. Sir William Crookes* concludes that the radiation from 
 uranium does not proceed from uranium itself, but from some 
 unknown impurity. The reason for this conclusion is that by a 
 process of fractionation he has obtained, starting from uranium salts, 
 two products, one of which is radio-active, while the other is not. 
 
 One of these processes consists in dissolving crystallised uranium 
 nitrate in ether, the uranium divides itself unequally between the 
 ether and the water present, the larger part which is in the ether 
 layer does not affect a photographic plate, while the smaller 
 portion which is in the water layer possesses all the photographic 
 activity of the original nitrate. Soddyf*, who repeated this 
 experiment using "for the radio-activity the electrical test, i.e. the 
 amount of ionisation produced, 'found that both portions were 
 equally active, so that apparently no separation had been effected. 
 The explanation of this discrepancy is that in the photographic 
 method the rays have to pass through glass or' card before 
 reaching the film, so that all the absorbable a rays are stopped 
 and only the ft rays are detected : in the electrical method however 
 the ionisation is practically -entirely produced by the a radiation, 
 thus the. photographic method detects the ft, the electrical method 
 the a radiation, so that the experiments show the separation 
 is confined to the substance producing the ft radiation. Another 
 process employed by Crookes to separate the active consti- 
 tuent UrX from the other consisted in precipitating solutions 
 of uranium nitrate with ammonium carbonate in excess, the small 
 amount of precipitate was collected an.d the filtrate evaporated, 
 another and much larger precipitate came down; the first of 
 these precipitates strongly affected a photographic plate, while 
 the second was almost inactive. On testing these by the elec- 
 trical method Soddy found that the second precipitate produced 
 a considerable ionisation, while the effect of the small quantity 
 of the first was barely perceptible ; the explanation of this is the 
 same as before, and Rutherford and GrierJ have shown by direct 
 experiment that the first precipitate emits nothing but the 
 cathodic-magnetically deflectable ft radiation, while the second 
 precipitate emits nothing but the a radiation. 
 
 * Crookes, Proc. Roy. Soc. Ixvi. p. 409, 1900. 
 
 t Soddy, Ghent. Soc. Journ. Ixxxi., Ixxxii. p. 860, 1902. 
 
 t Rutherford and Grier, Phil. Mag. vi. 4, p. 315, 1902. 
 
284 
 
 BECQUEREL RAYS. 
 
 [145 
 
 145. Becquerel* made the very interesting observation that 
 when he had enfeebled the radio-activity of uranium by precipi- 
 tating barium as sulphate from uranium solutions and transferred 
 most of the (/3) activity to the barium, on allowing the products to 
 stand for several months the enfeebled uranium had recovered its 
 normal activity, while the barium which had been made radio- 
 active had entirely lost this property ; a similar phenomenon was 
 discovered by Rutherford and Soddy in the case of thorium, and 
 their investigations on this point led to very important considera- 
 tions as to the production of radio-activity; these are discussed 
 on p. 292. 
 
 Radiation from Thorium. 
 
 146. Soon after the discovery of the Becquerel rays Schmidt J- 
 discovered that thorium gave out rays having very similar 
 properties. This radiation was subsequently studied by Ruther- 
 ford J and by Owens, and was found to present many features of 
 great interest. 
 
 When a thin layer of thorium oxide is used the radiation is 
 approximately homogeneous, as the following results given by 
 Rutherford show : successive layers of thin paper were placed 
 over a thin layer of thorium oxide, and the intensity of radiation 
 determined by measuring the rate of discharge through a volume 
 of gas sufficient to absorb the radiation completely. 
 
 Thickness of paper = -0027 cm. 
 
 Number of layers of thin paper 
 
 Rate of Discharge 
 
 
 
 1 
 
 1 
 
 37 
 
 2 
 
 16 
 
 3 
 
 08 
 
 The intensity of the radiation, which is proportional to the 
 rate of discharge, thus diminishes in approximately geometrical pro- 
 gression with the addition of equal thicknesses of paper, this shows 
 
 * Becquerel, Comptes Rendus, cxxxiii. p. 977, 1901. 
 t Schmidt, Wied. Ann. Ixv. p. 141, 1898. 
 J Rutherford, Phil. Mag. v. 49, pp. 1, 161, 1900. 
 Owens, Phil. Mag. \. 48, p. 360, 1899. 
 
147] 
 
 BECQUEREL RAYS. 
 
 285 
 
 that the radiation is roughly homogeneous. When however a thick 
 layer of the oxide is used there is in addition to the radiation of 
 the type given out by the thin layer other radiation of a much 
 more penetrating type ; this is proved by the following results, 
 which were also given by Rutherford. 
 
 Thick layer of oxide. 
 Thickness of paper = '008 cm. 
 
 Number of layers of paper 
 
 Bate of Discharge 
 
 
 
 1 
 
 1 
 
 74 
 
 2 
 
 74 
 
 5 
 
 72 
 
 10 
 
 67 
 
 20 
 
 55 
 
 Thus the first layer of paper produces an appreciable diminu- 
 tion in the intensity of the radiation due to the absorption of 
 the radiation of the type given out by the thin layer, but after 
 this is absorbed there is an appreciable amount of radiation left 
 which can pass through a considerable thickness of paper without 
 suffering much absorption. 
 
 147. The radiation from thick layers of thorium oxide when first 
 measured by Rutherford seemed to be extremely capricious ; thus, 
 for example, when its intensity was measured by the conductivity it 
 communicated to a gas, the slightest draught in the vessel through 
 which the current of electricity passed was sufficient to produce 
 a very sensible diminution in the current ; indeed so sensitive was 
 the current to external disturbances, that it was found exceedingly 
 difficult to get consistent results. Rutherford showed that those 
 irregularities had a most interesting cause, as he was able to trace 
 them to an ' emanation ' given off by the thorium. He found 
 that the thorium gave off something which was wafted about by 
 currents of air like a vapour; in order to avoid prejudging the 
 question as to the physical state in which the substance given 
 off by the thorium existed, Rutherford called it an emanation. 
 This emanation is radio-active, i.e. it gives off rays that can 
 penetrate a photographic plate or ionise a gas ; it can penetrate, 
 apparently by diffusion, thin sheets of metal or pieces of paper ; 
 
286 BECQUEREL RAYS. [147 
 
 it cannot, however, get through glass or mica, even when they are 
 in very thin films : in fact, its power of getting through substances 
 seems much more selective than the corresponding power possessed 
 by either Rontgen, Becquerel, or cathode rays ; in this respect it 
 resembles the effect coming from certain metals and resinous 
 substances studied by Russell. That the passage of the emanation 
 through solids is analogous to the slow diffusion of gas through 
 metal, as, for example, hydrogen through red-hot platinum, is 
 suggested by the fact that if the thorium oxide is covered up 
 with paper it takes a considerable time for the emanation to 
 get through. 
 
 The following experiment is one by which Rutherford demon- 
 strated the existence of the ' emanation,' and studied many of 
 its properties. 
 
 A thick layer of thorium oxide was enclosed in a narrow 
 rectangular vessel A, made up of two thicknesses of foolscap 
 paper. This paper was sufficiently thick to stop all the radiation 
 from a thin layer of thorium. The vessel containing the thorium 
 
 Fig. 75. 
 
 was placed inside a long metal tube B. One end of this tube 
 was connected with a large insulated vessel C, the end of this 
 vessel was perforated to allow air to pass through. An insulated 
 electrode D was inserted in G, and connected with one pair of 
 quadrants of an electrometer. C was connected with one terminal 
 of a battery giving an electromotive force of 100 volts, the other 
 terminal of this battery was put to earth. 
 
 A slow current of dust-free air was passed through the appa- 
 ratus. After a short time a current began to pass between C 
 and D, and gradually increased until it reached a certain value, 
 when it became steady. The flow of air was then stopped, and 
 
147] BECQUEREL RAYS. 287 
 
 it was found that the current between and D persisted for 
 about 10 minutes. As long as the current of air was passing 
 through the apparatus there would have been a current of elec- 
 tricity between C and D, if ordinary radiation and no emanation 
 had been coming from the thorium, for the radiation would have 
 produced ionised gas in the neighbourhood of A, and this would 
 have been carried by the current into C: but in this case the current 
 of electricity would have stopped within a fraction of a second 
 after the stoppage of the current of air, whereas, as we have seen, 
 the effect persisted for 10 minutes. This shows that fresh ions 
 must be continually produced in (7, in other words, the substance 
 carried over from A must be radio-active, and though its radio- 
 activity diminishes with time there is enough left to be appreci- 
 able after an interval of 10 minutes. 
 
 Rutherford measured the leak between G and D at regular 
 
 o 
 
 intervals after the stoppage of the current of air, and so was 
 able to measure the rate at which the intensity of the radiation 
 from the emanation died away: the intensity diminishes in 
 geometrical progression with the time, and is thus proportional 
 to e~ A ^, where t is the time and X a constant : the intensity is 
 reduced to about one-half its value in one minute, so that \ is 
 about 1/86. The rate at which the radiation falls off is not 
 affected by exposing the emanation to a strong electric field, nor 
 could any motion of the emanation as a whole be detected in 
 such a field : Rutherford showed that the average velocity of the 
 particles of the emanation, under an electric field of one volt per 
 centimetre, must be less than 10~ 6 cm./sec. 
 
 In consequence of the diffusion of the emanation from the 
 thorium the radiation from thick layers of this substance does 
 not cast shadows, the emanation getting by diffusion round the 
 opaque body and obliterating the shadow. 
 
 The emanation can pass through plugs of porous substances, 
 can bubble through water or the strongest acids, and can be 
 raised to temperatures far above a red-heat without losing its 
 radio-activity * : in fact, when once the ' emanation ' has been 
 produced no physical or chemical process which has yet been 
 tried has any effect upon its radio-activity: in this inertness it 
 
 * Rutherford and Soddy, Journal of Chemical Society, Ixxxi. p. 321, 1902. 
 
288 BECQUEREL RAYS. [148 
 
 resembles the gases argon and helium, the latter of which occurs 
 along with thorium in many minerals. 
 
 Since the emanation can penetrate several millimetres of a 
 thorium compound, the radiation from a layer of such a compound 
 will increase with the thickness of the layer when this is less 
 than a few millimetres; above a certain thickness the radiation 
 becomes practically constant. 
 
 The fact that the ' emanation ' can pass through porous plugs 
 and water traps, and can withstand temperatures which alter the 
 properties of thorium, is strong evidence that the emanation is 
 not thorium dust, i.e. not small particles of thorium in the solid 
 state ; this conclusion is strengthened by the fact that the ema- 
 nation does not give rise to a cloud when the air through which 
 it is diffused suffers an expansion sufficient to produce a fog in 
 dusty air. 
 
 No alteration has been detected in the pressure of an ex- 
 hausted bulb when the emanation is allowed to diffuse into it, 
 nor does this intrusion of the emanation produce apparently any 
 change in the spectrum given out by the bulb. 
 
 Effect of Physical Conditions on Emanating Power. 
 
 148. Effect of Temperature. This has been investigated by 
 Rutherford* and by Rutherford and Soddyf, who have shown that 
 an increase of temperature up to a certain limit about a red-heat 
 increases the emanating power of thorium oxide. The maximum 
 reached is between three and four times the value at ordinary 
 atmospheric temperatures, and is maintained at this value for 
 several hours without any sign of diminution with time. When 
 the thorium is allowed to cool the emanating power returns 
 to about the original value. When the thoria is heated beyond 
 a certain temperature the emanating power rapidly falls off to 
 a fraction of its former value, and on cooling the emanation is 
 found to be small compared with its previous value; by heating 
 thoria .to the highest temperature which could be safely employed 
 with platinum vessels and then allowing it to cool, the emanating 
 power was reduced to about 8 per cent, of its original value. 
 
 * Rutherford, Physikalische Zeitschrift, ii. p. 429, 1901. 
 
 t Rutherford and Soddy, Journal of Chemical Soc. Ixxxi. p. 321, 1902. 
 
149] BECQUEREL RAYS. 289 
 
 This change in the rate of emanation is accompanied by changes 
 in the physical and chemical properties of the thoria ; when first 
 the de-emanation sets in the thoria changes in colour from pure 
 white to a light brown, and then at the very highest tempera- 
 tures to a pure pink ; and at the same time the solubility of the 
 substance in sulphuric acid is greatly diminished. Though the 
 emanation is so greatly diminished by this intense heating, 
 the radiation from thin layers of the substance which, following 
 Rutherford, we shall call the 'straight line' radiation is not 
 affected. 
 
 Rutherford and Soddy have shown that the loss of emanating 
 power of thoria can be remedied by chemical treatment, they 
 found that if the de-emanated thoria was dissolved up and re- 
 precipitated it recovered completely its emanating power. 
 
 In another experiment made by Rutherford and Soddy the 
 thoria was cooled by a mixture of solid carbonic acid and ether, 
 the emanation fell to about 10/ of its value at the temperature 
 of the room, but it recovered its original value when the cooling 
 agent was removed. Thus though all changes of temperature 
 produce marked temporary effects, no permanent ones are pro- 
 duced unless the temperature exceeds red-heat. 
 
 149. Effects of Moisture. Dorn* showed that the emanation 
 from thoria was greater in a moist atmosphere than in a dry one. 
 Rutherford and Soddy subsequently confirmed this, and found 
 that the emanation in an atmosphere saturated with water 
 vapour was about 20 / greater than in a very dry atmosphere. 
 
 There are many phenomena which show that the emanating 
 power of a thorium compound does not depend merely upon the 
 quantity of thorium and other elements in the material ; the way 
 in which the different elements are combined and the previous 
 treatment and history of the compound have a great influence 
 upon the result. Thus, for example, the emanating power of 
 freshly prepared hydroxide goes on increasing for some time 
 after it has been dried, until when it reaches the steady state 
 the value may be three times that when it was first tested. 
 This seems to indicate that the emanation may be due to some 
 compound which is formed but slowly : the effect produced by 
 
 * Dorn, Abh. der Naturforsch. Ges.fiir Halle-a-S. 1900. Beiblatter, xxiv. p. 1343. 
 * T. G. 19 
 
290 BECQUEREL RAYS. [150 
 
 intense heating could be explained by supposing that at high 
 temperatures this compound is changed into one not giving the 
 emanation, the change being a permanent one, the new substance 
 not being destroyed by the subsequent cooling. 
 
 A good illustration of the effect of changes in the physical 
 condition of the substance on its emanating power is afforded by 
 the nitrate ; this salt when in the solid state gives out but little 
 emanation, when however the salt is dissolved in water and air 
 bubbled through the solution the air carries off more than 200 
 times the quantity of emanation that could be obtained by passing 
 the air over an equal quantity of the solid ; the quantity of 
 emanation obtained by bubbling depends only upon the quantity 
 of the salt and not upon the degree of dilution. 
 
 Source of the Emanation. 
 
 150. Rutherford and Soddy have made a series of experi- 
 ments to see whether the emission of the emanation is a property 
 of thorium itself, or whether it is due to some impurity. The con- 
 clusion they came to was that it was not emitted directly from the 
 thorium, since they could obtain from thorium salts substances 
 whose emanating power was enormously greater than that of the 
 original salt. One method of doing this was to dissolve a quantity 
 in the experiment 70 grams of thorium nitrate in water and 
 precipitate the thorium by adding ammonia. The nitrate was then 
 evaporated down to about 60 c.c., and was found to possess when 
 air was bubbled through it as much emanating power as 146 grams 
 of thoria; on evaporating to complete dryness and getting rid of 
 the ammonium salts the residue left only weighed '0583 gram. 
 Thus this residue consisted of a substance which when in solution 
 gave with a weight of '0583 gram as much emanation as 
 146 grams of thoria, or weight for weight its emanating power 
 was 2500 times that of thoria. The separation of this substance 
 was accompanied by a loss in the emanating power of the sub- 
 stance from which it was produced, for when the hydroxide pre- 
 cipitated in this experiment was converted into oxide, the ema- 
 nating power of this was only about one-third that of oxide 
 prepared from nitrate which had not been dissolved. Similar 
 results were obtained by testing the water used to wash the oxide. 
 Residues were obtained by evaporating the washings to dryness, 
 
151] 
 
 BECQUEREL RAYS. 
 
 291 
 
 and some of these residues were 1800 times more radio-active than 
 the original thoria. No substance other than thorium could be 
 detected in these residues ; the quantity of material available was 
 however too small to admit of a very searching examination. 
 
 151. In a subsequent paper Rutherford and Soddy* have 
 shown that the very active residues they obtain by those methods 
 gradually lose their radio-activity, while the thorium hydroxide 
 which had been deprived of its power by the abstraction of this 
 residue gradually recovers and ultimately regains its normal 
 activity ; thus in one case they found that in about three weeks 
 the recovery of the hydroxide whose strength had been reduced 
 to about 36 % of its normal value was practically complete, while 
 the residue which originally was so abnormally active had in the 
 same time lost the whole of its activity. This led to a series of 
 experiments on the rate of recovery of the hydroxide and the 
 rate of loss of the residue called by them Th X, the residue was 
 prepared by the ammonia process described on p. 290. The 
 
 No. of D 
 
 J 
 
 Fig. 76. 
 
 results of these experiments are shown in the curves given in 
 Fig. 76: it will be seen that the time taken by the hydroxide 
 
 * Rutherford and Soddy, Phil. Mag. vi. 4, pp. 370, 569, 1902. 
 
 192 
 
292 BECQUEREL RAYS. [151 
 
 to recover half of its lost radio-activity is about the same as that 
 taken for the radio-activity of the Th X (the residue) to lose half 
 of its original activity. Rutherford and Soddy by these experi- 
 ments were led to a theory of radio-activity which explains this 
 and many other phenomena. This view is as follows; the 
 radio-active constituent in the thorium compounds is not an 
 accidental impurity, but is a substance which we may call ThX, 
 which is being manufactured at a constant rate from the thorium ; 
 after its manufacture its radio-activity gradually dies away. The 
 normal radio-activity of a thorium compound is due to a state of 
 dynamical equilibrium in which the increase in radio-activity due 
 to the production of fresh ThX just balances the loss due to the 
 fading away of the activity of the Th X previously produced. 
 
 To put this in a mathematical form suppose that T is the 
 amount of thorium present at any time, let the amount of Th X 
 produced by this in unit time be aT; let the initial radio-activity 
 of unit mass of Th X be r, then the rate at which the radio- 
 activity of the mixture is increasing in consequence of the pro- 
 duction of fresh Th X is raT ; let R be the radio-activity of the 
 mixture, let this in consequence of the loss of energy by radiation 
 be decreasing at the rate \R ; then we have 
 
 when things are in a steady state dR/dt vanishes and we have 
 
 . 
 
 The general solution of (1) is, regarding T as constant, 
 
 R = ~ + C~ M ....................... (2) 
 
 A, 
 
 where G is a constant. Let us suppose that we remove all the 
 Th X and so deprive the substance of its radio-activity, then 
 initially when t = 0, R = and (2) becomes 
 
 thus the compound will have recovered half of its normal activity 
 when e~ M = J or when t = - log 2. 
 
 A. 
 
152] BECQUEREL RAYS. 293 
 
 Let us now consider the radio-activity of the Th X removed 
 from the mixture, as there is no thorium in the mixture T = 
 so (2) becomes 
 
 R = Ce- A , 
 
 thus the intensity of the radiation will fall to half its original 
 value when e~ M = or when t = - log 2 ; thus the time taken for 
 
 A. 
 
 the Th X to lose half its radio-activity is equal to the time taken 
 for the salt from which the Th X was removed to recover half of 
 its lost activity, and this as we have seen is approximately the 
 case. 
 
 On this view the energy required t6 maintain the radiation is 
 obtained from the chemical change which is taking place in the 
 thorium, the change from thorium to thorium X being accompanied 
 by a loss of energy. 
 
 Rutherford and Soddy consider that Th X is a distinct sub- 
 stance and not merely some chance substance that may have been 
 present along with the thorium in the salt. Their reason for 
 thinking that the latter view is not tenable is that if it were 
 true then any method of precipitating the thorium from a solution 
 ought to leave the solution radio-active after the loss of the 
 thorium ; this is not however the case, it is only certain special 
 methods of precipitation which deprive the precipitated thorium 
 of its activity and leave the solution radio-active ; this implies 
 that the substance which is the origin of the radio-activity is one 
 having definite chemical properties. 
 
 152. Emanating Power. The loss of radio-activity of the 
 thorium hydroxide treated in the way described above is accom- 
 panied also by a loss of emanating power, while the Th X possesses 
 this power to a very large extent when first formed : it is found 
 that as the thorium hydroxide recovers its radio-activity it also 
 recovers pari passu its emanating power, while the emanation 
 from the Th X becomes smaller and smaller and finally dis- 
 appears. This is what would happen if the Th X split up after 
 its formation, one of the products of the decomposition being the 
 emanation. 
 
 An interesting question is what becomes of the dead Th X 
 and the dead emanation ; since the Th X is only active for about 
 
294 
 
 BECQUEREL RAYS. 
 
 [153 
 
 a week, the amount of the spent Th X to the active will be the 
 ratio of the age of the thorium compound to one week. As the 
 life of the emanation is very much shorter the proportion of the 
 spent emanation to the active will be very much larger. Is it 
 possible that the gases like helium and argon which are so often 
 found in minerals containing radio-active substances represent 
 the accumulations of spent emanations ? The chemical inertness 
 which is so marked a feature of these gases is also as we have 
 seen a characteristic of the emanation. 
 
 153. Debierne* by extracting the thorium from pitchblende 
 obtained an exceedingly radio-active product, he ascribed this 
 activity to the presence of a new element, which he named 
 1 actinium ' ; he was not able to separate the actinium from the 
 thorium. 
 
 Induced Radio-activity produced by Thorium Emanation. 
 
 154. Rutherford f discovered that the emanation from thorium 
 makes any substance with which it comes in contact radio- 
 active. This can be shown by the following experiment (Fig. 77). 
 
 Fig. 77. 
 
 Two isolated plates B and C are placed parallel to one another 
 in a closed metallic vessel connected with the earth. In a shallow 
 depression, LM, in the plate (7, a layer of thorium oxide is placed 
 and covered with several layers of foolscap paper. The plate C 
 is connected to the positive pole of a battery, giving a potential 
 difference of at least 50 volts, and the other pole of this battery 
 is connected with the earth. The plate B is connected with an 
 electrometer. If this is left for several hours, and then the 
 
 * Debierne, Comptes Rendus, cxxix. p. 563, 1899 ; cxxx. p. 906, 1900. 
 t Rutherford, Phil. Mag. v. 49, p. 161, 1900. 
 
154] 
 
 BECQUEREL RAYS. 
 
 295 
 
 plate C with the thorium removed, and replaced by a clean 
 metallic plate, it will be found that the gas between the plates now 
 possesses considerable conductivity ; this will gradually diminish 
 with lapse of time and after a few days become inappreciable. 
 If, instead of leaving B in the vessel when C is removed, both 
 B and C are replaced by fresh plates, there will be no conduc- 
 tivity; the ionisation is thus due to some change produced in 
 the plate B by the action of the thorium. The plate B has been 
 made radio-active. That this effect is due to the action of the 
 emanation and not of the straight line radiation may be proved 
 in several ways. In the first place, the effect is absent if we use 
 *a thin layer of thorium oxide, which emits plenty of straight line 
 radiation but very little emanation. Again, when we de-emanate 
 thorium oxide by intense heating (see p. 289), we destroy its 
 power of producing induced radio-activity, although we do not 
 affect its power of emitting straight line radiation. 
 
 The close connection between the emanation and the induced 
 radio-activity is shown by the following experiment made by 
 Rutherford. 
 
 A slow current of air from a gas-bag passed down a rect- 
 angular wooden pipe, 60 cm. long ; the air passed through sul- 
 phuric acid to dry it, and through a plug of cotton-wool in the 
 pipe at W, this plug removed spray and equalised the flow of 
 air over the cross section of the tube. A metal plate charged 
 with positive electricity covered the bottom of the tube, four 
 insulated metal plates A, B, C, D, placed at equal intervals, had 
 a negative charge induced on them by being connected with the 
 earth. When the current of air passed through the vessel with 
 the velocity *2 cm./sec. for 7 hours, with a potential difference of 
 300 volts between the lower and upper plates, the following 
 results were obtained : 
 
 
 Eelative current due 
 
 Relative excited 
 
 
 to emanation 
 
 radio-activity 
 
 Plate A ... 
 
 1 
 
 r 
 
 B ... 
 
 55 
 
 43 
 
 C ... 
 
 18 
 
 16 
 
 I)- 
 
 072 
 
 061 
 
296 BECQUEREL RAYS. [155 
 
 Thus the induced radio-activity is approximately proportional 
 to the intensity of the radiation given out by the emanation. 
 
 The experiment shows that the emanation is in some way the 
 cause of the induced radio-activity ; it does not enable us to 
 decide whether the radio-activity is due to a deposit of the 
 substance of the emanation on the plate, or whether it is due 
 to a change in the surface layers of the plate produced by the 
 radiation coming from the emanation. We shall return to this 
 point when we have discussed more fully the properties of the 
 induced radio-activity. 
 
 If in the inclosure containing the thorium and the emanation* 
 there is a conductor strongly charged with negative electricity, the 
 induced radio-activity will be concentrated on this conductor and 
 there will be less on the walls of the inclosure than there would 
 be if the conductor were uncharged ; thus the excess of radio- 
 activity on the wire is obtained at the expense of that on the 
 surrounding objects. 
 
 The amount and quality of the induced radio-activity seem to 
 be independent of the material of which the walls of the inclosure 
 are made; the substitution of paper or cardboard for metal makes 
 no appreciable difference in the result. The radio-activity does 
 not depend upon the nature of the gas in the inclosure, nor upon the 
 pressure of the gas, although the concentration of the induced 
 radio-activity on negatively electrified surfaces is less complete at 
 low pressures than it is at high. Thus, for example, in an experi- 
 ment made by Rutherford the induced radio-activity on a nega- 
 tively electrified wire was practically unchanged when the pres- 
 sure was reduced from 760 mm. to 16 mm.; at a pressure of 5 mm. 
 however, it was about 1/20 of its value at the higher pressure ; 
 this diminution in the radio-activity of the wire is accompanied 
 by an increase in that of the walls of the inclosure. 
 
 155. Duration of the induced radio-activity. This induced 
 radio-activity dies away gradually with the time ; the rate of de- 
 crease is, however, very slow, as Rutherford's measurements show 
 that it takes about 11 hours for the intensity of the radiation to 
 fall to 1/2 of its original value. The rate at which the radiation 
 dies away does not depend upon the nature of the material which 
 is made radio-active. The duration of the induced radio-activity 
 
156] BECQUEREL RAYS. 297 
 
 is thus very much greater than that of the emanation which pro- 
 duced it, as we have seen that this fades away to one-half its 
 original value in one minute. We must remember, however, that 
 this relates to the emanation when it has escaped from solids and 
 is in a form analogous to that of a free gas, we do not know whether 
 the rate of decay is as great as this when the emanation is diffus- 
 ing through a solid : the results of experiments seem rather to 
 indicate that it is not, for the emanation is still active after passing 
 through a great many sheets of paper ; if its rate of decay when in 
 the paper is as rapid as it is when in the air it must be able to 
 diffuse through these in a very few minutes. 
 
 A surface once made radio-active can be exposed to very rough 
 usage without losing this property; thus Rutherford raised a piece 
 of radio-active platinum to a white heat and found after cooling 
 that it had lost little if any of its activity. Washing the surface 
 with hot or cold water, caustic soda, or nitric acid has no effect 
 upon the activity ; if, however, the wire is dipped in sulphuric or 
 hydrochloric acid the radio-activity is removed in a few minutes : 
 the radio-activity is however only removed from the metal to the 
 acid, for on evaporating down to dryness the residue left was found 
 to be strongly radio-active. It would thus appear that the radio- 
 active substance is dissolved in the acid and retains its radio- 
 activity. 
 
 No change in weight due to the induced radio-activity can be 
 detected, nor does microscopic examination of the metal reveal 
 the presence of any dust or any change in the surface. The radio- 
 activity can be removed by long scouring with sand or emery 
 paper, the pieces removed are radio-active. 
 
 156. Time taken to produce the Radio-activity. The radio- 
 activity takes considerable time to produce. On first exposure to 
 the emanation it increases nearly proportionally with the time, 
 afterwards the rate of increase falls off, and it ultimately attains a 
 constant value. The following diagram (from Rutherford's paper) 
 shows how the intensity of the induced radiation increases with 
 the time of exposure to the thorium. 
 
 The time taken to attain a steady state is fixed by the rate at 
 which the induced radiation fades away. For let I be the inten- 
 sity of the induced radio-activity at any time t, q the rate at which 
 
298 
 
 BECQUEREL RAYS. 
 
 [156 
 
 this is increasing in consequence of the presence of the thorium, 
 I IT the rate at which it would decay if no thorium were present, 
 then we have 
 
 dl I 
 
 or 
 
 I = qT(l-e~lr 
 
 thus the radio-activity will not reach a steady state until t is 
 considerably greater than T. Now T has been determined by 
 
 100 
 
 90 
 
 30 
 
 20 
 
 10 
 
 77/re ,n 
 
 10 20 30 40 50 60 70 80 90 100 
 Fig. 78. 
 
 Rutherford by measuring the rate at which the activity of the 
 surface disappears when it is not exposed to the action of thorium; 
 putting q = we get 
 
 where / is the value of / when t = ; Rutherford found that / fell 
 to / in about 11 hours, so that T= 16 hours ; thus it will take a 
 time greater than 11 hours but comparable with it for the induced 
 radio-activity to reach a steady state. We see from equation (1) 
 that the induced radio-activity should reach half its final value in 
 about 11 hours; an inspection of Fig. 78 will show that this is 
 the case. 
 
157] BECQUEREL RAYS. 299 
 
 Penetrating power of the induced Radio-activity. 
 
 157. Rutherford measured the penetrating power of the in- 
 duced radiation and found that it was considerably greater than 
 that from thin layers of the thorium itself. Thus the latter is 
 reduced to half its intensity after passing through about 1 cm. of 
 air at atmospheric pressure, while the induced radio-activity can 
 pass through 1*65 cm. before its intensity is reduced by the same 
 amount. The penetrating power of the induced radio-activity is 
 independent of the nature of the substance made radio-active; 
 this is a strong indication that the induced radio-activity is due 
 to a deposit of the emanation and not to an alteration of the sur- 
 face of the substance by radiation from the emanation. Further 
 evidence on this point could probably be obtained by observing 
 at different air pressures the distances from the thorium at which 
 a substance can be made radio-active. For if it is due to a 
 deposit of the emanation the experiment described on p. 295 shows 
 that the emanation must be deposited while it is radio-active, i.e., 
 not much longer than a minute after it has left the thorium. 
 If the substance to be made radio-active is placed so far away 
 from the thorium that the emanation takes much more than 
 a minute to diffuse to it, the emanation will be spent before it 
 reaches the surface and this will not become radio-active. Now 
 the distance through which the emanation can diffuse in a time T 
 is proportional to V DT where D is the coefficient of diffusion of 
 the emanation; as D varies inversely as the pressure of the gas the 
 distance at which a surface could become radio-active would be 
 inversely proportional to the square root of the pressure. If, 
 however, the induced radio-activity were due to the radiation 
 given out by the emanation, then since the transparency of a 
 gas to the radiation is inversely proportional to the pressure the 
 distance at which a surface could be made radio-active would 
 be inversely proportional to the pressure and not, as in the pre- 
 ceding case, to the square root of the pressure. 
 
 The effect produced by negative electrification in increasing 
 the induced radio-activity on a surface thus electrified is, I think, 
 probably connected with the property possessed by several radio- 
 active substances, for example uranium and radium, of emitting 
 negatively electrified corpuscles. Let us trace the consequences 
 
300 
 
 BECQUEREL RAYS. 
 
 [158 
 
 of supposing that the radio-active emanation from thorium pos- 
 sesses this property. As the radio-activity of the particles we 
 have seen only lasts for a short time, it is probable that most of 
 the particles will be spent before they have time to emit these 
 negative corpuscles. But the particles which succeed in doing 
 this and which thereby acquire a charge of positive electricity 
 will now be attracted by the negatively electrified surface and will 
 move rapidly up to it. The velocity with which the particle 
 moves in the electric field is very great compared with the velocity 
 with which it would have moved towards the surface if only diffu- 
 sion had come into play. Thus the emanation will in consequence 
 of the charge on the surface arrive at the surface very much 
 sooner than it would have done if there had been no charge ; it 
 thus arrives very much fresher and is much more efficient as a 
 producer of induced radio-activity. 
 
 158. The velocity acquired by the positively charged particles 
 of the emanation when in the electric field has been measured by 
 Rutherford*, using the following method, which is based on the 
 assumption justified by the extent to which the induced radio- 
 activity can be concentrated on a negatively electrified surface- 
 that the radio-activity of the surface is almost wholly due to the 
 number of positively electrified particles which reach it. 
 
 The emanation spreads between two parallel plates A and B, 
 Fig. 79, an electric field is produced between the plates, this field 
 
 Fig. 79. 
 
 consists of two parts, (1) a constant potential difference equal to 
 E making the top plate +, the lower plate , (2) a field in which 
 
 Rutherford, Physikalische Zeitschrift, iii. p. 210, 1902; Phil. Mag. vi. 5, p. 95, 1903. 
 
158] BECQUEREL RAYS. 301 
 
 the direction of the force is reversed at equal intervals of time T ; 
 thus it is equal to E^ for a time T, then changes to E l which lasts 
 for a time T, when it changes again to -f E l and so on. This 
 variable potential difference is placed in series with the constant 
 potential difference, so that in the first half of the alternation the 
 electric force acting downwards is (E^-^-E^jd where d is the dis- 
 tance between the plates, while in the second half of the alterna- 
 tion it is equal to (E l E )/d and acts upwards: E l is supposed 
 to be greater than E . There is thus on the average a tendency 
 to make the positive ions go to the lower plate, but during the 
 second half of the alternation some of the particles will be attracted 
 to the upper plate and will make it radio-active : the number of 
 such particles will depend upon the velocity of the particles and 
 may be calculated as follows. 
 
 Let K be the velocity of the particles under unit electric force 
 and let us suppose that the positive particles are being produced 
 uniformly between the plates, the number produced in one second 
 in a layer of unit thickness between the plates being q. The 
 particles which reach the upper plate when negatively electrified 
 will be of two classes: (1) those produced whilst the plate is nega- 
 tively electrified, and (2) those which were present between the 
 plates at the beginning of the alternation. Let us take first the 
 number in the first class; consider the number sent to the top 
 plate by a layer of thickness dx at a distance x away from it, any 
 particle from this layer, since it moves with the velocity JX l} will 
 take the time xj KX^ to reach the plate. X l is the electric force 
 between the plates and is equal to (E l )/d. Since the particle 
 must reach the plate before the end of the alternation the latest 
 time it can start is xjKX-^ before the end, and thus the particles 
 reaching the layer are only formed for a time TxjKX^ thus 
 the number of particles reaching the plate from this layer is 
 q(T -xjKX^dx and the total number of particles in class (1) is 
 equal to 
 
 CKX.T 
 
 JO 
 
 The number in class (2) will be the number of positive particles 
 at the beginning of the alternation in a layer next the upper plate 
 whose thickness is KX l T. The force in the preceding alternation 
 
302 BECQUEREL RAYS. [158 
 
 tending to drive the particles from the upper plate is X 2 where 
 X 2 = (E 4- -fi'i) / d : hence the velocity of the particles is KX Z : the 
 number of particles produced in a layer of thickness dx, at a dis- 
 tance x from the upper plate, which have not moved by the end 
 of the alternation to a distance from the upper plate greater than 
 
 XX l T is q - - =. dx ; hence the number of particles in the 
 jfx-A 2 
 
 second class is equal to 
 
 = 1 K.X*T* 
 
 Thus the total number of positive particles reaching the upper 
 plate in the time of a double alternation of length ZT 
 
 In this time the total number of positive particles produced is 
 2qdT, and if care is taken to make the electric field sufficiently 
 strong all these particles will reach one or other of the plates. 
 Hence p the ratio of the number of particles reaching the upper 
 plate to the sum of the numbers reaching the upper and lower 
 plates is given by the equation 
 
 or substituting for X 1 and X 2 their values we get 
 
 On the hypothesis already mentioned, that the induced 
 radio-activity is almost entirely caused by the positively charged 
 particles which come up to the plate, p is the ratio of the 
 radio-activity of the upper plate to the sum of the activities of 
 the upper and lower plates, and by measuring these activities p 
 can be determined ; when p is known equation (1) gives us the 
 means of determining K and hence the velocity of the positively 
 charged particles in an electric field. By this method Kutherford 
 got the following results. 
 
158] 
 
 BECQUEREL RAYS. 
 
 Plates 1*3 cm. apart. 
 
 303 
 
 E!+E 
 
 volts 
 
 E!-JB 
 
 volts 
 
 Alternations 
 per sec. 
 
 p 
 
 Velocity for one 
 volt per cm. 
 
 152 
 
 101 
 
 57 
 
 27 
 
 1-25 
 
 225 150 57 
 
 38 
 
 1-17 
 
 Plates 2 cm. apart. 
 
 272 
 
 207 
 
 44 
 
 37 
 
 1-47 
 
 300 
 
 200 
 
 53 
 
 286 
 
 1-45 
 
 These results relate to air at atmospheric pressure. Zeleny 
 (p. 47) found that the velocity of the positive ion produced by 
 Rontgen rays in air at this pressure was T36 cm. /sec. for the 
 potential gradient of a volt per cm. : the velocity of the positive 
 particles in the thorium emanation is thus within the limits of 
 experimental errors equal to the velocity of the ordinary positive 
 ions. 
 
 Rutherford has shown that at low pressures, say less than 1 mm., 
 of mercury there is less tendency for the radio-activity to be con- 
 centrated on the negative electrode than there is when the pressure 
 is higher. We see that if the mean free path of the particle were 
 comparable with the size of the vessel there ought not on the 
 preceding view to be much concentration unless the particles 
 were at rest, or at any rate were moving with a velocity small 
 compared with that which would be developed by the movement 
 of the charged particles through a fall of potential equal to that 
 between the negatively electrified body and the walls of the vessel : 
 for it is only in the latter case that the particle would strike 
 the attracting body, in all others it would describe an orbit round 
 it and would strike the walls of the vessel and not the electrode 
 itself. 
 
 Radio-activity of Radium, Polonium, Actinium. 
 
 The Becquerel rays have led to the discovery of some new sub- 
 stances possessing the power of radio-activity to a far greater 
 extent than uranium the original source of these rays, After 
 Becquerel's discovery Monsieur and Madame Curie* made a very 
 
 * Curie, Rapports, Congres International de Physique, t. iii. p. 79, Paris, 1900. 
 
304 
 
 BECQUEREL RAYS. 
 
 [158 
 
 systematic and extensive examination of a great number of 
 chemical elements and compounds, and also of minerals, to see 
 if other elements possessed powers similar to uranium ; the ex- 
 amination of the elements and compounds (which included the 
 rare elements, gallium, germanium, neodydymium, praseodydy- 
 mium, mobium, scandium, gadolinium, erbium, samarium, rubi- 
 dium, yttrium, ytterbium, holmium) did not lead to the discovery 
 of any substances other than uranium possessing this property. 
 The investigation of the minerals was more fruitful, for they found 
 that several minerals containing uranium were more active than 
 the same bulk of uranium. This is shown by the following table 
 in which i is the saturation current in amperes between two circular 
 plates 8 cm. in diameter and 3 cm. apart when one of the plates 
 is covered with the substance under consideration : 
 
 
 i x 10 11 amperes 
 
 
 i xlO 11 amperes 
 
 Metallic Uranium 
 
 2-3 
 
 Thorite 
 
 1-4 
 
 Pitch-blende from 
 
 
 Orangeite 
 
 2-0 
 
 Johanngeorgeustadt 
 
 8-3 
 
 Monazite 
 
 0-5 
 
 Joachimstal 
 
 7-0 
 
 Xenotime 
 
 0-03 
 
 Pribran 
 
 6-5 
 
 ^Eschynite . 
 
 0'7 
 
 Cornwall 
 
 1-6 
 
 Fergusonite 
 
 0'4 
 
 Cleocite 
 
 1-4 
 
 Samarskite 
 
 1-1 
 
 Chalcolite 
 
 5-2 
 
 Niobite 
 
 0-3 
 
 Autunite 
 
 2-7 
 
 Carnotite 
 
 6'2 
 
 
 
 
 
 All these minerals contain uranium and thorium, but it will 
 be seen that several of them are more radio-active than the pure 
 metals : this suggests that they may contain some exceedingly 
 active substantives other than uranium, this supposition was 
 strengthened when Monsieur and Madame Curie prepared Chal- 
 colite artificially from pure substances and found that it was only 
 about one-fifth as radio-active as the natural mineral. They then 
 set to work to search pitch-blende systematically; they tested the 
 radio-activity of a certain piece, then separated this chemically 
 and tested that of the constituents, and thus gradually separated 
 the active from the inert parts of the pitch-blende. This treat- 
 ment has led to the discovery of three different strongly radio- 
 active constituents of pitch-blende; radium discovered by Monsieur 
 and Madame Curie and Monsieur Bemont*, polonium discovered 
 * Curie and Bemont, Comptes Rendus, cxxvii. p. 1515, 1898. 
 
158] 
 
 BECQUEREL RAYS. 
 
 305 
 
 by Monsieur arid Madame Curie*, and actinium by Monsieur 
 Debiernef. Radium accompanies the barium prepared from 
 pitch-blende, and in its chemical actions is similar to that metal ; 
 it can, however, be separated from barium by fractionation, as its 
 chloride is less soluble in water, in alcohol and in hydrochloric 
 acid. The amount of radium in pitch-blende is exceedingly small, 
 many thousand kilograms of this mineral only yielding a few 
 decigrams of a radio-active substance, of which only a small fraction 
 is radium. The spectrum of radium was examined by Dema^ayJ: 
 the following are the principal lines between wave-lengths 5000 
 and 3500. 
 
 Wave-length 
 
 Intensity 
 
 Wave-length 
 
 Intensity 
 
 4826-3 
 
 10 
 
 4600-3 ? 
 
 3 
 
 4726-9 
 
 5 
 
 4533-5 
 
 9 
 
 4699-8 
 
 3 
 
 4436-1 
 
 8 
 
 4692-1 
 
 7 
 
 4340-6 
 
 12 
 
 4683-0 
 
 14 
 
 3814-7 
 
 16 
 
 4641-9 
 
 4 
 
 3649-6 
 
 12 
 
 There are also two nebulous bands in the spectrum, one ex- 
 tending from 4631*0 to 4621*9 with the maximum at 4627*5; 
 
 i 
 
 Fig. 80. 
 
 the second begins suddenly at 4463'7, has a maximum from 4455"2 
 to 4453'4, fading away at 4390. The appearance of the spectrum 
 is shown in Fig. 80. 
 
 The sensitiveness of the test by radio-activity is shown by the 
 fact that it required several thousand times more radium to give 
 
 * Curie, op. cit. p. 175. 
 
 t Debierne, Comptes Rendus, cxxix. p. 593, 1899 ; cxxx. p. 906, 1900. 
 
 J Demar(;ay, Ib. cxxvii. p. 1218, 1898 ; cxxix. p. 116, 1899 ; cxxxi. p. 258, 1900. 
 
 T. G. 20 
 
306 BECQUEREL RAYS. [158 
 
 an appreciable spectrum than to give an amount of radio-activity 
 quite appreciable by electrical methods. 
 
 The atomic weight of radium has been determined by Mon- 
 sieur and Madame Curie* to be 225. Runge and Prechtf from 
 consideration based on its spectrum estimate the atomic weight 
 as 257-8. 
 
 The radiation from radium is extraordinarily intense. Mon- 
 sieur and Madame Curie have prepared specimens of radium 
 which when enclosed in a lead tube '5 cm. thick will discharge an 
 electroscope more readily than uranium, even although the latter 
 is brought without any covering close up to the electroscope. 
 
 The radiation comprises rays of three classes': (1) easily 
 absorbed rays not deflected by a magnet nor by an electric field f, 
 
 (2) much more penetrating rays which are deflected by magnetic 
 or electric fields and which carry a charge of negative electricity, 
 
 (3) rays still more penetrating which are not deflected. 
 
 All the radium salts are luminous and retain this property for 
 long periods: Giesel found that the luminosity diminished in 
 damp air but recovered its brightness on drying. 
 
 The activity of the radium salts like some of those of thorium 
 (see p. 289) increases for some time after precipitation. The fol- 
 lowing numbers are given by Curie ; initial activity 95, after 1 day 
 120, after 2 days 165, after 3 days 210, after 9 days 310, after 
 24 days 381, after 300 days 410. If the chloride after attaining 
 its maximum activity is dissolved and reprecipitated the activity 
 of the new product diminishes as the time it is kept in solution/ 
 increases; it reaches, however, a limit after the salt has been four 
 or five days in solution. It would be interesting to know if the 
 increase in activity observed for some time after the preparation 
 of the radium compounds occurs in all the three classes of rays 
 given out by these substances or is confined to one class. 
 
 * Curie, Comptes Rendus, July 21, 1902. 
 
 t Eunge and Precht, Physik. Zeit'. iv. p. 285, 1903. 
 
 Rutherford has quite recently shown that the rays of class 1 are slightly 
 deflected by magnetic or electric fields and that they carry a positive charge ; he 
 found that the velocity of these rays was of the order 2 x 10 9 cm. /sec. and ejm of 
 the order 6 x 10 3 . Phil. Mag. vi. 5, p. 177, 1903. Strutt (Phil. Trans., A, 1901, 
 vol. cxcvi. p. 525) had previously suggested that the undeflected rays consisted of 
 positive ions. 
 
 Giesel, Wied. Ann. Ixix. p. 91, 1899. 
 
159] 
 
 BECQUEREL RAYS. 
 
 307 
 
 159. The magnetic deflection of rays given out by some radio- 
 active substances was observed almost simultaneously by Giesel*, 
 Meyer and v. Schweidlerf, and Becquerel*. Giesel used impure 
 polonium (polonium free from radium does not give deviable 
 rays), Meyer and v. Schweidler impure polonium and radium, and 
 Becquerel radium. Becquerel's experiments on radium, proving 
 both the magnetic and electric deflections of the rays and showing 
 that these deviable rays consist of corpuscles projected with a 
 velocity about two-thirds of that of light, have already been de- 
 scribed. M. and Mme Curie showed that radium gave out non- 
 deviable as well as deviable rays and that the former were much 
 more easily absorbed than the latter. The arrangement they used 
 is represented in Fig. 81. A is the radio-active substance placed 
 
 BATTED. 
 
 B' 
 
 Fig. 81. 
 
 between blocks of lead, B, B', the radiation from A passes be- 
 tween these blocks into the space between the parallel plates 
 P, P', making the air between these a conductor and allowing a 
 current to pass between the plates, the magnitude of the current, 
 serving as a measure of the intensity of the radiation reaching the 
 space between the plates. P is charged up to 500 volts and P' 
 connected with an electrometer. The arrangement B, B', B" can 
 
 * Giesel, Wied. Ann. Ixix. p. 831, 1899. 
 
 t Meyer and v. Schweidler, Wien. Ber. p. 323, 1899. Physik. Zeitsc^r. i. p. 113, 
 1899. 
 
 Becquerel, Comptes Eendus, cxxix. p. 997, 1899. 
 Curie, 16. cxxx. p. 73, 1900. 
 
 202 
 
308 BECQUEREL RAYS. [160 
 
 be placed between the poles of an electro- magnet which produces 
 a strong magnetic field at right angles to the plane of the paper ; 
 if the rays are deflected even to a slight extent they will strike 
 against the block B, B' and be suppressed. 
 
 The effects produced by the magnet depend essentially upon 
 the distance AD between the radio-active substance and the 
 place where it is tested ; if this distance is greater than 7 cm. all 
 the rays are suppressed by a magnetic field of 2500 units ; at a 
 distance of 6' 5 centimetres only a portion of the rays are sup- 
 pressed and this portion gets smaller and smaller as the plates 
 P and P' approach the radio-active substance A ; that the escape 
 of the rays from the magnetic field is not due to a deficiency in 
 the strength of the field is shown by the fact that when the mag- 
 netic field is on no further diminution in the current is produced 
 when the strength of the field is increased from 2500 to 7000 
 units. The following numbers show the effects observed at dif- 
 ferent distances, the current when the magnetic field is off being 
 taken as 100, so that the numbers representing the current with 
 the field on may be taken as the percentage of non-deviable rays 
 which are able to penetrate the various distances through air at 
 atmospheric pressure. 
 
 Distance AD in centimetres 7'1, 6'9, 6'5, 6'0, 51, 3'4 
 Current with magnet on 0, 0, 11, 33, 56, 74 
 
 If the radio-active substance is covered with a piece of thin 
 aluminium foil or a piece of black paper all the non-deviable rays are 
 absorbed by it and the current is completely stopped by the mag- 
 netic field. It will be seen from the preceding figures that only a 
 small fraction of the total ionisation produced by the radium is 
 due to the rays which are deflected by a magnet; by far the larger 
 part of it is produced by the non-deviable easily absorbed rays. 
 
 160. That these deviable rays carry a charge of electricity is 
 proved by the fact discovered by Becquerel (see p. Ill) that they 
 are deflected when placed in an electric field, a fact also observed 
 by Dorn*. M. and Mme Curie f had previously shown by direct 
 experiment the existence of the negative charge on these rays. If 
 we place a body near a sample of radium surrounded by air at 
 
 * Dorn, Comptes Rendus, cxxx. p. 1126, 1900. 
 t Curie, 16. p. 647. 
 
160] BECQUEREL KAYS. 309 
 
 atmospheric pressure we cannot expect to observe any appreciable 
 negative charge on the body, for the radium makes the air a con- 
 ductor so that the electricity escapes from the body through the 
 air as fast as it arrives. To observe the effect we must work in a 
 high vacuum where there is not enough gas to produce appreciable 
 conductivity or else replace the air by a solid dielectric; the Curies 
 employed the latter method ; the arrangement they used is shown 
 in Fig. 82. A metal disc MM is connected by a wire with an 
 
 Fig. 82. 
 
 electrometer, the disc and wire being completely surrounded by a 
 solid insulator, ebonite or paraffin, the whole is placed in a 
 metallic case connected with the earth, the layer of insulating 
 material and the metal of the case are very thin next the lower 
 face of the disc MM. This lower face is exposed to the radiation 
 from the radium R placed in a cavity in a block of lead A A. It 
 is found that under these circumstances the disc receives a con- 
 stant stream of negative electricity. This current is only small; 
 from a layer of radium with a surface of 2'5 sq. cm. and *2 cm. 
 thick, and with the rays passing on their way to the disc through 
 aluminium foil "01 mm. thick and a layer of ebonite *3 mm., the 
 current was 10~ n amperes. 
 
 The Curies also detected the positive charge left behind on 
 the radium ; to do this they connected the lead containing the 
 radium with the electrometer and surrounded it by an insulating 
 substance as is shown in Fig. 82 ; under these circumstances they 
 found that the electrometer received a positive charge. 
 
 Since e/m = 10~ 7 a current of 10~ n amperes from the radium 
 corresponds to a loss in weight of about one three-hundredth part 
 of a milligram in a million years. 
 
 No charge could be detected on the non-deviable rays, but 
 with those rays on account of the great absorption the experiment 
 is exceedingly difficult. 
 
310 
 
 BECQUEREL RAYS. 
 
 [161 
 
 161. The properties of the deviable rays, i.e. their deflection 
 by magnetic and electric fields, and the possession of a negative 
 charge show that like the cathode rays they consist of negatively 
 electrified corpuscles moving with great velocities ; the velocity of 
 some of the particles projected from radium, viz. 2 x 10 10 cm./sec., is 
 greater than that we have yet been able to give to any corpuscles 
 by purely electrical means. Additional confirmation of the simi- 
 larity between the deviable radium rays and cathode rays is given 
 by the study of the absorption of these rays by various bodies. 
 Lenard* showed that if a bundle of cathode rays is travelling 
 parallel to the axis of as, and if 7 is the intensity of the rays 
 when # = and / the intensity after travelling a distance x, 
 then / = / e^ Aa; , where X is a constant, called the coefficient of 
 absorption of the cathode rays. By testing a great number of 
 substances with densities varying from that of solid platinum to 
 that of hydrogen gas at 3 mm. pressure, Lenard found that what- 
 ever the state of the substance might be, solid or gaseous, X was 
 very approximately proportional to the density of the substance ; 
 how nearly this law holds will be seen from the following table in 
 which X is the coefficient of absorption and d the density ; the 
 
 Substance 
 
 X cm." 1 
 
 d . gr./cm. 3 
 
 X/d 
 
 Hydrogen at 3 mm. pressure... 
 Air at *78 mm. pressure 
 
 00149 
 00416 
 
 3-6xlO- 7 
 l'2x 10~ 6 
 
 4040 
 3330 
 
 Hydrogen at 760 mm. pressure 
 
 Air ' 
 -- 11 55 
 
 SOg 55 55 55 
 
 476 
 3-42 
 8-51 
 3310 
 
 8-5 xlO- 6 
 1-2 x 10~ 3 
 2-7xlO- 3 
 1*1 
 
 5610 
 2780 
 3110 
 3010 
 
 
 2690 
 
 1-30 
 
 2070 
 
 Glass 
 
 7810 
 
 2-47 
 
 3160 
 
 Aluminium 
 
 7150 
 
 2'70 
 
 2650 
 
 
 7250 
 
 2 '80 
 
 2590 
 
 Dutch Metal 
 
 23800 
 
 8-90 
 
 2670 
 
 Silver 
 
 32200 
 
 10-5 
 
 3070 
 
 Gold 
 
 55600 
 
 19-3 
 
 2880 
 
 
 
 
 
 rays were produced by a tube for which the potential difference 
 between the electrodes was about that which would produce a 
 spark in air about 2'8cm. long: from some later determinations 
 
 * Lenard, Wied. Ann. Ivi. p. 255, 1895. 
 
161] 
 
 BECQUEREL RAYS. 
 
 311 
 
 made by Lenard*, I should conclude that this corresponded to a 
 velocity of the cathode rays of about 6 x 10 9 cm./sec. 
 
 Thus though the density of the lightest substance is only 
 about one sixty-millionth of that of the heaviest, the values of 
 \/d only range from 2070 to 5610 : and if we leave out hydrogen, 
 which as we shall see exhibits peculiarities in its absorption of 
 all rays, the range is only from 2070 to 3330 ; considering the 
 difficulties of the experiment this is strong evidence in favour of 
 \jd being very nearly constant. 
 
 R. J. Strutt { has measured the coefficient of absorption of the 
 deviable radium rays for a considerable number of substances ; his 
 results are given in the following table. 
 
 Substance 
 
 X 
 
 d 
 
 \jd 
 
 Platinum 
 
 157-6 
 
 21-5 
 
 7-34 
 
 Lead 
 
 62-5 
 
 11-4 
 
 5-48 
 
 Silver 
 
 657 
 
 10-6 
 
 6'20 
 
 Copper 
 
 49-2 
 
 8-95 
 
 5-50 
 
 Iron 
 
 52-2 
 
 776 
 
 6'74 
 
 Tin 
 
 51-2 
 
 7-3 
 
 7-01 
 
 Zinc 
 
 40-3 
 
 7-2 
 
 5'58 
 
 Mica 
 
 10-8 
 
 2-74 
 
 3-94 
 
 Glass 
 
 12-5 
 
 2*73 
 
 4'58 
 
 Aluminium 
 
 11-6 
 
 2-7 
 
 4-30 
 
 Celluloid 
 
 5-45 
 
 1-36 
 
 4-01 
 
 Ebonite 
 
 4-77 
 
 1-14 
 
 4-18 
 
 Card 
 
 3-84 
 
 ro 
 
 3-84 
 
 Sulphur dioxide... 
 
 0413 
 
 00758 
 
 5-45 
 
 Thus though there is a very wide range in the values of X and 
 d, the values of \/d differ comparatively little from each other. 
 The coefficients of absorption for the cathode rays are roughly about 
 500 times those for the radium rays ; this difference is probably 
 due to the much greater velocity of the radium rays, which wa,s 
 found by Becquerel to be as great as 2 x 10 10 cm. /sec., while the 
 velocity of the cathode rays used by Lenard was probably only 
 about one-quarter of this. 
 
 StruttJ has made a series of measurements of the amount of 
 ionisation produced by the two types of radium rays and the 
 
 * Lenard, Wied. Ann. Ixv. p. 504, 1898. 
 
 t Hon. R. J. Strutt, Nature, Ixi. p. 539, 1900. 
 
 J Hon. R. J. Strutt, Phil. Trans. A. 196, p. 507, 1901. 
 
312 BECQUEREL RAYS. [162 
 
 rays from polonium when they pass through different gases. 
 Rutherford's results (see p. 249) indicate that the amount of 
 ionisation would be proportional to the coefficient of absorption 
 of the rays in the gas. Strutt's results are given in the following 
 table (p. 313), which for convenience of comparison contains the 
 relative ionisation produced by Rontgen rays as determined by 
 Perrin and J. J. Thomson and also the relative ionisation pro- 
 duced by cathode rays as determined by M c Clennan*. 
 
 162. Thus for the cathode rays and the deflectable Becquerel 
 rays, the coefficient of absorption depends only upon the density 
 and not upon the chemical composition or physical state of the 
 substances; the non-deviable, easily absorbable Becquerel rays 
 approximate to this law but deviate from it sensibly more than 
 the deflectable rays, while in the case of the Rontgen rays there 
 is no approximation to this law. An inspection of the result 
 shows that hydrogen is anomalous, the ionisation for the deflect- 
 able rays being very considerably greater than its density 
 warrants. The law of absorption for those rays which consist 
 of rapidly moving negatively electrified corpuscles is of great 
 interest in connection with the theory of the structure of matter. 
 For it is exactly the result we should expect if the molecules of 
 the different chemical elements consisted of differently arranged 
 aggregations of a primordial atom, the number of these atoms in 
 the molecule being proportional to the mass of the molecule, 
 i.e. to its molecular weight ; then if the corpuscles forming the 
 cathode or deflectable Becquerel rays are so small that they can 
 thread their way between the individual primordial atoms in the 
 molecules of the chemical elements, the collisions the corpuscles 
 make when passing through any body are collisions with the 
 primordial atoms in the molecule rather than with the molecule 
 as a whole. Thus the mean free path of a corpuscle will be 
 inversely proportional to the number of primordial atoms in unit 
 volume ; this number since all these atoms are to be considered as 
 having the same mass will be proportional to the mass of unit 
 volume of the substance, hence the mean free path of the cor- 
 puscles will be inversely proportional to the mass of the substance 
 and will, if the mass is kept constant, not be affected by any 
 changes in its chemical composition or physical state. If L is the 
 
 * M c Clennan, Phil. Trans. A. 195, p. 49, 1901. 
 
162] 
 
 BECQUEREL RAYS. 
 
 313 
 
 s 
 
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 H *"* 
 
 r-l CM < 
 
 
 
 P 
 
 
 
 f*" t 1 
 
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 CO 
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 CM O 7-1 C35 O Tt* l 
 
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 rH rH C 
 
 
 
 r* bo 
 
 ?i .9 
 
 t- 
 
 
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 oOr-icor-cocMOic 
 
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 1 1 
 
 
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 PH 
 
 99-1 3 i i 
 
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 i-H 00 PH CD 
 
 
 S PH 
 
 
 
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 CO Q iO 
 CO O 1 O5 Tj O -^ 1 
 
 1 
 
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 r-l 00 r-t r-l CO 
 
 
 If 
 
 CO 
 
 for-it-cocoaiCMr 
 Or- iCM>OOOiicOC 
 
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 ! 
 
 ,lrHrHi (i (CMT^iT 
 
 5 
 
 
 
 
 
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 73 
 
 
 
 
 
 
 S 3 4 
 
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 2 So^2l 
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 g .ft ^^S ^33^: 
 W^oWoo^oS 
 
 J 
 
314 BECQUEREL BAYS. [163 
 
 mean free path of a corpuscle and if we suppose that at each 
 collision the corpuscle loses the fraction (3 of its kinetic energy, 
 then X the coefficient of absorption = J3/L, and as L is inversely 
 proportional to the density of the substance we see that X ought 
 to be proportional to the density, a law which the results we have 
 quoted show to be very approximately true. 
 
 163. The penetrating power of the radium rays is much 
 greater than that of the cathode rays produced by electrical means; 
 this can readily be accounted for by the greater velocity of the 
 corpuscles in the former rays if we regard the collisions which 
 take place between the corpuscles and the primordial atom as 
 analogous to the deflection two bodies exerting forces on each 
 other experience when they pass one another at close quarters. 
 Taking this view of a collision let us define a collision as a case 
 where the corpuscle and the primordial atom come so close 
 together that the angle through which the direction of motion 
 of the path of the former is twisted exceeds a certain value. 
 This deflection depends upon the initial velocity of the corpuscle 
 and its minimum distance from the atom ; and the theory of 
 central forces shows that a collision will not occur if the kinetic 
 energy of the corpuscle, when so far away from the atom that the 
 force between them is inappreciable, exceeds a certain multiple of 
 the work done on the corpuscle by the atom when the former 
 moves from an infinite distance to its point of nearest approach 
 to the atom. To take a definite case, let us suppose that the 
 forces between the corpuscle and the atom are electrical in their 
 origin and that the charges on the atom and corpuscle are equal, 
 then if m is the mass of a corpuscle, e its charge in electrostatic 
 measure, v its velocity at an infinite distance from the atom, d the 
 least distance between the atom and corpuscle; then the work 
 done on the corpuscle is e*/d and the condition for a collision is 
 that 
 
 02 
 
 -j should not be less than 
 
 where & is a numerical constant. Thus d cannot be greater than 
 2e z /kmv*. We may get a rough idea of the effect due to the 
 velocity if we take 'this value of d as the radius of the sphere of 
 action of the atom, and suppose a collision to occur whenever a 
 corpuscle passes through this sphere. Now the mean free path 
 
163] BECQUEREL RAYS. 315 
 
 varies inversely as the square of the radius of the sphere of action, 
 thus for this law of force the mean free path will be directly 
 proportional to the fourth power of the velocity. The coefficient 
 of absorption (which see p. 314) is equal to @/L, where L is the 
 mean free path, hence neglecting any variation in /3 the coefficient 
 of absorption will vary inversely as the fourth power of the velocity 
 of the corpuscles : thus a theory of this kind will explain why the 
 penetrating power of the more rapidly moving corpuscles in the 
 deflectable radiation is so much greater than that of the cathode 
 rays in Lenard's experiments. The essential condition for the 
 penetrating power of the corpuscles to be independent of every- 
 thing except the density of the substances through which they 
 are passing is that the collisions which impede the progress of 
 the corpuscles should be collisions with the individual primordial 
 atoms and not collisions with the molecule as a whole ; for this 
 condition to be satisfied it is evident that the sphere of action of 
 one primordial atom must not include other atoms, or if D is the 
 distance between two atoms, D must be greater than 2e s /kmv* t 
 or v* must be greater than 2e*/kmD. If v 2 is smaller than this we 
 cannot expect the simple law of absorption which holds for the 
 very rapidly moving corpuscles to apply. Now in electrostatic 
 measure efm. = 3 x 10 17 , e = 3*4 x 10~ 10 , and we shall assume that D 
 is 10~ 9 . Substituting these values we see that v* must be greater 
 than 2 x 10 16 /& or v greater than T4 x 10 8 /&*. Thus if the 
 velocity of the corpuscle falls below a value somewhere between 
 10 8 and 10 7 cm./sec., we should expect the law \/d = constant to 
 fail. 
 
 For velocities smaller than this the collisions made by a cor- 
 puscle are to be regarded as taking place between the corpuscle 
 and the molecule of the substance rather than with the constituent 
 primordial atoms of the molecule, and when this is the case the 
 mean free path of the corpuscle, say in hydrogen, will be four times 
 that of a molecule of hydrogen at the same pressure : the factor 4 
 has to be introduced because the size of a corpuscle is negligible 
 compared with that of a molecule, so that the radius of the sphere 
 of action in a collision between a corpuscle and a molecule is 
 one-half of that between two molecules. 
 
 It is of some interest to form an estimate of the mean free 
 path of a rapidly moving corpuscle, although we are not yet in a 
 
316 BECQUEREL RAYS. [164 
 
 position to evaluate all the constants that occur in the expression 
 for the free path. By the Kinetic Theory of Gases, L, the mean 
 free path of a particle, is given by the equation 
 
 L- - 1 - 
 
 where cr is the radius of the sphere of action in a collision, n the 
 number of systems in unit volume of the gas through which the 
 particle is moving. Putting for cr the value 2e 2 /kmv 2 , we find for 
 the value of L the free path of a corpuscle 
 
 ~ 
 
 Let us suppose that the gas through which the corpuscle is 
 moving is hydrogen at atmospheric pressure, and assume further 
 that the mass of the primordial atom is the same as that of a 
 corpuscle, then nm = 8'5 x 10~ 5 and we get 
 
 since e is measured in electrostatic units m/e=J10~ 17 , e=3'4x lO" 10 , 
 substituting these values we get 
 
 for a velocity equal to that of some of the corpuscles in the 
 radium rays, i.e. 2 x 10 10 , L is equal to 7& 2 centimetres. 
 
 The influence of the velocity of a corpuscle on the effects of a 
 collision is considered more fully on p. 344. 
 
 Emanation from Radium and induced Radio -activity 
 produced by it. 
 
 164. M. and Mme Curie* have shown that the walls of a 
 vessel containing radium become radio-active. Radium, like 
 thorium, gives out an emanation which is also radio-active. The 
 persistence of the radio-activity of the emanation from radium is, 
 however, very much greater than that from thorium : the latter, 
 as we have seen, falls to half its value in about one minute, 
 while the activity of the radium emanation lasts for several 
 
 * Curie, Rapports presentes au Congres International de Physique, iii. p. 108, 
 1900. 
 
164] BECQUEREL RAYS. 317 
 
 hours; this has been shown by Dorn* and Rutherford f. The 
 latter filled a cylinder with the emanation and observed the 
 saturation current from time to time; after the lapse of 3*5 hours 
 the current was 1*31 times its initial value, after 20 hours the 
 current had sunk to its initial value. On blowing out the air 
 from the cylinder and refilling with air free from the emanation 
 the current fell to half its value, showing that half the current 
 was due to the emanation and half to the induced radio-activity 
 on the walls of the vessel. Thus, in this experiment, it took 
 20 hours for the activity of the emanation to fall to one-half 
 of its original value, a great contrast to the 1 minute required 
 for the same fall in the thorium emanation. On the other hand 
 the radio-activity induced on neighbouring bodies by the radium 
 emanation dies away more rapidly than that due to the thorium 
 emanation. The induced radio-activity due to radium, like that 
 due to thorium, concentrates on negatively electrified bodies. 
 
 Rutherford f has shown that heating has an enormous effect 
 on the issue of the emanation from radium. The radium to be 
 heated was placed in a platinum tube, and a constant current 
 of air passed over the radium and through a testing vat in which 
 the saturation current was measured : this current was due to 
 the ionisation of the air in the vat by the radiation from the 
 emanation, and also by the radiation from the walls of the vessel 
 which became radio-active. On heating the tube containing the 
 radium with a small gas flame, the saturation current in the 
 vat was increased 300 times : blowing the emanation from the vat 
 reduced the current to 1/20 of its value when the emanation 
 was present, showing that 19/20 of the ionisation was due to 
 the emanation, the remaining 1/20 being due to induced radio- 
 activity on the walls of the vat. The experiment was repeated 
 with a larger gas flame, when the current in the vat increased to 
 650 times the value when the radium was cold ; with a still larger 
 flame the current increased to 1800 times its value, and when 
 the platinum tube was red-hot it increased to 5000 times the 
 value when cold. Heating the tube to a white heat produced 
 no further increase in the current. Blowing out the emanation 
 from the vat when the current was greatest reduced the current 
 
 * Dorn, Abh. d. naturf. Ges. Halle, 1900. 
 
 t Rutherford, Physikalische Zeitschr. ii. p. 429, 1901. 
 
318 BECQUEREL RAYS. [165 
 
 to one-fourth, showing that three-fourths of the ionisation was 
 due to the emanation and one-fourth to the induced radio-activity. 
 The radium was then allowed to cool ; on heating it to a red heat 
 the next day the current was only increased 65 times, and this 
 increase was maintained on subsequent coolings and heatings. 
 This experiment suggests that the radium contains a radio-active 
 gas which can be driven out by heating, and which ordinarily sup- 
 plies a part of the emanation. M. and Mme Curie (I.e.) obtained 
 from radium a radio-active gas, producing phosphorescence on 
 the walls of the glass vessel in which it was contained ; the 
 radiation from this gas was sufficiently powerful to penetrate 
 the walls of the tube and ionise the gas in the neighbourhood. 
 No new lines were found when the spectrum of the gas was 
 examined. 
 
 165. Molecular Weight of the Emanation from Radium. We 
 can form some estimate as to the molecular weight of the radium 
 emanation from the determination made by Rutherford and Miss 
 Brooks* of its coefficient of diffusion through air. The measure- 
 ments which have been made of the coefficients of inter-diffusion 
 of a large number of simple gases have shown that the coefficient 
 of diffusion of one gas into another is approximately inversely 
 proportional to the square root of .the product of their molecular 
 weights: if then we know the rate of diffusion of the radium 
 emanation through air we can, by the aid of the preceding rule, 
 determine its molecular weight. , 
 
 The method used by Rutherford and Miss Brooks to determine 
 the coefficient of diffusion through air was as follows. A long 
 brass cylinder AB, Fig. 83, was divided into two equal parts 
 by a smooth metal slide 8, the ends of the cylinder were closed 
 by ebonite stoppers, which supported the brass tubes a and b: 
 the cylinder was insulated and connected with one pole of a 
 battery of 300 volts, the other pole of the battery was earthed: 
 the rods a and b were connected with a sensitive electrometer. 
 The cylinder was packed round with felt, so as to keep the 
 temperature as constant as possible. To get sufficient emanation 
 into the cylinder the radium was slightly heated, and the ema- 
 nation was carried by a slow current of air into the cylinder. 
 
 * Rutherford and Brooks, Trans. Roy. Soc. Canada, vii. p. 21, 1901. 
 
165] BECQUEREL RAYS. 319 
 
 When a sufficient quantity of the emanation had been obtained 
 the current was stopped, and the apparatus left to stand for 
 several hours: the slide S was then opened and the current 
 began to diffuse from a to b. The electrical currents through 
 a and b were measured at regular intervals. Initially there is no 
 current in B, but after opening the slide the current in B begins 
 
 UC7 
 \ 
 
 PLAT//WM TUB 
 
 Fig. 83. 
 
 to increase and that in A to decrease : measurements were made 
 of the currents at regular intervals, these currents (when corrected 
 for the part due to the induced radio-activity on the electrodes 
 and walls of the vessel) give the amount of emanation present 
 in the two cylinders. From the ratio of the amounts of the 
 emanation in the two cylinders, the coefficient of diffusion K 
 through air can be calculated from the formula 
 
 here a is the length of the cylinder, t the duration of the ex- 
 periment in seconds, 8 l and $ 2 the amounts of the emanation in 
 the cylinders A and B respectively at the end of the experiment. 
 The values obtained for K varied between '08 and '15. The 
 authors state that the emanation given off when the radium is 
 first exposed to the air diffuses more rapidly than that given 
 off at a later period. Applying the law that the coefficient of 
 diffusion of one gas into another varies inversely as the square 
 root of product of the molecular weights of the gases, the values 
 of K found for radium would indicate a' molecular weight be- 
 tween 40 and 100. This shows that the emanation is not the 
 vapour of radium, as M. and Mme Curie have shown that the 
 atomic weight of that substance is about 225. 
 
320 BECQUEREL RAYS. [166 
 
 166. Chemical Effects produced by Radium*. Radium dis- 
 colours glass with which it is in contact ; the discoloration seems 
 analogous to that which is observed in the glass of a discharge 
 tube exhausted to a very high vacuum : it produces in the chlorides 
 of the alkali metals changes in colour like those produced by 
 the impact of cathode rays on these salts, it also gives rise to 
 ozone, a strong smell of which is perceptible on opening a bottle 
 in which strong radium has been kept. 
 
 Polonium. 
 
 167. Polonium, discovered by M. and Mme Curie*, is found 
 in company with the bismuth extracted from pitch-blende : they 
 obtained bismuth richer and richer in polonium by the following 
 
 methods of fractionation : 
 
 
 
 1. Sublimation of the sulphide in vacuo. The sulphide of 
 polonium is much more volatile than that of bismuth. 
 
 2. Precipitation of solutions in nitric acid by water. The 
 precipitated nitrate is much more active than that remaining 
 behind in the solution. 
 
 3. Precipitation by hydrogen sulphide from a solution in 
 hydrochloric acid. The precipitated sulphide is much more active 
 than the salt which remains behind. 
 
 Polonium has not been obtained in a pure enough state to 
 give a spectrum. As far as is known the radiation from it is 
 entirely of the non-deviable kind: polonium does not give out 
 negative corpuscles, and its radiation is very easily absorbed, a 
 thin sheet of aluminium being able to stop it. The radiating 
 power of polonium is not permanent, it continually gets weaker 
 and weaker. Mme Curie f, who measured the absorption by a 
 thin plate of aluminium of the radiation from polonium after it 
 had traversed a certain thickness of air, found the very remarkable 
 result that the further the polonium rays go through air the more 
 easily are they absorbed by aluminium. 
 
 The arrangement they used to show this is represented in 
 Fig. 84: PP, FP' are two metallic plates between which the 
 
 * Curie, Comptes Rendus, cxxvii. p. 175, 1898. 
 t 16. cxxx. p. 76, 1900. 
 
167] 
 
 BECQUEREL RAYS. 
 
 321 
 
 current produced by a considerable potential difference is mea- 
 sured in the usual way: the polonium is placed at A and the rays 
 from it go through wire-gauze at T. When the polonium is 
 
 BATTERY 
 
 ELECTROMETER 
 
 Fig. 84. 
 
 covered with a thin layer of aluminium foil the absorption of the 
 rays increases with the distance AT, and if a second layer of 
 aluminium foil is placed over the polonium the absorption pro- 
 duced by the second layer is greater than that produced by the 
 first ; this is the opposite to what is observed with the Rontgen 
 rays, but in the Rontgen rays we have a mixture of rays of very 
 varying powers of penetration, and when this is the case the 
 first layer must as we have seen (p. 246) produce greater absorp- 
 tion than the second. The effects observed with polonium (and 
 they also occur as Mme Curie has shown with the non-deflect- 
 able rays of radium) are those which would be produced if the 
 polonium rays were homogeneous but became less penetrating 
 after passing through an absorbing medium. We should expect 
 rays which consist of rapidly moving negatively charged parti- 
 cles to become more easily absorbed after passing through an 
 absorbing medium, as the velocity of the particles diminishes in 
 consequence of the absorption, and we have seen that slow parti- 
 cles are more absorbed than fast ones. The rays from polonium 
 however resemble Rontgen rather than cathode rays, as they are 
 not deflected either by electric or magnetic forces. We shall see 
 reasons for thinking that these rays consist of pulses of electric 
 T. G. 21 
 
322 BECQUEREL RAYS. [168 
 
 and magnetic force, the thickness of the pulse determining the 
 nature of the rays; thick pulses corresponding to easily absorbed 
 rays, thin ones to penetrating rays. Thus, if the thickness of a 
 pulse increased as the rays passed through an absorbing medium 
 we should get the results observed by Mme Curie. Now, if we 
 suppose that the absorption of the rays is due to the communica- 
 tion of kinetic energy to charged ions struck by the pulse we 
 can see that such a thickening of the pulse would take place, as 
 some of the tubes of force in the pulse would be temporarily 
 attached to the ion; thus the ion would tend to hold them back 
 after the pulse passed on; the tubes would ultimately break away 
 from the ion, but the result of the temporary detention would be 
 a separation of the tubes and a broadening of the pulse. If this 
 effect is produced in air it will evidently have the effect of making 
 the intensity of the rays die away very rapidly as they get weaker 
 and thus make the appearance of measurable effect more abrupt 
 than it is in cases where the ordinary law of absorption holds : as 
 an illustration of this point Mme Curie found that a very slight 
 change in the distance AT (Fig. 84) was sufficient to make the 
 current between the plates increase from a value too small to be 
 measurable to one of very considerable magnitude. 
 
 Actinium. 
 
 168. Actinium, which is the name given to a very radio-active 
 substance which accompanies the thorium extracted from pitch- 
 blende, was discovered by Debierne*; it occurs in such minute 
 quantities that its investigation presents great difficulties. It 
 seems to possess to a very high degree the power of producing 
 induced radio-activity, in this it resembles Th X (see p. 291) and it 
 seems not improbable that it may turn out to be this substance. 
 
 Induced Radio-activity on Negatively Electrified Bodies in Air. 
 
 169. Elster and Geitel'f have found that a strongly negatively 
 electrified body suspended in the open air or in a large room 
 becomes temporarily radio-active. They showed that if a body was 
 connected with the negative terminal of a Wimshurst machine for 
 
 * Debierne, Comptes Rendus, 129, p. 593, 1899 ; 130, p. 906, 1900. 
 f Elster and Geitel, Physikalische Zeitschr. iii. p. 76, 1901. 
 
169] 
 
 BECQUEREL RAYS. 
 
 323 
 
 some hours, on detaching the body from the machine it was found 
 to be radio-active, ionising the air in its neighbourhood and affect- 
 ing a photographic plate. It is necessary for the success of 
 this experiment that a very large volume of air should be exposed 
 to the electric field, thus the wire must be in the open air or in a 
 large room. I was not able to get any induced radio-activity 
 with the air in the normal state when the wire was placed in a 
 closed vessel of about 500 litres capacity. The material of which 
 the negatively electrified body is made does not seem to have 
 much effect upon the amount of induced radio-activity, paper 
 giving as large an effect as metal.. A piece of metal made radio- 
 active in this way can be heated to redness without losing its 
 activity; if the surface of the radio-active metal is dissolved in acid 
 the acid becomes radio-active ; this is most conveniently proved 
 by evaporating the acid to dryness and testing the residue. The 
 radio-activity produced in this way gradually dies away. Ruther- 
 ford and Allen*, who have measured the rate at which it decays, 
 
 Curve 1. Induced radio-activity from air. 
 Curve 2. ,, ,, ,, thorium. 
 
 Curve 3. Thorium rays. 
 
 Curve 4. Uranium rays. 
 
 0123 
 
 Layers of tinfoil. 
 
 Fig. 85. 
 
 found that the induced radio-activity falls to about half its value 
 
 in three-quarters of an hour ; the induced radio-activity due to 
 
 * Rutherford and Allen, Physikalische Zeitschr. iii. p. 225, 1902. 
 
 212 
 
324 BECQUEREL RAYS. [170 
 
 thorium emanation is as we have seen much more persistent than 
 this. Rutherford has also compared the penetrating power of the 
 radiation from the negatively electrified wire in air with that of 
 the rays from substances made active by the thorium emanation 
 and with the non-deviable rays from thorium and uranium ; the 
 results which represent the proportion which pass through 1, 2, 3, 
 4 layers of tinfoil each 3'4 x 10~ 4 cm. thick are represented in 
 Fig. 85 ; it will be seen that of the radiations tested that induced 
 in air is the most penetrating. Elster and Geitel ascribe the 
 induced radio-activity to the deposition on the wire of some 
 unknown radio-active substance which is diffused through the 
 atmosphere. 
 
 lONISATION DUE TO PHOSPHORUS; IN NEWLY PREPARED GASES 
 AND IN AIR WHICH HAS BEEN IN CONTACT WITH WATER. 
 
 lonisation due to Phosphorus. 
 
 170. Air which has passed over phosphorus at not too low a 
 temperature has the power of discharging both positively and 
 negatively electrified bodies. This was known by Matteucci*, 
 it was also studied by Naccarif, and was subsequently indepen- 
 dently discovered by Shelford Bid well J. Barus, who has made 
 a very extensive series of observations on this phenomenon, found 
 that air which had been treated in this way was very active as 
 a cloud producer. If hydrogen is passed over phosphorus it does 
 not become a conductor of electricity. 
 
 There are two points of view from which we may regard the 
 action of the phosphorus : the first is that the air in passing 
 over the phosphorus gets ionised, and after its escape from the 
 phosphorus consists of a mixture of positive and negative ions 
 uniformly distributed through the gas ; in fact, that the gas is 
 in much the same condition as if it had been drawn past an 
 incandescent metal whose temperature was high enough to produce 
 both positive and negative ions at its surface. The other view 
 is that the air passing over the phosphorus carries off phosphorus 
 
 * Matteucci, Encyclopaedia Britannica (1855 edition), viii. p. 622. 
 
 t Naccari, Atti della Scienze de Torino, xxv. p. 252, 1890. 
 
 J Bidwell, Nature, xlix. p. 212, 1893. 
 
 Barus, Experiments with Ionised Air, Washington, 1901. 
 
170] BECQUEREL RAYS. 325 
 
 dust or nuclei, and that each of these nuclei acts as a centre of 
 ionisation, ionising the gas in its immediate neighbourhood ; the 
 state of the gas on this view would be similar to that of a gas 
 containing a large number of incandescent metallic particles, 
 each of these particles being surrounded by an envelope of 
 conducting gas. On this view, when the conducting gas was 
 placed in an electric field, the conduction would be due to the 
 motion of ions dragged out of the gas in contact with the nuclei 
 by the electric force, while the nuclei themselves would not be 
 displaced. The evidence is hardly sufficient to enable us to decide 
 with certainty between these two views: the second one, however, 
 seems to me the more probable, for Barus found that the rate 
 at which the conductivity died away from the phosphorised air 
 was not increased by the application of a strong electric field. 
 The decrease in conductivity seems consistent with the view 
 that it arises from the diffusion of the nuclei to the sides of 
 the vessel, a nucleus ceasing to be active as soon as it becomes 
 attached to the walls of the vessel. The rate of decay of conduc- 
 tivity would thus be proportional to the number of nuclei striking 
 the walls of the vessel in one second ; in the case of a gas of 
 density p, and whose average velocity of translation is v, this num- 
 ber is per unit area of surface equal to ^pv ; from measurements 
 of the rate at which the phosphorised gas lost its conductivity 
 Barus concluded that the nuclei moved about like the molecules 
 of a gas, only very much more slowly, the average velocity of 
 the nuclei being only about 3 cm. per second. Another reason 
 for supposing that the phosphorus supplies the gas which has 
 passed over it with nuclei capable of producing ions rather than 
 with ready-made ions, is the very considerable analogy that exists 
 between the behaviour of the phosphorised air and that of air 
 which has passed through water ; the properties of the latter we 
 shall consider in the next paragraph. 
 
 Barus made experiments to see if the ionising properties of 
 the phosphorised air could be exerted through thin films of 
 various materials: the only films which he found to transmit 
 any appreciable effect were those made of thin tissue-paper, and 
 here the effect seemed to make its way through the pores rather 
 than through the material itself, as on oiling the paper so as to 
 stop up the pores the transmission ceased. 
 
326 BECQUEREL RAYS. [171 
 
 Conductivity produced by bubbling air through water. 
 
 171. As we have seen (Chap. I.) air when in its normal state 
 conducts electricity to a certain extent, the saturation current 
 through the air in a small closed vessel being proportional to the 
 mass of the air contained in the vessel, the saturation current per 
 unit mass of air showing but little variation in samples of air taken 
 from different places. I have found, however, that air which has 
 passed through tap water acquires and retains for some time very 
 much greater conductivity than normal air. One way in which 
 this was proved was to use as the vat containing the air a cylin- 
 drical gasometer about 103 cm. high and 75 cm. in diameter, 
 down the axis of which was a conducting wire; the conductivity 
 of the air was tested by measuring the saturation current 
 between this wire and the walls of the vat. If now the air in 
 this vat was made to bubble through water the conductivity 
 increased to a very large extent. One way of forcing the air 
 through water was to pump the air from the vat by means of 
 a water pump into a second vessel (the process of pumping of 
 course making the air bubble vigorously through the water), 
 and then force the air back from this vessel into the vat; when 
 this circulation had been kept up for about an hour it was found 
 on stopping the circulation that the conductivity of the air was 
 very much greater than it was before. I often found, for example, 
 that it had increased 30 or 40 times, and I have no reason for 
 supposing that this increase was any approach to a limit. Another 
 convenient way of putting a gas into this conducting condition 
 is by passing it through a Gouy sprayer. When once a gas has 
 got into this condition it remains in it for a very considerable 
 time; thus, for example, I found that after the lapse of several 
 days after the passage of the gas through water, the conductivity 
 was still many times its value before the bubbling through the 
 water had occurred. 
 
 This conducting gas can be transferred from one vessel to 
 another, it can pass through plugs of glass-wool without losing 
 its conductivity, nor does it lose this property when passed over 
 wire-gauze heated to a red heat or through white-hot platinum 
 tubes or over hot copper. 
 
 The conductivity of the gas is due to the continued pro- 
 
171] 
 
 BECQUEREL RAYS. 
 
 327 
 
 duction of ions around some nuclei introduced into the gas by 
 its passage through the water; it cannot be explained by the 
 simple ionisation of the gas by this process, i.e. by a production 
 of ions while the air is bubbling through the water, this pro- 
 duction ceasing as soon as the air leaves the water, for if this 
 were the cause of the conductivity the current through the gas 
 would continue to increase as the electromotive force was in- 
 creased : there would in this case be no ' saturation ' of the 
 current. If no fresh ions were being produced the increase 
 of electric force would at first produce a continual increase in 
 the current, but as the old ions got used up by the current, 
 and no fresh ones being by hypothesis produced, the current 
 would gradually decrease. The relation between the current 
 and the potential difference is not of this character, but, as 
 the following numbers show, exhibits all the characteristics of 
 conduction through a medium in which ions are being generated 
 at an approximately constant rate ; the numbers in the following 
 table are proportional to the current passing between a wire 
 placed along the axis of the cylindrical gasometer in which the 
 gas was contained and the walls of the gasometer, when differ- 
 ences of potential, indicated by the numbers in the first column of 
 the table, were maintained between the wire and the walls of the 
 vessel. It will be noticed that for equal differences of potential, 
 the current is greater when the wire is the positive electrode 
 than when it is the negative. 
 
 Potential difference between 
 
 Current 
 
 the wire and sides of the 
 
 
 vessel in volts 
 
 
 
 
 wire + 
 
 wire - 
 
 1000 
 
 250 
 
 150 
 
 800 
 
 220 
 
 140 
 
 600 
 
 205 
 
 140 
 
 400 
 
 150 
 
 128 
 
 200 
 
 125 
 
 97 
 
 160 
 
 105 
 
 80 
 
 120 
 
 80 
 
 70 
 
 80 
 
 67 
 
 45 
 
 40 
 
 40 
 
 30 
 
 The difference can be explained by supposing that the negative 
 ions produced round the nuclei can be more easily detached by 
 
328 BECQUEREL RAYS. [172 
 
 the electric field from its neighbourhood than the positive ions; 
 this is what we should expect from the greater mobility of the 
 negative ions, part of the positive ions may get attached to the 
 nuclei and as these are almost immovable the positive ions en- 
 gaged in this way could not take any part in carrying the current. 
 
 The behaviour of the gas when it contains the nuclei intro- 
 duced into it by bubbling through water is very analogous to that 
 of a gas containing the emanation from thorium ; the ionising 
 power of the nuclei introduced by the water is however much 
 more persistent than that of the emanation ; on the other 
 hand the radiation from the nuclei is very much less pene- 
 trating than that from the emanation : for gas which had been 
 bubbled through water was passed for 6 hours over a photo- 
 graphic plate without producing any effect upon it. No increase 
 in conductivity was found by bubbling air through alcohol, ether, 
 or turpentine. The increase in conductivity produced in air by 
 the nuclei introduced into it by contact with water may explain 
 the interesting result found by Elster and Geitel*, that the air in 
 closed caves in which there is no circulation has a much higher 
 conductivity than the air in open spaces, for these nuclei might 
 slowly diffuse from the walls of the cave and so increase the ionisa- 
 tion in the air. If the explanation given below of the action of 
 the nuclei is correct, then the increase in conductivity might be 
 produced by nuclei of many substances besides water; all that is 
 required on this explanation is that there should be chemical action 
 between the air and the substance forming the nuclei. 
 
 Effects produced on a negatively electrified wire immersed in the 
 
 conducting gas. 
 
 172. We have seen (p. 294) that a negatively electrified wire 
 in a gas containing the emanation from thorium acquires the power 
 of ionising the air in its neighbourhood and retains this power for 
 a considerable time. Elster and Geitel have shown that the same 
 property is acquired by a negatively electrified rod exposed to the 
 open air, or to the air in a large cave or cellar, the effect in the 
 latter case being considerably greater than in the open air. I 
 have found that effects of a similar character are produced by 
 
 * Elster and Geitel, Physikalisch^e Zeitschrift, iii. p v 76, 1901. 
 
172] BECQUEREL RAYS. 329 
 
 negatively electrifying a wire in air whose conductivity has been 
 increased by bubbling it through water. I first tested the effect 
 of negatively electrifying the central wire in the cylindrical gaso- 
 meter when the gas in it was in the normal state; the wire was 
 connected to the negative pole of a Wimshurst machine, the other 
 terminal of which was put to earth and maintained at a potential 
 of about 30000 volts for 6 hours, the outside of the gasometer was 
 kept connected with the earth ; in this case no change could be 
 detected in the wire, the saturation current in the gasometer was 
 the same after the electrification of the wire as it had been before, 
 while if the wire had ionised the air around it the saturation current 
 would have been increased; the volume of air in the vessel, about 
 5 x 10 5 c.c., is thus too small to give the effect observed by Elster 
 and Geitel in the open air and* in large rooms. I next tried the 
 effect of largely increasing the current passing through the gas 
 during the negative electrification of the wire ; this was done by 
 exposing the air in the gasometer to Rontgen rays during the 
 whole of the time the wire was kept connected with the Wims- 
 hurst machine ; the rays make the conductivity of the gas very 
 much greater than when it is in the normal state, and so largely 
 increase the number of positive ions which come up to the nega- 
 tively electrified wire. In this case after disconnecting the wire 
 from the Wimshurst machine and stopping the rays the saturation 
 current was found to have slightly increased, the increase being 
 from 15 to 20 per cent.; that this was due to a change in the 
 property of the wire and not of the gas in the vessel was shown 
 by replacing the wire by one which had not been electrified, when 
 the saturation current was found to have its normal value. The 
 ionisation due to the negatively electrified wire (shown by the 
 increase in the saturation current) gradually died away and was 
 not perceptible after about 45 minutes. The experiment was 
 repeated with the wire connected with the positive instead of the 
 negative terminal of the Wimshurst machine, but in this case not 
 the slightest increase in the saturation current could be detected. 
 When the air was made a conductor by bubbling it through 
 tap water very much larger effects were obtained. To measure 
 these effects a second vessel was used in which the air was kept 
 in its normal state, the wire to be electrified was placed in this 
 vessel and the saturation current through the vessel measured, 
 (1) before the wire had been electrified, (2) after the wire had 
 
330 BECQUEREL RAYS. [173 
 
 been placed in the gasometer containing the conducting air and 
 negatively electrified : in most cases the wire itself was used as 
 one of the electrodes in the second vessel. When the air in the 
 gasometer had been got into a highly conducting state by bubbling 
 through water, the wire to be tested was placed in it and nega- 
 tively electrified by connecting it with the negative terminal of a 
 Wimshurst machine ; it was found that even with no more than 
 half-an-hour's electrification the wire acquired strong ionising 
 power. Thus, to give an example, the saturation current in the 
 second vessel before the wire was electrified (the wire being used 
 as one of the electrodes) was 15, after 30 minutes' negative elec- 
 trification in the gasometer the saturation current rose to 75, a 
 five- fold increase. If the wire was positively electrified when in 
 the gasometer the saturation current through the second vessel 
 was increased but to a very much smaller extent than if it had 
 been negatively electrified ; no increase was produced if the wire 
 was not electrified. The ionising power given to the wire by its 
 negative electrification gradually dies away after the electrification 
 has ceased ; the rate of decay varied somewhat in different cases, 
 it generally took about 40 minutes for the ionisation to fall 
 to one-half its initial value. Though it is convenient to use the 
 electrified wire as the electrode in the second vessel, it is not 
 necessary to do this, an increase in the saturation current is pro- 
 duced when the wire is merely placed in the second vessel and 
 another wire used as the electrode. The ionising power does not 
 seem to depend much upon the material of which the negatively 
 electrified body is made ; the following experiment illustrates this. 
 Four wires, one copper, one zinc, one copper covered with sodium 
 amalgam and the other copper covered with a layer of glycerine 
 and water, were metallically connected together and placed in 
 symmetrical positions in the gasometer and negatively electrified, 
 these wires were then used separately as electrodes in the second 
 vessel when they all gave approximately equal currents, much 
 larger than the normal one. 
 
 173. When the wire has by negative electrification once been 
 put in the state in which it ionises the surrounding gas it remains 
 in this state in spite of very rough treatment. Thus it can be 
 washed with water and then dried with filter-paper without losing 
 this property; it can be heated to a bright red heat without much 
 
173] BECQUEREL RAYS. 331 
 
 detriment to its ionising power; an amalgamated wire was heated 
 until the mercury was driven off and still retained its activity. If, 
 however, the active wire is rubbed with emery-paper so as to 
 remove the outside layers, or if in the case of a wire covered with 
 a layer of water the water is wiped off, then the activity of the 
 wire is destroyed. The ionising power of the wire corresponds to 
 a very easily absorbed type of radiation, about half the radiation 
 being absorbed by a layer of air at atmospheric pressure about 
 2 cm. thick, its effects can be detected through thin layers of 
 aluminium foil. 
 
 The properties of the wire after having been negatively elec- 
 trified in the conducting gas are very analogous to those possessed 
 by a wire after negative electrification in the open air or in air 
 containing an emanation ; the radio-activity in these cases has 
 usually been ascribed to some radio-active substance adhering to 
 the wire. There are indications that when air bubbles through 
 water it carries away with it a radio-active gas which can also 
 be extracted by boiling the water. For I have found that the 
 conductivity acquired by the air varies considerably with different 
 samples of water. The conductivity produced by Cambridge tap 
 water is very large, although the deposit obtained when the water 
 is evaporated to dry ness is not appreciably radio-active; with rain- 
 water the increase in conductivity is very small, it is increased 
 when certain salts such as lead nitrate are dissolved in the water. 
 I have found a small but appreciable increase in conductivity from 
 the water produced by the combustion of coal gas. 
 
 The conductivity is retained by the air after it has passed 
 through a porous plug. As the radio-active constituent can diffuse 
 through a porous plug it is possible by measuring the rate of 
 diffusion to determine the density of the emanation. By com- 
 paring the rates at which the emanation and carbonic acid gas 
 diffused through the same plate I found that the density of the 
 emanation was between 5 and 6 times that of carbonic acid. 
 
 The following considerations indicate that certain changes in 
 the physical conditions might make a body radio-active indepen- 
 dently of the deposition of an intrinsically radio-active substance. 
 We have, when considering the phenomena of electrification by 
 incandescent metals and of photo-electricity, regarded a metal 
 
332 BECQUEREL RAYS. [174 
 
 when in its normal state as being full of negatively electrified 
 corpuscles ; at ordinary temperatures these corpuscles have 
 not sufficient kinetic energy to enable them to overcome the 
 attraction of the metal arid shoot out from the metal into the 
 surrounding gas; when, however, the kinetic energy of the corpus- 
 cles is sufficiently increased, either by raising the temperature of 
 the metal or by the action of ultra-violet light, they escape into 
 the gas and produce electrical effects. Now in the case of a 
 negatively electrified wire placed in a conducting gas a state of 
 things will be set up at the surface of the metal which will assist 
 the corpuscles to escape into the gas. For in consequence of the 
 negative electrification of the wire positive ions travel up to it : 
 let us suppose that some at least of these do not get discharged 
 but stick to the wire, forming a layer of positive electrification 
 close to the surface of the metal, the positive electrification will 
 induce negative on the metal so that there will be at the surface 
 of the wire two oppositely electrified layers close together, the 
 negative layer on the wire, the positive layer outside ; there will 
 thus be a very intense electric field, tending to pull the negative 
 electricity out of the wire and thus making the metal into a 
 cathode emitting cathode rays ; if these corpuscles are moving with 
 sufficient rapidity to ionise the gas through which they pass the 
 gas around the metal will be surrounded by positive and negative 
 ions and will thus be able to discharge both positive and nega- 
 tive electricity from the wire; if the corpuscles come out, but with 
 so little kinetic energy that they are not able to ionise the mole- 
 cules of the gas against which they strike, then we should expect 
 the wire to discharge negative electricity more easily than positive, 
 for the positive electricity in this case would have to be carried 
 by the positive ions in the outer coating of the double layer and 
 the experiments we have described show that this is only detached 
 with great difficulty. 
 
 174. The measurements made by H. A. Wilson (see p. 190) 
 show that to ionise a molecule requires the expenditure of an 
 amount of energy equal to the work required to move the charge 
 on an ion through about 2 volts, hence we see that to give to 
 the corpuscles from the ions sufficient energy to ionise the gas 
 through which they pass, there must be a difference of potential 
 between the positive and the negative layers of at least 2 volts. 
 
175] BECQUEREL RAYS. 333 
 
 If the potential difference between these layers exceeds this 
 value the corpuscles dragged out of the metal may ionise the 
 gas ; the corpuscles in the cathode rays in a vacuum tube acquire 
 a velocity equivalent to that due to a fall through several hundred 
 volts; hence their velocity will greatly exceed that of the cor- 
 puscles extracted from the metal by^ the double layer, the latter 
 correspond to very slow and easily absorbed cathode rays. If 
 these views are correct it is not necessary to suppose that all 
 cases of induced radio-activity are due to the deposit of a radio- 
 active substance ; the formation of a suitable double layer of 
 electrification at the surface of any substance would impart this 
 property to that substance. 
 
 175. The existence of a double layer of electrification has long 
 been recognised in certain cases, it is by means of such a layer 
 that the polarisation of the electrodes immersed in an electrolyte 
 is usually explained ; it seemed therefore of interest to try 
 whether such electrodes possessed any properties analogous to 
 tnose possessed by a wire which has been negatively electrified 
 in a conducting gas. Two platinum wires were immersed in 
 dilute sulphuric acid, and a current of about 1 ampere was sent 
 through the acid ; these wires were used as electrodes for about 
 half-an-hour and then taken out, dried with filter-paper, and 
 then tested to see whether any ionisation was produced by them 
 in the air around them ; in many cases considerable ionisation 
 was found in the air round the wire which had been used 
 as the negative terminal (the one at which the hydrogen 
 ions arrive), but in no case was any such effect observed near 
 the wire which had been used as the positive terminal. The 
 amount of ionisation round the wire used as the negative terminal 
 varied a good deal, even when the intensity and the duration of 
 the current between the electrodes was kept the same, in some 
 few cases it seemed to be absent altogether; when present the 
 ionising power died away more rapidly than for a wire which 
 had been negatively electrified in the air, and was destroyed by 
 processes which hardly affected the wire. 
 
334 BECQUEREL RAYS. [176 
 
 Electrification produced by the bubbling of air through water, the 
 splashing of drops, the liberation of gases by chemical action 
 or by electrolysis. 
 
 176. The preceding experiments relate to the conductivity 
 of the gas, and show that the process of bubbling through water 
 produces both positive and negative ions in the gas ; the electrifi- 
 cation in the gas, i.e. the excess of the number of positive over 
 that of the negative ions, had previously been the subject of 
 many investigations. Thus Lord Kelvin * showed that air bubbled 
 through water carried with it a negative charge, the amount of 
 this charge depending upon the purity of the water, the addition 
 of salts or acids to the water diminishing the effect, and in some 
 cases reversing the sign of the electrification. The closely con- 
 nected effect connected with the splashing of drops had previously 
 been investigated by Lenard f, whose attention was called to 
 the question by the well-known fact that there is something 
 exceptional in the phenomena of atmospheric electricity at the 
 foot of a waterfall when the water falls upon the rocks and 
 breaks into spray. Lenard found that when a drop of water 
 splashes against a plate, a positive charge goes to the water, 
 while the surrounding air is negatively electrified. The amount 
 of the electrification is influenced to a remarkable extent by the 
 purity of the water ; thus Lenard found that while the effect 
 was very marked with the exceptionally pure water at Heidel- 
 berg, it was alfnost insensible with the less pure water at Bonn. 
 He found too that the splashing of a weak solution of sodium 
 chloride produced positive instead of negative electrification in 
 the air; thus while the splashing of rain electrifies the air 
 negatively, the breaking of waves on the sea-shore will electrify 
 it positively. 
 
 In some experiments that I made on the subject^, I found 
 that the effects produced by exceedingly minute traces of some 
 substances were exceedingly large ; thus, although rosaniline is 
 a very powerful colouring agent, I found that its presence in 
 
 * Lord Kelvin, Proc. Roy. Soc. Ivii. p. 335, 1894. 
 
 f Lenard, Wied. Ann. xlvi. p. 584, 1892. 
 
 t J. J. Thomson, Phil. Mag. v. 37, p. 341, 1894. 
 
176] BECQUEREL RAYS. 335 
 
 water could be detected by the electrical effect before any change 
 in the colour was apparent. 
 
 Kosters* found that while air bubbled through pure water 
 was negatively electrified, the addition of '007 per cent, of 
 sulphuric acid to the water made the air coming through electri- 
 cally neutral, while the addition of more acid caused the air to 
 be positively electrified, although the amount of this was small 
 compared with the negative electrification due to pure water. 
 
 The effect produced by the addition of salts and acids to the 
 water on the electrification of air passing through, has also been 
 investigated by Lord Kelvin, Maclean, and Gait"!". 
 
 The increased conductivity of air, produced by its passage 
 through water, is not nearly so sensitive to impurities in the 
 water as the charge carried away by the air. Thus I could find 
 no appreciable difference in the conductivity when salt, rosaniline 
 or methyl violet was added to the water, although the amount 
 and even the sign of the charges carried away by air passing 
 through the solution are very different. Very different considera- 
 tions are involved in the case of the conductivity given to air 
 by the water, and the amount of charge given to it by splashing 
 and bubbling. The former corresponds to a steady state which 
 continues for hours and even days after the passage of the air 
 through the water: the latter is no doubt largely influenced by 
 what occurs at the instant when a fresh liquid surface, due either 
 to the bubbles forcing their way through the liquid or by the 
 large increase in area produced by the splashing of a drop, is 
 exposed to the gas. 
 
 LenardJ found that electrification was produced by many 
 liquids besides water and aqueous solutions ; thus, mercury pro- 
 duced a very large effect of the same sign as water; if mercury 
 is vigorously shaken up in a bottle, and the air drawn off, it is 
 found to be strongly charged with negative electricity ; turpentine, 
 too, gives a large effect of the opposite sign to that of water, 
 the air being positively, the turpentine negatively, electrified. 
 The splashing of carbon bisulphide also gives rise to considerable 
 
 * Kosters, Wied. Ann. Ixix. p. 12, 1899. 
 
 t Lord Kelvin, Maclean, and Gait, Phil. Trans. A. 1898. 
 
 I Lenard, Wied. Ann. xlvi. p. 584, 1892. 
 
336 BECQUEREL RAYS. [176 
 
 electrification, the sign of the electrification being the same as 
 for water. 
 
 The nature of the gas surrounding the liquid has also a very 
 considerable effect upon the electrification; thus Lenard found 
 that the electrification due to the splashing of water surrounded 
 by hydrogen was much less than when the water was surrounded 
 by air ; using very carefully purified hydrogen, I got only a very 
 small electrification, and that of the opposite sign to the effect 
 in air. 
 
 Electrification due to Chemical Action. 
 
 In many cases of chemical combination in which gases take 
 part we get electrification of the gas; Pouillet* was the first 
 to discover an example of this effect ; he found that while 
 a carbon cylinder is burning, the air round the cylinder is posi- 
 tively while the cylinder itself is negatively electrified. Lavoisier 
 and Laplace f showed that the same effect occurs with glowing 
 coal. Pouilletj also found that when a jet of hydrogen burns 
 in air, there is positive electrification in the surrounding air, 
 negative electrification in the hydrogen. Lavoisier and Laplace 
 found that when hydrogen is rapidly liberated by the action of 
 sulphuric acid on iron there is considerable positive electrification 
 in the gas ; in this case the interpretation of the results is made 
 difficult by the electrical effects produced by the bubbling of the 
 gas through the liquid, these we should expect to be very con- 
 siderable as the gas is liberated in small bubbles, which is the 
 most favourable case for getting a considerable electrification in 
 a given volume of air. This and other cases of electrification 
 by chemical action have been investigated by Enright|| and by 
 TownsendV, the latter showed that the hydrogen produced by 
 the action of sulphuric acid on iron retained its electrification 
 after passing through tubes filled with tightly packed glass-wool, 
 thus proving that the electrification could not be carried by the 
 coarse spray produced by the bursting of the bubbles, as this is 
 
 * Pouillet, Pogg. Ann. ii. p. 422. 
 t Lavoisier and Laplace, Phil. Trans. 1782. 
 J Pouillet, Pogg. Ann. ii. p. 426. 
 
 Lavoisier and Laplace, Memoires de V Academic des Sciences, 1782. 
 || Enright, Phil. Mag. v. 29, p. 56, 1890. 
 
 II Townsend, Proc. Camb. Phil. Soc. ix. p. 345, 1898 ; Phil. Mag. v. 45, p. 125, 
 1898. 
 
176] BECQUEREL RAYS. 337 
 
 stopped by the wool. Townsend also showed that when chlorine 
 is liberated by the action of hydrochloric acid on manganese 
 dioxide the chlorine has a strong positive electrification ; and that 
 the oxygen produced by heating potassium permanganate carries 
 with it a strong positive charge. 
 
 Townsend has shown that gases liberated by electrolysis carry 
 with them considerable charges of electricity. Thus the hydrogen 
 evolved by the electrolysis of sulphuric acid at temperatures as 
 high as 40 or 50 C. has a considerable positive charge ; the 
 charge on the oxygen is exceedingly small in comparison, it is also 
 positive. When these gases are liberated by the electrolysis of a 
 solution of caustic potash the electrification on the hydrogen is 
 very small, while the oxygen has a much larger negative charge 
 the amount of which rapidly increases with the temperature; the 
 nature of the electrode too has a considerable influence on the 
 amount of electrification which comes off in the gas. The interpre- 
 tation of these results, like those of the evolution of gases by the 
 action of acids on metals, is made difficult by the electrical effects 
 produced by the bubbling of the gases through the liquid. 
 Rosters*, who has also investigated this subject, ascribes most of 
 the electrification to the bubbling. 
 
 Townsendf found that these electrified gases possess the 
 remarkable property of producing a cloud when they pass into 
 a vessel containing aqueous vapour; this cloud is produced even 
 when the air in the vessel is far from saturated with moisture, and 
 does not require any lowering of temperature such as would be 
 produced by the expansion of the air in the vessel. Townsend 
 found that when the gas liberated by electrolysis was not charged 
 no cloud was produced, and that the weight of cloud produced, other 
 circumstances being the same, was proportional to the charge in 
 the gas. Clouds are produced, however, in some cases in which .-to 
 charges are perceptible; thus H. A. Wilsonj has shown that if 
 solutions of salts or acids, or even of sugar or glycerine, are sprayed 
 by a Gouy sprayer into a vessel and the air from this vessel passed 
 through sulphuric acid a cloud is formed when this air emerges 
 into a damp atmosphere. The cause of this seems fairly clear, 
 
 * Rosters, Wied. Ann. Ixix. p. 12, 1899. 
 
 t Townsend, Proc. Comb. Phil. Soc. ix. p. 345, 1897. 
 
 J H. A. Wilson, Phil. Mag. v. 45, p. 454, 1898. 
 
 T. G. 22 
 
338 BECQUEREL RAYS. [177 
 
 although the passage through the sulphuric acid robs the drops of 
 the solution of the water, the acid or salt in the drop is carried 
 along with the air through the sulphuric acid; when this emerges 
 into the moist atmosphere the water condenses round the salt or 
 acid and forms a drop of the solution, thus the drops in the cloud 
 are not pure water, but solutions, and as the vapour pressure for 
 these solutions is smaller than that for pure water the drops do 
 not evaporate, even although the atmosphere is not saturated with 
 moisture. Meissner* has also described clouds not accompanied 
 by electrification which are produced when air containing ozone is 
 passed through a solution of potassium iodide: these can be ex- 
 plained in a similar way by supposing that the ozone acting on 
 the potassium iodide produces some substance which readily dis- 
 solves in water when it comes into contact with it. I think that 
 a similar explanation may hold for the clouds produced by the 
 electrified gas, for the carriers of the electricity are evidently 
 complex bodies of very considerable size, since Townsendf* found 
 that the velocity of these carriers under a potential gradient of 
 1 volt per cm. was only about 1/8000 of the velocity under the 
 same electric field of the ions produced by the action of the Rontgen 
 rays on the gases : if we suppose that these systems can dissolve 
 in water like an acid or salt and lower the vapour pressure, the 
 process by which the cloud is formed would be the same as that 
 in H. A. Wilson's experiment. 
 
 Townsend measured the rate of fall, the weight of the cloud, 
 and the amount of electrification carried by it ; the first of these 
 measurements gives the size of a drop, the second the number of 
 drops, and the third the charge on a drop ; he found, assuming 
 each drop to be charged, that the magnitude of the charge on the 
 carrier of the electricity in electrolytic oxygen was about 5*1 x 10~ 10 
 electrostatic units. 
 
 lonisation produced by the motion of negatively electrified 
 corpuscles. 
 
 177. The motion of negatively electrified corpuscles plays an 
 exceedingly important part in the electrical properties of gases ; 
 
 * Meissner, Jahresber. f. Chem. 1863, p. 126 ; see also Townsend, Proc. Camb. 
 Phil. Soc. x. p. 52, 1899. 
 t 16. ix. p. 345, 1897. 
 
177] BECQUEREL RAYS. 339 
 
 we have already seen that it is of fundamental importance in the 
 phenomena connected with incandescent solids and with photo- 
 electric effects, and we shall find subsequently that it ia of equal 
 importance in the phenomena connected with sparks and dis- 
 charges through vacuum tubes where the conductivity of the gas 
 is produced by the electric field itself: it is therefore desirable 
 to consider the laws of ionisation by moving corpuscles indepen- 
 dently of the method of production of the corpuscles. 
 
 The fact that gas traversed by Lenard rays can discharge 
 electrified bodies whether the electrification is positive or negative 
 shows that the rapidly moving corpuscles constituting those rays 
 ionise a gas when they pass through it. The ionisation of a gas 
 due to the passage through it of cathode rays inside a vacuum 
 tube was shown by the author* using the arrangement represented 
 in Fig. 86. A pencil of cathode rays from the cathode C passed 
 
 Fig. 86. 
 
 through holes in two metal plugs connected with the earth and 
 then between two parallel metal plates D, E ; one of these plates 
 was connected with one pole of a battery, the other pole of which 
 was put to earth, and the other plate to one pair of quadrants of 
 an electrometer, the other pair of quadrants being to earth ; the 
 plates were so arranged that the pencil of cathode rays did not 
 strike against either of them. When the cathode rays were not 
 passing between the plates there was no appreciable current of 
 electricity between the plates, but when the rays passed between 
 the plates the current if the pressure of gas was not too low 
 was very appreciable. The relation between the current and the 
 potential difference between the plates was of the character typical 
 of an ionised gas ; the current very soon reached a maximum value, 
 beyond which it did not increase for a considerable range of poten- 
 
 * J. J. Thomson, Phil. Mag. v. 44, p. 293, 1897. 
 
 222 
 
340 BECQUEREL RAYS. [178 
 
 tial difference; when the pressure was very low the current between 
 the plates got very small, as now there were very few molecules 
 for the cathode rays to strike against and ionise. This and the 
 case of the Lenard rays show that rapidly moving corpuscles ionise 
 the gas through which they pass. Since it requires a definite 
 amount of energy to ionise a molecule of a gas it is evident that 
 ionisation will not occur unless the corpuscles possess more than a 
 certain amount of energy, i.e. are moving above a certain speed : 
 if we assume that the work required to ionise a gas is that required 
 to move the charge on an ion through a potential difference of 
 2 volts the minimum velocity which must be possessed by a 
 corpuscle before it can ionise the molecules of a gas by colliding 
 against them is about 6*3 x 10 7 cm./sec. If any corpuscles are 
 present in a gas acted upon by an electric field the corpuscles will 
 move under the electric force, and if under this force they acquire 
 a velocity greater than the minimum velocity required to ionise 
 the gas these corpuscles will produce fresh ions, and these again 
 will generate other ions, so the gas will rapidly become a con- 
 ductor. The velocity acquired by a corpuscle in an electric field 
 will depend not only upon the intensity of the electric field but 
 also upon the free path of the corpuscle; after a collision the direc- 
 tion of motion of the corpuscle will be changed, it may be that it 
 is reversed, in which case the action of the electric field after the 
 collision will be to destroy the velocity communicated to the par- 
 ticle by the field before the collision took place : these considera- 
 tions show that the maximum kinetic energy communicated to 
 the corpuscles will be the work done on the corpuscle by the 
 electric field when the corpuscle moves over a space comparable 
 with its mean free path. Thus the kinetic energy communicated 
 to a corpuscle by a given electric field when the free path is long, 
 i.e. when the pressure of the gas is low, will be greater than when 
 the free path is short, i.e., when the pressure of the gas is high; thus 
 it is much easier to make a gas a conductor by this means when 
 the pressure is low than when it is high : these considerations 
 were first given by the writer in a paper read before the Cam- 
 bridge Philosophical Society, Jan., 1900. 
 
 178. The mathematical development of this conception has 
 already been given on page 231 ; it is shown there that in the 
 case when the ions are all moving parallel to the axis of x, under 
 
178] BECQUEREL RAYS, 341 
 
 an electric force X, and when the only source of ionisation in 
 the gas is the negative corpuscles, 
 
 where n is the number of corpuscles, u is the velocity of a 
 corpuscle parallel to the axis of x and the electric force, X the 
 mean free path of the corpuscle ; f(Xe\) the ratio of the number 
 of cases, in which a collision leads to ionisation, to the whole 
 number of collisions ; 7 the ratio of the number of cases, in which 
 collision leads to the recombination of the corpuscle, to the whole 
 number of collisions. Since (nu/\)f(Xe\) is the number of 
 fresh ions produced by the corpuscles in unit time, and as they 
 move in this time through ucm., f(Xe\)/\ is the number of 
 ions produced by a corpuscle in moving over 1cm.: denoting 
 this quantity by a, we get * 
 
 d , 
 
 or nu=e 
 
 where G is the value of nu when x 0. 
 
 If the field is strong enough to make the corpuscles reach 
 the electrodes before they have time to recombine, 7 = 0, and 
 we have 
 
 nt* 
 
 nu is the quantity of negative electricity passing in unit time 
 through unit area of a plane at right angles to the axis of X 
 at a distance x from the origin, and can be measured by placing 
 a metal plate at this distance, connecting it with an electrometer, 
 and measuring by means of this instrument the rate at which 
 negative electricity is reaching the plate. A very valuable series 
 of experiments on this effect have been made by Townsend* and 
 Townsend and Kirbyf who have determined the values of a for 
 gases under different pressures and for electric fields of different 
 intensities. The following are the values of a found by Townsend 
 for air: 
 
 * Townsend, Phil. Mag. vi. 1, p. 198, 1901. 
 t Townsend and Kirby, ib. p. 630. 
 
342 
 
 BECQUEREL RAYS. 
 
 [178 
 
 X volts 
 
 Pressure 
 17 mm. 
 
 Pressure 
 38 rnm. 
 
 Pressure 
 1-10 mm. 
 
 Pressure 
 2'1 mm. 
 
 Pressure 
 4*1 mm. 
 
 per cm. 
 
 a 
 
 a 
 
 a 
 
 a 
 
 a 
 
 20 
 
 24 
 
 
 _ 
 
 _ 
 
 _ 
 
 40 
 
 65 
 
 34 
 
 
 
 
 
 
 
 80 
 
 1-35 
 
 1-3 
 
 45 
 
 13 
 
 
 
 120 
 
 1-8 
 
 2-0 
 
 1-1 
 
 42 
 
 13 
 
 160 
 
 2-1 
 
 2-8 
 
 2'0 
 
 9 
 
 28 
 
 200 
 
 
 
 3'4 
 
 2'8 
 
 1-6 
 
 5 
 
 240 
 
 2-45 
 
 3-8 
 
 4-0 
 
 2-35 
 
 99 
 
 320 
 
 27 
 
 4'5 
 
 5-5 
 
 4-0 
 
 2'1 
 
 400 
 
 
 
 5-0 
 
 6'8 
 
 6-0 
 
 3'6 
 
 480 
 
 3-15 
 
 5-4 
 
 8-0 
 
 7'8 
 
 5-3 
 
 560 
 
 
 
 5-8 
 
 9-3 
 
 9'4 
 
 71 
 
 640 
 
 3-25 
 
 6-2 
 
 10-6 
 
 10-8 
 
 8-9 
 
 Thus we see that for a given value of X, a. begins by increasing 
 with the pressure, it attains a maximum at a particular pressure, 
 and then diminishes as the pressure increases ; we see too that 
 the larger the value of X the higher the pressure at which 
 a is a maximum. The values given for a at the two lowest 
 pressures show that, as the force is increased, a approaches 
 a constant value. 
 
 These results follow at once from the value we have obtained 
 for a, viz. 
 
 If X is constant, then at the pressure when a is a maximum, 
 
 da 
 
 or 
 
 where 
 
 = 0, 
 
 ct/v 
 
 f'(Xe\)Xe /(ZeX) 
 
 X-\ 2 "~ ' * ' 
 
 /v 
 
 
 - d.Xe\ 
 equation (1) may be written 
 
 Xe\f'(Xe\)=f(Xe\) .................... (2). 
 
 This equation determines the value of X when a is a maximum ; 
 we see from the form of the equation that the solution of (2) 
 
 is of the form 
 
 Xe\ c, 
 
178] BECQUEREL RAYS. 343 
 
 where c is independent of both X and X ; thus the value of X, 
 when a is a maximum, is inversely proportional to X, and since 
 \ is inversely proportional to the pressure, it follows that the 
 pressure at which a has its maximum value is proportional to X. 
 
 When the electric field is so strong that the kinetic energy 
 acquired by the corpuscle between two collisions is great enough 
 to make the corpuscle ionise the molecule whenever it collides 
 with it, f(Xe\) = 1 and a. = 1/X, ; hence a becomes in strong fields 
 equal to the reciprocal of the mean free path, i.e. to the number 
 of collisions made by the corpuscle in moving over 1 cm. Thus, 
 from the table, we may infer that a corpuscle makes about 3'25 
 collisions per cm. when moving through air at a pressure of 
 17 mm. of mercury. Townsend has shown that the number of 
 collisions determined in this way agree well with the number de- 
 duced from the Kinetic Theory of Gases for the collisions between 
 a body of negligible size and one of the size of a molecule of air. 
 The number of collisions made by a corpuscle moving through 
 air at a pressure of 1 mm. of mercury, as determined by the 
 above method, is about 21. Townsend and Kirby have shown 
 that the numbers of collisions made by a corpuscle moving 
 through hydrogen or carbonic acid at this pressure are respec- 
 tively 11 '5 and 29: these, again, agree well with the values 
 deduced from the Kinetic Theory. 
 
 When we are dealing with corpuscles moving with the velo- 
 city of those in the Lenard rays, i.e. with velocities between 
 10 9 and 10 10 cm./sec., the number of ions produced is much smaller 
 than those produced by the comparatively slow corpuscles dealt 
 with in the preceding experiment: thus, Durack* has sLown 
 that a corpuscle moving with a velocity of 5 x 10 9 cm./sec. only 
 produces about *4 ions when moving through 1 centimetre of 
 air at the pressure of 1 mm. of mercury, and with the still more 
 rapidly moving corpuscles shot out from radium the ionisation is 
 still smaller. The effect of velocity on the ionisation may, I think, 
 be explained by considerations of the following kind: let us 
 suppose that the molecules of a gas consist of a large number 
 of smaller particles, and that each of these repels the corpuscle ; 
 for the sake of taking a definite case, let us consider a molecule 
 as analogous to a metallic cage enclosing a large number of nega- 
 * J. J. E. Durack, Phil. Mag. vi. 4, p. 29, 1902. 
 
344 BECQUEREL RAYS. [178 
 
 tively electrified particles, the force due to these outside the cage 
 being balanced by a positive charge on the cage itself, equal in 
 magnitude to the sum of the negative charges on the particles 
 inside the cage ; then if a slowly moving corpuscle were to 
 penetrate the cage, the repulsions exerted on it by the particles 
 would at once drive it out before it had penetrated an appreciable 
 distance inside the cage : thus, in this case, the number of 
 collisions made by the corpuscle in its journey through the gas 
 would be the same as the number it would make if the molecules 
 of the gas were hard, impenetrable, elastic solids ; we have seen 
 that this hypothesis agrees well with the results of experiments 
 on slowly moving corpuscles. If, however, the velocity of the 
 corpuscle is very great, the repulsion of the particles inside the 
 cage will not stop the corpuscle ; the corpuscle will penetrate 
 the cage, being deflected by every particle it passes. The con- 
 ditions of the problem are now quite different from those when 
 the corpuscle was moving so slowly that it could not penetrate 
 the cage ; we proceed briefly to consider the collisions in this 
 case. The problem of the collision between bodies repelling each 
 other with a force varying inversely as the n th power of the 
 distance has been investigated by Maxwell*, who solved the 
 problem when the two bodies were moving with any velocities. 
 We shall suppose that the velocity of the particles is so small 
 with respect to that of the corpuscle that they may be supposed 
 to be at rest. In this case, if T is the kinetic energy of a cor- 
 puscle, T the change in T due to a collision, then Maxwell's 
 
 result gives 
 
 4JM/ 2 
 
 - 1 
 
 where M l} M 2 are the masses of the corpuscl'e and the particle 
 respectively, and 6 is given by the equation 
 
 - dx 
 
 2 
 
 - e = r 
 
 I 
 
 Jo 
 
 the force between the bodies is supposed to vary inversely as the 
 n th power of the distance between them, and 
 
 
 * Maxwell, Collected Papers, Vol. ii. p. 26. 
 
178] BECQUEREL RAYS. 345 
 
 where V is the velocity of the corpuscle before collision, 6 the 
 length of the perpendicular let fall from the particle on the line 
 of flight of the corpuscle before collision, and K the force at 
 unit distance. 
 
 x is the positive root of the equation 
 
 (n - 1) W 
 
 Let us take the case when the force varies inversely as the 
 square of the distance, i. e. n = 2, then we have 
 
 7T - l x> dx 
 
 2~ e = 
 
 A 2a 
 
 o ^/ 1 - a? - 
 
 TT 
 = - sm 
 
 thus sin 
 
 \/l+a 2 (, . 6 2 F' 
 and hence BT = ,,, * , 2 . 
 
 r 
 
 Since T varies as F 2 we see that when F is small ST will 
 increase with F and will be proportional to F 2 , it will reach a 
 
 maximum value when F 2 = -7- J^. 2 , while for larger values of 
 
 F, ST will decrease as F increases and will ultimately vary 
 
 as 1/F 2 . 
 
 Now BT is the energy lost by the corpuscle and given up 
 to the particle ; thus ST will measure the energy available for 
 dissociating the molecule, the ionising effect will therefore reach a 
 maximum value and will then diminish as the velocity increases. 
 When a is large, 6 is proportional to I/a, i.e. to 1/F 2 ; now 20 
 is the angle through which the direction of motion is deflected, 
 thus, for corpuscles moving with different speeds, the ionisation 
 of the gas and the diffusion of the corpuscles will be proportional 
 to each other. 
 
CHAPTER XIII. 
 
 SPAEK DISCHARGE. 
 
 179. WE have hitherto mainly been discussing cases in which 
 the ionisation was produced independently of the electric field 
 acting upon the gas, we shall now proceed. to the consideration of 
 cases in which the ionisation is mainly due to the action of the 
 electric field itself, and when the electric field before sending the 
 electric current through the gas has first to make the gas a con- 
 ductor. Cases when ionisation is produced by an electric field have 
 already been considered on pp. 2 31 et seq., we shall now consider 
 the most familiar case of this kind, the electric spark. To take 
 as simple a case of this as possible, let us suppose that we have two 
 large metal plates parallel to one another and near together, let the 
 plates be placed in connection with a large battery of cells or some 
 other means of producing a difference of potential between them ; 
 then if we start with a very small difference of potential between 
 the plates the only current which will pass from one plate to the 
 other will be the very small one due to the spontaneous ionisation 
 of the gas between the plates ; this current is npt luminous and is 
 proportional to the distance between the plates, and so by pushing 
 the plates near together may be made as small as we please. On 
 measuring the potential difference, however, a stage is reached 
 when a current accompanied by luminosity passes between the 
 plates, and when this, the sparking stage, is reached the potential 
 differences between the plates remain approximately constant, even 
 when the number of cells in the circuit connecting the two plates 
 is increased. The potential difference between, the plates when 
 the spark passes depends upon the distance between the plates, 
 i.e. the length of the spark, and on the nature and pressure of the 
 gas in which the plates are immersed ; the investigation of the 
 
180] SPARK DISCHARGE. 347 
 
 connection between these quantities has occupied the attention 
 of many observers. Before we consider their results, it will be 
 useful to consider some properties of the spark which have an 
 important effect on the accuracy of such observations. 
 
 180. We shall call the greatest potential difference, which can 
 be applied to the electrodes for an indefinitely long time without 
 causing the spark to pass, the spark potential difference. It must 
 not be supposed, however, that whenever a potential difference 
 just greater than this is applied to the plates a spark always 
 passes; it frequently happens that if the potential difference is 
 only applied for a short time the air between the plates can sustain 
 a much greater difference of potential than the spark potential 
 without a spark passing through it. Thus Faraday* long ago 
 observed that it takes a greater potential difference to start the 
 first spark than is required to keep up the sparks when once they 
 have been started, and that the effect of one spark in facilitating 
 the passage of its .successors does not die away until the gas has 
 rested for several minutes. I found that if the gas is dried with 
 extreme care it is possible to get it to stand without a spark pass- 
 ing a potential difference three or four times as large as that 
 which is sufficient to produce a spark in less perfectly dried gasf. 
 The dry gas seems, however, to be in an unstable state as far as its 
 electrical properties are concerned, for when once a spark has been 
 forced through it the potential difference between the plates falls 
 to the value for a moist gas, and the gas is riot again able to 
 stand a greater potential difference until it has rested for several 
 minutes ; this result suggests that if we had a perfectly dry gas it 
 might not be possible to start a spark through it. The gas would, 
 however, be in an unstable state, and may be compared to a super- 
 saturated solution into which a foreign body has to be introduced 
 before crystallisation begins, though the process once started con- 
 tinues until the solution ceases to be supersaturated. Another 
 analogy would be a gas supersaturated with aqueous vapour, 
 when for condensation to take place we require the presence of 
 nuclei round which the drops may condense. The tendency of 
 the gas to get into this electrically unstable state is much dimi- 
 nished by the presence of moisture, or of gases from flames, sparks, 
 i 
 
 * Faraday, Experimental Researches, 1417. 
 t J. J. Thomson, Phil. Mag. v. 36, p. 313. 
 
348 SPARK DISCHARGE. [180 
 
 or arcs, by the illumination of the cathode by ultra-violet light, or 
 by the exposure of the spark-gap to Rontgen or Becquerel rays, in 
 short by any agent which introduces ions into the field. War- 
 burg* has made very extensive researches on the effect produced 
 by several of these agents on the passage of sparks ; the method 
 he used consisted in measuring the interval between the applica- 
 tion of a potential difference greater than the spark potential and 
 the passage of the spark ; this interval, which may be several 
 minutes when the potential only just exceeds the spark potential, 
 diminishes as the potential difference increases, we shall call it 
 the ' lag ' of the spark. The amount of the ' lag ' has an import- 
 ant effect on many phenomena connected with sparks ; thus for 
 example if it is great and an induction coil or some other machine 
 furnishing a very rapidly changing potential be used ta produce 
 the spark, the terminals may support for the short time during 
 which the electric field lasts a potential difference which would 
 produce a spark if the lag were short; in a case like this an agent 
 might make the spark pass by diminishing the time of lag 
 even though it had no effect on the spark potential. A notable 
 instance of this is the effect produced by ultra-violet light on 
 sparks passing between the terminals of an induction coil. Hertzf 
 showed that the exposure of the spark-gap to such light facilitated^ 
 the passage of the spark ; E. Wiedemann and EbertJ showed that 
 if the negative electrode is screened off from the light, leaving the 
 spark-gap and positive electrode illuminated, no effect is produced ; 
 we have seen (Chapter X.) that the illumination of a negatively 
 electrified body leads to a discharge of negative ions, and that no 
 ions are produced when the body is positively electrified. Swyn- 
 gedauw found that if the positive electrode was large its illu- 
 mination helped the spark: it is possible that with large electrodes 
 sufficient light may be reflected from the positive to the negative 
 electrode, or to some body in the neighbourhood of the positive 
 electrode which is negatively electrified by induction, to cause the 
 negatively electrified body to emit ions. 
 
 * Warburg, Sitz. Akad. d. Wissensch., Berlin, xii. p. 223, 1896 ; Wied. Ann. lix. 
 p. 1, 1896; Ixii. p. 385, 1897. 
 
 t Hertz, Wied. Ann. xxxi. p. 983, 1887. 
 
 t E. Wiedemann and Ebert, Wied. Ann. xxxiii. p. 241, 1888. 
 
 Swyngedauw, Rapports presentes au Congres International de Physique, Paris, 
 iii. p. 164. 
 
180] 
 
 SPARK DISCHARGE. 
 
 349 
 
 Wiedemann and Ebert (I.e.) showed that the nature of the 
 gas had considerable influence upon the amount of the effect 
 produced by ultra-violet light, the effect being especially large in 
 carbonic acid gas (the currents due to photo-electric effects in this 
 gas are much larger than in air). Warburg* showed that the 
 chief effect of the ultra-violet light was to diminish the ' lag ' and 
 that the effect on the spark potential was comparatively small. 
 This is clearly shown by the figures given in the following table, 
 taken from Warburg's paper: the potential difference was produced 
 by a battery of storage cells, and a contact make and break was 
 used, by means of which the potential difference was applied to 
 the air-gap for a short interval, in this case '0012 sec. The frac- 
 tions in the table have for their numerators the number of times 
 a spark passed when the potential difference was applied for this 
 time, and for their denominators the number of times the potential 
 difference was applied ; thus the fraction T ^ indicates that the 
 spark never passed, and the fraction -{- that it always did so. The 
 gas used in these experiments was hydrogen at a pressure of 
 11 mm. of mercury, the spark potential was 960 volts in daylight, 
 1080 in the direct light from an arc lamp, and 1260 when this 
 light had passed through glass. The electrodes were platinum 
 spheres, 7 mm. in diameter, and the spark length was 4*5 cm. 
 
 Potential Difference 
 
 8 
 
 3 
 
 o 
 
 
 
 3 
 
 $ 
 
 o 
 
 
 
 s 
 
 o 
 
 o 
 
 o 
 
 1 
 
 in volts 
 
 OS 
 
 *< 
 
 iH 
 
 
 
 O 
 
 8 
 
 OS 
 
 <N 
 
 
 
 3 
 
 3 
 
 
 
 t- 
 
 
 
 00 
 
 In the dark 
 
 
 
 
 
 
 
 <L 
 
 A 
 
 -Ar 
 
 A 
 
 A 
 
 T 7 iT 
 
 A 
 
 
 
 
 
 
 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 In daylight 
 
 
 
 -L 
 
 
 JL 
 
 A 
 
 
 
 
 
 
 
 
 In the arc light 
 
 
 
 10 
 
 
 Iff 
 
 10 
 
 
 
 
 
 
 
 
 through glass 
 
 
 i8 
 
 
 }$ 
 
 
 
 
 
 
 
 
 
 
 In the arc light 
 
 1% 
 
 
 ft 
 
 
 
 
 
 
 
 
 
 
 
 It will be seen from this table that while in the dark the 
 spark does not always pass even when the potential difference 
 is 9 times that required to produce a spark when the field is con- 
 tinuous, in the arc light a potential difference only a little greater 
 than the minimum required to produce a spark, always produces 
 a spark ; the table shows too that daylight produces a very per- 
 ceptible diminution of the ' lag.' 
 
 * Warburg, Sitz. Akad. der Wissenschaften, Berlin, xii. p. 223, 1896. 
 
350 SPARK DISCHARGE. [181 
 
 Warburg* showed that the 'lag' in a very dry gas was much 
 longer than in one containing a small quantity of water vapour; 
 the difficulty of starting the electric discharge in very carefully 
 dried gas has already been alluded to (see p. 347). 
 
 The importance of the 'lag' in relation to the mechanism of 
 the spark discharge seems first to have been realised by Jaumannf, 
 who pointed out that while it lasted some process must be going 
 on in the gas which converts it from an insulator to a conductor. 
 During this process no light can be detected even in the darkest 
 room, and both Jaumann and Warburg failed to find by direct 
 experiments with electroscopes any indication of a current passing 
 through the gas at this stage. Warburg J, however, at low pres- 
 sures observed some effects which seem to indicate that during the 
 lag there is a current passing through the gas although it is too 
 'small to be detected by an electroscope or to produce any lumi- 
 nosity. The evidence for this is based on the effect produced by 
 a magnet on the discharge through a gas at low pressure ; a dis- 
 charge is hindered by the action of a transverse magnetic field 
 owing to the deflection of the ions which carry the current ; 
 Warburg showed that the magnetic field not only hampered 
 the luminous discharge, it also produced a great increase in the 
 duration of the 'lag,' he concluded from this that during the lag 
 there is a feeble current which is essential for the production of 
 the spark, and that the magnetic field by hampering this current 
 prolongs the time which has to elapse before the spark can pass. 
 Walter by taking photographs of sparks on rapidly moving 
 plates has shown that a bright spark is preceded by faintly lumi- 
 nous brush discharges. We shall see when we consider the theory 
 of the spark discharge that the formation of a preliminary current 
 is necessary for the production of the spark. 
 
 Effect of rapid variations in the potential of the terminals on 
 the passage of a spark. 
 
 181. Jaumann || has made some interesting experiments on 
 the effect on the spark length of rapid changes in the electrical 
 
 * Warburg, Wied. Ann. Ixii. p. 385, 1897. 
 
 + Jaumann, Ib. Iv. p. 656. 
 
 J Warburg, Ib. Ixii. p. 385. 
 
 Walter, Ib. Ixvi. p. 636, Ixviii. p. 776. 
 
 H Jaumann, Wien. Sitz. xcvii. p. 765, 1888. 
 
181] 
 
 SPARK DISCHARGE. 
 
 351 
 
 condition of the electrodes. The experiments are of the following 
 type. The main current from an electrical machine charged the 
 
 Fig. 87. 
 
 I 
 
 condenser. B, while the condenser C could be charged through 
 the air space F, G being a small condenser whose capacity was only 
 55 cm., while B was a battery of Leyden jars whose capacity was 
 about 1000 times that of C ; a wire was connected to the inside 
 coating of B and terminated about 5 mm. above the plate E, 
 which was connected with the earth. A glow discharge passed 
 from the wire to the plate, and the difference of potential between 
 the outside and inside coatings of the jars B was constant and equal 
 to about 12 electrostatic units. When the knobs of the air break 
 F were suddenly pushed together a spark about 5 mm. in length 
 passed across the air break and in addition a bright spark 5 mm. 
 long jumped across the air space at e where there was previously 
 only a glow. The passage of the spark at F put the condenser G 
 in connection with B, and thus produced a rapid variation in the 
 potential of the wire, and the spark at E was the result. From 
 experiments of this kind Jaumann came to the conclusion that if 
 V is the potential difference between the electrodes the condition 
 
 dV 
 
 for sparking is that V -=- and not V should have a definite value, 
 dt 
 
 so that if we could make the potential difference vary with great 
 rapidity it might produce a spark even though its magnitude were 
 much below the sparking value. I cannot see, however, that the 
 experiments justify this conclusion ; it must be remembered that 
 when we add on the small condenser we start electrical vibrations, 
 
352 SPARK DISCHARGE. [182 
 
 and that while these are going on the maximum value of the 
 potential in certain parts may greatly exceed the value when the 
 vibrations have died away. Thus, to take a very simple case, 
 suppose A is a very large Leyden jar, while B is a very small one, 
 originally A is charged, B is not, the outsides of both are connected 
 with the earth ; if the in sides of A and B are suddenly connected, 
 then though the final potential of B will be smaller than the 
 initial value of the potential of A, yet the maximum value during 
 the oscillations will be nearly twice as large as the initial poten- 
 tial of A, and thus if B were suddenly connected with A a spark 
 might pass across the plates of B although B might stand without 
 sparking a potential difference equal to that originally existing 
 between A : the passage of this spark would, however, be due to 
 the oscillation producing a great increase in the maximum poten- 
 tial difference, and would not necessarily indicate that with a given 
 potential difference the spark would pass more easily if this were 
 changing than if it were steady. This question has been the 
 subject of much controversy, it is often called the question of 
 'constant spark potential' and has been discussed by Jaumann*, 
 Swyngedauwf, and K. R. Johnson J. 
 
 Variation of the spark potential difference with the spark length 
 and pressure of the gas. 
 
 182. The first measurements of the potential difference re- 
 quired to produce a spark through air at atmospheric pressure were 
 made by Lord Kelvin in 1860, since then the subject has attracted 
 much attention and important investigations have been made by 
 Baille||, LiebigH, Paschen**, Peaceft> Orglerft, Struttg, Bouty||||, 
 EarhartlfH and Carr***. The values of the spark potential differ- 
 
 * Jaumann, Wied. Ann. Iv. p. 656, 1895 ; Wien. Sitz. xcvii. p. 765, 1888. 
 
 f Swyngedauw, These : Contribution a VEtude des Decharges, 1897. 
 
 J Johnson, Drude's Ann. iii. p. 460, 1900 ; v. p. 121, 1901. 
 
 Lord Kelvin, Collected Papers on Electrostatics and Magnetism, p. 247. 
 
 || Bailie, Annales de Chimie et de Physique [5], xxv. p. 486, 1882. 
 
 IT Liebig, Phil. Mag. v. 24, p. 106, 1887. 
 ** Paschen, Wied. Ann. xxxvii. p. 79, 1889. 
 ft Peace, Proc. Roy. Soc. Iii. p. 99, 1892. 
 $$ Orgler, Drudc's Ann. i. p. 159, 1900. 
 
 Strutt, Phil. Trans. 193, p. 377, 1900. 
 || || Bouty, Comptes Rendus, 131, pp. 469, 503, 1900. 
 HIT Earhart, Phil. Mag. vi. 1, p. 147, 1901. 
 *** Carr, Proc. Roy. Soc. Ixxi. p. 374, 1903. 
 
182] SPARK DISCHARGE. 353 
 
 ence given by the earlier experimenters are as a rule somewhat 
 larger than those found under similar circumstances by more 
 recent observers, probably because latterly more attention has been 
 paid to eliminating the effects due to 'lag'; whenever 'lag' is 
 present the potential difference when the spark passes is higher 
 than the minimum required to produce a spark. We shall first 
 give a general account of the laws which have been brought to 
 light by the experiments made on this subject, reserving until the 
 end of the chapter the tables which embody the numerical results 
 obtained by the above-mentioned physicists. 
 
 Let us first take the case where the electrodes are so large 
 compared with the distance between them and placed in such a 
 position that the lines of electric force are parallel to each other, 
 this condition would be fulfilled if the electrodes were parallel 
 planes placed at a distance from each other not greater than a 
 small fraction of their diameter; it is approximately fulfilled in 
 the arrangement most frequently used where the electrodes are 
 portions of spheres of large radius placed close together. 
 
 In the first place the potential difference required to produce 
 a spark of given length does not aepend upon the metal of which 
 the electrodes are made (it is possible that aluminium and magne- 
 sium electrodes may be exceptions to this rule). Experiments 
 on this point have been made by Righi*, Peace, and Carr. Righi 
 tried electrodes of carbon, bismuth, tin, lead, zinc, and copper and r 
 got the same potential difference with all these substances. Peace 
 (I.e.) who made very careful experiments with electrodes of zinc 
 and brass could not detect the slightest difference in the 
 potential difference required to spark across them. Carr found 
 the spark potential to be the same with electrodes of brass, iron, 
 zinc, and aluminium. On the other hand, De la Rue and Hugo 
 Miillerj- came to the conclusion that sparks pass more easily 
 between aluminium electrodes than between electrodes of any 
 other metal, but that with this exception the nature of the elec- 
 trodes has no influence upon the spark length. It is worthy of 
 remark that the cathode fall of potential which is very closely con- 
 nected with the spark potential is nearly the same for electrodes 
 
 ** 
 
 * Righi, Nuovo Cimento (2), xvi. p. 97, 1876. 
 
 t De la Rue and Miiller, Phil. Trans. 169, Pt. 1, p. 93, 1898. 
 
 T. G. 23 
 
354 SPARK DISCHARGE. [182 
 
 of all the metals used by Righi ; for aluminium and magnesium 
 electrodes, however, it is decidedly smaller. 
 
 The connection between the spark potential and the spark 
 
 COAL GAS. 
 
 100 200 300 *oo 500 coo 700 800 900 iooo Centimeters 
 
 length is represented by the curves given in Figs. 88, 89, 90, 
 and 91 for air, hydrogen, and carbonic acid and coal gas at 
 
 AIR. 
 
 100 200 soo 400 500 600 700 800 900 iooo C 'e utitncfcrs 
 Fig. 89. 
 
 atmospheric pressure, the ordinates are proportional to the 
 
182] 
 
 SPARK DISCHARGE. 
 
 355 
 
 potential difference required to produce a spark of a length repre- 
 sented by the abscissae. 
 
 The curves in Figs. 88 91 are due to Liebig (I. c.), who 
 used spherical electrodes 19*5 cm. in diameter. The curves 
 
 HYDROGEN. 
 
 100 2OO 300 400 500 600 700 
 
 800 900 1000 Centime.te.rs 
 
 Fig. 90. 
 
 running up to the vertical axes represent the connection between 
 the average value of the electric intensity, i.e. V/d where V is the 
 spark potential and d the spark length, and the spark length. 
 
 100 200 300 400 50 
 
 600 700 800 900 1000 
 
 Fig. 91. 
 
 It will be seen that except for very short sparks the curves 
 representing the relation between V and d are approximately 
 
 232 
 
356 SPARK DISCHARGE. [183 
 
 straight lines, so that for moderately long sparks the relation 
 between F and d would be of the form 
 
 where a and b are constants. Chrystal* has shown that the 
 simple relation 
 
 F= 4-997 + 9 
 
 where F is measured in electrostatic units and d in centimetres 
 agrees with Bailie's very numerous experiments on the spark poten- 
 tial in air at atmospheric pressure quite as well if the spark length 
 exceeds 2 mm. as the more complicated formula 
 
 F 2 = 10500 (d + 0*08) d 
 
 proposed by Bailie himself. Carey Foster and Prysonf also 
 found that the linear relation V=a + bd was the one which best 
 represented the results of their experiments on the potential 
 difference required to spark through gas at atmospheric pressure. 
 
 183. The curves we have given do not however give any indica- 
 tion of the relation between the spark potential and the spark 
 length when the latter is exceedingly small. When the spark length 
 falls below a certain value which is inversely proportional to the 
 pressure, and which we shall call the critical spark length, the 
 potential difference has a minimum value, and if the spark length is 
 still further diminished the spark potential begins to increase and 
 goes on increasing until the spark length gets down to about 10~ 4 cm., 
 when it very rapidly diminishes. The increase of the spark poten- 
 tial due to a diminution in the spark length was first observed by 
 Peace ; as the critical spark length at atmospheric pressure is 
 exceedingly small, only about '01 mm., it is difficult to experiment 
 with sparks short enough to show the effect, as however the 
 critical spark length varies inversely as the pressure, we can by 
 diminishing the pressure increase the critical spark length until its 
 observation becomes comparatively easy. Perhaps the simplest way 
 of showing the effect is to use slightly curved electrodes and to 
 observe 'the position of the spark as these are brought closer 
 together. When the electrodes are at some distance apart the 
 spark passes along the shortest line between them; as the electrodes 
 
 * Chrystal, Proc. Eoy. Soc. Edin. xi. p. 487, 1882. 
 
 t Catey Foster and Pryson, Chemical News, xlix. p. 114, 1884. 
 
183] 
 
 SPARK DISCHARGE. 
 
 357 
 
 are pushed together it will be found that a stage is reached when 
 the spark no longer passes along the shortest line, but goes to 
 one side, taking a longer path, showing that it is easier to pro- 
 duce a long spark than a short one ; with this arrangement the 
 potential difference required to produce the spark does not vary, 
 as the electrodes are moved nearer together it remains constant 
 and equal to the minimum potential difference required to pro- 
 duce a spark ; the spark length too is constant and equal to the 
 critical spark length ; the position of the spark is determined by 
 the condition that it. passes at the place where the distance be- 
 tween the electrodes is equal to the critical spark length. In order 
 to measure the increase of potential difference due to the dimi- 
 nution in spark length it is necessary to use perfectly flat and 
 parallel electrodes, when these are pushed together the length of 
 the spark is necessarily diminished. , The electrodes used by Carr 
 (I. c.) are represented in Fig. 92 ; they were plane brass plates em- 
 bedded in ebonite and separated by ebonite rings of different 
 
 -- 
 
 ToBofcry 
 
 thicknesses. With this apparatus Carr obtained the results given 
 in the following table : 
 
 Pressure 2'02 mm. : gas air. 
 
 Spark length 
 
 Spark potential 
 
 in volts 
 
 1 rnm. 
 
 558 
 
 
 2 mm. 
 
 371 
 
 
 3 mm. 
 
 357 
 
 
 5 mm. 
 
 376 
 
 
 10 mm. 
 
 472 
 
 
 
358 
 
 SPARK DISCHARGE. 
 Pressure T05 mm.: gas air. 
 
 [183 
 
 Spark length 
 
 Spark potential 
 
 in volts 
 
 1 mm. 
 
 1826 
 
 
 2 mm. 
 
 594 
 
 
 3 mm. 
 
 397 
 
 
 5 mm. 
 
 355 
 
 
 10 mm. 
 
 37 
 
 
 The effect is even more strongly marked in hydrogen, as the 
 following table shows. 
 
 Pressure 2*6 mm.: gas hydrogen. 
 
 Spark length 
 
 Spark potential 
 
 in volts 
 
 1 mm. 
 
 1781 
 
 
 2 mm. 
 
 462 
 
 
 3 mm. 
 
 398 
 
 
 5 mm. 
 
 285 
 
 
 10 mm. 
 
 317 
 
 
 In each of these cases the spark potential for the shortest 
 spark is greater than for the longest. When the spark length 
 falls below about 5 x 10~ 4 cm. the spark potential, as Earhart has 
 shown, falls off rapidly; we shall return to this point later on. The 
 existence of a critical spark length is also proved by the remark- 
 able changes which take place in the appearance of the discharge 
 when the electrodes are brought very near together. Thus in the 
 course of some experiments on the discharge between large parallel 
 plates I observed* that at very low pressures the discharge went 
 from the under side of the lower plate, which was the positive elec- 
 trode, and round to the top of the upper plate, the space between 
 the plates was quite free from any luminous discharge : showing 
 the discharge went more easily round the longer path than by the 
 much shorter one between the plates. The same thing is shown 
 in Figs. 93 and 94, which are drawings given by Lehmann'f* of 
 the appearance as seen through a microscope of the discharge 
 
 * J. J. Thomson, Proc. Camb. Phil. Soc. v. p. 395, 1886. 
 f Lehmann, Moleciilare Physik, ii. p. 295. 
 
18*] 
 
 SPARK DISCHARGE. 
 
 359 
 
 between electrodes of different shapes placed very near together. 
 A very famous experiment due to Hittorf*, represented in Fig. 95, 
 
 Fig. 93. 
 
 Fig. 94. 
 
 is another illustration of this. The two electrodes were only 1 mm. 
 apart, the regions around them were connected together by a long 
 
 Fig. 95. 
 
 spiral tube 375 cm. long; in spite of the enormous difference be- 
 tween the lengths of the paths the discharge, when the pressure 
 was very low, all went round through the spiral, the space between 
 the electrodes remaining quite dark. 
 
 184. The curves in Figs. 88 91 show how rapidly the 
 value of V/d (V being the spark potential and d the distance 
 
 Hittorf, Wied. Ann. xxi. p. 96, 1884. 
 
360 
 
 SPARK DISCHARGE. 
 
 [185 
 
 between the plates) increases as d diminishes. This was observed 
 by Lord Kelvin in 1860. If the electric field were uniform V/d 
 would be the electric intensity between the plates; in general, 
 however, when a current of electricity passes through a gas the 
 field is not uniform but is greater at one or both of the electrodes 
 than in the rest of the field, we are not justified therefore in 
 assuming that V/d is the maximum electric intensity between 
 the electrodes. 
 
 Variation of the spark potential with the pressure. 
 
 185. If the spark length is constant and not too small then, 
 starting with air at atmospheric pressure, as the pressure is 
 diminished the spark potential decreases, the relation between the 
 potential and pressure being at first a linear one ; on further diminu- 
 tion of the pressure the spark potential reaches a minimum value r 
 after this any further diminution in the pressure is accompanied by 
 an increase in the spark potential. The relation between the spark 
 potential and the pressure is represented by the curve in Fig. 96, 
 
 Pressure in Millimetres 
 Fig. 96. 
 
 taken from a paper by Carr (I.e.); in this curve the ordinates 
 represent the spark potential, the abscissae, the pressure ; the 
 
185] 
 
 SPARK DISCHARGE. 
 
 361 
 
 electrodes were parallel planes and the spark length 3 mm. The 
 pressure at which the spark potential is a minimum is called the 
 critical pressure. Peace (I.e.) showed that the critical pressure 
 depended upon the spark length, the shorter the spark length the 
 greater the critical pressure. He showed too that the minimum 
 spark potential was constant, being independent of the spark 
 length ; in air it was equal to about 351 volts, so that unless thej 
 spark length is less than about 5 x 10~ 4 cm., a potential difference) 
 of less than 351 volts cannot produce a spark. 
 
 These points are well illustrated by the curves in Fig. 97, taken 
 from Carr's paper; they represent the relation between the pres- 
 sure and the spark potential, for sparks of 1, 2, 3, 5, and 10 mm. 
 
 / 2 J 
 
 Pressure in Millimetres of Mercury 
 Fig. 97. Air. 
 
 The critical pressures for these spark lengths as given by Carr are 
 as follows. 
 
 Spark length 
 
 Critical pressure 
 
 Product of spark length 
 and critical pressure 
 
 1 mm. 
 
 4-98 mm. 
 
 4-98 
 
 2 mm. 
 
 2'71 mm. 
 
 5-42 
 
 3 mm. 
 
 1-89 mm. 
 
 5-67 
 
 5 mm. 
 
 1-34 mm. 
 
 6'7 
 
 10 mm. 
 
 679 mm. 
 
 6-79 
 
362 
 
 SPARK DISCHARGE. 
 
 [185 
 
 It will be seen that the product of the critical pressure and 
 the spark length is approximately constant: we must remember 
 that owing to the flatness of the curves in the neighbourhood of 
 the critical pressure the exact determination of the critical pres- 
 sure is a matter of some difficulty, especially with the shorter 
 
 tr -$-&" D 
 
 400 480 StO 610 720 800 
 
 Pressure in Millimetres 
 Fig. 98. Air. 
 
 1040 U20 1200 
 
 Pressure in Millimetres 
 
 Fig. 99. Hydrogen. 
 
 sparks : the differences in the product of the critical pressure and 
 the spark length are not greater than could be accounted for by 
 the errors in the determination of the critical pressure. 
 
 The same features are shown by sparks through hydrogen and 
 
185] SPARK DISCHARGE. 363 
 
 carbonic acid; the curves for these as given by Carr are shown in 
 
 / 2 3 4 S" 
 
 Pressure in Millimetres 
 Fig. 100. Carbon Dioxide. 
 
 Figs. 99 and 100, and the connection between the critical pressure 
 and the spark length shown in the following tables: 
 
 Hydrogen. Minimum potential 280 volts. 
 
 Spark length 
 
 
 Critical pressure 
 
 Product of spark length 
 and critical pressure 
 
 1 mm. 
 
 10-3 mm. 
 
 10-3 
 
 2 mm. 
 
 5-93 mm. 
 
 11-8 
 
 3 mm. 
 
 4-02 mm. 
 
 12-06 
 
 5 mm. 
 
 2-8 mm. 
 
 14-0 
 
 10 mm. 
 
 1'46 mm. 
 
 14-6 
 
 Carbonic acid. Minimum potential 420 volts. 
 
 Spark length 
 
 Critical pressure 
 
 Product of spark length 
 and critical ^pressure 
 
 1 rnm. 
 
 5-02 mm. 
 
 5-02 
 
 2 mm. 
 
 2*52 mm. 
 
 5-04 
 
 3 mm. 
 
 1-63 mm. 
 
 4-89 
 
 5 rnm. 
 
 1-07 mm. 
 
 5-35 
 
 10 mm. 
 
 510mm. 
 
 5-1 
 
364 
 
 SPARK DISCHARGE. 
 
 [185 
 
 / The constancy of the product of spark length and critical 
 /pressure in the case of carbonic acid is very marked. 
 
 Carr has also given curves for the connection between spark 
 length and pressure for H 2 S, SO 2 , CO 2 , C 2 H 2 , O 2 , N 2 O ; these are 
 shown in Fig. 101. 
 
 2-2 2-4 26 2-8 
 
 _.__/ 1-2 /-+ 1-6 1-8 Z 
 
 Pressure in Millimetres 
 Fig. 101. 
 
 The spark length for these gases was 3 mm. 
 
 Very careful experiments on the relation between the pressure 
 and the spark potential were made by Strutt* for air, hydrogen, 
 nitrogen, and helium ; the experiments on nitrogen and helium are 
 especially interesting, as the minimum spark potential in these 
 gases was found by him to be greatly affected by minute traces 
 of impurity. Thus the presence of a very minute quantity of 
 oxygen in nitrogen increased the minimum spark potential from 
 251 volts to 388 volts. Thus nitrogen from which the oxygen had 
 been removed by passing the gas over metallic copper gave a 
 minimum spark potential of 388 volts, the value of this potential 
 for a specjmen of nitrogen prepared from air by the absorption of 
 the oxygen by alkaline pyrogallol was 347 volts ; when, however, 
 the oxygen was more completely removed by bubbling the gas 
 repeatedly through the liquid alloy of sodium and potassium the 
 minimum spark potential fell to 251. The curves obtained by 
 
 * Hon. R. J. Strutt, Phil. Trans. 193, p. 377, 1900. 
 
185] 
 
 SPARK DISCHARGE. 
 
 365 
 
 Strutt for nitrogen are shown in Fig. 102. Curve No. 2 refers to 
 the purest specimen, curve No. 1 to a specimen which had been 
 
 _t 600 
 
 3 
 
 ~ 500 
 
 I 
 
 4 
 
 | 
 
 OQ* 300 
 
 10 20 30 40 60 60 70 80 
 
 Pressure in Millimetres of Mercury 
 Fig. 102. Nitrogen. 
 
 passed several times through the sodium and potassium alloy, but 
 not so often as that to which curve No. 2 relates : the minimum 
 spark potential for this specimen was 276 volts. The curves after 
 passing the critical pressure are parallel. 
 
 The discharge through helium, which was also studied by Strutt, 
 presents many interesting features. Ramsay and Collie * first drew 
 attention to the ease with which the discharge passed through 
 
 -2 
 I 
 
 I 
 
 I 
 o 
 
 
 I 
 
 800 
 
 400 
 
 300 
 
 \ 
 
 10 20 30 40 50 60 
 
 Pressure in Millimetres of Mercury 
 Fig. 103. Helium. 
 
 helium. Strutt's experiments, the results of which are represented 
 in Fig. 103, show that for a given length of spark the critical 
 
 Ramsay and Collie, Proc. Roy. Soc. lix. p. 257, 1896. 
 
366 
 
 SPARK DISCHARGE. 
 
 [186 
 
 pressure is exceedingly high, being about 5 times that of air for 
 the same spark length and more than twice that of hydrogen. The 
 great effect of small impurities on the minimum spark potential 
 is shown by the different curves in Fig. 103, which refer to samples 
 purified in different ways : the smallest value of this potential 
 obtained by Strutt was 261 volts. 
 
 186. We have seen that the product of the critical pressure and 
 the spark length is constant and is also independent of the nature 
 of the electrodes, it is thus a property of the gas : the following table 
 contains the values of this product q, calculated from the measure- 
 ments of Carr and Strutt, and also the mean free paths (X) of the 
 molecules of the gases at atmospheric pressure, these with the 
 exception of helium are taken from the table in 0. E. Meyer's 
 Kinetische Theorie der Gase, p. 142, that of helium is deduced from 
 Lord Rayleigh's* experiments on the viscosity of helium : though 
 these free paths are taken for a particular pressure, the ratio of 
 the free paths of the molecules of different gases is independent 
 of the pressure. The numbers in column (3) are the spark length 
 in millimetres multiplied by the critical pressure : 
 
 Gas 
 
 Minimum spark 
 potential 
 
 2 
 
 X x 10 5 cm. 
 
 10 5 x \lq 
 
 Air 
 
 341 S. 
 
 5-7 
 
 95 
 
 17 
 
 Nitrogen . .. 
 
 251 S. * 
 
 6-7 
 
 98 
 
 14 
 
 Oxygen . 
 
 455 C. 
 
 
 1-05 
 
 
 Hydrogen 
 
 (302308 S.) 
 
 14-4 
 
 1-8 
 
 12 
 
 Carbonic acid 
 
 ( 278 C. J 
 419 C. 
 
 5-1 
 
 68 
 
 13 
 
 Sulphur dioxide 
 
 457 C. 
 
 3-3 
 
 48 
 
 14 
 
 Nitrous oxide 
 
 418 C 
 
 5 
 
 68 
 
 14 
 
 Sulphuretted hydrogen 
 Acetylene 
 
 414 C. 
 468 C. 
 
 6 
 
 628 
 
 10 
 
 Helium 
 
 261 S. 
 
 27 
 
 2-6 
 
 10 
 
 
 
 
 
 
 The letters S. and C. indicate that the measurements were 
 made by Strutt or Carr : no very great accuracy can be claimed 
 for the values of q, as the determination of the critical pressure is 
 difficult; a small error in the determination of the spark potential 
 near this pressure would lead to a large error in the value of the 
 
 Lord Rayleigh, Proc. Roy. Soc. Ixix. p. 198, 1896. 
 
187] SPARK DISCHARGE. 367 
 
 critical pressure. Taking this into account, I think the differences 
 shown in the preceding table for q/\ from the constant value 
 1*3 are not, except in the case of sulphuretted hydrogen and 
 helium, greater than might be explained by errors of experiment. 
 In the two exceptions sulphuretted hydrogen and helium there 
 are special circumstances which make us hesitate to accept the 
 results as final without further experiment. Sulphuretted hydro- 
 gen is decomposed by the spark, hydrogen being liberated; if such 
 a decomposition had occurred in the experiments we have used 
 for the determination of q the spark would have passed through a 
 mixture of hydrogen and sulphuretted hydrogen, the hydrogen 
 would increase the critical pressure and hence the value of q. 
 Again as Strutt's experiments show, the numbers for helium are 
 very greatly affected by the presence of small amounts of impurity, 
 so that it would hardly be safe to draw conclusions from this gas 
 unless the free path determination had been made with the same 
 specimen of gas as the electrical determinations. 
 
 We may, I think, conclude that for a large number of gases 
 the value of qj\ is approximately constant, i.e. that with a given 
 spark length the critical pressure is proportional to the mean free 
 path of the molecules of the gas. 
 
 Paschen s Law. 
 
 187. As the result of a very numerous series of experiments on 
 the relation between spark potential and pressure, Paschen* came 
 to the conclusion that the spark potential depended only upon the 
 product of the pressure and the spark length : i.e. upon the mass 
 of gas between unit area of the electrodes. Thus, if the spark 
 length d and pressure p of the gas are both altered, but in such a 
 way that their product does not change, the spark potential V 
 will remain constant ; or in other words V is a function of pd. 
 
 The following results taken from Paschen's paper show how 
 nearly the law is obeyed over the range of pressures studied by 
 him ; all these pressures it ought to be noticed are considerably 
 above the critical pressures. V is the spark potential measured in 
 electrostatic units, p the pressure measured in cm. of mercury, 
 
 * Paschen, Wied. Ann. xxxvii. p. 79, 1889. 
 
368 SPARK DISCHARGE. [187 
 
 and d the spark length in cm.: the electrodes in these experiments 
 were spheres 1 cm. in radius. 
 
 Air : pd = 7'5 
 
 P 
 
 d 
 
 V 
 
 10 
 
 0-75 
 
 16-23 
 
 15 
 
 0-50 
 
 16-54 
 
 20 
 
 0-38 
 
 16-75 
 
 25 
 
 0-30 
 
 17-00 
 
 30 
 
 0-25 
 
 16-83 
 
 40 
 
 0-17 
 
 16-86 
 
 50 
 
 0-15 
 
 16-68 
 
 75 
 
 o-i 
 
 16-33 
 
 
 Mean 
 
 16-65 
 
 Hydrogen : pd=7'5 
 
 P 
 
 d 
 
 F 
 
 10 
 
 0-75 
 
 9-50 
 
 15 
 
 0-50 
 
 9-32 
 
 20 
 
 0-38 
 
 9-47 
 
 25 
 
 0-30 
 
 9-59 
 
 30 
 
 0-25 
 
 9-58 
 
 40 
 
 0-187 
 
 9-69 
 
 50 
 
 0-15 
 
 9-90 
 
 75 
 
 o-io 
 
 10-44 
 
 
 Mean 
 
 9-68 
 
 Carbonic acid : pd=7'5 
 
 P 
 
 d 
 
 F 
 
 12-5 
 
 0-6 
 
 16-45 
 
 15-0 
 
 0-5 
 
 16-48 
 
 20-0 
 
 0-38 
 
 17-02 
 
 25-0 
 
 0-30 
 
 17-92 
 
 30-0 
 
 0-25 
 
 17-79 
 
 40-0 
 
 0-187 
 
 18-33 
 
 50-0 
 
 0-15 
 
 17-77 
 
 75-0 
 
 o-io 
 
 17-21 
 
 
 Mean 
 
 17-37 
 
 Air : pd = 20 
 
 p 
 
 d 
 
 F 
 
 28-6 
 
 0-7 
 
 34-30 
 
 33-3 
 
 0-6 
 
 34-63 
 
 40-0 
 
 0-5 
 
 35-12 
 
 50-0 
 
 0-4 
 
 34-77 
 
 66-66 
 
 0-3 
 
 35-39 
 
 
 Mean 
 
 34-64 
 
 Hydrogen : pd = 20 
 
 p 
 
 d 
 
 F 
 
 28-6 
 
 0-7 
 
 " 19-12 
 
 33-33 
 
 0-6 
 
 19-25 
 
 40-00 
 
 0-5 
 
 19-43 
 
 50-00 
 
 0-4 
 
 19-43 
 
 68-66 
 
 0-3 
 
 20-00 
 
 
 Mean 
 
 19-45 
 
 Carbonic acid : pd = 20 
 
 P 
 
 d 
 
 F 
 
 33-33 
 
 40-00 
 50-00 
 6666 
 
 0-6 
 0-8 
 0-4 
 0-3 
 
 Mean 
 
 33-03 
 
 32-86 
 33-46 
 34-11 
 
 33-6 
 
187] 
 
 SPARK DISCHARGE. 
 
 369 
 
 The relation between the spark potential and the product pd 
 is shown in the curves for air, hydrogen, and carbonic acid in 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r 
 
 s 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 '- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 ' 
 
 
 
 
 
 
 
 
 Nv 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 X 
 
 ,,- 
 
 & 
 
 ) I* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 X^ 
 
 - 
 
 
 
 
 
 
 
 
 
 
 . 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 x '' 
 
 
 
 
 
 
 
 
 
 J 
 
 -' 
 
 
 
 
 
 "J 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 , 
 
 'A 
 
 rO 
 
 ^ e 
 
 ^ ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X f 
 
 * 
 
 
 
 
 
 
 ft 
 
 - 
 
 " 
 
 ^ 
 
 r 
 
 
 
 
 
 
 
 
 "} OQ 
 
 
 
 
 
 t 
 
 x 
 
 
 
 
 
 = 
 
 .-- 
 
 >- ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,; 
 
 ? 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 * 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J 
 
 - 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 It 
 
 1 
 
 I 
 
 \- 
 
 
 2( 
 
 D 
 Fi 
 
 J. - 
 
 LO^ 
 
 L 
 
 3 
 
 D 
 
 
 
 
 4 
 
 9 
 
 
 
 
 
 Fig. 104, the ordinates^are the spark potentials in electrostatic 
 measure, the abscissae the values of pd. 
 
 O 
 
 I 
 I 
 
 Q AM 
 
 2 mrr 
 
 5 mr> 
 /O. 
 
 Product of Pressure and Distance between Electrodes 
 Fig. 105. Air. 
 
 Paschen's experiments were all made at pressures considerably 
 greater than the critical pressure ; it has, however, quite recently 
 T. G. 24 
 
370 
 
 SPARK DISCHARGE. 
 
 [187 
 
 been shown by Carr (I.e.) that Paschen's law holds at all pressures. 
 This is very clearly shown by the curves in Figs. 105, 106, which 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 + 
 X 
 
 </- 
 </- 
 
 / /T7/7 
 2/TT/7 
 
 
 += 
 
 3 * 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d = 
 of - 
 
 5 mr 
 /O mr 
 
 
 .2 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 o> ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 n /ceo 
 1 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ft * 
 
 "eS 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 1 * 
 
 
 
 
 
 V 
 
 ***L 
 
 DTT-4U 
 
 w-a 
 
 A^ 
 
 -** 
 
 K3 g> 
 
 * 
 
 -* 
 
 t 
 
 ==f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 2 
 
 Product of Pressure and Distance between Electrodes 
 
 Fig. 106. Carbon Dioxide. 
 
 represent the relation between the spark potential V (in this case 
 measured in volts) and the product pd (p was measured in milli- 
 metres of mercury and d in millimetres) ; five different values of d 
 were used, ranging from 1 to 10 mm. ; the results of these are 
 represented on the curve by symbols attached to the points on the 
 curve determined by the various experiments. It will be seen 
 that the points for all the spark lengths all lie on the same curve, 
 and in this case the range of pressures extended far below the 
 critical pressure. The results of Paschen's law are very important; 
 we see that to find the spark potential corresponding to any spark 
 length and any pressure it is only necessary to possess the results 
 of experiments made with a constant spark length over the whole 
 range of pressures. We see, too, that it follows from this law that 
 the critical pressure must vary inversely as the spark length, a 
 result for which as we have seen there is direct experimental 
 evidence. It follows too from this law that if we know the values 
 of the spark potential required to produce a spark of constant 
 length for all pressures we can deduce the value of the spark 
 potential for a spark of any length at any pressure. 
 
188] 
 
 SPARK DISCHARGE. 
 
 371 
 
 X188. For pressures considerably greater than the critical 
 pressure the relation between the spark potential and the spark 
 length is a linear one; if Fis the spark potential and a; the spark 
 length at atmospheric pressure, then 
 
 F= ax + b, 
 
 where, if V is measured in electrostatic units and x in centi- 
 metres, the experiments by Bailie, Liebig, Paschen, Orgler give 
 the following values for the constants in hydrogen, air, and 
 carbonic acid. 
 
 Gas 
 
 BAILLE 
 
 LIEBIG 
 
 PASCHEN 
 
 ORGLER 
 
 a 
 
 6 
 
 a 
 
 & 
 
 a 
 
 & 
 
 a 
 
 6 
 
 Air 
 
 99-6 
 
 5 
 
 87'4 
 55-8 
 91-8 
 
 
 92'5 
 43-0 
 91-1 
 
 
 93-6 
 46-3 
 85-6 
 
 
 Hydrogen ... 
 Carbonic acid 
 
 Wolf*, who measured the spark potential required to produce 
 a spark 1 mm. long at pressures varying from 1 to 5 atmo- 
 spheres, found that (as we should expect from Paschen's law) the 
 relation at these high pressures between spark potential and pres- 
 sure is a linear one ; if V is the spark potential in electrostatic 
 measure and x the pressure in atmospheres, then Wolf found that 
 V was given by the following expressions : 
 
 For hydrogen V= 6*509 x + 6'2 
 For oxygen F=9'6# + 4'4 
 
 For air F=10'7^ + 3'9 
 
 For nitrogen F = I2'08x + 5'0 
 
 For carbonic acid V= 10'22# + 7*2. 
 
 If F is the average electric force between the electrodes 
 in these experiments, then ^ T =10F. 
 
 The order of the spark potential for different gases as will be 
 seen from the preceding table depends upon the pressure ; thus 
 at the pressure of 1 atmosphere F for CO 2 is greater than F for 
 air, while at high pressures it is less. 
 
 * Wolf, Wied. Ann. xxxvii. p. 306, 1889. 
 
 242 
 
372 SPARK DISCHARGE. [189 
 
 189. Bouty* has made a series of experiments on the electric 
 field required to make a gas into a conductor, using a method which 
 dispensed with the use of metallic electrodes. In this method the 
 gas at a low pressure is contained in a glass vessel with parallel 
 sides, and this vessel is placed in the space between two parallel 
 plates parallel to the walls of the vessel, the difference of potential 
 between these plates is increased until the gas in the glass vessel 
 becomes luminous, indicating that a discharge is passing through 
 it; the strength of the electric field, i.e. the electric force (not the 
 potential difference), when this occurs is called by Bouty the cohe- 
 sion dielectrique of the gas. A very considerable number of gases 
 were examined by this method. Bouty found that the cohesion 
 dielectrique F for gases up to 6 cm. pressure could be represented 
 by the formula 
 
 F=a + bp, 
 
 where a and b are constants and p is the pressure. When F is 
 measured in absolute electrostatic units and p in atmospheres, 
 Bouty found that 
 
 For hydrogen F = 1-4 + 63'33^ 
 For air F= T593 + 119'09j9 
 
 For carbonic acid ,F= T703 + 144*4 p; 
 
 he compares these expressions with those given by Wolf and 
 points out that while the coefficients of p are not so very different 
 the constant terms are of quite a different order; he ascribes this 
 difference to the electrodes in Wolfs experiments being metal, 
 while in his experiments they were glass; it seems to me that the 
 following explanation is more probable. If V is the potential 
 difference required to produce a spark of length I through gas at 
 a pressure p considerably greater than the critical pressure, then 
 we have approximately, if A and B are constants, 
 
 since we know by Paschen's law that F is a function of Ip ; hence 
 F, the average electric intensity when the spark passes, is given 
 by the equation 
 
 hence the constant term varies inversely as the length of the spark 
 * Bouty, C. R. 131, p. 469, 1900. 
 
189] 
 
 SPARK DISCHARGE. 
 
 373 
 
 while the coefficient of p is independent of the spark length. In 
 Wolf's experiments the spark length was only 1 mm., while the 
 distance between the plates in Bouty's experiments was much 
 greater so that the difference in the spark length would explain the 
 difference in the constant term, and it is not necessary to ascribe 
 it to the nature of the electrodes. Bouty* has determined the 
 constants a, b, in the expression F=a-)-bp for the cohesion 
 dielectrique for a number of vapours, the results are given in 
 the following table. Bouty's measurements were made at pres- 
 sures ranging from '0055 cm. to 2 cm. of mercury. The constants 
 apply when the pressure is measured in cm. of mercury and F in 
 volts per cm. 
 
 Vapour of 
 
 a 
 
 b 
 
 Water 
 
 333 
 
 500 
 
 Methyl-alcohol ... 
 Ethyl-alcohol 
 Ether 
 
 375 
 
 364 
 360 
 
 616 
 
 800 
 1000 
 
 Methyl formate ... 
 Ethyl propionate 
 Acetone 
 
 364 
 312 
 355 
 
 1020 
 1083 
 1100 
 
 Ethyl formate 
 Methyl acetate . . . 
 Carbon bisulphide 
 Toluol 
 
 360 
 369 
 330 
 
 380 
 
 1110 
 1250 
 1510 
 1610 
 
 Benzol . 
 
 377 
 
 1670 
 
 
 
 
 It will be seen that the values of a vary very little in com- 
 parison with those of b. The values of b are in nearly every 
 case in the same order as those of 1/X, where X is the mean free 
 path of the molecules of the gas, and are in many cases roughly 
 proportional to this quantity. If the law which is suggested by 
 these results actually holds and b is inversely proportional to 1/X 
 the spark potential V required for a constant spark length must 
 at pressures greater than the critical pressure be expressed by an 
 equation of the form 
 
 where X is the mean free path of the molecules and a and b are 
 constants which are the same for all gases. 
 
 * Bouty, C. E. 131, p. 503, 1900. 
 
374 SPARK DISCHARGE. [190 
 
 190. v. Rontgen* arrived at the conclusion that the spark 
 potential for a constant spark length was inversely proportional to 
 the mean free path of the molecules of the gas through which the 
 spark passed ; we have seen, however, that the ratio of the spark 
 potential for different gases varies with the pressure and the spark 
 length, so that this statement does riot give complete expression 
 to the laws of the spark -discharge. If we look at the question 
 from the point of view of Paschen's law we see that from that law 
 
 F=/Y? 
 
 where x is the spark length and X the mean free path of the mole- 
 cules of the gas; if the spark potential for different gases depended 
 only upon the mean free path of the molecules of the gases the 
 function / would be the same whatever were the nature of the 
 gas ; but, if this were the case the minimum potential required 
 to produce a spark would be the same for all gases, a result which 
 is inconsistent with the determinations made of this quantity. I 
 have tried an equation of the form 
 
 where F is the same function for all gases and A a constant which 
 may vary from one gas to another. Practically the only gases for 
 which we possess sufficient materials to test this law adequately 
 are air, hydrogen and carbonic acid. I have found that the obser- 
 vations in air and hydrogen are in fair agreement with this law, 
 while those in carbonic acid are not : it is desirable, however, that 
 the law should be tested over a far wider range of gases, as there 
 are special circumstances connected with carbonic acid which make 
 one hesitate to accept conclusions drawn from this gas alone; in the 
 first place the experiments made by different observers differ 
 more widely for this gas than for any of the others tested, it is 
 one in which the 'lag' of the spark is exceedingly pronounced, and 
 in other cases of discharge, such for example as that produced by 
 ultra-violet light, it exhibits peculiarities not shown by air or 
 hydrogen. Careful observations on the spark discharge in a gas 
 which has a mean free path differing considerably from either 
 hydrogen or air are much wanted. 
 
 * Rontgen, Gottingen Nach. 1878, p. 390. 
 
191] 
 
 SPARK DISCHARGE. 
 
 375 
 
 191. Natterer* tested for a large number of gases the length 
 of spark produced at constant pressure by a small induction coil ; the 
 measurements made by this method are of necessity exceedingly 
 rough but they are for many gases the only measurements we 
 possess relating to the passage of the spark. Part of Natterer's 
 results are given in the following table, the temperature when not 
 stated is to be taken as about 20 C., the spark lengths are in 
 millimetres. 
 
 Gas 
 
 Spark length 
 
 Gas 
 
 Spark length 
 
 H 2 . 
 
 1520 
 
 HCN (80 C.) . 
 
 23 
 
 No 
 
 1015 
 
 CO 
 
 1014 
 
 NO 
 
 9 14 
 
 CH, 
 
 813 
 
 O 2 
 
 810 
 
 C 2 He 
 
 1013 
 
 HC1 
 
 57 
 
 CH 3 OH (100 C.) 
 
 912 
 
 C1 2 
 
 24 
 
 C0 2 
 
 811 
 
 HBr ... 
 
 23-5 
 
 CH 3 .CHO(100C.)... 
 
 68 
 
 HI 
 
 1-5 2 
 
 CoH.OH (110 C) . 
 
 7 9 
 
 Br 2 (100 C ) 
 
 23 
 
 CH 3 C1 
 
 811 
 
 I 9 (230 C ) . 
 
 2-53 
 
 C 2 N 2 
 
 1-52 
 
 H 2 (130 C.) ... . 
 
 47 
 
 (CHA,CO (100 C.) .. 
 
 69 
 
 H 2 S ... . 
 
 35 
 
 C 2 H 6 CHO (100C.)... 
 
 47 
 
 N 
 
 35 
 
 C 2 H 5 C1 
 
 4 7 
 
 S0 2 
 
 1-52 
 
 (C 2 H 6 ) 2 (100 C.) ... 
 
 58 
 
 HgCl 2 (271 C ) 
 
 22-5 
 
 CS 2 (100C.) 
 
 23 
 
 
 58 
 
 C 6 H 6 (110 C.) 
 
 79 
 
 p| 3 3 :::;:;: 
 
 47 
 
 C 4 H 4 S (110 C.) 
 
 45 
 
 SoCL (135C.) .. 
 
 1-752 
 
 C 2 H 3 2 C 2 H 5 (110C.) 
 
 37 
 
 PC1 3 (137-5 C.) 
 AsCl 3 (181-5C.) 
 PBr 3 (271C.) 
 
 1-52 
 1-251-5 
 l-75_2 
 
 C 2 H 5 Br (100 C.) 
 CHC1 3 (100C.) 
 C 3 H 7 Br (100 C.) 
 
 33-5 
 
 1-752 
 2-252-75 
 
 SiF 4 (101C.) 
 
 57 
 
 (CH' 3 ) 2 CHBr (100 C.) 
 
 22-5 
 
 PC1 3 0(153C.) 
 
 2-252-5 
 
 CH 3 I (100 C.) 
 
 22-25 
 
 SiCl 4 (170C.) 
 
 1-752 
 
 OGL(110C.) 
 
 1-51-75 
 
 SnCL (260 C.) 
 
 1-51-75 
 
 C 2 H 5 I (100 C.) 
 
 1-752 
 
 CH/ 
 
 710 ' 
 
 CHBro (180C.) ., 
 
 22-5 
 
 C 9 H 9 . 
 
 34 
 
 Hg(uSA,(195 C.)... 
 
 67 
 
 
 
 
 
 It will be noticed that the spark lengths are short in vapours 
 of complicated chemical constitution in which the mean free paths 
 are small ; the halogen elements chlorine, bromine and iodine seem 
 to exert a great influence in shortening the spark, these elements 
 and their compounds have short free paths. 
 
 Natterer found that the spark length was exceptionally long 
 
 * Natterer, Wied, Ann. xxxviii. p. 63, 1889. 
 
376 SPARK DISCHARGE. [192 
 
 in the monatomic vapours of mercury and cadmium, we have seen 
 that it is also long in the monatomic gas helium. 
 
 Theory of the Spark Discharge. 
 
 192. At this stage it may be useful to give an account of 
 a theory which explains many of the peculiarities of the spark 
 discharge. On this theory, which was given by the writer in 
 a paper read before the Cambridge Philosophical Society, Feb. 
 1900, and published in the Philosophical Magazine, [5], 50, p. 278, 
 1900, the ionisation which is necessary to put the gas into the 
 conducting state required for the passage of the spark is effected 
 by means of ions which under the influence of the electric field 
 producing the spark acquire so great a velocity that when they 
 come into collision with the molecules of the gas through which 
 they are moving they ionise the molecules. We have already had 
 instances of the ionisation of a gas by rapidly moving ions in the 
 cases of cathode and Lenard rays, and we have seen that the view 
 (which was suggested by the consideration of the spark discharge) 
 that ions in a strong electric field can acquire sufficient energy to 
 enable them to act as ionising agents was of service in explaining 
 some of the phenomena connected with the discharge of electri- 
 city produced by the action of ultra-violet light. Townsend (see 
 p. 341) has shown that in the case of a gas ionised by means of 
 Rontgen rays the negative corpuscles' present in the gas can in 
 a strong electric field produce fresh ions by their collision with 
 the molecules of the gas ; we have tnus from several sources 
 direct evidence that rapidly moving negative ions can by means 
 of collision give rise to fresh ions. 
 
 Let us now consider the case of a gas between two parallel 
 metal plates, between which there is an electric field, then if there 
 were a few negative ions present these would be set in motion by 
 the field, and if the strength of the field exceeded a certain value 
 would acquire sufficient energy to ionise the molecules of the gas 
 with which they came into collision, fresh ions would be produced 
 and a current of electricity would flow through the gas. If, how- 
 ever, the conditions are such that only the negative ions in the 
 field produce fresh ions, this current will only be transitory, in a 
 short time all the negative ions will be driven up to the cathode 
 and the current will stop. If, however, the positive ions in their 
 
193] SPARK DISCHARGE. 377 
 
 journey to the cathode can produce fresh ions, then negative ions 
 are continually being produced, these under the action of the field 
 will produce new ions and so the number of the ions and the 
 conductivity of the gas will increase in geometrical progression ; 
 this increase will not, however, go on indefinitely, for with the 
 increased conductivity of the gas the strength of the electric field 
 between the plates will diminish until it falls to such a point that 
 the number of ions produced in unit time by the field is equal to 
 the number lost in the same time through the combination of the 
 ions and through the motion of the ions up to the electrodes. To 
 maintain the current it is not necessary for the positive ions to 
 produce fresh ions at all parts of the field between the electrodes, 
 it is sufficient for them to do so close to the cathode. The posi- 
 tive ions will strike against the cathode; we shall suppose that 
 under this bombardment by the positive ions the cathode emits 
 negative corpuscles in fact cathode rays so that the continuous 
 supply of negative corpuscles comes on this view from the metal 
 of the cathode stimulated by the positive ions striking against it. 
 The action of the positive ions as ionising agents is thus confined 
 to the effect produced by their impacts on the cathode, it is not 
 necessary to suppose that they, like the negative corpuscles, ionise 
 the molecules of a gas by striking against them. The expression 
 for the potential difference is however the same whether we suppose 
 that the positive ions cause the cathode to emit corpuscles by their 
 impact with it, or whether we suppose that they ionise the gas 
 close to the cathode, the positive ions in other parts of the field 
 not possessing sufficient energy to ionise the gas. 
 
 193. Before attempting to obtain by these principles the con- 
 nection between spark potential, spark length and pressure it will 
 be helpful to consider some facts as to the distribution of electric 
 force along the spark, obtained by the study of the discharge at 
 low pressures when the structure of the discharge is much more 
 obvious than it is at atmospheric pressure. This structure as w$ 
 shall see later shows many variations, but an example which may 
 be taken as typical is that shown in Fig. 107. The distribution of 
 electric intensity along the line of discharge is shown in Fig. 108. 
 Next to the cathode there is a dark space called the Crookes dark 
 space, the thickness of which does not depend upon the distance 
 between the electrodes, then comes a luminous piece called the 
 
378 
 
 SPAKK DISCHARGE. 
 
 [193 
 
 negative glow, then comes a dark space called the Faraday dark 
 space, and then a stretch of luminosity reaching to the anode, 
 
 Fig. 107. 
 
 called the positive column. From the curve giving the electric 
 intensity we see that this is approximately uniform along 
 
 01234 
 
 Positive column 
 
 12 13! 14 
 
 Negative glow 
 
 Fig. 108. 
 
 the positive column; but that in the Crookes dark space the 
 electric intensity is very much greater. The potential difference 
 
193] SPARK DISCHARGE. 379 
 
 between the cathode and the negative glow, called the cathode 
 potential fall, is as we shall see later independent of the pressure 
 of the gas or the distance between anode and cathode, as long as 
 this is greater than the thickness of the dark space. Recent 
 measurements made by Strutt have proved that the cathode fall 
 of potential is equal to the minimum spark potential. We see, 
 too, that it is only in the Crookes dark space that the electric 
 intensity is greater than in the uniform positive column, it is 
 therefore only in this space that the positive ions would be likely 
 to produce fresh ions by collisions with molecules of the gas. To 
 sum up we have a uniform electric intensity along the positive 
 column and a variable but very much greater intensity inside the 
 Crookes dark space. The thickness of the dark space does not 
 depend upon the distance between the electrodes, so that the 
 further these are apart the longer the region of uniform electric 
 intensity along the positive column. 
 
 We shall now proceed to find the connection between the 
 spark potential and the spark length. We found (p. 341) that if n 
 is the number of corpuscles per unit volume at a distance x from 
 the cathode, u the velocity of these corpuscles, X their mean free 
 path, e the charge on a corpuscle, then when the system is in a 
 steady state 
 
 where f(Xe\) is the ratio between the number of collisions which 
 produce fresh ions and the whole number of collisions, and 7 the 
 ratio of the number of collisions in which the corpuscles remain 
 attached to the molecule to the whole number of collisions. If 
 the electric field is very strong the corpuscles acquire so much 
 energy that every collision produces ions, in this ca,SGf(Xe\) = l, 
 if Xe\ falls below a certain value iheuf(Xe\) = 0, we shall sup- 
 pose that in the Crookes dark space the electric field is so strong 
 that/(ZeX) = 1, and that in the rest of the field where the electric 
 intensity is much less f(Xe\} = ftXe\ w, where ft and w are 
 constants. 
 
 From equation (1) we have 
 where n Q u is the value of nu when x 0, i.e. at the cathode; if we 
 
380 SPARK DISCHARGE. [193 
 
 put x = d in this expression we shall get the value of nu at the 
 anode, this, if no positive ions come from the anode itself, is equal 
 to i/e, where i is the current per unit area through the gas. Let us 
 first take the case where d is greater than c, the thickness of the 
 Crookes layer: then from x=Q to x = c, f(Xe\) = l ) and from 
 x = c to d, f(Xe\) = 13 Xe\ - w, hence in this case, 
 
 /^/v^\ \ dx c >Q*nr v\ ^ d w(d-c) 
 
 (f(Xe\) 7) = - 4- pe ( V VQ) , 
 
 o J ^ X X X X 
 
 where F is the fall of potential in crossing the Crookes dark 
 space, i.e. the cathode fall of potential. Hence we have from (2) 
 putting nu = i/e 
 
 Now n u is the number of corpuscles emitted in unit time by 
 unit area of the cathode. We suppose that this emission is due 
 to the bombardment of the cathode by the positive ions, and that 
 the number of corpuscles emitted per second is proportional to the 
 energy given to the cathode by the positive ions. The question 
 now arises as to the energy possessed by the ions when they strike 
 the cathode ; before they reach the Crookes space they are moving 
 in a weak part of the field, and their energy is proportional to Xe\ 
 where X is the electric intensity ; when however they get into the 
 dark space the field rapidly becomes more intense, and the energy 
 of the positive ions rapidly increases, we shall therefore get a close 
 approximation to the truth if we suppose that the energy of the 
 positive ions is given to them in the dark space, and that the energy 
 of each ion is equal to V e, V being the cathode fall of potential. 
 The number of positive ions which strike unit area of the cathode 
 in unit time is (i w w e)/e, and the energy given up by these to 
 the cathode is therefore (i w ^ e)F . We suppose that n u 
 the number of corpuscles emitted in unit time is proportional to 
 the energy of bombardment, so that 
 
 n u = k(i n u e) F , 
 where A; is a constant. 
 
 Substituting this value of n u Q in equation (3) we get 
 
 _ 
 - 
 
193] SPARK DISCHARGE. 381 
 
 hence we have 
 
 or 
 
 F= F -f- 
 
 X $e pe X* 
 
 This gives us the relation between F the spark potential, d the 
 spark length and X, which is inversely proportional to the pressure. 
 We see that the relation is a linear one, and since c is proportional 
 to X we see also that this equation satisfies Paschen's law that 
 F is a function of d/\, 
 
 We shall return to the discussion of this equation after we 
 have considered the case when d the spark length is^ftss than c, 
 i.e. when the anode comes into the Crookes dark space. In this 
 casef(Xe\) is equal to unity throughout the field, and the energy 
 with which the positive ions strike the cathode is now eFand not 
 eV , where F is the potential difference between the plates. Hence 
 we have 
 
 ,cfo? d 
 
 and n Q Uoe = k(i n u e) Ve (5). 
 
 Hence instead of equation (3) we have 
 
 from which we get 
 
 1 + kVe 
 
 or =~ 
 
 ke 
 
 A 1 
 
 from this equation we see that V the spark potential increases 
 very rapidly as d/\ diminishes ; we see too that Paschen's law is 
 again obeyed since F is a function of d/\. 
 
 If we combine equations (4) and (6), and represent the result 
 graphically by a curve whose ordinates are proportional to F and 
 abscissae to d/\, we get a curve similar to that shown in Fig. 109. 
 A reference to the figures given on pages 360 5 will show that 
 except just in the neighbourhood of the minimum spark potential 
 the theoretical curve agrees well with those determined by experi- 
 
382 
 
 SPARK DISCHARGE. 
 
 [193 
 
 ment ; we could have anticipated the want of smoothness of the 
 theoretical curve in this region, for here to simplify the calculation 
 
 Fig. 109. 
 
 we assumed values for f(Xe\) which were discontinuous at this 
 point. 
 
 It is of interest to see what light the theory throws on the 
 questions raised by the experiments. We saw that the measure- 
 ments made on the spark potential suggest (we can hardly use 
 a stronger term) that the spark potential could be expressed by 
 
 an equation of the form V=k +/(-}, where d is the spark 
 
 \X/ 
 
 length, and X the mean free path, and / a function which is the 
 same for all gases. Now for sparks whose length is greater than 
 
 the critical spark length the theory gives V= constant + ^--5 ; 
 
 /j6 A 
 
 if this is of the form under discussion (>y+w)//3e must be independent 
 of the nature of the gas : 7 measures the chance of a corpuscle 
 sticking to a molecule against which it strikes, and ft and w the 
 chance of a molecule being ionised when struck by a corpuscle 
 moving with a given velocity. We have not any independent 
 measurements of these quantities ; we should anticipate that they 
 would depend to some, although probably not to any large extent, 
 
194] SPARK DISCHARGE. 383 
 
 on the nature of the molecule. We saw too (p. 366) that there is 
 considerable evidence that for a given pressure the critical spark 
 length in different gases is proportional to the mean free paths of 
 the molecules : thus if c is the critical spark length when the free 
 path is X, c/\ is the same for all gases. 
 
 Let us now consider the minimum potential F required 
 to produce a spark ; by equations (4) and (6) this is given by the 
 equation 
 
 Thus neglecting variations in 7 we see that the values of F 
 in different gases are proportional to I/ke. From equation (5) 
 it follows that l/ke is the potential difference through which 
 a positive ion must fall in order to acquire such an amount of 
 energy that when it strikes against the cathode it produces the 
 emission of one corpuscle, either from the cathode itself or from 
 a layer of gas next the cathode. 
 
 194. This view we have taken of the spark discharge accounts 
 for the ' lag,' i.e. the interval between the application of the electric 
 field and the passage of the spark which, as we have seen, is very 
 noticeable under certain circumstances. For before the spark 
 reaches a steady state there is a preliminary stage during which 
 the number of ions is continually increasing. On the first appli- 
 cation of the field the number of ions and the current through the 
 gas is small, but in consequence of the collisions of these ions with 
 the molecules of the gas, the number of ions and the current 
 rapidly increase until finally a steady state is reached : this interval 
 is what we have called the ' lag, 5 and we see that its duration will 
 be diminished by any agent, such as ultra-violet light shining on 
 the negative electrode, which increases the number of negative 
 ions initially in the gas. 
 
 The view that the emission of negative corpuscles from the 
 cathode is due to the impact against it of the positive ions is 
 strongly supported by some experiments made by Schuster* and 
 Welmeltf on the effect of placing solid obstacles in the Crookes 
 dark space : these obstacles cast a shadow on the cathode, and 
 
 * Schuster, Proc. Roy. Soc. xlvii. p. 557, 1890. 
 t Wehnelt, Wied. Ann. Ixvii. p. 421, 1899. 
 
384 SPARK DISCHARGE. [195 
 
 from the region of this shadow there is no emission of cathode rays. 
 This effect is illustrated in Fig. 110, taken from Wehnelt's paper ; 
 in this figure D is the obstacle and K the cathode. 
 
 1 
 
 K D 
 
 Fig. 110. 
 
 Potential difference required to produce very short sparks. 
 
 195. Earhart* has made a series of experiments on the differ- 
 ence of potential required to produce sparks whose length is 
 comparable with the wave-length of sodium light ; the electrodes 
 used were steel spheres, and the connection between the spark 
 potential and the distance between the spheres is shown in Fig. Ill, 
 in which the abscissae are the spark potential and the ordinates 
 the shortest distance between the spheres. In consequence of the 
 curvature of the* electrodes, the least distance between the spheres 
 is not necessarily equal to the spark length ; thus when the 
 distance is less than the critical spark length the spark will pass, 
 not across the shortest distance, but across a place where the 
 distance is equal to the critical spark length. Thus Earhart's 
 curves do not show the increase in potential difference with 
 diminishing distance between the electrodes as they would have 
 done if they had been plane : the most interesting feature of the 
 curves is the very rapid diminution in the spark potential when 
 the distance between the electrodes falls to less than about 
 3 x 10~ 4 cm. ; when the distance is less than this the spark 
 potential falls off rapidly with the distance, and seems from 
 Earhart's results to become directly proportional to the distance. 
 The smallest potential difference actually measured was 32 volts 
 when the distance Between the electrodes was 3 x 10~ 5 cm. : this 
 is only about one-tenth of the minimum spark potential. Earhart 
 made some observations on the effect of pressure ; diminution 
 
 * Earhart, Phil. Mag. vi. 1, p. 147, 1901. 
 
195] 
 
 SPARK DISCHARGE. 
 
 385 
 
 of the pressure from three atmospheres to one atmosphere did not 
 seem to affect the discharge potential when the electrodes were 
 
 00 200 300 40O 500 600 700 800 900 1000 1100 
 
 Potential in Volts 
 Fig. 111. 
 
 very close together; when the pressure was diminished below 
 one atmosphere however the discharge potential also diminished. 
 An inspection of the curves suggests that the character of the 
 discharge changes when the electrodes are brought within a certain 
 distance of each other, or what is equally consistent with the 
 curves, when the average electric intensity, F, between the plates 
 reaches a certain value (about a million volts per cm.) : when F 
 has once reached this value Earhart's experiments suggest that 
 the discharge is determined by the condition that F, i.e. V/d, 
 if V is the potential difference and d the distance between the 
 electrodes, should have this value. These experiments raise many 
 
 25 
 
 T. G. 
 
386 SPARK DISCHARGE. [195 
 
 important points, and it is to be hoped that they will be carried 
 much further. 
 
 The following considerations seem to afford a possible explana- 
 tion of the behaviour of the discharge when the electrodes are 
 very close together. We have had occasion before to make use 
 of the hypothesis that in a metal, even at ordinary temperature, 
 free corpuscles are moving about in every direction; if these 
 corpuscles could escape from the metal under ordinary conditions 
 the metal would be unable to retain a charge of negative electricity. 
 Now one of the reasons the corpuscles do not escape is that as 
 soon as they leave the metal there is an electrostatic attraction 
 between the corpuscle and the metal equal to e 2 /4r 2 , where e is the 
 charge on the corpuscle and r the distance of the corpuscle from 
 the surface of the metal ; this attraction, unless the kinetic energy 
 with which the corpuscle leaves the metal exceeds a certain very 
 high limit, will drag the corpuscle back into the metal. Let us 
 now suppose that an external electric force F acts on the corpuscle, 
 tending to make it move away from the metal ; then if Fe is 
 comparable with e 2 /4r 2 , the external field will give appreciable 
 assistance to the corpuscle in escaping from the metal, and will 
 enable corpuscles to leave the metal, whose kinetic energy is too 
 small to enable them to escape in the absence of an external field. 
 If Fe is comparable with e 2 /4r 2 , F must be comparable with e/4r 2 . 
 Now in electrostatic measure e = 3*4 x 10~ 10 , let us put r = 10~ 7 , 
 then e/4r 2 = 8'5 x 10 3 . Now in Earhart's experiments F was about 
 10 6 volts per cm., or in electrostatic measure 3*3 x 10 3 ; this is 
 more than one-third of the value of e/4r 2 , so that if, as is quite 
 possible, r is somewhat greater than 10~ 7 , the pull exerted by the 
 external field would be able to drag the corpuscles away from the 
 metal : as soon however as corpuscles can leave the electrode, that 
 electrode will act like a cathode, and a discharge of negative 
 electricity will pass from this to the opposite electrode. If this 
 explanation is correct the discharge across these very- small 
 distances is entirely carried by the corpuscles and no part of it 
 by positive ions ; in the discharge we have previously considered, 
 corpuscles and positive ions both take a share in carrying the 
 discharge. 
 
196] 
 
 SPARK DISCHARGE. 
 
 387 
 
 Discharge when the electric field is not uniform. 
 
 196. Bailie* and Paschenf have made some very interesting 
 experiments on the potential difference required to spark between 
 spheres small enough to make the variations in the strength of 
 the electric field considerable. Bailie's results are given in table A 
 Paschen's in table B : 
 
 A. POTENTIAL DIFFERENCES. 
 Pressure 760 mm., Temp. 15 20 C. 
 
 Spark 
 Length 
 in cms. 
 
 Planes 
 
 Spheres 
 6cm. 
 diam. 
 
 Spheres 
 3cm. 
 diam. 
 
 Spheres 
 1 cm. 
 diam. 
 
 Spheres 
 6cm. 
 diam. 
 
 Spheres 
 35 cm. 
 diam. 
 
 Spheres 
 1 cm. 
 diam. 
 
 05 
 
 8-94 
 
 8-96 
 
 9-18 
 
 9-18 
 
 9-26 
 
 9-30 
 
 9-63 
 
 10 
 
 14-70 
 
 14-78 
 
 14-99 
 
 15-25 
 
 15-53 
 
 16-04 
 
 16-10 
 
 15 
 
 20-20 
 
 20-31 
 
 20-47 
 
 21-28 
 
 21-24 
 
 21-87 
 
 19-58 
 
 20 
 
 25-42 
 
 25-59 
 
 25-95 
 
 26-78 
 
 26-82 
 
 27-13 
 
 21-91 
 
 25 
 
 30-38 
 
 30-99 
 
 31-33 
 
 32-10 
 
 32-33 
 
 31-96 
 
 23-11 
 
 30 
 
 35-35 
 
 36-12 
 
 36-59 
 
 37-32 
 
 37-38 
 
 36-29 
 
 24-12 
 
 35 
 
 40-45 
 
 41-45 
 
 41-47 
 
 42-48 
 
 42-16 
 
 39-39 
 
 25-34 
 
 40 
 
 45-28 
 
 46-34 
 
 46-77 
 
 47-62 
 
 46-34 
 
 41-77 
 
 26-03 
 
 45 
 
 50-48 
 
 51-46 
 
 51-60 
 
 51-56 
 
 50-44 
 
 43-76 
 
 26-62 
 
 40 
 
 44-80 
 
 45-00 
 
 45-00 
 
 45-50 
 
 44-80 
 
 41-07 
 
 26-58 
 
 45 
 
 49-63 
 
 50-33 
 
 49-63 
 
 52-04 
 
 48-42 
 
 43-29 
 
 28-49 
 
 50 
 
 54-35 
 
 55-06 
 
 54-96 
 
 54-66 
 
 53-25 
 
 47-21 
 
 30-00 
 
 60 
 
 63-82 
 
 65-23 
 
 65-23 
 
 65-23 
 
 59-69 
 
 53-75 
 
 31-51 
 
 70 
 
 74-09 
 
 ' 75-40 
 
 73-79 
 
 72-28 
 
 64-22 
 
 56-47 
 
 32-92 
 
 80 
 
 84-83 
 
 87-98 
 
 84-76 
 
 77-61 
 
 67-75 
 
 58-79 
 
 33-82 
 
 90 
 
 94-72 
 
 97-44 
 
 94-62 
 
 80-13 
 
 70-56 
 
 59-09 
 
 34-93 
 
 1-00 
 
 105-49 
 
 112-94 
 
 104-69 
 
 83-05 
 
 72-38 
 
 59-49 
 
 36-24 
 
 We see from the tables that with a given spark length between 
 two equal spheres, one charged and insulated and the other put to 
 earth, the potential difference varies with the diameter of the 
 spheres; starting with planes the potential difference at first 
 increases with the curvature and attains a maximum when the 
 sphere has a certain diameter. This critical diameter depends 
 upon the spark length, the shorter the spark the smaller the 
 critical diameter. 
 
 * Bailie, Annales de Chimie et de Physique [5], xxv. p. 486, 1882. 
 t Paschen, Wied. Ann., xxxvii. p. 79, 1889. 
 
 252 
 
388 SPARK DISCHARGE. 
 
 B. SHORT SPARKS. LONG SPARKS. 
 
 [11 
 
 Spark 
 Length 
 in cms. 
 
 Spheres 
 1 cm. 
 radius 
 
 Spheres 
 5 cm. 
 radius 
 
 Spheres 
 25 cm. 
 radius 
 
 01 
 
 3-8 
 
 3-42 
 
 3-61 
 
 02 
 
 5-04 
 
 5-18 
 
 5-58 
 
 03 
 
 6-62 
 
 6-87 
 
 6-94 
 
 04 
 
 8-06 
 
 8-82 
 
 8-43 
 
 05 
 
 9-56 
 
 9-75 
 
 9-86 
 
 06 
 
 10-81 
 
 10-87 
 
 11-19 
 
 07 
 
 11-78 
 
 12-14 
 
 12-29 
 
 08 
 
 13-40 
 
 13-59 
 
 13-77 
 
 09 
 
 14-39 
 
 14-70 
 
 14j89 
 
 10 
 
 15-86 
 
 15-97 
 
 16-26 
 
 . -11 
 
 16-79 
 
 17-08 
 
 17-26 
 
 12 ' 
 
 18-28 
 
 18-42 
 
 18-71 
 
 14 v 
 
 20-52 
 
 20-78 
 
 21-26 
 
 Spark 
 Length 
 in cms. 
 
 Spheres 
 1 cm. 
 
 radius 
 
 Spheres 
 5 cm. 
 radius 
 
 Spheres 
 25 cm. 
 radius 
 
 10 
 
 15-96 
 
 16-11 
 
 16'45 
 
 15 
 
 21-94 
 
 22-17 
 
 22-59 
 
 20 
 
 27-59 
 
 27-78 
 
 28-18 
 
 25 
 
 32-96 
 
 33-42 
 
 33-60 
 
 30 
 
 38-59 
 
 39-00 
 
 38-65 
 
 35 
 
 43-93 
 
 44-32 
 
 43-28 
 
 40 
 
 49-17 
 
 49-31 
 
 47-64 
 
 45 
 
 54-37 
 
 54-18 
 
 51-56 
 
 50 
 
 5971 
 
 59-03 
 
 54-57 
 
 55 
 
 64-60 
 
 63-35 
 
 57-27 
 
 60 
 
 69-27 
 
 67-80 
 
 59-95 
 
 V -70 
 
 ' J 78-51 
 
 75-04 
 
 63-14 
 
 80 
 
 ' 87-76 
 
 81-95 
 
 66-39 
 
 90 
 
 
 
 68-65 
 
 1-00 
 
 
 ; 
 
 70-6 
 
 1-20 
 
 
 
 74*94 
 
 1-50 
 
 
 
 79-42. 
 
 The results given in these tables show that when the spheres 
 .are very small the potential difference required to produce a spark 
 
 Fig. 112. 
 
197] 
 
 SPARK DISCHARGE. 
 
 389 
 
 of given length is, if the spark is not too short, very much less 
 than the potential required to produce the same length of spark 
 between parallel planes, and that the spark potential difference 
 with points as electrodes only increases slowly with the length of 
 the spark. The effect of the shape of the electrode on the spark 
 length is shown by the curves represented in Fig. 112, which is 
 taken from a paper by De la Rue and Miiller*. The curves give 
 the relation between . spark potential and spark length for two 
 planes, two spheres one 3 cm. in radius, the other 1*5 cm. in 
 diameter, two coaxial cylinders, a plane and a point, and two 
 points. 
 
 197. Schusterf has by the aid of Kirchhoff's solution of the 
 problem of the distribution of electricity over two spheres, calcu- 
 lated from Bailie's and Paschen's results the maximum electric 
 intensity in the field before the spark passed: the results for 
 Bailie's experiments are given in the following table. 
 
 Spark 
 Length 
 in cms. 
 
 Planes 
 
 Spheres 
 6 cm. 
 diam. 
 
 Spheres 
 3cm. 
 diam. 
 
 Spheres 
 1cm. 
 diam. 
 
 Spheres 
 6cm. 
 diam. 
 
 Spheres 
 35 cm. 
 diam. 
 
 Spheres 
 1 cm. 
 diam. 
 
 05 
 
 179 
 
 180 
 
 186 
 
 190 
 
 197 
 
 206 
 
 292 
 
 10 
 
 147 
 
 149 
 
 153 
 
 163 
 
 176 
 
 198 
 
 376 
 
 15 
 
 135 
 
 138 
 
 141 
 
 157 
 
 170 
 
 206 
 
 425 
 
 20 
 
 127 
 
 131 
 
 137 
 
 154 
 
 170 
 
 219 
 
 460 
 
 25 
 
 122 
 
 127 
 
 134 
 
 154 
 
 180 
 
 236 
 
 478 
 
 30 
 
 118 
 
 124 
 
 130 
 
 156 
 
 189 
 
 253 
 
 494 
 
 35 
 
 116 
 
 122 
 
 129 
 
 159 
 
 197 
 
 263 
 
 516 
 
 40 
 
 113 
 
 122 
 
 129 
 
 164 
 
 204 
 
 272 
 
 528 
 
 45 
 40 
 
 112 
 
 120 
 
 127 
 
 166 
 
 214 
 
 278 
 
 540 
 
 112 
 
 118 
 
 124 
 
 157 
 
 197 
 
 268 
 
 539 
 
 45 
 
 110 
 
 119 
 
 122 
 
 167 
 
 206 
 
 275 
 
 578 
 
 50 
 
 109 
 
 117 
 
 125 
 
 166 
 
 218 
 
 296 
 
 608 
 
 60 
 
 106 
 
 116 
 
 125 
 
 181 
 
 233 
 
 327 
 
 639 
 
 70 
 
 106 
 
 117 
 
 126 
 
 188 
 
 234 
 
 339 
 
 667 
 
 80 
 
 106 
 
 123 
 
 130 
 
 192 
 
 250 
 
 349 
 
 685 
 
 90 
 
 105 
 
 120 
 
 132 
 
 191 
 
 255 
 
 349 
 
 708 
 
 1-00 
 
 106 
 
 128 
 
 133 
 
 194 
 
 258 
 
 349 
 
 733 
 
 It will be seen that the smaller the spheres, i.e. the more 
 irregular the electric field, the greater the maximum electric 
 
 * De la Rue and Miiller, Phil Tram. 1878, Pt. i. p. 55. 
 t Schuster, Phil. Mag., v. 29, p. 182, 1890. 
 
390 SPARK DISCHARGE. [197 
 
 intensity. We must be careful to distinguish between the electric 
 field before the spark passes and the electric field during the 
 discharge or even during the interval between the application of 
 the potential difference and the passage of the discharge, for during 
 this interval ions are moving about in the field and producing 
 fresh ions ; both of these effects will modify the distribution of the 
 electric field. Thus to take an example, suppose we have a nega- 
 tively electrified point near to a positively electrified plate ; if 
 there are no ions in the field the electric force would be a 
 maximum at the point, and would steadily diminish as we 
 approach the plate ; if, however, there are ions present in the 
 neighbourhood of the point the negative ions will be repelled 
 from the point, while the positive ions will be pulled into it ; 
 this will have the effect of increasing the electric intensity at 
 a distance from the point at the expense of that close to the 
 point : if the negative ions congregate at the plate, so as to form 
 a layer of negative electrification close to the plate, the electric 
 intensity at the plate may rise to very high values. This is what 
 actually occurs, for Mr Blyth has measured at the Cavendish 
 Laboratory the distribution of electric intensity between a point 
 and a plate when the discharge is passing, and has shown that 
 it is large close to the point, is then comparatively small for 
 some distance but becomes large again close to the plate. 
 
 The alteration of the electric field during the 'lag' will explain 
 why a spark does not necessarily pass when one or both of the 
 electrodes are small, even although the potential difference between 
 one of the electrodes a and a point in the field P near to A 
 (calculated on the assumption that there are no ions in the field) 
 is greater than that required to produce a spark of length aP 
 between plane electrodes, for during the 'lag' the movement of 
 the ions in the field may have so reduced the potential difference 
 between a and P that it is less than that required to produce 
 a spark of length aP. 
 
 Although the processes going on during the lag may reduce the 
 inequalities in the electric field between small electrodes they 
 cannot be expected to remove them entirely, and when the field is 
 far from uniform, as is the case with pointed electrodes, we can 
 easily see that the potential difference required to produce a long 
 spark is less than that required to produce a spark of the same 
 
198] 
 
 SPARK DISCHARGE. 
 
 391 
 
 length between plane electrodes. For let the curve APQ (Fig. 
 113) represent the distribution of potential between small elec- 
 trodes AB, and let CD be the curve which represents the potential 
 
 Fig. 113. 
 
 difference required to produce a spark in a uniform field (the 
 ordinate of a point on CD represents the spark potential required 
 to produce a spark whose length is equal to the abscissa of the 
 point); then we see that although the potential difference BQ 
 between the small electrodes may be less than BD, that required 
 to produce a spark of length AB in a uniform field, the two curves 
 may intersect ; if they do so at P, then a spark will pass from 
 A to P, the whole potential difference will be thrown on the 
 region between P and B, so that the strength of this part of the 
 field will increase and the spark will travel on to B. 
 
 198. When the electrodes are of different sizes Faraday* 
 found that the spark potential is different according as the smaller 
 electrode is positive or negative ; De la Rue and Mtillerf also 
 observed the same effect; according to WesendonckJ this differ- 
 ence only occurs when a brush discharge accompanies the spark, 
 when the conditions are such that the discharge passes entirely 
 as a spark the spark potential is the same whichever way the spark 
 passes. 
 
 * Faraday, Experimental Researclies, 1480. 
 
 t De la Rue and Muller, Phil. Trans., 1878, Pt. i. p. 55. 
 
 J Wesendonck, Wied. Ann., xxviii. p. 222. 
 
392 SPARK DISCHARGE. [199 
 
 Pressure in the Spark. 
 
 199. The ions in the electric field acquire kinetic energy and 
 as the pressure in a gas is proportional to the kinetic energy 
 per unit volume the pressure along the path of the spark will be 
 increased. This increase in pressure may be very large ; for it is 
 easy to show that the kinetic energy given to the ions, when a 
 quantity of electricity equal to Q passes through the spark, is equal 
 to VQ, where V is the spark potential. To take an example, let 
 us suppose that we have a spark one cm. long through air at atmo- 
 spheric pressure, and that we discharge by this spark the charge 
 in a condenser of 1000 cm. capacity charged to the potential 
 difference required to produce the spark, this potential difference 
 is about 30000 volts, i.e. 100 in electrostatic units, hence in this 
 case F=10 2 and Q = 10 2 x 10 3 , thus the energy given to the gas 
 is 10 7 ergs. Now if this energy were distributed throughout 1 c.c. 
 of gas it would increase the pressure by 6'6 atmospheres, it is 
 however confined to the very much smaller volume traversed by 
 the spark, the pressure in this region will be proportionately 
 greater ; to take -^ of a c.c. as the volume of gas traversed by 
 the spark would probably be a very large over-estimate, and yet 
 even if the volume were no less than this the initial pressure 
 along the path of the spark would be 660 atmospheres. This 
 high pressure would spread as a pulse from the region of the 
 spark-gap, the pressure in the pulse, when this had got so far 
 from the spark-gap that it might be regarded as spherical, 
 varying inversely as the square of the distance from the spark - 
 
 A well-known instance of the effects produced by this pressure 
 is what is called the ' electrical bomb/ where a loosely-fitting plug 
 in a closed vessel is blown out when a spark passes through the 
 vessel. The effect can easily be observed if a pressure-gauge, in 
 which the pressure is indicated by the motion of a small quantity 
 of a light liquid, is attached to an ordinary discharge-tube, the 
 pressure in the gas being most conveniently from 2 to 10 mm. 
 of mercury. At the passage of each spark there is a quick move- 
 ment of the liquid in the gauge as if it had been struck by a blow 
 coming from the tube ; immediately after the passage of the spark 
 
199] SPARK DISCHARGE. 393 
 
 the liquid in the gauge springs back within a short distance of its 
 position of equilibrium and then slowly creeps back the rest of the 
 way. This latter effect is probably due to the slow escape of the 
 heat produced by the passage of the spark, the gauge behaves 
 just as it would if a wave of high pressure rushed through the 
 gas when the spark passed. The increased pressure due to the 
 discharge has been described by Meissner* and by De la Rue 
 and Miillerf. 
 
 The existence of a pulse spreading from the spark has been 
 beautifully demonstrated by ToplerJ who studied by the method 
 of instantaneous illumination the region round the spark imme- 
 diately after it had passed. As the density of the air in the pulse 
 differs from that of the surrounding gas, the pulse is optically 
 different from the rest of the field and so can be made visible. 
 Fig. 114 a, taken from Topler's paper, represents the appearance 
 
 Fig. 114. 
 
 of the field looking so as to see the whole length of the spark, 
 Fig. 114 6 the appearance when the spark is looked at end-on. 
 
 Tb'pler noticed that the initial disturbance close to the spark 
 gap showed periodic expansions and contractions, as if the regions 
 of greatest disturbance were distributed at equal intervals along 
 the length of the spark. There was an exceptionally large pro- 
 tuberance in the neighbourhood of the cathode. 
 
 * Meissner, Abhand. der kimig. Geselhchaft Gottingen, xvi. p. 98, 1871. 
 
 t De la Rue and Miiller, Phil. Trans., 1880, p. 86. 
 
 Topler, Pogg. Ann., cxxxi. pp. 33, 180, 1867 ; cxxxiv. p. 194, 1868. 
 
394 SPARK DISCHARGE. [199 
 
 In an experiment due to Hertz which also illustrates well 
 the explosive effects due to the spark the explosion seemed to be 
 more vigorous at the anode than at the cathode*; in this experi- 
 ment the anode was placed at the bottom of a glass tube with 
 a narrow mouth, while the cathode was placed outside the tube 
 and close to the open end. The tube and the electrodes -were in 
 a bell-jar filled with dry air at a pressure of 40 50 mm. of 
 mercury. When the discharge from a Leyden jar charged by 
 an induction coil passed through the tube, the glow accompanying 
 the discharge was blown out of the tube and extended several 
 centimetres from the open end; the effect was not so marked when 
 the electrodes were reversed. 
 
 Haschek and Machef by measuring the pressure at the surface 
 of a vessel through which sparks from a high tension transformer 
 were passing have calculated the pressure in the spark ; with brass 
 electrodes amj sparks 3 mm. long they estimated the pressure of 
 the spark in air at a pressure of 704 mm. of mercury'as 51*7 atmo- 
 spheres, in carbonic acid at the same pressure 52*2 atmospheres, 
 and in coal gas as 72'7 atmospheres ; they found that the pressure 
 in the spark was, as might be expected from the diminution in 
 the spark potential, less wheijjtfthe pressure of the gas through 
 which the spark passed was* low than when it was high : thus in 
 one of their experiments Jftie pressure in the spark was estimated 
 by them to be 27 '2 atmospheres when the pressure of the air was 
 585 mm. of mercury, when the air pressure was reduced to 96 mm. 
 of mercury the spark pressure fell to one atmosphere. They found 
 too that the spark pressure depended upon the nature of the 
 electrodes; thus under similar conditions they found that the 
 spark pressures in air with electrodes of carbon, iron and brass 
 were respectively 124, 79, 64 atmospheres. When as in these 
 experiments sparks follow each other in rapid succession, the spark 
 is carried to a considerable extent by the metallic vapour from the 
 electrode. 
 
 Haschek and Exner J and Mohler have published estimates of 
 
 the spark pressure derived from observations of the displacement 
 
 
 
 * Hertz, Wied. Ann., xix.*p. 87, 1893. 
 t Haschek and Mache, Wied. Ann., Ixviii. p. 740, 1899. 
 Haschek and Exner, Wien. Sitzungs., cvi. p. 1127, 1897. 
 Mohler, Astrophysical Journal, iv. p. 175, 1896. 
 
200] SPARK DISCHARGE. 395 
 
 of the lines in the spectrum of the spark due to the electrode. 
 Humphreys* has shown that the effect of increased pressure in 
 the vapour of a metal is to displace the lines towards the red end 
 of the spectrum, and has measured the. displacement for various 
 pressures ; hence if we assume that the displacement of the lines 
 in the spark spectrum is due to the pressure of the spark, if we 
 measure this displacement we can deduce the pressure in the spark. 
 
 The magnitude of the pressures in the spark explains the 
 mechanical effects produced by sparks, such as the perforation of 
 pieces of cardboard or thin plates of glass. 
 
 Heating Effects produced by Sparks. 
 
 200. A large part of the energy given to the ions during 
 the discharge will appear as heat and will raise the tempera- 
 ture of the gas and the vessel in which it is contained. 
 Measurements of the heat produced by sparks have been made 
 by Riessf, PaalzowJ, G. Wiedemann, Naccari and Bellati||, Pog- 
 gendorfff, Dewar**, Rollmannff, Naccarift, Villari, Mugna|||| : 
 measurements in absolute measure have been made by Heyd- 
 willerTfl and Kauffmann***. These experiments have mostly 
 been made on the heat developed by the sparks produced by 
 discharging Leyden jars ; the most 'definite result obtained is that- 
 the heat produced in the spark ga^ is only a small fraction of 
 the energy in the jar before it was discharged. The discharge of 
 the jar is oscillatory, so that in this case we have a series of 
 sparks following one another across the gap in quick succession ; 
 under these circumstances there is a great tendency for the spark 
 to change into an arc, and in the arc the potential difference 
 
 * Humphreys, Astrophysical Journal, vi. p. 169, 1897. 
 
 f Eiess, Eeibungselektricitdt. 
 
 J Paalzow, Pogg. Ann., cxxvii. p. 126, 1866. 
 
 G. Wiedemann, Pogg. Ann., clviii. p. 35, 1876. 
 || Naccari and Bellati, Beib., ii. p. 720, 1878. 
 
 IT Poggendorff, Pogg. Ann., xciv. p. 632, 1855. 
 ** Dewar, Proc. Roy. Soc. Edin., vii. p. 699, 1872. 
 ft Kollmann, Pogg. Ann., cxxxiv. p. 605, 1868. 
 JJ Naccari, Att. di Torino, xvii. p. 1, 1882. 
 
 Villari, Beib., iii. p. 713 ; iv. p.-404; v. p. 460; vi. p. 699 ; vii. p. 782. 
 
 Ill) Mugna, Beib., vi. p. 953. 
 
 1H1 Heydwiller, Wied. Ann., xliii. p. 310, 1891 ; Ixi. p. 541, 1897. 
 *** Kauffmann, Wied. Ann., Ix. p. 653, 1897. 
 
396 SPARK DISCHARGE. [201 
 
 between the electrodes, and therefore the heat produced by a 
 given current, is very much less than for the spark. The relation 
 between the electromotive force and the current in the case of the 
 discharge through gases is in general so different from that for 
 metals that it is somewhat misleading to speak of the resistance 
 of the spark gap : it may, however, give some idea of the small 
 amount of energy dissipated in the spark gap to say that the 
 heating effect for sparks six millimetres long has been found in 
 some cases investigated by Miss Brooks* to be not greater than 
 that which would have occurred if a wire about 2 ohms resist- 
 ance occupied the position of the spark. 
 
 201. Schuster and Hemsalechf have made some very interest- 
 ing researches on the constitution of sparks following rapidly one 
 after another, such as are produced by the oscillatory discharge of 
 a Leyden jar. The sparks were photographed on a rapidly moving 
 film mounted on the rim of a wheel making about 30 revolutions 
 per second, the motion of the film was at right angles to the length 
 of the spark, so that the line traced on the film by a source of 
 light moving with finite velocity along the spark length would be 
 inclined to the direction of the spark, and its inclination would 
 (if the velocity of the film were known) give the velocity of the 
 source of light. By sending the light from the spark on its way 
 to the film through a spectroscope the velocity corresponding to 
 any line in the spectrum could be determined. 
 
 The conclusion arrived at by the authors from these experi- 
 ments is that the first spark passes through air, but that if the 
 sparks follow each other in rapid succession (as they do when pro- 
 duced by the oscillatory discharge of a Leyden jar) and are not 
 too long the succeeding ones pass through the vapour of metal, the 
 electrodes being vaporised by the heat produced by the first spark. 
 This view is confirmed by a very interesting experiment made by 
 the authors : they found that if self-induction was put into the 
 spark circuit by which the jars were discharged the air lines almost 
 disappeared from the spectrum of the spark while the metal lines 
 were very bright: the self-induction increases the time the oscilla- 
 tions last and so enables the vapour of the metal to get well diffused 
 
 * Miss Brooks, Phil. Mag., vi. 2, p. 92, 1901. 
 
 t Schuster and Hemsalech, Phil Trans. 1899, vol. cxciii. p. 189. 
 
202] SPARK DISCHARGE. 397 
 
 through the spark gap, the discharge passing for by far the greater 
 part of the time through the vapour so that most of the energy is 
 spent in heating this and not the air. 
 
 The authors found that the velocity of the metallic vapours in 
 the spark was greater for the metals of low atomic weight than 
 for those of high ; thus the velocity of aluminum vapour was 1890 
 metres per second, that of zinc and cadmium only about 545. 
 
 The very interesting result was obtained that the velocities 
 of the vapours of some metals and especially of bismuth indicated 
 by some of the lines in the spectrum were not the same as those 
 indicated by other lines, thus in bismuth some of the lines indi- 
 cated a velocity of 1420 metres per second, others a velocity of only 
 about 550, while one line (X = 3793) gave a still smaller velocity. 
 This result raises some very interesting questions, as for instance 
 whether bismuth is a mixture of different elements, some of the 
 lines in the spectrum being due to one constituent, others to the 
 other constituents ; ano.ther possibility is that the molecules even 
 of an element are not all of the same kind, and that the different 
 lines in the spectrum are emitted by molecules of different kinds ; 
 we should also get a similar effect if the relative intensities of 
 the lines varied greatly with the kinetic energy possessed by a 
 molecule, if for example the intensity of a line a was very much 
 greater than that of a line /3, for a rapidly moving molecule, and 
 very much less for a slowly moving one, then, if the molecules of 
 the vapour were projected with different velocities, the line a would 
 indicate a higher velocity than ft ; on these points Schuster and 
 Hemsalech reserve their opinion until they have made further 
 experiments. 
 
 Effect of a Magnetic Field on the Spark. 
 
 202. We shall see later on that a magnetic field produces a 
 very great effect on the discharge through gases when the pressure 
 is low. At atmospheric pressure, however, the effects on the spark 
 itself are very slight, although the halo of luminous gas which 
 surrounds the course of the sparks when a number of sparks 
 follow each other in rapid succession is drawn out into a broad 
 band by the magnetic field. This halo, it may be observed, is 
 deflected by a current of air though the spark itself is not affected. 
 
398 SPARK DISCHARGE. [203 
 
 Precht* has observed a distinct effect of a magnet on a spark at 
 atmospheric pressure when the sparks pass between a sharp point 
 and a blunt wire ; the spark is deflected by a transverse magnetic 
 field in the same direction as a flexible wire conveying a current 
 in the same direction as that passing through a spark would be 
 deflected. He found, too, that the magnetic field affected the 
 spark potential; thus when the distance between the electrodes 
 was 8 mm. and the transverse magnetic force 7017 he found that 
 when the pointed electrode was the anode, the rounded one the 
 cathode, the magnetic field reduced the spark potential from 8670 
 volts to 7520 volts, while when the point was cathode, the rounded 
 electrode anode the same magnetic field increased the potential 
 from 6250 to 6450 volts. 
 
 Appearance of Long Sparks. 
 
 
 
 203. When sparks are of considerable length they exhibit a 
 branched appearance, as shown in Fig. 115, the branches pointing 
 
 Fig. 115. 
 
 to the negative electrode ; the electricity flowing along those 
 branches which terminate abruptly must ultimately find its way to 
 the electrodes by a dark discharge. The appearance of the spark 
 is different at the positive and negative terminals, there is a single 
 straight stem at the positive, while at the negative the discharge 
 is divided into several threads. The spark along its course 
 exhibits abrupt changes in direction as if it made its way by 
 a series of jumps rather than as an uninterrupted stream. 
 
 * Precht, Wied. Ann., Ixvi. p. 676, 1896. 
 
205] SPARK DISCHARGE. 399 
 
 Discharge of Electricity from Points. 
 
 204. A very interesting case of electric discharge is that 
 between a sharply pointed electrode, such as a needle, and a neigh- 
 bouring metallic electrode of considerable area. In this case the 
 luminosity is confined at atmospheric pressure to the neighbourhood 
 of the electrode, the current through the rest of the gas is carried 
 almost entirely by ions of the same sign as the charge on the point. 
 
 Chattock (see page 53) has shown that the velocity of these 
 ions under unit electric force is the same as that of the ions pro- 
 duced by Rontgen or Becquerel rays, and Townsend (see page 29) 
 has shown that the charge on the ions is also the same. If the 
 point is placed at right angles to a large metal plane, then for 
 electricity to stream from the point the potential of the point 
 must exceed^ that of the plane by an amount called by v. Rontgen * 
 the minimum potential ; this minimum potential depends upon 
 the sharpness of the point, the pressure and nature of the gas and 
 the sign of the electrification of the point, being less if the point 
 is negatively than if it is positively electrified ; according to War- 
 burg f, the minimum potential does not depend upon the distance 
 of the point from the plane. When the potential difference be- 
 tween the point and the plane exceeds the * minimum potential ' 
 a current of electricity passes from the point to the plane; the 
 magnitude of this current for a given potential difference between 
 the point and the plane rapidly diminishes as the distance from 
 the plane increases: Warburg (I.e.) has shown that if d is the 
 shortest distance between the point and the plane, then for a given 
 difference of potential the current is proportional to I/d 3 ' 17 , this 
 law holds whatever be the sharpness of the point. 
 
 Value of the Minimum Potential. 
 
 205. As this depends upon the sharpness of the point we can 
 only compare the values of this quantity for the same point under 
 different circumstances. The following table gives the value for 
 
 * v. Rontgen, Gottingen. Nach. p. 390, 1878. 
 t Warburg, Wied. Ann., Ixvii. p. 69, 1899. 
 
400 
 
 SPARK DISCHARGE. 
 
 [205 
 
 the minimum potential with the same point at different pressures 
 as determined by Tamm* : 
 
 Pressure in cm. of mercury 
 
 Point - 
 
 Point + 
 
 76 
 
 2140 volts 
 
 3760 volts 
 
 70 
 
 2135 
 
 3755 
 
 60 
 
 2105 
 
 3705 
 
 50 
 
 2035 
 
 3585 
 
 40 
 
 1905 
 
 3350 
 
 30 
 
 1690 
 
 2970 
 
 20 
 
 1360 
 
 2390 
 
 10 
 
 910 
 
 1580 
 
 Thus the change in the minimum potential with the pressure 
 is very slow when the pressures are high but becomes much faster 
 at lower pressures. 
 
 The ratio of the minimum potential for positive and negative 
 points is approximately the same at all pressures. Observations 
 of the minimum potential in different gases have been made by 
 v. Rontgen f and by Precht J; the results of their observations are 
 given in the following table, the numbers in the first two columns 
 are due to v. Rontgen, those in the third and fourth to Precht. 
 
 
 Minimum potential, point + 
 
 Minimum potential, pressure 
 760 mm. 
 
 Gas 
 
 
 
 
 Pressure 205 mm. 
 
 Pressure 110 mm. 
 
 Point + 
 
 Point - 
 
 H 2 .... 
 
 1296 volts 
 
 1174 volts 
 
 2125 volts 
 
 1550 volts 
 
 2 .... 
 CO .... 
 
 2402 
 2634 
 
 1975 
 2100 
 
 2800 
 
 2350 
 
 CH 4 .... 
 
 2777 
 
 2317 
 
 
 
 NO .... 
 
 3188 
 
 2543 
 
 
 
 C0 2 .... 
 
 3287 
 
 2655 
 
 3475 
 
 2100 
 
 N 2 .... 
 
 
 
 2600 
 
 2000 
 
 Air .... 
 
 
 
 2750 
 
 2050 
 
 * Tamm, Drude's Ann., vi. p. 259, 1901. 
 
 t v. Rontgen, Gottingen. Nach., 1878, p. 390. 
 
 J Precht, Wied. Ann., xlix. p. 150, 1893. 
 
206] SPARK DISCHARGE. 401 
 
 Connection between Potential Difference and Current. 
 
 206. Warburg (I.e.) found that using the same point and keep- 
 ing it at the same distance from the plate the relation between 
 the current i and the potential V can be expressed by the relation 
 
 where M is the minimum potential. Sieveking* considered that 
 the linear relation i = b ( V M) represented his experiments with 
 sufficient accuracy: in a recent paper by Tammf this question is 
 discussed, and a formula of the type of Warburg shown to give 
 better agreement: in place of the minimum potential M Tamm 
 writes J (M l + M^) where M 1 is the potential at which the discharge 
 begins when the potential is gradually increased, M 2 that at which 
 it leaves off when it is gradually lowered, the two are not identical 
 the latter being the smaller : the application of the formula in 
 this form is limited to potential differences considerably greater 
 than M. 
 
 The current with the same potential difference increases as the 
 pressure diminishes, this is shown by the following results due to 
 Tamm (1. c.). (See Tables, p. 402.) 
 
 It will be noticed that the current with the point positive is 
 always less than that with the point negative, the potential differ- 
 ence being the same in the two cases. The increase of the current 
 as the pressure diminishes is more rapid at small pressures than 
 at high pressures ; the current seems to be roughly proportional 
 to the reciprocal of the pressure, while at low pressures it varies 
 as the square of this quantity. 
 
 Tamm gives as the relation between i x the current at a pres- 
 sure of x centimetres, and i 78 the current at 76 cm. pressure, the 
 potential difference being V in both cases, the empirical equation 
 
 76 3/T , 76 
 
 * Sieveking, Drude's Ann., i. p. 299, 1900. 
 t Tamm, Drude's Ann., vi. p. 259, 1901. 
 T. G. 26 
 
402 
 
 SPARK DISCHARGE. 
 
 [207 
 
 Current in micro-amperes. 
 
 Potential difference... 
 Pressure 
 
 -4000 
 
 -6000 
 
 -8000 
 
 -10000 
 
 76 
 
 1-4 
 
 4-2 
 
 8-0 
 
 13'4 
 
 70 
 
 1-6 
 
 4-6 
 
 8-6 
 
 14-5 
 
 60 
 
 2-0 
 
 57 
 
 10-5 
 
 17-6 
 
 50 
 
 2-6 
 
 7-8 
 
 13-7 
 
 22-8 
 
 40 
 
 3-7 
 
 11-3 
 
 20-4 
 
 33-7 
 
 30 
 
 6-8 
 
 19-5 
 
 35'3 
 
 58-0 
 
 20 
 
 14-6 
 
 44.7 
 
 80-9 
 
 134-2 
 
 Potential difference... 
 
 + 4000 
 
 + 6000 
 
 + 8000 
 
 + 10000 
 
 Pressure in cm. of Hg. 
 
 
 
 
 
 76 
 
 0-7 
 
 2-1 
 
 4-8 
 
 9-3 
 
 70 
 
 0-8 
 
 2-3 
 
 51 
 
 10-1 
 
 60 
 
 1-0 
 
 2-8 
 
 6-3 
 
 12-3 
 
 50 
 
 1-3 
 
 3-8 
 
 8'2 
 
 16-0 
 
 40 
 
 1-9 
 
 5-6 
 
 12-3 
 
 23-5 
 
 30 
 
 3-3 
 
 9-7 
 
 21-1 
 
 40-4 
 
 20 
 
 7-3 
 
 224 
 
 48-0 
 
 93-0 
 
 207. Warburg* has shown that the presence of minute traces 
 of oxygen in gases such as hydrogen or nitrogen produces a great 
 diminution in the current from a negative point while it has but 
 little effect on that from a positive one ; thus the removal of a trace 
 of oxygen from nitrogen increased the current from a negative point 
 in that gas fifty times ; this may be taken as indicating that 
 oxygen has a great tendency to collect round the carriers of the 
 negative charge and either make them less efficient as ionisers or 
 else make them move more slowly in the electric field. 
 
 208. Warburgf ^ as investigated the proportion of current 
 received at different portions of the plane opposite the electrified 
 point ; he finds that the amount received per unit area at a point 
 Q on the plane is proportional to cos m 6 where 6 is the angle QPO, 
 P being the electrified point and the normal from P on the 
 
 * Warburg, Drude's Ann., ii. p. 295, 1900. 
 t Warburg, Wied. Ann., Ixvii. p. 69, 1899. 
 
209] SPARK DISCHARGE. 403 
 
 plane, the electrified conductor is supposed to be at right angles 
 to the plane ; he finds that m for a negatively electrified point is 
 equal to 4*65, for a positively electrified point 4*82, and that it is 
 independent of the sharpness of the point. 
 
 The Electrical Wind. 
 
 209. The current of electrified ions which constitutes the dis- 
 charge from the point sets the air in the neighbourhood in motion. 
 For when the ions have settled down into the state in which their 
 velocity is proportional to the electric force acting upon them 
 the mechanical force acting upon them is transferred to the air 
 through which they are moving, this gives rise to currents of air 
 directed from the point, and these air currents are what is known 
 as the electrical wind. This motion of the air forwards is accom- 
 panied by a reaction on the point, tending to drive it backwards. 
 This reaction has been measured by Arrhenius*, who finds that 
 when positive electricity is escaping from a point into air the 
 reaction tending to drive the point backwards is, when the 
 current is kept constant, proportional to the pressure of the gas, 
 and for different gases at the same pressure (air, hydrogen, and 
 carbonic acid) varies as the square root of the molecular weight 
 of the gas. The reaction when an equal current of negative 
 electricity is escaping from the point is much less, the proportion 
 between the two depending on the pressure of the gas; thus in air 
 at a pressure of 70 cm. the reaction on the positive point was 
 1*9 times that of the negative, at 40 cm. 2*6 times, at 20 cm. 3'2 
 times, at 10'3 cm. 7 times, and at 5'1 cm. 15 times the reaction of 
 the negative point. The reaction on the discharging point is due 
 to the repulsion between the electrified point and the ions carry- 
 ing the discharge ; we can easily calculate this force. Suppose that 
 the needle from which the electricity is discharged points in the 
 direction of the axis of z ; let p be the density of the ions at any 
 part of the field, Z the electric force at the same point, then F, 
 the force parallel to z acting on the ions, is equal to 
 
 jjjZpdxdydz ; 
 
 I but if w is the velocity of the ion parallel to z, w = kZ where k is 
 
 I , - 
 
 * Arrhenius, Wied. Ann., Ixiii. p. 305, 1897. 
 
 262 
 
404 SPARK DISCHARGE. [209 
 
 the velocity of the ion under unit electric force ; substituting this 
 value for Z we get 
 
 F= I j pdxdydz] 
 
 but if i is the current 
 
 i jjwpdxdy, 
 
 hence if k is constant throughout the field 
 
 (1). 
 
 The reaction on the point is equal to F, hence for a constant 
 
 current F varies inversely as k ; this conclusion agrees when the 
 
 point is positively electrified with the results of Arrhenius's experi- 
 
 ments. For let us first consider the effects of pressure, k varies 
 
 inversely as the pressure ; hence F should be directly proportional 
 
 to the pressure, this is in agreement with Arrhenius's result ; 
 
 next consider the reaction of different gases, if we refer to the 
 
 values given on page 56, we see that the velocities of the ions 
 
 under unit electric force are roughly inversely proportional to the 
 
 square roots of the densities of the gases, hence F should be approxi- 
 
 mately directly proportional to the square roots of these densities. 
 
 Since the velocity of the negative ion is greater than that of the 
 
 positive the reaction on the negative point should be less than 
 
 that on the positive; the ratio of the reaction on the positive 
 
 point to that on the negative is however much greater than the 
 
 ratio of the velocity of the negative ion to that of the positive. 
 
 We have seen however reasons for believing that a rapid con- 
 
 densation of the gas takes place around the newly-formed negative 
 
 ions after they are produced at the point, so that the velocity of 
 
 the negative ion will be greater at first than after it has been for 
 
 some time in the gas, it is only however for these aged ions that 
 
 we know the velocity, while in the case of the point discharge a 
 
 large part of the reaction will be due to the more rapidly moving 
 
 freshly-formed ions in the immediate neighbourhood of the point, 
 
 so that the value of F will be less than that determined by equa- 
 
 tion (1) when we substitute for k the observed velocity of the 
 
 negative ion. 
 
211] SPARK DISCHARGE. 405 
 
 Discharge from a point whose electrification is rapidly 
 changing sign. 
 
 210. If a point is charged up to a high and rapidly alternating 
 potential, such as can be produced by the electrical oscillations 
 started when a Leyden-jar is discharged, then in hydrogen, 
 nitrogen, ammonia, and carbonic acid gas, a conductor placed near 
 the point gets a negative, while in air and oxygen it gets a 
 positive charge*. Himstedtf has shown that the distribution of 
 electrification in these gases differs only in degree; he finds that in 
 air and oxygen, although the electrification is positive near the 
 point, yet it changes sign as we recede from it and ultimately 
 becomes negative ; while in hydrogen and the other gases 
 mentioned above we get positive electrification if we go close 
 up to the point; the difference between the gases is that in 
 air the place where the electrification changes sign is some 
 distance from the point, while in hydrogen it is close up to it. 
 This outer zone of negative electrification is what we should 
 expect from the greater velocity of the negative ions, for under an 
 alternating electric field the amplitude of the path of the faster 
 ions would be greater than that of the slower, and thus at a 
 distance from the point greater than the amplitude of the slower 
 ions there would be nothing but negative electricity. The de- 
 termination of the distance at which the electrification changes 
 sign would be a very complicated investigation, as it would involve 
 in addition to the relative velocities of the positive and negative ions 
 the difference in the values of the current proceeding from the point 
 according as it is positively or negatively electrified, as well as the 
 difference in the minimum potential at which the discharge begins. 
 
 211. The condition of a point from which electricity is discharg- 
 ing seems to suffer some modification as the discharge goes on, and 
 this gives rise to variations in the current: PrechtJ found that a 
 point from which positive electricity had been discharged some- 
 times got hollowed out into a kind of crater, as if some of the 
 metal had been torn away ; he found that a negatively electrified 
 point did not suffer any change of shape. 
 
 * Harvey and Hird, Phil. Mag. [5], xxxvi. p. 45, 1893. Himstedt, Wied. Ann., 
 lii. p. 473, 1894. J. J. Thomson, Phil. Mag. [5], xl. p. 511, 1895. 
 f Himstedt, Wied. Ann., Ixviii. p. 294, 1899. 
 Precht, Wied. Ann., xlix. p. 50, 1893. 
 
406 
 
 SPARK DISCHARGE. 
 
 [212 
 
 Theory of the discharge from fine points. 
 
 212. We may suppose that the escape of electricity from a sharp 
 point occurs in the following way. When the electric field at the 
 point reaches a certain intensity a short spark passes from the 
 point to the air a little distance away, along the path of this spark 
 ions are produced, positive as well as negative ; if the point is 
 positively electrified the positive ions are driven out from this 
 region into the surrounding gas and under the influence of the 
 electric field find their way to the metal plate to which the point 
 is discharging; if the point is negatively electrified it is the 
 negative ions which are driven to the plate, and which carry the 
 electricity which is discharging from the point. 
 
 Let us apply these considerations to explain some of the 
 features of the discharge. We shall first consider the strength of 
 the field required to produce the small spark from the point. 
 
 The relation between the potential difference required to pro- 
 duce a spark and the spark length is (see page 360) represented 
 by a curve similar to a, Fig. 116, where the ordinates represent the 
 
 Fig. 116. 
 
 spark potential and the abscissae the spark length. Let us sup- 
 pose that the point is equivalent in its electrical effect to a small 
 sphere of radius a ; thus if V is the potential of the sphere the 
 potential difference between the sphere and a point at a distance x 
 
 from its surface is V ; let the equation to the curve 
 
212] SPARK DISCHARGE. 407 
 
 a* 
 
 (Fig. 116) be y=F- -, then if the curve ft intersects the 
 
 Gb ~F SO 
 
 curve a a spark will pass from the point, if the curves do not intersect 
 no spark will pass, the smallest value of V which will produce a 
 spark is when the corresponding curve /3 just touches the curve a. 
 Now when a is very small dyfdx for is very small compared with 
 yjx, but for the curve a it is only in the neighbourhood of the 
 minimum spark potential that this is the case, hence we conclude 
 that when {3 touches a it does so close to A, the point correspond- 
 ing to critical spark X Q and to F the minimum potential difference 
 required to produce a spark, hence we have approximately 
 
 F here is the value of the minimum potential required to produce 
 a spark; we see that V diminishes as a diminishes, i.e. the sharper 
 the point the smaller the discharge potential, it also diminishes as 
 the critical spark length increases, and as the critical spark length 
 is greater at low pressures than at high the minimum potential 
 will diminish as the pressure diminishes. In consequence of the 
 conductivity of the gas round the point, the radius of the sphere 
 taken as equivalent in its electrical action to the point may be 
 considerably larger than the actual radius of the point, and the 
 proportions between these quantities may depend upon the 
 pressure of the gas. 
 
 Difference between the minimum potential for positive 
 and negative points. 
 
 The minimum potential required for the discharge of positive 
 electricity from a point is greater than that for negative : this is, 
 I think, consistent with the preceding view, for the minimum 
 potential difference F depends (1) upon the energy a corpuscle 
 must possess to ionise a molecule against which it strikes, 
 (2) upon the energy a positive ion must possess in order to make 
 the cathode against which it strikes emit negative corpuscles; 
 an increase in either of these quantities would be attended by 
 an increase in the minimum spark potential. Now when the 
 
408 SPARK DISCHARGE. [212 
 
 discharging point is negatively electrified the conditions are the 
 same as in the ordinary spark discharge, for there is a metallic 
 cathode for the positive ions to strike against ; when however the 
 point is positively electrified, the cathode consists of the molecules 
 of the gas, and it is very probable that a positive ion would require 
 greater energy to detach a corpuscle from a molecule of a gas than 
 from a piece of metal which we have reason to think is very easily 
 ionised, this would have the effect of making F for the positive 
 point greater than for the negative and thus making the minimum 
 potential required for point discharge greater. 
 
 Relation between the current from a point and the potential differ- 
 ence between the point and the plane to which it discharges. 
 
 In order to simplify the mathematical analysis we shall take a 
 case which, while presenting the same physical features as the 
 point discharge from a needle, is yet from its symmetry more 
 amenable to calculation, the case is that of the discharge from a 
 very fine wire discharging to a coaxial cylinder. Almy* has made 
 a series of experiments on this kind of discharge. Let us take a 
 point on the wire as the origin for polar coordinates and let r be 
 the distance of a point in the gas from the wire, R the electric 
 force at this point and p the density of the electrification, then we 
 have 
 
 ........................ (1). 
 
 When we get beyond the region of the spark the discharge will be 
 carried by ions of one sign, hence if i is the current per unit length 
 of the wire, u the velocity of the ions, we have 
 
 but u = kR, where k is the velocity of the ion under unit force, 
 hence we have from equation (1) 
 
 d /T? \ 2t 
 
 3r (Ai) -B; 
 
 integrating this equation, we get 
 
 (Rry* = jr* + C ........................ (2), 
 
 where C is a constant. To determine 0, let a be the smallest 
 
 * Almy, American Journal of Science .[I], xii. p. 175, 1902. 
 
212] SPARK DISCHARGE. 409 
 
 value of r, for which the ions are all of one sign (a will exceed 
 the radius of the wire by a quantity of the order of the minimum 
 spark length) ; when r = a, R will be comparable with the electric 
 force required to produce a spark ; thus R will at atmospheric 
 pressure be greater than 10 2 in electrostatic units : in these units 
 k for air at this pressure is 450, hence unless i were comparable 
 with the value 2 x 10 6 in electrostatic measure, i.e. with | x 10~ 3 
 amperes, which is much larger than the currents used by 
 observers of the spark discharge, (2i/k) a 2 will be small compared 
 with (Rdf, i.e. C will be approximately independent of the current, 
 
 2t 
 and at the surface of the wire C .will be large compared with -y-r 2 . 
 
 iC 
 
 At the surface of the cylinder, on fche other hand, in general, 2ir*/k 
 will be large compared with C, for suppose the radius of the cylin- 
 der were 10 3 times that of the wire, then a current of a few micro- 
 coulombs per second (which is of the order of the currents made 
 by Tamm in his experiments) would make 2ir 2 /k at the surface 
 of the cylinder very large compared with (Ra) 2 and therefore with C. 
 
 If V is the potential at the distance r from the wire, we have 
 from (2) 
 
 7 i T 
 
 dr r (k 
 
 integrating this equation we find, if V is the potential difference 
 between the cylinder and the point near the wire where the current 
 begins to be carried by ions of one sign, and b is the radius of the 
 cylinder, 
 
 where i is so large that 2tb 2 /k is large compared with C, this 
 becomes approximately, 
 
410 SPARK DISCHARGE. [212 
 
 the second term on the right-hand side varies very slowly with t, 
 treating it as a constant and writing a for this term, we get 
 
 &* = (F'-a)* ...................... (1): 
 
 if V is the potential difference between the wire and the cylinder 
 we have seen that F= V + F where F is the least potential that 
 can produce a spark (for air it is about 351 volts), thus we have 
 from (1) 
 
 * = ~(F-F -y ..................... (2), 
 
 so that for large values of V, i varies as F 2 ; thus the current 
 varies as the square of the potential difference. Almy* found 
 that the current was proportional to V(V ft), thus for values of 
 V large compared with j3 it is proportional to F 2 ; according to 
 Almy's experiments the current is more nearly proportional to the 
 inverse cube of the radius of the cylinder than to the inverse 
 square as indicated by equation (2) ; it is to be noted that any want 
 of symmetry in the apparatus which would make the discharge 
 tend to concentrate on a particular radius would make the current 
 vary more rapidly with the radius than if the discharge were 
 quite symmetrical. We see from equation (2) that the current 
 varies as k, the velocity of the ion under unit force, thus since the 
 negative ion moves faster than the positive, the discharge under 
 given potential should be greater when the point is negative than 
 when it is positive ; from Tamm's observations the ratio of the 
 negative current to the positive in air at atmospheric pressure is 
 equal to 1*44, this is not far from the ratio of the velocities of the 
 negative and positive ions for dry air. 
 
 Again, since i is proportional to k, and k is inversely propor- 
 tional to the pressure, the current should vary inversely as the 
 pressure when the potential difference is large ; a reference to the 
 table on page 402 will show that although this is approximately 
 true at high pressures it ceases to be an approximation to the truth 
 when the pressure is low, when the current varies more nearly as 
 the inverse square of the pressure. At low pressures and with 
 large currents the discharge is accompanied by luminosity right 
 up to the plate ; an example of this is shown in Fig. 117, taken 
 
 * Almy, American Journal of Science [4] xii. p. 175, 1902. 
 
212] SPARK DISCHARGE. 411 
 
 from a paper by v. Obermayer*: the appearance presented by the 
 discharge suggests that ionisation is taking place at the plate as 
 well as at -the point, in which case ions of both signs would be 
 present between the plate and the point, and our investigation 
 
 Fig. 117. 
 
 which is founded on the supposition that the current is carried 
 entirely by ions of one sign would not apply. Even at atmospheric 
 pressure there is evidence in some cases of the presence of ions 
 of opposite sign to that of the electrification of the discharging 
 point : thus C. T. R. Wilson -f* notices a case in which when a 
 positive point was discharging into his expansion apparatus (see 
 p. 136) an expansion which was sufficient to bring down negative 
 but not positive ions produced a cloud, showing that negative ions 
 were present. 
 
 We shall see that from a spark rays are given out (Entladung- 
 strahlen) which can ionise a gas ; some rays are thus given out 
 from the small spark at the end of the discharging point, and 
 these rays may in certain cases produce appreciable ionisation 
 at a considerable distance from the point. The discharge from a 
 point seems to possess very considerable actinic power+. 
 
 Earhart's experiments (p. 384) seem to indicate that when 
 the electric force reaches a certain very high value the ions can 
 come from the metal, it would be interesting to further test this 
 view by seeing if a moderate potential was able to produce a 
 discharge from an exceedingly fine point in a good vacuum. 
 
 * v. Obermayer, Wien. Sitzungsberichte, c. p. 127, 1891. 
 
 t C. T. R. Wilson, Phil. Trans. A. vol. cxcii. p. 403, 1899. 
 
 J Cook, Phil. Mag. [5], xlvii. p. 40, 1899. Leduc, Eclair. Electr. xxi. p. 144, 1899. 
 
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CHAPTER XIV. 
 
 THE ELECTRIC ARC. 
 
 213. IN the electric spark and the discharge from a point the 
 difference of potential between the electrodes is several hundred 
 volts, while the current is only a fraction of a milliampere; in 
 the case we now proceed to consider, the electric arc, where the 
 electrodes are in a state of incandescence, the potential difference 
 is very much smaller, while the current is enormously greater, 
 often amounting to many amperes. We can produce the arc 
 discharge if we take a battery of cells of small resistance, numerous 
 enough to give a potential difference of 60 to 80 volts, and connect 
 the electrodes with two carbon terminals which are at first pushed 
 against each other, a current of electricity flows through the 
 carbons and warms the junction ; if while the current is still 
 passing the carbons are drawn apart a bright discharge which 
 may carry a current of many amperes passes from one carbon 
 terminal to the other. This discharge, which is called the electric 
 arc, is characterized by intense heat and light which make it of 
 great practical importance. The main sources of the light are 
 the extremities of the carbon rods which are in a state of vivid 
 incandescence. The temperature of the extremity of the positive 
 terminal is much higher than that of the negative ; according to 
 Violle* the temperature of the former is about 3500 C., that of 
 the latter about 2700 C., while the temperature of the arc itself 
 he found to be higher than that of either terminal. The terminals 
 if similar to begin with soon present marked differences in their 
 appearance, the extremity of the positive terminal gets hollowed 
 out into a crater-like shape, while the negative terminal if pointed 
 to begin with remains so. Both terminals in general lose weight, 
 
 * Violle, Comptes Rendus, cxv. p. 1273, 1892. 
 
214] 
 
 THE ELECTRIC ARC. 
 
 417 
 
 the positive, however, far more than the negative. The appearance 
 of the terminals is shown in Fig. 118; these figures are due to 
 Mrs Ayrton *. a and b represent the appearance when the arc is 
 quiet, d when it is giving out a hissing sound ; in some cases a 
 mushroom-shaped body forms at the end of the negative terminal. 
 
 Fig. 118. 
 
 The temperature of the crater of the positive terminal remains 
 constant even when the current varies, an increase of current 
 increases the area of the luminous crater, but the amount of 
 light given out by each unit area remains unaltered ; the tem- 
 perature of the crater is probably the temperature at which 
 carbon melts or volatilizes. E. W. Wilson f has shown that when 
 the arc passes through gas at a very high pressure, say 20 atmo- 
 spheres, the luminosity of the positive crater is sensibly less than 
 at atmospheric pressure ; in a later paper he gives reasons for 
 thinking that this may be explained by the increased absorption 
 of light by the gas surrounding the arc. 
 
 Connection between the difference of potential between the 
 electrodes, the length of the arc, and the current. 
 
 214. If V is the potential difference between the terminals, 
 I the length of the arc, FrohlichJ showed that the linear relation 
 
 where ra and n are constants, i.e. independent of I, exists between 
 
 * Mrs Ayrton, Proc. Inst. Electrical Engineers, xxviii. p. 400, 1899. 
 t E. W. Wilson, Proc. Roy. Soc., Iviii. p. 174, 1895 ; Ix. p. 377, 1897. 
 Frohlich, Elektrotechnische Zeitschrift, iv. p. 150, 1883. 
 
 T. G. 
 
 27 
 
418 
 
 THE ELECTRIC ARC. 
 
 [214 
 
 V and I. Mrs Ayrton* has shown that both m and n are functions 
 of the current i passing through the arc, and that 
 
 where a, /3, 7, 8 are constants. 
 
 Ayrton-f- made a long series of experiments on the relation 
 between the potential difference and the current through the arc, 
 some of the curves representing the results of these experiments 
 are given in Fig. -119, where the ordinates represent the potential 
 
 a 20 22 24 26 28 30 Amperes 
 
 difference and the abscissae the current; it will be seen from 
 these curves that for a quiet arc an increase in current is accom- 
 panied by a decrease in the potential difference, while in the 
 hissing arc the potential difference is independent of the current. 
 
 The constants m and n in Frohlich's formula have been 
 measured by several experimenters, by Frohlich himself, EdlundJ, 
 Peukert, v. Lang||, Gross and ShephardU, Nebel**, Aronsff, 
 
 * Mrs Ayrton, The Electric Arc, chap. iv. 
 
 f W. E. Ayrton. Mrs Ayrton, The Electric Arc. 
 
 J Edlund, Fogg. Ann., 134, pp. 251, 337, 1868. 
 
 Peukert, Zeitschrift fur Elektrotechnik, Wien, iii. p. Ill, 1885. 
 
 || v. Lang, Wied. Ann., xxvi. p. 145, 1885 ; xxxi. p. 384, 1887. 
 
 IT Gross and Shephard, Proc. Amer. Acad. of Sciences, 1886, p. 2. 
 
 ** Nebel, Centralblatt fiir Elektrotechnik, viii. pp. 517, 619, 1886. 
 
 ft Arons, Wied. Ann., Iviii. p. 73, 1896. 
 
214] THE ELECTRIC ARC. 419 
 
 Luggin*; for carbon electrodes in air at atmospheric pressure m 
 is about 39 volts, varying somewhat with the size and purity of 
 the carbons; it is diminished by soaking these in salt solution; 
 the value of n given by different experimeters varies considerably, 
 this may be due to their haviog used currents of different inten- 
 sities, as Mrs Ayrton has shown that it depends upon the current, 
 diminishing as the current increases. When metallic instead of 
 carbon terminals are used the value of m depends upon the metal 
 being in general larger the higher the temperature at which the 
 metal volatilizes; the values in volts found by v. Langf for m for 
 terminals of different substances are as follows : C = 35, Pt = 27 '4, 
 Fe = 25, Ni= 26-18, Cu = 23'86, Ag=15'23, Zn = 19*86, Cd = 10'28. 
 Lecher J gives Pt = 28, Fe = 20, Ag = 8. Arons found for Hg the 
 value 12*8, in this case the fall of potential along the arc itself 
 was abnormally small. In interpreting these results it is important 
 to notice that with some terminals the arc is intermittent. 
 Lecher has shown that this is the case with iron or platinum 
 terminals, and Arons that it is so with mercury terminals; no 
 intermittence has been detected with carbon, silver or copper 
 terminals. The potential differences given above are mean values, 
 and if the arc is intermittent they may differ greatly from the 
 actual potentials during the passage of the arc. 
 
 If the two terminals are of different materials the potential 
 difference may depend upon the direction of the currents, this 
 is especially the case when one of the electrodes is carbon and the 
 other metal ; the arc passes much more easily when the carbon is 
 the negative terminal and the metal the positive one than it does 
 in the opposite direction. So marked is this effect that if such 
 a pair of terminals is connected up with an alternating electro- 
 motive force the arc may pass only in the direction in which the 
 carbon is the negative terminal, the potential difference being 
 insufficient to drive it the opposite way. For experiments on this 
 point we may refer to papers by Blondel||, by Duddell and 
 MarchantH, and by Eichberg and Kallir**. 
 
 * Luggin, Wien. Ber., xcviii. p. 1192, 1889. 
 
 t v. Lang, Wied. Ann., xxxi. p. 384, 1887. 
 
 $ Lecher, Wied. Ann., xxxiii. p. 609, 1888. 
 
 Arons, Wied. Ann. Iviii. p. 73, 1896. 
 
 || Blondel, Comptes Bendus, 127, p. 1016, 1898; 128, p. 727, 1898. 
 
 IT Duddell and Maxchant, Inst. Elect. Eng., xxviii. p. 1, 1899. 
 
 ** Eichberg and Kallir, Wien. Sitz. 107, p. 657, 1898. 
 
 272 
 
420 
 
 THE ELECTRIC ARC. 
 
 [215 
 
 Non-arcing Metals. 
 
 215. With some metals as terminals the arc has a great 
 tendency to go out and is only maintained with difficulty; brass, 
 cadmium, and bismuth are examples of such metals ; in some cases 
 this is a very useful property, it has been investigated by Wurtz* : 
 a great deal depends upon the size and shape of the electrodes, as 
 well as of the material they are made ; conditions which promote 
 a rapid flow of heat from the hot extremities of the terminals are 
 favourable to the extinction of the arc. 
 
 Effect of pressure on the potential difference in the 
 arc discharge. 
 
 216. The potential difference is not independent of the pres- 
 sure of the gas through which the arc passes. Duncan, Rowland 
 and Todd ( have made an extensive series of experiments on this 
 point ; the results of some of their experiments are represented 
 graphically in Fig. 120: it will be seen from the curves that for 
 
 80 
 
 70 
 
 60 
 
 50 
 
 40 
 
 30 
 
 Aimosphe 
 
 es 
 
 Fig. 120. 
 
 short arcs the potential difference increases continuously with the 
 pressure, while for longer arcs there is a critical pressure at which 
 the potential difference is a minimum ; this critical pressure seems 
 to increase with the length of the arc. 
 
 * Wurtz, Lum. EL, xlv. p. 79, 1892. 
 
 f Duncan, Rowland and Todd, Electrician, xxxi. p. 60. 
 
217] 
 
 THE ELECTRIC ARC. 
 
 421 
 
 Effect of the nature of the gas on the potential difference. 
 
 217. The nature of the gas affects the arc, thus it is difficult 
 to get good arcs in pure hydrogen ; this may be due in part at least 
 to the more rapid convection of heat from the terminals in this gas. 
 Arons* has measured the potential difference required to produce 
 an arc 1*5 mm. long, carrying a current of 4*5 amperes between 
 terminals of different metals in air and pure nitrogen ; his results 
 are given in the following table : 
 
 
 Potential 
 
 difference 
 
 
 Potential 
 
 difference 
 
 Terminal 
 
 Air 
 
 Nitrogen 
 
 Terminal 
 
 Air 
 
 Nitrogen 
 
 Ag 
 
 21 
 
 ? 
 
 Pt 
 
 36 
 
 30 
 
 Zn!; 
 
 23 
 
 21 
 
 Al 
 
 39 
 
 27 
 
 Cd 
 
 25 
 
 21 
 
 Pb 
 
 
 18 
 
 Cu 
 
 27 
 
 30 
 
 Mg .. 
 
 
 22 
 
 Fe 
 
 29 
 
 20 
 
 
 
 
 
 
 
 
 
 
 The case of silver is interesting as, though it gives good arcs 
 in air, Arons could not obtain an arc in pure nitrogen ; he ascribes 
 this to the absence of any chemical combination between the 
 silver and the nitrogen ; he was able in the case of the other 
 metals to get evidence of the formation of nitrides. With the 
 exception of copper the potential differences in nitrogen are smaller 
 than in air, the difference being very noticeable in the cases of 
 iron and aluminium. 
 
 Arons also made a series of experiments in hydrogen, but 
 found the greatest difficulty in producing the arc in this gas, and 
 could only obtain it by using large currents and having the gas at 
 a low pressure ; cadmium, zinc, and magnesium gave the best arcs 
 in hydrogen. 
 
 We must in the case of the arc remember that since the metal 
 or the carbon volatilizes the arc goes through a mixture of the 
 vapour of the metal and the air, nitrogen or hydrogen in which 
 the terminals are immersed, so that the conditions of the experi- 
 ment are very complicated ; the presence of this vapour makes 
 
 * Arons, Drude's Annalen, i. p. 700, 1900. 
 
422 THE ELECTRIC ARC. [218 
 
 ambiguous the interpretation of the effect of changes of pressure 
 in the gas around the terminals, as we do not know the pressure of 
 this vapour. 
 
 218. The distribution of potential between the terminals 
 generally shows the following characteristics : there is a consider- 
 able fall of potential close to the anode, a smaller one close to the 
 cathode, and a very gentle potential gradient in the space between 
 the terminals ; the general nature of this distribution is shown by 
 the curve in Fig. 121: the curve shows many of the characteristics 
 
 CATHODE ANODE 
 
 Fig. 121. 
 
 of the distribution of potential between two hot electrodes in 
 flames; see p. 191. 
 
 Luggin* found that with carbon terminals and a current of 
 15 amperes there was a fall of potential of 33'7 volts close to the 
 anode, and one of 87 close to the cathode. The difference between 
 the potential falls at the anode and cathode is not so large with 
 iron or copper electrodes as it is with carbon. With mercury 
 terminals Arons found that the cathode fall was 5 '4 volts, the 
 anode fall 7'4 volts. When the current is increased so much 
 that the discharge passes from the quiet to the hissing arc there 
 is a sudden fall of potential. Luggin f and Mrs AyrtonJ have 
 shown that this diminution in the potential occurs almost entirely 
 at the anode, the potential gradients in the other parts of the 
 discharge being but little atfected. 
 
 * Luggin, Centralblatt filr Elektrotechnik, x. p. 567, 1888. 
 t Luggin, Wien. Sitz., xcviii. p. 1192, 1889. 
 J Mrs Ayrton, The Electric Arc. 
 
219] THE ELECTRIC ARC. 423 
 
 219. Some experiments which are very suggestive as to the 
 parts played by the two terminals in the arc discharge have been 
 made by Fleming*. In these experiments a third exploring carbon 
 electrode was used which was either inserted in the arc, or what was 
 often more convenient, placed outside the undisturbed path of 
 the arc, and the arc directed on to it by means of a magnet. 
 Fleming found that when the third terminal was connected 
 with the negative terminal of the arc by a circuit which con- 
 tained a battery of a few cells and a galvanometer to register the 
 current, a current passed round the circuit under a very small 
 electromotive force when the direction of the current was from 
 the cold electrode placed in the arc through the arc to its negative 
 terminal and then through the galvanometer, but that it would 
 not pass in the other direction : another way of stating this result 
 is to say that with one electrode hot and the other cold, a current 
 can pass in the direction in which the negative electricity comes 
 from the hot electrode into the gas, but not in the other direction. 
 Thus although in ordinary arcs the positive terminal is the hotter, 
 this experiment shows that a high temperature of the negative 
 electrode is the essential condition for the arc discharge, and that 
 if we can keep the temperature of the negative terminal up by 
 independent means we can get a discharge, even although the 
 temperature of the positive electrode is comparatively low. No 
 arc, however, will pass if the negative terminal is cold. 
 
 Fleming found that if he connected the exploring electrode 
 up to the positive electrode, without introducing any battery into 
 the circuit, enough current passed through the exploring electrode 
 to ring an electric bell or light an incandescent lamp placed 
 between the electrode and the positive terminal : but that no 
 appreciable current passed if the electrode were connected with 
 the negative instead of the positive terminal ; this result indicates 
 that the potential of the spare electrode is brought nearly to an 
 equality with that of the cathode. From these experiments 
 Fleming concluded that the arc discharge consists of a torrent 
 of negatively electrified particles of carbon shot off from the 
 cathode, these carry the current and striking with great violence 
 against the anode hollow it out, just as a body is hollowed out ' 
 when struck by a sand blast. 
 
 * Fleming, Proc. Roy. Soc., xlvii. p. 123, 1890. 
 
424 THE ELECTRIC ARC. [219 
 
 The phenomena connected with the discharge of electricity 
 from incandescent bodies (see Chap. VIII.) seem to me to indicate 
 a somewhat different explanation of the arc discharge. We saw 
 that an incandescent body such as a piece of carbon, even when 
 at a temperature far below that of the terminals in the arc 
 discharge, emits negatively electrified corpuscles at a rate corre- 
 sponding to a current of the order of an ampere per square 
 centimetre of incandescent surface, and that the rate of emission 
 increases very rapidly with the temperature ; thus at the tem- 
 perature of the negative carbon in the arc the rate of emission 
 probably corresponds to a current of a large number of amperes 
 per square centimetre of hot surface. If then a piece of carbon 
 were maintained by independent means at this high temperature 
 and if this were used as the negative electrode a current could 
 be sent through a gas to another electrode, whether this second 
 electrode were cold or hot. 
 
 Let us first suppose that the anode is cold, then the current would 
 be carried entirely by negative ions, there would . be free negative 
 ions in the space between the electrodes, these would cause the 
 electric force to increase as we pass from the cathode to the anode 
 and would make the current increase rapidly with the potential 
 difference. Now suppose that the anode becomes hot and that 
 there is some gas in contact with it which can be ionised, yield- 
 ing a supply of positive ions ; this current will no longer be 
 carried entirely by negative ions, though inasmuch as (p. 192) 
 the velocity of the negative ion at these high temperatures is 
 very much greater than that of the positive, by far the larger part 
 of the current is carried by the negative ions. The presence of 
 the positive ions, however, modifies very considerably the distri- 
 bution of potential between the electrodes : the positive ions 
 diffuse into the region of the discharge until they are sensibly 
 equal in number to the negative ions ; when this is the case the 
 electric force is sensibly uniform between the terminals except close 
 to the electrodes, and we have a distribution similar to that given 
 in Fig. 49, p. 191, which is taken from a paper by H. A. Wilson on the 
 conductivity through hot gases, and represents the distribution of 
 potential between two hot electrodes : by comparison with Fig. 121 
 it will be seen that this bears a great resemblance to the distri- 
 bution of potential between the terminals in the arc discharge. 
 
220] THE ELECTRIC ARC. 425 
 
 The view we take of the arc discharge is that it is similar to the 
 discharge between the incandescent terminals just considered, the 
 only difference being that in the flame the temperature of the 
 terminals is maintained by independent means, while in the arc it is 
 maintained by the work done by the discharge itself; this requires 
 that the potential difference between the electrodes also and the 
 current passing between them should not sink below certain values. 
 On the other hand when the temperature is maintained by external 
 aid the smallest potential difference is able to send a current. 
 
 On this view the cathode is bombarded by the positive ions 
 which maintains its temperature at such a high value that negative 
 corpuscles come out of the cathode ; these which carry by far the 
 larger part of the arc discharge bombard the anode and keep it 
 at incandescence, they ionise also either directly by collision or 
 indirectly by heating the anode, the gas or vapour of the metal of 
 which the anode is made producing in this way the supply of 
 positive ions which keep the cathode hot. It will be seen that 
 the essential feature in the discharge is the hot cathode, as this 
 has to supply the carriers of the greater part of the current in the 
 arc ; the anode has in general to be hot, otherwise it could not 
 supply the positive ions which keep the cathode hot ; in such a 
 case as that of a third electrode put in the arc and acting as 
 one of the anodes we may regard the discharge as having two 
 anodes, and as one is sufficient to keep the cathode hot we 
 can get the arc to pass to the other anode even although it 
 is cold. 
 
 220. The conditions that determine the current when a 
 given electromotive force acts round the whole circuit of the 
 arc are that the work supplied to the cathode and anode should 
 be sufficient to maintain them at incandescence. Although we 
 have not the data which would make a numerical calculation 
 possible, yet an expression in an analytical form of these con- 
 ditions may serve to make the preceding theory clearer and more 
 definite. 
 
 We have seen that the number of corpuscles emitted in one 
 second by unit area of a hot body increases very rapidly with the 
 
 temperature, being represented with considerable accuracy by 
 
 _> 
 a formula of the form AO^e *, where 6 is the absolute temperature; 
 
426 THE ELECTRIC ARC. [220 
 
 we shall call this function /(#), then if 6 is the temperature and 
 w l the area of the luminous part of the cathode the number of 
 corpuscles coming from the cathode in one second is equal to 
 w-if(6). If i is the current, R 1} R^ the velocities of the positive 
 and negative ions under unit electric force, the part of the 
 current carried by the negative ions is R. 2 i/(R l + R 2 ), and this 
 when divided by e, the charge on an ion, is equal to the number 
 of negative ions passing a section of the arc per second ; hence 
 we have 
 
 Let us now consider the temperature equilibrium of the 
 cathode. Let w^ (0) be the rate at which it is losing heat by 
 radiation and conduction, w the work expended when the cathode 
 emits one corpuscle, then to maintain thermal equilibrium the 
 rate at which energy must be given to the cathode is 
 
 w ^2 
 
 this work has to be supplied by the positive ions coming up to 
 the cathode in unit time ; the number of such ions is 
 
 we shall suppose that the energy they possess is got in passing 
 through the fall of potential at the cathode; let this fall be 
 denoted by E , then equating the rate at which energy is com- 
 municated to the cathode to the rate at which the cathode is 
 losing energy we get 
 
 or 
 
 I 
 
 Let 6 l be the temperature and o> 2 the area of the hot part of 
 the anode, w^r (6^ the rate at which it is losing energy by 
 radiation, conduction, and vaporisation, W the amount of work 
 required to produce a positive ion. 
 
 The number of positive ions produced in unit time is 
 
 R! 
 
 RI + R 2 e ' 
 
220] THE ELECTRIC ARC. 427 
 
 thus the work absorbed per second at the cathode is 
 
 Ri Wi 
 
 The number of negative ions striking against the anode in 
 unit time is 
 
 let us suppose that the energy with which they strike against 
 the anode is that due to passing through the anode fall of 
 potential E lf equating the rate at which the anode is losing 
 energy to that at which it is gaining it we have 
 
 thus 
 
 #! , as we have seen, does not depend on the current but only on the 
 material of which the anode is made. 
 
 If E is the external electromotive force acting on the circuit, 
 R the resistance of the leads, then E Ri is the potential 
 difference between the arc terminals ; when the arc is so short 
 that we may neglect the changes in potential along the arc, apart 
 from those at the anode and cathode, this difference of potential 
 is equal to E -f E l ; hence we have 
 
 E-Ri=E + E, ........................ (4); 
 
 thus we have four equations (1), (2), (3), and (4) to determine the 
 four quantities 6, i, E , and E lf 
 
 Mrs Ayrton has shown that o> 2 the area of the crater is a linear 
 function of the current and may be represented by an equation of 
 the form o> 2 = a + bi ; if o>! follows the same law then equations (2) 
 
 ft 
 
 and (3) suggest that E + E^ will be of the form a + , where 
 
 a and ft are independent of i, and this is in accordance with the 
 results of the experiments made on the relation between the 
 current through the arc and the potential difference between its 
 terminals. 
 
428 
 
 THE ELECTRIC ARC. 
 
 [221 
 
 221. 
 
 Taking the equation 
 E 
 
 .(5), 
 
 we see that the graph representing this relation is a hyperbola. 
 E has a minimum value at the point A, this value is 
 
 2 V^K + a. 
 
 The portion of the graph to the left of A corresponds to an unstable 
 state, for suppose the current is changed from i Q to i + x and 
 
 Fig. 122. 
 
 that there is self-induction L in the external circuit, let E' be the 
 steady electromotive force due to batteries, &c., in this circuit, 
 then from (5) we have 
 
 or when x is small 
 
 or 
 
 dx 
 
 /3 
 
 Now to the left of A, ~ R is positive, hence x will increase 
 
 indefinitely with t and the current will be unstable ; to the right 
 of A this quantity is negative and x will diminish to zero as the 
 time increases, the current under these conditions will be stable. 
 Thus for stability the current cannot be less than its value at A, 
 i.e. (ft/R)*, hence if i m is the minimum current, E m the minimum 
 external electromotive force, we have 
 
 4,= (/SAB)*, 
 
222] THE ELECTRIC ARC. 429 
 
 or if the external electromotive force is E the arc will go out if 
 the resistance R in the external circuit is greater than 
 
 (E-af 
 ~4 
 
 Thus as one numerical example let us take the case of the 
 arc 6 mm. in length for which the curve representing the relation 
 between the current through the arc and the potential difference 
 between the terminals is represented in Fig. 119, page 418; from 
 the curve we find that /3 = 3'4 x 10 8 in absolute measure ; we may 
 take a as about 40 volts, or in absolute measure 4 x 10 9 if E the 
 electromotive force in the external circuit is 80 volts or 8 x 10 9 
 absolute units ; we find that the arc will go out if the resistance 
 is greater than 
 
 16 x 10 18 
 
 4x3'4xl0 8 
 
 l-2xl0 10 =12ohms. 
 
 222. Another way of treating the problem of the arc graphically 
 is, instead of tracing the curve 
 
 where F(i) is the potential difference between the terminals of the 
 arc when it is carrying the current i, to trace the curve 
 
 y=F(i) 
 
 and the straight line 
 
 y^E-Ri', 
 
 if these intersect in two points P and Q (Fig. 123) we can show as 
 before that the state corresponding to P is unstable, and that the 
 current under the given external electromotive force and resistance 
 is represented by the abscissa of the point Q ; if the resistance is too 
 great the line may not cut the curve at all, while if it is too small 
 the point Q may be so far away that the corresponding value of 
 the current may be too great for a silent arc and a hissing arc will 
 necessarily be formed. 
 
 The minimum current for a given external resistance is got 
 by finding the point 8 when the tangent to the curve is parallel 
 to the line y Ri. The current at 8 is the minimum current, 
 and the value of OT, T being the point where the tangent at 8 
 intercepts the axis i = 0, is the minimum external electromotive 
 force. 
 
430 
 
 THE ELECTRIC ARC. 
 
 [223 
 
 To find the maximum value of R for which the arc can exist 
 under a given external electromotive force, EI take ON=E ly and 
 from N draw a tangent to the curve; let this tangent cut the 
 axis y = in M, then ON/OM is the required resistance. 
 
 223. Hissing Arcs. When the current is increased beyond 
 a certain value, the potential difference between the terminals 
 falls in the case of carbon electrodes by about 8 or 10 volts and 
 does not change when the current is increased ; when in this state, 
 the arc emits a hissing sound. Mrs Ayrton*, who has made a 
 study of the hissing arc, has shown that it occurs when the 
 incandescence of the anode covers such a large area that it 
 expands beyond the crater up the sides of the terminal : see 
 Figs. 118, c and a, which represent the appearance of the arc in 
 
 CURRENT 
 Fig. 123. 
 
 the hissing and quiet stages. The hissing of the arc is closely 
 connected with the oxidation of the terminal by the air ; for when 
 the incandescence extends up the sides of the carbon, the glowing 
 carbon is no longer completely protected by the carbon vapour 
 
 * Mrs Ayrton, The Electric Arc. 
 
224] THE ELECTRIC ARC. 431 
 
 from oxidation. It is then that the arc hisses. Mrs Ayrton has 
 shown that if the arc is formed in a closed vessel an increase of 
 current ceases to make it hiss as soon as the oxygen in the vessel 
 has been burnt up; whenever, however, fresh oxygen is intro- 
 duced into the vessel the hissing recommences. 
 
 We can see why chemical combination should tend to diminish 
 the potential difference between the terminals of the arc, for the 
 heat evolved by the burning of the terminals would tend to 
 maintain them at incandescence, so that the whole of the energy 
 required for this purpose would no longer have to be supplied by 
 the electric field. 
 
 Trotter* has shown that parts of the arc are in rapid motion 
 in the unstable state between the hissing and the quiet arc. 
 
 224. Effect of a magnetic field on the arc. The arc is 
 deflected by a magnetic field in the same direction as a flexible 
 conductor would be if it carried a current flowing in the same 
 direction as that through the arc. The curved course corresponds 
 to a longer path and the effect of the magnetic field on the 
 potential difference is of the same character as an increase in the 
 length of the arc, and just as it is possible to extinguish an arc 
 by increasing its length, so the arc can be blown out by the 
 application of a strong magnetic field. 
 
 * Trotter, Proc. Roy. Soc. Ivi. p. 262, 1894. 
 
V 
 
 CHAPTER XV. 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 225. WHEN the electric discharge passes through a gas at 
 a low pressure differences in the appearance of the discharge at 
 various points in its path become very clearly marked. The 
 discharge (Fig. 124) presents the following features : starting from 
 the cathode there is a thin layer of luminosity spread over its 
 
 Fig. 124. 
 
 surface, next to this there is a comparativelyjdark space, called 
 the Crookes dark space, the width of which depends on the 
 pressure of the gas, increasing as the pressure diminishes, it also 
 
225] DISCHARGE THROUGH GASES AT LOW PRESSURES. 433 
 
 * 
 as Schuster* has shown depends to some extent on the intensity 
 
 of the current, being greater for large currents than for small ; 
 the boundary of the dark space is approximately the surface 
 traced out by normals of constant length drawn to the surface 
 of the cathode; beyond the dark space there is a luminous region 
 called the 'negative glow'; beyond this again is another com- 
 paratively dark region called by some writers the 'second negative 
 dark space/ and by others the ' Faraday dark space/ its length is 
 very variable even when the pressure is constant ; beyond this; 
 again there is a luminous column reaching right up to the anode 
 and called the 'positive column'; when the current and pressure 
 are within certain limits this column exhibits remarkable alter- 
 nations of dark and bright spaces, these are called striations and 
 are shown in Fig. 125. The figure is taken from a paper by 
 
 mm : m*mmm mm m m mm r? 
 ~i*ii*ttt*ifiiiif itiiii t*.. 
 
 Mill!! ** 
 
 
 Fig. 125. 
 
 De la Rue and Mtiller, Phil. Trans., 1878, pt. 1, p. 155. In long 
 tubes the positive column constitutes by far the greater part of 
 
 * Schuster, Proc. Eoy. Soc. xlvii. p. 557, 1890. 
 T. G. 28 
 
434 DISCHARGE THROUGH GASES AT LOW PRESSURES. [226 
 
 the discharge, for the Crookes space, the negative glow, and the 
 Faraday dark space -do not depend markedly upon the length of 
 the tube, so that when the length of the discharge is increased, 
 the increase is practically only in the length of the positive 
 column; thus for example in a tube used by the writer about 
 15 metres long the positive column occupied the whole of the 
 tube with the exception of two or three centimetres close to 
 the cathode. 
 
 Distribution of the Electric Force along the discharge. 
 
 226. The electric force varies greatly along the discharge, it 
 has been measured by Hittorf*, Graham -f-, A. Here}, Skinner , 
 and H. A. Wilson ||. The method employed by these observers 
 was to measure the potential acquired by a metal wire placed in 
 various positions along the line of discharge, if the potential of 
 the wire is the same as that of the gas with which it is in contact 
 we get from these observations the means of determining the dis- 
 tribution of electric force along the tube. As an example of how 
 this method is carried out in practice we may take the apparatus 
 used by H. A. Wilson and shown in Fig. 126. The discharge 
 
 To fi/Atp ere 
 
 Fig. 126. 
 
 passed between two aluminium discs C and D supported by thin 
 glass rods which kept them a constant distance apart. Flexible 
 wire spirals connected these electrodes with wires sealed through 
 the ends of the tube. A piece of iron H was fixed to the frame 
 carrying the electrodes and enabled it to be moved along the 
 tube by means of a magnet. Two electrodes E, F about 1 mm. 
 
 * Hittorf, Wied. Ann. xx. p. 705, 1883. 
 
 t Graham, Wied. Ann. Ixiv. p. 49, 1898. 
 
 J A. Herz, Wied. Ann. liv. p. 246, 1895. 
 
 Skinner, Wied. Ann. Ixviii. p. 752, 1899. 
 
 || H. A. Wilson, Phil. Mag. v. 49, p. 505, 1900. 
 
227] DISCHARGE THROUGH GASES AT LOW PRESSURES. 435 
 
 apart were fused through the side tube G, these electrodes were 
 connected with a quadrant electrometer whose deflection gave the 
 difference of potential between E and F, and hence the electric 
 force at this part of the tube. By moving the framework, EF 
 could be brought into any part of the discharge between G and D, 
 and thus the distribution of electric force between the electrodes 
 mapped out. Another method which has been used is to keep 
 the electrodes C and D fixed and move E, F by attaching them to 
 a support floating on the top of a column of mercury the height of 
 which could be altered. 
 
 For methods such as those just described to be successful the 
 secondary electrodes must take up the potential of the gas with 
 which they are in contact ; to enable them to do this quickly 
 there must be a plentiful supply of both positive and negative 
 ions in the gas which by giving up their charges to the wire can 
 raise or lower its potential to equality with the surrounding 
 gas ; the results obtained seem to justify the assumption that at 
 moderate pressures the secondary electrodes do in most parts of 
 the discharge acquire the potential of the gas, but the method is 
 a dangerous one when the pressure is very low, or when the 
 wire is placed in the Crookes space where the conductivity is 
 very low. 
 
 Thus, to take an extreme case, suppose that a secondary 
 electrode is placed in an enclosure in which there" are torrents 
 of negative ions but no positive ones, then the wire will go on 
 receiving negative electricity until it gets so highly charged that 
 it is able to repel the negative ions sufficiently to prevent any 
 more striking it ; when this stage is arrived at its potential may 
 be lower than that at any point in the enclosure previous to its 
 introduction. 
 
 227. I have suggested for discharge at low pressures the use 
 of a method in which the deflection of the- cathode rays is used 
 to measure the strength of the electric field. The apparatus used 
 to carry out this method is shown in Fig. 127. A and B are 
 the electrodes kept at a constant distance apart and attached 
 to springs, by means of which they can be moved along the 
 tube. E and F are side tubes placed in line with each other, 
 in E cathode rays are produced by a Wimshurst machine, 
 
 282 
 
436 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [228 
 
 a pencil of these rays passes through a small hole in the disc G, 
 traverses the electric discharge passing between A and B, then 
 travels down the tube F producing a bright patch on a phos- 
 
 B 
 
 Fig. 127. 
 
 phorescent screen placed at the end of the tube. As the cathode 
 rays are deflected by the electric force along the line of discharge 
 the patch on the screen will be deflected from the position it 
 occupies when the discharge is not passing ; by measuring this 
 deflection we can determine the electric force at the part of the 
 discharge traversed by the rays ; by moving the electrodes A and 
 B along the tube we can map out the electric field at all parts of 
 the discharge. Mr Strachan at the Cavendish Laboratory has in 
 this way obtained the distribution of electric force in gases at low 
 pressure. 
 
 228. The distribution of electric force in a discharge tube 
 under various circumstances as to pressure and current is repre- 
 sented in. the following figures in which the ordinates represent 
 the value of the electric force at a point in the tube whose position 
 is fixed by the abscissa. From these curves we infer that the 
 electric force is very large indeed in the Crookes dark space, 
 diminishes rapidly towards the negative glow, and in the negative 
 
228] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 437 
 
 glow itself it is very small ; it reaches a minimum either in the 
 glow itself or in the portion of the Faraday dark space just 
 
 & 
 
 80 
 70 
 6o 
 so 
 40 
 
 2o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 F^. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 t 
 
 
 + 
 
 
 
 
 
 
 
 
 
 
 -> 
 
 /It 
 
 \ 
 
 QATI 
 
 *L 
 
 i. 
 
 
 
 Pos 
 
 T/V 
 
 C 
 
 
 /v 
 
 
 
 O 1 7. 3 4- 5 6 7 8 9 10 II 1% 13 f+ 
 
 Nitrogen. Pressure T06 mm. Current 0*676 m.a. 
 Fig. 128. 
 
 outside the negative glow, after which it increases, towards the posi- 
 tive column ; in the case of a uniformly luminous positive column 
 (Fig. 128) the electric force is constant along it until we get quite 
 
 70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 60 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S so 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <s 
 
 ? 40 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 8, 
 
 _ 30 
 
 \A 
 
 C 
 
 ^ ^ 
 
 s r 
 
 ^ 
 
 ^ 
 
 L/\ 
 
 /\ 
 
 
 
 
 
 
 
 5 
 S ao 
 
 
 V 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 L. 
 
 k .../-, 
 
 
 fo 
 
 . .- 
 
 S/f'J 
 .'""! 
 
 e <:< 
 
 /M ,T 
 
 
 . 
 
 
 ^ 
 
 ^f 
 
 9 />; 
 
 t/^ 
 
 J 
 
 5123 
 Hydrogen. 
 
 4-5 6 7 8 9 'O it 12 13 14- Cms 
 
 Pressure 2-25 mm. Current 0-586 m.a. 
 Fig. 129. 
 
 close to the positive electrode ; a sudden jump in the potential 
 called the anode fall of potential occurs quite close to the anode ; 
 in many of Wilson's experiments this drop was preceded by the 
 
438 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [228 
 
 electric force falling to an exceedingly low value ; in some cases 
 indeed it was apparently reversed ; it is not certain however that 
 this apparent reversal may not have been due to disturbances 
 produced by the introduction of the wires, &c., used to measure 
 the potential. When the positive column was striated then, as 
 we see from Fig. 129, the alternations of luminosity in the 
 positive column are accompanied by alternations in the value of 
 the electric force, maxima of the electric force occurring at the 
 bright parts of the striae, minima at the dark parts. Graham 
 
 
 
 
 
 
 
 - 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 + f 
 
 * 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 1 
 
 
 
 
 
 
 
 
 
 ^ 
 
 *^ 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 " s - 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 
 
 ^ 
 
 1=-. 
 
 
 ^ 
 
 J 
 
 
 20 40 60 80 too HO '40 ilo MO 70 
 
 Fig. 130. 
 
 showed that when the gas was impure there were considerable 
 variations in the electric force even in the luminous positive 
 column ; this is shown in Fig. 130 and Fig. 131, which repre- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 g 
 
 
 
 
 
 
 
 
 
 
 
 \, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 *x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 1 i 
 
 
 ^ 
 
 $ 
 
 
 20 40 60 8O loo I'iO /4p I6o 
 
 Fig. 131. 
 
 il 
 
 90 
 
 1 
 
 DQ 
 
 sent the distribution of electric force in an impure gas and in one 
 which had been carefully purified. When there is no positive 
 
229] DISCHARGE THROUGH GASES AT LOW PRESSURES. 439 
 
 column there is no region of constant intensity between the anode 
 and the negative glow. 
 
 If X is the electric force, supposed parallel to x, and p the 
 density of the electrification, then from the equation 
 
 dX 
 
 we see that the slope of the curves for x enables us to find the 
 excess of the positive over the negative ions at each point of the 
 discharge ; an inspection of the curves shows that there is a very 
 large excess of positive over negative in the Crookes dark space ; 
 in the negative glow the positive and negative ions are about 
 equal in number ; in the Faraday dark space there is an excess of 
 negative ions ; in the uniform positive column the two kinds of 
 ions are about equal in number, while in a striated positive 
 column there is a negative charge on the cathode side of the 
 bright part of a striation and a positive charge on the anode 
 side. 
 
 229. Distribution of electric force near the cathode., The 
 electric field in the neighbourhood of the cathode has been the 
 subject of many researches. Hittorf * showed that the potential 
 difference between the cathode and a point in the negative glow was 
 independent of the current, provided this was not great enough to 
 cause the negative glow to enclose the whole of the cathode. When 
 that stage was reached the potential between the cathode and the 
 glow increased with the current. Thus if the cathode is a wire, 
 then when the current is small the negative glow only surrounds 
 the tip of the wire ; as the current is increased the negative glow 
 encloses more and more of the wire, but it is not until the glow 
 reaches the end of the cathode that the difference of potertial 
 between the cathode and the glow begins to be affected by the 
 current. This difference of potential is called the cathode fall of 
 potential. Warburg*)- showed that it was independent of the pres- 
 sure of the gas, and that the potential fall was practically the same 
 whether platinum, zinc, copper, silver or iron electrodes were 
 used ; it was, however, considerably less when the electrodes were 
 
 * Hittorf, Wied. Ann. xx. p. 705, 1883. 
 
 t Warburg, Wied. Ann. xxxi. p. 545, 1887 ; xl. p. 1, 1890. 
 
440 DISCHARGE THROUGH GASES AT LOW PRESSURES. [229 
 
 made of aluminium or magnesium. Mey* has recently shown 
 that the cathode fall of potential depends more than had been 
 thought on the nature of the cathode, and that it falls to com- 
 paratively low values for the strongly electro-positive alkali metals 
 (see also Lyman, Proc. Camb. Phil. Soc. xn. p. 45, 1902). With 
 zinc, copper and iron electrodes the cathode fall of potential 
 is often abnormally small when the electrodes are new ; it 
 rises however to its normal value after the electrodes have 
 been used for some time. Warburg ascribes this effect to the 
 presence of a thin layer of oxide on the new electrode, which gets 
 removed in course of time by the disintegration which occurs when 
 the metal is used as a cathode. Hittorf-J- discovered that the 
 cathode fall became exceedingly small when the cathode was 
 raised to a red heat. Goldstein J and Warburg (loc. cit.) found 
 that the diminution in the cathode fall became much less when 
 the heating was continued for a long time. It is worthy of remark 
 in this connection that the emission of negative electricity from 
 an incandescent wire often falls off very considerably after long- 
 continued heating. Warburg found that a trace of impurity in 
 the gas produced surprisingly large effects on the cathode fall of 
 potential. Thus he found that the cathode fall in nitrogen which 
 contained traces of moisture and oxygen was with a platinum 
 cathode 260 volts, while the same nitrogen, after being very care- 
 fully dried, gave a cathode fall of 343 volts ; thus a mere trace of 
 moisture had diminished the cathode fall by 25 per cent. As long 
 as the total quantity of water vapour is small, the lowering of the 
 cathode fall does not seem to depend much upon the amount of 
 aqueous vapour present; when however there is much water 
 vapour present the fall is greater than in pure nitrogen ; thus in 
 a mixture of aqueous vapour and nitrogen in which the pressure 
 due to the aqueous vapour was 2*3 mm., that due to the nitrogen 
 3'9 mm., the cathode fall was 396 as against 343 in nitrogen with 
 a trace of oxygen ; the increase in the cathode fall was, however, 
 not nearly so great as that in the potential differences along the 
 positive column. In hydrogen Warburg found that a trace of 
 aqueous vapour increased the cathode fall of potential. 
 
 * Mey, Verhand. Deutschen Physikalischen Gesellschaft, v. p. 72, 1903. 
 t Hittorf, Wied. Ann. xxi. p. 133, 1884. 
 t Goldstein, Wied. Ann. xxiv. p. 91, 1885. 
 
229] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 441 
 
 Warburg* also investigated the effect of removing from the 
 gas all traces of oxygen. This was done by depositing on the 
 inside of the tube a thin layer of sodium, which was produced by 
 placing the tube in sodium amalgam, heating the glass and sending 
 a current of electricity from the amalgam through the hot glass to 
 an electrode inside the tube : the sodium thus deposited combined 
 with any oxygen there might be in the tube. The removal of the 
 oxygen produced a very great effect on the potential fall ; thus in 
 nitrogen with platinum electrodes the cathode fall was reduced by 
 the removal of a trace of oxygen from 343 to 232 volts, while with 
 magnesium electrodes the cathode fall when there was no oxygen 
 was 207 volts. In hydrogen free from oxygen the cathode fall was 
 300 with platinum electrodes and 168 with magnesium electrodes ; 
 thus with platinum electrodes the cathode fall is greater in 
 hydrogen than in nitrogen while with magnesium electrodes it is 
 less. 
 
 The following table contains the results of the measurements of 
 the cathode fall of potential in various gases by Warburg (loc. cit.), 
 Capstickf and Strutt J; it also contains the measurements by 
 
 Gas 
 
 Cathode fall in volts 
 Platinum electrodes 
 
 Cathode 
 fall with 
 aluminium 
 electrodes. 
 WARBURG 
 
 Minimum po- 
 tential differ- 
 ence required 
 to produce a 
 spark. STRUTT 
 
 WARBURG 
 
 CAPSTICK 
 
 STRUTT 
 
 Air .. 
 
 340350 
 about 300 
 
 230 if free 
 from 
 340 
 
 298 
 369 
 232 
 
 469 
 
 582 
 
 226 
 
 168 
 207 
 
 341 
 302308 
 
 251 
 261326 
 
 H 2 . 
 
 2 .. 
 
 N 2 
 
 Hg vapour 
 Helium . . . 
 H'O 
 
 NH 3 
 
 
 Strutt of the least potential difference able to produce a spark 
 through the various gases. We see from the results that there is 
 very considerable evidence in favour of the view that the minimum 
 
 * Warburg, Wied. Ann. xl. p. 1, 1890. 
 
 t Capstick, Proc. Ray. Soc. Ixiii. p. 356, 1898. 
 
 J Strutt, Phil. Tram, cxciii. p. 377, 1900. 
 
442 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [230 
 
 potential difference required to produce a spark through a gas is 
 equal to the cathode fall of potential in that gas. 
 
 The influence of the material of the electrode is shown by the 
 results quoted in the following table which is due to Mey (Lc.). 
 
 CATHODE FALL. 
 
 Gas 
 
 Electrode 
 
 Pt 
 
 Hg 
 
 Ag 
 
 Cu 
 
 Fe 
 
 Zn 
 
 Al 
 
 Mg 
 
 Na 
 
 Na-K 
 
 K 
 
 :: 
 
 &:: 
 
 Arg. . 
 
 369 
 300 
 232 
 226 
 167 
 
 
 
 
 
 
 
 
 
 
 226 
 
 295 
 
 280 
 
 230 
 
 213 
 
 190 
 
 168 
 
 207 
 
 185 
 
 178 
 80 
 
 169 
 125 
 
 78-5 
 
 172 
 
 170 
 69 
 
 
 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 
 
 
 
 
 Capstick found that if in dry gases a trace of oxygen was 
 present the cathode fall was approximately the same as in pure 
 oxygen. This is borne out by the results of the experiments of 
 Warburg already quoted on the effect produced by a trace of 
 oxygen in the presence of nitrogen. When water vapour is 
 present it would appear from Warburg's experiments that this 
 effect of the oxygen is to a large extent neutralised. We have 
 already (p. 402) alluded to Warburg's experiments on the great 
 diminution in the rate of escape of negative electricity from 
 a point in nitrogen produced by the presence of a trace of oxygen ; 
 it seems probable that this effect is connected with that of a trace 
 of oxygen on the cathode fall. The latter effect can hardly be due 
 to any oxidation of the electrode, for Warburg has shown that the 
 potential fall at slightly oxidised surfaces is less than that at 
 bright ones. 
 
 230. For the compound gases H 2 and NH 3 , the only ones 
 hitherto observed, the cathode fall seems to obey the additive 
 law, thus the cathode fall in H 2 = cathode fall in H 2 + J cathode 
 fall in 2 , while the cathode fall in NH 3 = J cathode fall in 
 N 2 -f | cathode fall in H 2 ; it would be very interesting to see if the 
 connection between the cathode fall in a gas and its chemical 
 
 o 
 
 composition suggested by the two results just quoted is confirmed 
 by further observations on the cathode fall in other compound 
 
231] DISCHARGE THROUGH GASES AT LOW PRESSURES. 443 
 
 gases. Carr came to the conclusion that the minimum spark 
 potential also followed the additive law. The experimental diffi- 
 culties are, however, very great, as it is exceedingly difficult to 
 get a continuous discharge through a compound gas. If a circuit 
 containing a telephone is placed in. series with the discharge tube 
 Capstick found that it is almost impossible to get the telephone 
 silent when a compound gas is in the tube, while there is no diffi- 
 culty whatever in doing so with an elementary gas. The singing 
 of the telephone indicates that the discharge is intermittent, and 
 when this is the case the cathode fall cannot be measured. 
 
 231. Current density at the cathode. H. A. Wilson* has 
 measured the current density at a cylindrical wire cathode when 
 the negative glow does not envelope the whole of the negative 
 electrode. Under these circumstances the glow assumes the appear- 
 ance shown in Fig. 132, its shape resembling a test tube with a well 
 
 TO PUMP ETC 
 
 Fig. 132. 
 
 marked lip at the end furthest from the anode; as the current 
 increases the glow reaches further along the electrode, the length 
 of the glow being proportional to the current. Wehneltf has 
 shown that the discharge from the cathode is confined to the area 
 covered by the glow and that the current density is constant over 
 this area; this shows that the current density at the cathode is inde- 
 pendent of the total current flowing through the tube, provided 
 that this is not so large as to make the glow envelope the whole of 
 the cathode. Wilson made a series of experiments in air at dif- 
 ferent pressures, ranging from 6'7 mm. to "023 mm., and found that 
 if C is the total current flowing through the tube in milliamperes, 
 I the length of wire covered by the glow in centimetres, d the 
 diameter of the wire in centimetres, p the pressure of the gas 
 in mm. of mercury, then C/l7r(d + 'Q5)p was approximately con- 
 stant and equal to '4 ; this result indicates that the current 
 density at a point "25 mm. from the surface of the cathode is 
 
 * H. A. Wilson, Phil, Mag. vi. 4, p. 608, 1902. 
 t Wehnelt, Drude'-s Ann. vii. p. 237, 1902. 
 
444 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [232 
 
 constant when the pressure is constant whatever the diameter 
 of the wire, and is proportional to the pressure when this alters. 
 It is remarkable that the current density is the same for aluminium 
 as for platinum electrodes, though the cathode fall is different. 
 An inspection of Wilson's numbers shows that though C/p is 
 approximately constant there is a tendency for it to slowly 
 decrease to a minimum and then slightly increase again. 
 
 232. The distribution of electric force in the dark space and 
 negative glow. The first determination of the electric force in the 
 dark space was made by Schuster*, who showed that if V is the 
 difference of potential between the cathode and a point in the 
 dark space or negative glow at a distance x from the cathode, then 
 the relation 
 
 where F" is the cathode fall and k a constant (for constant pressure), 
 represented very approximately the results of his experiments. 
 
 This distribution of potential would, since -^ = 4<7rp, where p 
 
 (Lx 
 
 is the density of the free electricity, involve in the dark space the 
 
 30 
 
 40 
 
 20 
 
 045 
 
 0-2? 
 
 o-o 
 
 10 20 30 10 20 30 40 
 
 Fig. 133. 
 
 existence of a positive charge of electricity, whose density de- 
 creases, in geometrical progression as the distance from the cathode 
 increases in arithmetical progression. 
 
 Graham -f-, who also measured the distribution of the electric 
 
 * Schuster, Proc. Roy. Soc. xlvii. p. 526, 1890. 
 t Graham, Wied. Ann. Ixiv. p. 49, 1898. 
 
233] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 445 
 
 force in the dark space near the cathode in nitrogen, obtained 
 for the distribution of potential results represented by the curves 
 in Fig. 133. From these curves it would follow that although 
 throughout the greater part of the dark space the electrical charge 
 is positive, there is a layer of negative electricity just in front of 
 the cathode. Wehnelt has repeated Graham's experiments without 
 finding the nicks in the curve near the cathode ; he ascribes them 
 to the two exploring wires not being in the line of the current. 
 Wehnelt gives the following figures as representing the distribu- 
 
 Fig. 134. 
 
 tion of the equipotential surfaces near the cathode ; they probably 
 are influenced to some extent by the walls of the tube. Both 
 Schuster and Graham found that the electric force increased very 
 rapidly close to the cathode ; it was however very appreciable 
 throughout the dark space. Skinner*, in some recent experi- 
 ments, came to the conclusion that the whole of the cathode 
 fall takes place quite' close to the cathode, and that the electric 
 force in the rest of the dark space is exceedingly small. I think 
 the latter result must be due to the exploring wire not having 
 taken up the potential of the gas around it ; for Strachan, using 
 the method described on page 436, has found in agreement with 
 Schuster and Graham that although the force increases exceedingly 
 rapidly near the cathode, it is quite appreciable throughout the 
 rest of the dark space. 
 
 233. The cathode fall of potential ceases to be constant when 
 the negative glow covers the whole of the electrode, or when it 
 
 t * Skinner, Phil. Mag. vi. 2, p. 616, 1902. 
 
446 DISCHARGE THROUGH GASES AT LOW PRESSURES. [234 
 
 reaches to the walls of the tube; its value under these circumstances 
 is always greater than the normal fall and may rise to a very high 
 value. Stark* has given the following formula connecting the 
 cathode fall of potential K with the intensity of the current when 
 this is large enough to cover the whole of the cathode with negative 
 glow 
 
 where K n is the normal cathode fall, p the pressure of the gas, 
 f the area of the cathode, C the current through the tube, and k 
 and x constants. 
 
 234. Thickness of the dark space. As the pressure diminishes 
 the dark space gets broader and broader : the connection between 
 the pressure of the gas and the width of the dark space has been 
 investigated by Puluzf, Crookesj, and more recently by Ebert . 
 According to Ebert the width of the dark space is not in general 
 inversely proportional to the pressure of the gas, i.e. directly 
 proportional to the mean free path of the molecules of the gas. 
 The law found by Ebert when the cathode was so remote from the 
 walls of the tube that the latter did not exert any restriction on 
 the growth of the negative glow may be expressed as follows. 
 
 Let d l , dj be the thicknesses of the dark space in the same gas 
 at the pressures p l , p 2 respectively, then 
 
 d, 
 
 where m is a positive quantity in general less than unity; he 
 found that for the gases examined, air, O 2 , H 2 , N 2 , CO, and C0 2 , 
 that there was a discontinuity in the relation between d and p 
 when a certain pressure II, different for the different gases, was 
 reached, the value of m for pressures greater than II differing 
 from its value for lower pressures; thus to take oxygen as an 
 example, Ebert found that for pressures greater than '7 mm. of 
 Hg m had the value '459, while for lower pressures m was equal 
 to '738. It is remarkable that the pressure '7 mm. is the pressure 
 
 * Stark, Physikalische Zeitschrift, iii. p. 274, 1902. 
 t Puluz, Wien. Sitz. Ixxxi. p. 874, 1880. 
 Crookes, Phil. Trans, clxx. p. 138, 1879. 
 Ebert, Wied. Ann. Ixix. pp. 200, 372, 1899. 
 
235] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 447 
 
 at which Bohr*, Baly and Ramsay f found a discontinuity in the 
 relation between the pressure and the volume of the gas to occur. 
 Battellij also obtained this result. Lord Rayleigh who made 
 a very careful examination of the relation between the pressure 
 and the volume of oxygen was unable to detect any such dis- 
 continuity. Newalljl discovered that the electrodeless discharge 
 through oxygen behaved very differently according as the pres- 
 sure was greater or less than a certain critical pressure which 
 was about '7 mm. EbertIF gives the following values for II, the 
 pressure at which the change in the law connecting p and d 
 appears, and for d the thickness of the dark space at a pressure 
 of 1 mm. 
 
 Gas 
 
 n 
 
 d 
 
 H 9 .. 
 
 2'0 mm. 
 
 3-8 
 
 CO 
 
 1*3 mm 
 
 2-6 
 
 N 9 
 
 1*0 mm 
 
 2-2 
 
 C0 9 
 
 1*1 mm. 
 
 2-1 
 
 TT2 
 
 Air 
 
 0'9 mm. 
 
 1-9 
 
 0, 
 
 0*7 mm 
 
 1*6 
 
 \^2 
 
 
 
 He states that II is approximately proportional to the reciprocal 
 of the linear dimensions of the cathode ; if this is the case there 
 seems no reason for connecting II with the stage where there is 
 a change in the relation between the pressure and volume of the 
 gas. 
 
 235. The following results taken from Ebert's paper will 
 give some idea of the thickness of the dark space d at different 
 pressures p in different gases. 
 
 p in mm. of Hg I 2-06 
 din mm... T2 
 
 1-24 
 1-8 
 
 Air 
 
 0-61 I 0-47 
 2-4 3-1 
 
 0-27 
 4-6 
 
 0-19 
 7-0 
 
 Oxygen 
 
 p I 1-18 I 0-73 I 0-45 
 
 d ., 1-64 2-09 2-93 
 
 0-29 
 4'16 
 
 0-183 I 0-129 I 0-083 
 5-48 7-69 10-43 
 
 0-051 
 14-3 
 
 * Bohr, Wied. Ann. xxvii. p. 459, 1886. 
 
 f Baly and Ramsay, Phil. Mag. v. 38, p. 307, 1894. 
 
 $ Battelli, Physikalische Zeitschrift, iii. p. 17, 1901. 
 
 Rayleigh, Phil. Trans., A. 196, p. 205, 1901. 
 
 || Newall, Proc. Camb. Phil. Soc., ix. p. 295, 1897. 
 
 IT Ebert, Verhand. Deutsch. Physik. Ges. ii. p. 99, 1900. 
 
448 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [235 
 
 Hydrogen 
 
 p in mm. of Hg I 3'05 I 2'04 
 din mm | 1-5 | 2'0 
 
 1-37 
 
 2-8 
 
 0-95 
 4-0 
 
 Nitrogen 
 
 2-85 
 1-0 
 
 1-91 
 1-5 
 
 1-25 
 2-0 
 
 0-82 
 2-7 
 
 0-72* 
 5-0 
 
 0-54* 
 4-0 
 
 0-54 
 5-6 
 
 0-35 
 6-5 
 
 0-40 
 7-0 
 
 0-26 
 8-0 
 
 The results for hydrogen and nitrogen are plotted in Fig. 135, 
 where the ordinates represent the thickness of the dark space 
 and the abscissae the reciprocals of the pressure. It will be seen 
 that the points representing the experiments at the higher pres- 
 sures lie very well on straight lines, while at lower pressures they 
 no longer do so. The pressures when the curvature becomes 
 marked are close to the pressures called by Ebert the 'critical 
 pressure.' He found that* as the pressure diminished the potential 
 
 Fig. 135. 
 
 difference between the terminals at first diminished until this 
 critical pressure was reached ; when the pressure was still further 
 reduced the potential difference increased as the pressure was 
 diminished. The critical pressure was found to depend upon the 
 size of the vessel, the larger the vessel the lower the critical pressure. 
 The critical pressure marks the stage when the walls of the vessel 
 begin to restrict the formation of the glow and to complicate the 
 phenomena. In studying the laws governing the formation of the 
 dark space it is better to confine ourselves to pressures higher 
 than the critical pressure, when the walls of the tube do not 
 exert any influence. Confining our attention to such pressures 
 I am inclined to interpret Ebert's experiments somewhat differ- 
 
235] DISCHARGE THROUGH GASES AT LOW PRESSURES. 449 
 
 ently from Ebert himself. I think they show that d, the thickness 
 of the dark space, may be expressed in the form 
 
 6 
 
 a a + - , 
 P 
 
 where p is the pressure, and a and b are constants. If X is the 
 mean free path of a molecule of the gas, X is proportional to 1/jp, 
 and the preceding equation may be written in the form 
 
 d = a + l3\ (1), 
 
 or the dark space measured from a distance a in front of the 
 cathode is proportional to the mean free path of a molecule of the 
 gas. If we plot the curve in which the ordinate is the thickness 
 of the dark space and the abscissa the mean free path of a mole- 
 cule of the gas, then taking Xfor nitrogen at atmospheric pressure 
 to be equal to 9'86 x 10~ 6 cm. and for hydrogen to T85 x 10~ 5 cm. 
 (see Meyer, Kinetische Theorie der Gase), we find that the curves for 
 hydrogen and nitrogen are almost identical ; this indicates that in 
 equation (1) the constants a and /3 are the same for the two gases, 
 i.e. that if instead of measuring the dark space from the cathode 
 itself we measure it from a constant distance from the cathode 
 the thickness of the dark space bears to the mean free path of 
 the molecules of the gas a ratio which is the same for all gases. 
 The discharge in fact behaves as if the negative carriers came 
 from a region a little in front of the cathode, and not from the 
 cathode itself. H. A. Wilson's experiments on the current density 
 at the surface of the cathode suggest the same view ; the value of 
 a, the constant in equation (1) as given by the curves in Fig. 135, 
 is about '4 mm. The thickness of the layer at the surface, of 
 which Wilson found the current density to be constant, is in air 
 25 mm. : these two quantities are of the same order, and we 
 cannot claim for the value of a as determined by the curve in 
 Fig. 135 any great accuracy, as a slight error in the observations 
 might produce a large percentage error in a; for this reason 
 I think it possible that the identity of the values of a found for 
 hydrogen and nitrogen may be partly accidental, and more experi- 
 ments are needed before it can be considered as established that 
 a is the same for all gases. It would be interesting to see if the 
 thickness of the velvety glow which covers the surface of the 
 cathode is equal to a. 
 
 T. G. 29 
 
450 DISCHARGE THROUGH GASES AT LOW PRESSURES. [236 
 
 Connection between the thickness of the dark space and the free 
 path of a corpuscle, 
 
 236. The mean free path of a hydrogen molecule at C. 
 and 760mm. pressure is 1'85 x 10~ 5 cm. (Meyer, Kinetische Theorie 
 der Gase). The mean free path of a corpuscle will be greater than 
 this, first because the corpuscle is smaller than the molecule ; if 
 for the sake of definiteness we take the view that the collisions 
 between two molecules and between a corpuscle and a molecule 
 are analogous to those between two elastic spheres, then, neglect- 
 ing the radius of a corpuscle in comparison with that of a molecule, 
 the distance between the centres of a molecule and a corpuscle 
 when in collision will be half the distance between the centres of 
 two molecules when in collision. Now the free path is inversely 
 proportional to the square of the distance between the centres 
 when the spheres are in collision ; thus the free path of the 
 corpuscle will be four times that of the molecule. Again, under 
 the electric field the corpuscles move with a velocity very great 
 compared with the average velocity of translation of the molecules, 
 so that the latter may be considered to be at rest. Maxwell* has 
 shown that the free path of a body moving through a collection 
 of molecules at rest is A/2 times the free path if the molecules 
 were moving with an average velocity of translation equal to that 
 of the moving body; thus the mean free path of a corpuscle 
 moving through hydrogen at C. and 760mm. pressure will be 
 4 \/2 x 1'85 x 10~ 5 cm. ; the free path at a pressure of Jxfnm. will 
 therefore be 4 \/2 x 1*85 x 760 x 10- 5 cm., or about '8 of a milli- 
 metre. The thickness of the dark space in hydrogen at this 
 pressure reckoned from a distance '4 mm. from the cathode is 
 about 3'3 mm., or roughly 4 times the mean free path of the 
 corpuscle, and we have seen that the proportion between the 
 thickness of the dark space and the free path is probably the 
 same at all pressures and in all gases. Thus the thickness of the 
 dark space is a quantity of the same order of magnitude as the 
 free part of a corpuscle calculated on the very special hypothesis 
 used above. 
 
 Schuster*!" found that the thickness of the dark space de- 
 pended to some extent on the current passing through the gas, 
 
 * Maxwell, Collected Papers, vol. i. p. 386. 
 + Schuster, Proc. Roy. Soc. xlvii. p. 556, 1890. 
 
237] DISCHARGE THROUGH GASES AT LOW PRESSURES. 451 
 
 increasing slightly with an increase in current. Wehnelt* on 
 the other hand found that the dark space contracted as the 
 current increased ; this seems to indicate that the dark space may 
 have a stationary value for some particular current, increasing or 
 decreasing with the current, according as the current is on one 
 side or the other of this particular value. 
 
 237. Disintegration of the cathode. When the discharge 
 passes through the tube^portions of metal shoot out normally from 
 the cathode and form a thin metallic film on the walls of the tube 
 or any body in the neighbourhood of the cathode; indeed thin metal- 
 lic films for serni-transparent mirrors are now frequently made by 
 placing a piece of glass in a vacuum tube near a cathode made of the 
 metal it is wished to deposit and sending a current through the 
 tube. The amount of metal shot off from the cathode depends on 
 the pressure of the gas in the tube, it is much greater at low 
 pressures than at high. It depends also on the nature of the gas; 
 thus there is very little disintegration of aluminium electrodes in 
 air, but a large amount in the monatornic gases, helium, argdn and 
 mercury vapour. It depends largely on the nature of the metal. 
 According to Crookes f the order of the metals in descending order 
 of disintegration is Pd, Au, Ag, Pb, Sn, Pt, Cu, Cd, Ni, In, Fe. 
 GranqvistJ found that the order depended on the pressure of the 
 gas. Thus at high pressures he found that Pt lost more than Au, 
 at low pressures less. His results showing the connection between 
 disintegration and pressure are represented by the curves in 
 Fig. 136, where the ordinates are the loss of weight in milli- 
 grammes in an hour for electrodes 12 mm. long, 4'8 mm. broad, 
 and '0(5 thick when a current of 2'46 milliamperes passed 
 through the tube, and the abscissae the pressures. Granqvist 
 found also that the loss in weight in a given time is prop^r- 
 tional to the square of the current when the pressure is constant. 
 Crookes found that if the cathode consisted of the alloy of gold 
 and aluminium discovered by Roberts- Austen the gold was de- 
 posited while the aluminium was not ; thus the composition of the 
 cathode was changed by the discharge. The amount of metal 
 volatilised from a cathode is very much greater than that from 
 
 * Wehnelt, Physikalische Zeit. ii. p. 518, 1901. 
 
 t Crookes, Proc. Eoy. Soc. 1. p. 88, 1891. 
 
 t Granqvist, Oefversigt. Kgl. Vetensk. Akad. Fork. Stockholm, 1898, p. 709. 
 
 292 
 
452 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [238 
 
 the same wire when incandescent; thus Granqvist* found that he 
 got as much from a cathode in a few minutes as he got from the 
 same wire when incandescent and without charge, or when used as 
 
 25 
 
 10 
 
 O millimeCres 
 
 t-0 
 Fig. 136. 
 
 /' 
 
 20 
 
 an anode, in twelve hours. The streams of metal from the cathode 
 are deflected by a magnet, although not to anything like the 
 same extent as the cathode rays. 
 
 238. The cause of this disintegration of the cathode has not 
 been fully determined ; it is possible that it is due to the same 
 cause as the disintegration of incandescent wires, a very thin layer 
 of cathode close to the surface being in a state analogous to that 
 of a wire at a very high temperature; the surface of the cathode is 
 bombarded by the positive ions which have fallen through a 
 potential equal to the cathode drop; this might easily raise the 
 surface layers to such a temperature that the energy would be 
 radiated away and would not escape by conduction to heat the 
 inside of the cathode. As a matter of fact the surface of the 
 cathode is often to all appearance in a state of incandescence. It 
 
 * Granqvist, Kgl. AJcad. Stockholm, liv. p. 595, 1897. 
 
239] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 453 
 
 would be interesting to test this view by seeing if the presence of 
 even a trace of oxygen increased the disintegration of the cathode, 
 as it produces a large increase in that of an incandescent wire. 
 I am inclined to think, too, that gases absorbed in the metal have 
 a considerable effect upon the disintegration and indeed upon the 
 passage of the electricity from the cathode to the metal ; in high 
 vacua the potential difference between an anode and various 
 cathodes in the same tube will often change capriciously, the order 
 at one time being quite different from that a few minutes later. 
 This would be readily explained if the amount of absorbed gas 
 influenced the potential difference. If the disintegration does 
 depend on absorbed gas, then we should expect the rate to fall off 
 after long-continued use of a cathode in a high vacuum. 
 
 The Faraday dark space and the Positive Column. 
 
 239. Measurements of the electric force in the Faraday dark 
 space were first made by Hittorf *. Graham j* and H. A. Wilson J 
 also made numerous determinations of the force in this as in other 
 parts of the discharge, while Skinner has recently investigated the 
 influence of pressure and of the magnitude of the current on the 
 force in the dark space and on its length. The results of Skinner's 
 experiments, which were made on carefully purified nitrogen, 
 
 to 10 30 40 fO do Jo 90 9o 100 no no '50 ><* 
 Millimetres. 
 Fig. 137. 
 
 and with disc electrodes of considerable area, are represented 
 in Fig. 137. An inspection of these curves shows that when 
 
 * Hittorf, Wied. Ann. xx. p. 705, 1883. 
 
 t Graham, Wied. Ann. Ixiv. p. 49, 1898. 
 
 J H. A. Wilson, Phil. Mag. [5], xlix. p. 505, 1900. 
 
 Skinner, Phil. Mag. [5], 1. p. 563, 1900. 
 
454 DISCHARGE THROUGH GASES AT LOW PRESSURES. [239 
 
 the pressure is kept constant the width of the dark space 
 increases as the current increases. (The boundaries of the dark 
 space were found by Skinner to be at the points corresponding to 
 the intersection of the straight line II with the curves giving the 
 electric force.) The current drives as it were the luminous positive 
 column back on the anode, until with the largest current used the 
 luminous positive column was reduced to a patch close to the 
 anode. With the same current the width of the dark space is 
 greater at low pressures than at high. 
 
 Skinner made an interesting experiment in which the gas in 
 the tube was shielded from any disturbance travelling normally 
 from the cathode. The cathode was a disc placed with its plane in 
 the axis of the tube. This was surrounded by a piece of glass 
 tubing, the axis of the tube being at right angles to the disc; 
 thus any disturbance travelling from the cathode at right angles is 
 prevented from reaching any but a small part of the gas between 
 the electrodes. With this apparatus it was found that the 
 luminous positive column occupied nearly the whole of the 
 space up to the cathode : the dark space was very small, and 
 increased but little with an increase in the current. Skinner 
 observed that (with a tube of the normal type with the electrodes 
 facing each other) when once by means of a large current 
 the luminous positive column had been driven back on the 
 anode, the gas took a considerable time before it recovered the 
 power of transmitting a luminous discharge ; the time required 
 for the recovery depended upon the time the large current had 
 been kept flowing through the tube. Skinner mentions times 
 of one or two hours as having been required in some of his 
 experiments. 
 
 The potential difference between the electrodes is represented 
 by the area in Fig. 137, bounded by the -axis of abscissae, the 
 two vertical ordinates through the electrodes, and the curve 
 representing the electric force ; we see from an inspection of the 
 figure that this area diminishes as the current increases. Thus 
 the curve representing the relation between the potential dif- 
 ference between the electrodes and the current through the tube 
 slopes downwards. Hence to find the potential difference between 
 the electrodes and the current through the tube when an external 
 electromotive force E acts on a circuit including the tube, we pro- 
 
240] DISCHARGE THROUGH GASES AT LOW PRESSURES. 455 
 
 ceed as in Art. 222 by drawing the line y E^ Rx, where R is the 
 external resistance in the circuit, and finding the points P, Q where 
 this line cuts in the curve representing the relation between the 
 potential difference and the current through the tube. For the 
 reason given in Art. 222 the point P to the left corresponds to 
 an unstable state, the other point Q to the stable one. Just as 
 in the case of the arc we see that with a given external electro- 
 motive force the current through the tube cannot sink below a 
 certain finite value if the discharge is to be continuous*. 
 
 Since with the exception of the cathode dark space the only 
 dark part of the discharge is that where the curve representing 
 the electric force is below the line II (Fig. 137), it follows from 
 Skinner's experiment that there is luminosity at all parts of 
 the tube (with the exception of the cathode dark space), when 
 the electric force exceeds a certain value depending on the 
 pressure. 
 
 The Positive Column. 
 
 240. The potential gradient along a uniform unstriated 
 positive column is uniform ; its value has been investigated 
 by Hittorff, A. Herz]:, Graham, Wiison||, Skinnerlf. The 
 potential gradient in the positive column depends (1) upon the 
 diameter of the discharge tube, (2) upon the pressure and nature 
 of the gas through which the discharge is passing, and (3) the 
 current passing through the gas. 
 
 The potential gradient diminishes as the diameter of the 
 discharge tube increases, as the following table given by Herz 
 (loc. cit.) shows. The influence of the size of the tube is not 
 confined to tubes which are so narrow that their diameter is 
 comparable with the mean free path of the molecules and cor- 
 puscles in the tube, but extends to the cases when the diameter 
 of the tube is hundreds of times the mean free path. The results 
 in the table relate to pure nitrogen ; v is the potential gradient in 
 volts per centimetre, 2R the diameter of the tube (the current 
 
 * Kauffmann, Drude's Ann. ii. p. 158, 1900. 
 t Hittorf, Wied. Ann. xx. p. 726, 1883. 
 J Herz, Wied. Ann. liv. p. 244, 1895. 
 Graham, Wied. Ann. Ixiv. p. 49, 1898. 
 
 || Wilson, Phil. Mag. [5], xlix. p. 505, 1900 ; Proc. Camb. Phil. Soc. xi. pp. 249, 
 391, 1902. 
 
 IT Skinner, Phil. Mag. [6], xi. p. 616, 1901. 
 
456 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [240 
 
 passing through the tube was in all cases 1*2 milliamperes), p is 
 the pressure of the gas expressed in millimetres of mercury, and b 
 the constant occurring in the equation 
 
 v v = - b (i i ), 
 
 which Herz found expressed the relation between the gradients 
 v and V Q corresponding to the currents i and i ; in this equation 
 i and i are expressed in milliamperes. 
 
 
 
 i 
 
 
 
 P 
 
 2R = W mm. 
 
 2R = 15 mm. 
 
 , 2E = 20 mm. 
 
 2 J R = 25mm. 
 
 8-0 
 
 
 156-8 
 
 
 
 7-5 
 
 . .. 
 
 148-4 
 
 
 
 7-0 
 
 144-4 
 
 140-1 
 
 
 
 6-5 
 
 139-2 
 
 131-9 
 
 , 
 
 
 6-0 
 
 132-6 
 
 123-8 
 
 
 
 5-5 
 
 126-1 
 
 115-8 
 
 
 
 5-0 
 
 118-2 
 
 107-8 
 
 
 
 4-5 
 
 109-4 
 
 99-9 
 
 977 
 
 
 4-0 
 
 99-7 
 
 92-2 
 
 893 
 
 
 3-5 
 
 89-2 
 
 84-5 
 
 805 
 
 
 3-0 
 
 77-7 
 
 76-1 
 
 71-2 
 
 
 2-5 
 
 
 66-2 
 
 615 
 
 602 
 
 2-0 
 
 
 55-4 
 
 51-4 
 
 487 
 
 1-5 
 
 
 43-6 
 
 40-8 
 
 375 
 
 I'O 
 
 ... 
 
 
 29-8 
 
 26-9 
 
 b 
 
 10-0 
 
 8-5 
 
 3-5 
 
 3-4 
 
 The potential gradient in the positive column increases with 
 the pressure, the results of Herz's experiments are represented 
 by the curves in Fig. 138 in which the ordinates represent the 
 potential gradient and the abscissae the pressure, the dotted curve 
 relates to experiments with hydrogen, the others to experiments 
 with nitrogen in tubes of different dimensions, the curves seem 
 very approximately linear. H. A. Wilson* concluded from his 
 experiments that the potential gradient in the positive column 
 was proportional to the square root of the pressure ; the linear 
 relation v a + bp, where v is the potential gradient, p the pressure 
 
 H. A. Wilson, Proc. Camb. Phil. Soc. xi. pp. 249, 391, 1902. 
 
242] DISCHARGE THROUGH GASES AT LOW PRESSURES. 457 
 
 and a and b constants, represents the results of his experiments 
 almost equally well. 
 
 270 
 Z40 
 ZiO 
 
 180 
 (50 
 
 12 
 90 
 60 
 
 JO 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 R x y 
 
 
 
 
 
 
 
 
 
 
 2=/ 
 
 ;X 
 
 
 
 
 
 
 
 
 
 
 / 
 
 x 
 
 
 2/ , a 
 
 /^, 
 
 
 
 
 
 
 x 
 
 / / 
 
 / 
 
 
 , 
 
 ''" 
 
 
 
 
 
 
 . 
 
 x^r 
 
 ^ 
 
 2o 
 
 ^ ' 
 
 *^ 
 
 
 
 
 
 
 
 fa 
 
 
 f ' 
 
 '' 
 
 
 
 
 
 
 
 
 ^2 
 
 =2f 
 
 - ,' 
 
 
 
 
 
 
 
 
 
 ^ 
 
 / 
 
 ,' 
 
 
 
 
 
 
 
 
 
 jf 
 
 ' . 
 
 ''' 
 
 
 
 
 
 
 
 
 
 
 * , 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 075 I'S 2'2ST VO 375 45 S-2S 6-0 &-JS -J-S 25 9 
 
 Fig. 138. 
 
 Herz showed that under similar conditions as to pressure and 
 current the potential gradient in nitrogen was 1*4 times that in 
 hydrogen. He found that a trace of aqueous vapour had no 
 effect upon the gradient in the positive column, but that the 
 presence of a small quantity of oxygen in the nitrogen increased 
 the potential gradient. 
 
 241. Relation between the potential gradient and the current. 
 From the relation v v = b (i 1 ) given by Herz it would 
 follow that the potential gradient in the positive column con- 
 tinually increases as the current diminishes. H. A. Wilson has 
 however shown recently that the potential gradient attains a 
 maximum value for a certain value of the current and that when 
 the current falls below this value the potential gradient rapidly 
 diminishes. 
 
 242. When the positive column is striated the variations in the 
 luminosity are accompanied by variations in the electric intensity, 
 
458 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [243 
 
 the places of maximum luminosity are places of maximum poten- 
 tial gradient, this is clearly shown by the curve in Fig. 129, which 
 is one given by Wilson for the striated discharge in hydrogen. 
 
 243. Anode drop in potential. Skinner* has shown that 
 there is a finite difference in potential between the anode itself 
 and a point in the gas close to the anode. The magnitude of 
 this drop in potential was investigated by him for the discharge 
 through pure nitrogen ; he found that it was independent of the 
 current density, it increased slightly with the pressure, and de- 
 pended upon the metal of which the anode was made, being 
 greatest for aluminium and magnesium, for which the cathode 
 fall of potential is least ; the value of the anode drop at different 
 pressures and for different metals is represented in the curves in 
 Fig. 139. It will be observed that the anode drop is much smaller 
 
 4-0 
 
 30 
 
 ro 
 
 M 
 
 0'5 
 
 ro 
 
 rs 
 
 20 
 Fig. 139. 
 
 1' 5 
 
 than the cathode one, it is also much more abrupt; there does not 
 seem any region comparable in dimensions with the cathode dark 
 space in which the drop of potential occurs; in none of the ex- 
 periments hitherto made has it been found possible to get so 
 close to the anode that the potential of the exploring wire differed 
 by less than the anode fall of potential from the potential of the 
 anode. 
 
 * Skinner, Wied. Ann. Ixviii. p. 752, 1899. 
 
244] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 459 
 
 There is frequently a region in which the electric intensity is 
 very small just in front of the anode; in some of the experiments 
 made by H. A. Wilson, the electric intensity was apparently 
 negative; we must remember that the introduction of the ex- 
 ploring wire disturbs the field, and that this reversal of the 
 electric intensity may be due to this cause. 
 
 244. Number of ions at various points along the discharge. 
 H. A. Wilson* has made a series of investigations on this point; 
 his method was to determine the current flowing between two 
 small parallel platinum plates, the planes of the plates being 
 parallel to the current flowing through the tube, a small potential 
 difference (that due to one Clark's cell) was maintained between 
 the plates, previous experiments having shown that with potential 
 differences of this order the current was proportional to the 
 potential difference, and therefore that the presence of a field 
 of this intensity did not appreciably reduce the number of free 
 ions. Under these circumstances if n^ n 2 are the numbers of 
 positive and negative ions respectively, k lt & 2 the velocities of these 
 ions under unit electric force, the current between the plates is 
 proportional to k^ + k 2 n 2 . The results of Wilson's experiments 
 
 oeo 
 
 0-15 
 
 010 
 
 o-c: 
 
 0-20 
 
 (NO 
 
 0-05 
 
 5 6 7 8 9 10 II 12 13 
 Fig. 140. 
 
 are represented in Fig. 140. It will be noticed that the current is 
 very small in the cathode dark space, rises to its maximum value 
 
 * H. A. Wilson, Phil. Mag. [5], xlix. p. 505, 1900. 
 
460 DISCHARGE THROUGH GASES AT LOW PRESSURES. [245 
 
 in the negative glow, sinks again in the Faraday dark space and 
 increases in the positive column, while in the striated discharge 
 the current is a maximum in the luminous parts of a striation, 
 a minimum in the dark ones. 
 
 245. It is interesting to compare the distribution of the 
 electric intensity along the tube with these transverse currents. If 
 X is the force along the tube, i the current through unit area, 
 and if the velocity of the ions is proportional to the electric force 
 at the point, then we have 
 
 X k 
 
 as i is constant along the tube, k^ + k 2 n 2 should be inversely 
 proportional to X ; as k^ + k 2 n 2 is proportional to the transverse 
 current, we should expect the maxima for the transverse current 
 to coincide with the minima for X. An inspection of the curves 
 will show that this is not the case; thus the electric intensity in the 
 Faraday dark space is less than in the positive column ; the trans- 
 verse current is also less, instead of being greater as indicated 
 by the preceding reasoning. Again, both the electric intensity 
 and the transverse current are greater at the bright parts of a 
 striation than at the dark ; in fact, luminosity seems to be accom- 
 panied by abnormally great transverse currents; it was this that 
 led H. A. Wilson to suggest that the transverse current in the 
 luminous parts was increased by secondary ionisation due to the 
 illumination of the testing electrodes by the luminosity of the 
 discharge. Skinner has suggested as another explanation for the 
 discrepancy between the values of X and the transverse current 
 that the velocity of the ions may not be proportional to the 
 electric force ; that, for example, though the electric force in 
 the Faraday dark_jspace is very small the ions there may be 
 moving with high velocities , which they acquired in moving 
 through the strong electric field in the cathode dark space ; thus 
 the number of free ions necessary to carry the current may be 
 very considerably less than that calculated from the assumption 
 that the velocity was that due to the electric force in the Faraday 
 dark space. If this were the explanation of the distribution of 
 the transverse force, then the velocity of the ions in the Faraday 
 dark space ought to be greater than in the uniform positive 
 column. Now we can get information about the distribution of 
 
245] DISCHARGE THROUGH GASES AT LOW PRESSURES. 461 
 
 the velocity of the ions at different parts of the tube by measur- 
 ing the ' Hall effect.' H. A. Wilson * has shown that when a 
 magnetic force acts at right angles to the current passing through 
 a vacuum tube, then a difference of potential proportional to the 
 magnetic force is established between two electrodes, placed so 
 that the line joining them is at right angles both to the current 
 and to the magnetic force. The theory of this effect, called the 
 'Hall effect/ has been given in Art. 115; we showed that when 
 equal quantities of positive and negative ions are present, then if 
 Z be the difference of potential between two electrodes 1 cm. 
 apart due to a magnetic force H, then 
 
 where u and v are respectively the velocities of the negative and 
 positive ions. Thus a series of measurements of Z along the 
 tube will enable us to deduce the distribution of velocities; 
 
 Transverse force in volts per era. for constant magnetic field 
 
 O ro <_w -P* C_n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N^ 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 "-*- 
 
 
 
 
 ^ 
 
 \ 
 
 
 
 
 r 
 
 
 
 *^ 
 
 
 
 
 
 
 
 4 
 
 ^< 
 
 ^-x- 
 
 ^ 
 
 -* t 
 
 
 i- 
 
 
 2 34 56 789 10 II 12 13 cmz 
 
 Positive Column. Faraday Dark Space. Negative 
 Glow. 
 
 Fig. 141. Discharge in Air. Pressure 0-5 mm. Magnetic Field 22-1. 
 
 such measurements have been made by H. A. Wilson, and his 
 
 results are represented in the curves given in Figs. 141 and 142. 
 
 * H. A. Wilson, Proc. Camb. Phil. Soc. xi. pp. 249, 391, 1902. 
 
462 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [245 
 
 It will be seen that the curves are similar in character to 
 those giving the distribution of electric force ; thus the value 
 of Z in the Faraday dark space is less than in the positive column, 
 
 IJ 
 12 
 11 
 10 
 9 
 8 
 7 
 6 
 5 
 
 4 
 3 
 
 a 
 i 
 
 ( 
 
 S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 jt 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 * 
 
 
 
 
 
 
 s 
 
 *> 
 
 
 
 *s 
 
 2 1 
 
 3 cms 
 
 ) 
 i 
 
 ft 
 
 fegati 
 
 * ^ 
 
 ? 
 
 ve 
 
 -* 
 3 ^ 
 Fara 
 
 -x 
 
 ; 
 
 lay Da 
 
 5 ( 
 rkSps 
 
 5 
 ce. 
 
 L 
 
 7 ! 
 S 
 
 m. 
 
 3 < 
 tria. 
 
 L 
 
 ? i 
 
 A 
 
 1 
 s 
 
 E 
 
 i i 
 
 tria. 
 
 Glow. 
 Fig. 142. Discharge in Air. Pressure 0-3 mm. Magnetic Field 29 '4. 
 
 and in a striated discharge Z, like X, is a maximum at the bright 
 parts of the striation, a minimum at the dark. These results 
 seem to indicate that though a certain amount of lag between the 
 values of X and the velocity of the ions is probable, especially 
 at low pressures, it is not sufficiently large to explain the dis- 
 crepancies between the curves for X and those for the trans- 
 verse currents. 
 
 On Wilson's hypothesis that there is an additional ionisation 
 due to the incidence of the light from the discharge on the metal 
 of the electrodes, the current between electrodes made of wire- 
 gauze might be expected to be less than that between solid 
 electrodes, as the area of metal exposed to the light is so much 
 less in the first case than in the second. 
 
247] DISCHARGE THROUGH GASES AT LOW PRESSURES. 463 
 
 246. The striated discharge. This form of discharge, examples 
 of which are represented in Fig. 125, taken from papers by 
 De la Rue and Mtiller*, has from its very striking and beautiful 
 character attracted a great deal of attention. It only occurs, or at 
 any rate is only well developed, when the pressure of the gas and 
 the current through the tube are within certain limits; it does 
 not however depend upon the means used to produce the dis- 
 charge ; thus we get striations in discharges produced by induction 
 coils, electric machines, or large batteries of storage or voltaic 
 cells. 
 
 The striations are especially well developed in mixed gases, 
 especially those which contain organic vapours, such as turpentine. 
 Indeed some physicists consider they would not occur in perfectly 
 pure gases f ; it is however certain that they occur in gases which 
 have been purified with the greatest care ; according to Morren 
 they do not occur in oxygen. Crookesj observed in a tube con- 
 taining hydrogen three sets of striations, one set red, another 
 blue, and the third grey ; by spectroscopic examination he showed 
 that the luminosity in the first set was due to hydrogen, that in 
 the second to mercury vapour, and that in the third to hydro- 
 carbons. It will be noticed from Fig. 125 that in some cases the 
 s.trise seem to occur in sets of two or three individual striae 
 situated quite close together. It will be seen that the luminous 
 parts of the striaB are curved ; the concavities being turned to- 
 wards the positive electrode. When the tube is not of uniform 
 width the striations are nearer together in the narrower than in 
 the broad parts of the tube. 
 
 247. Investigations on the conditions determining the distance 
 between successive striations have been made by Goldstein, and 
 by R. S. Willows||. Goldstein came to the conclusion that if d 
 and d were the distances between the striations at the pressures 
 p and p 0) then 
 
 * De la Rue and Muller, Phil. Tram. 1878, pt. i. p. 155. 
 
 f E. C. Baly, Phil. Mag. xxxv. p. 200, 1893. 
 
 J Sir W. Crookes, Proc. Roy. Soc. Ixix. p. 399, 1902. 
 
 Goldstein, Wied. Ann. xv. p. 277, 1882. 
 
 II Willows, Proc. Camb. Phil. Soc. x. p. 302, 1900. 
 
464 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [247 
 
 where m is a quantity less than unity (compare Art. 234). The 
 distance between the striations increases as the pressure diminishes, 
 but the percentage change in the distance is not so great as that 
 in the pressure. 
 
 Willows found that in nitrogen the distance between the striae 
 increased with the current. Beginning with the smallest current 
 capable of maintaining the discharge the distance at first increased 
 very rapidly with the current. The rate of increase fell off how- 
 ever as the current increased ; the connection between the current 
 and the distance between the striae in nitrogen is represented by 
 the curve in Fig. 143. 
 
 50 
 
 70 90 110 130 
 
 GA L . DfL EX/ON 
 Fig. 143. 
 
 150 
 
 170 
 
 In hydrogen the distance between the striae at first increases 
 with the current; it then attains a maximum, and then any 
 further increase in the current produces a diminution in the 
 distance between the striae the lower the pressure the smaller 
 the current for which the distance between the striae is a maximum. 
 At very low pressures this current may be very little larger than 
 the smallest current consistent with a continuous discharge, so 
 that at these pressures the phase where an increase in current 
 causes the striae to separate may be almost effaced. The relation 
 between the current and the distance between the striae for 
 hydrogen at two different pressures in a tube 12 mm. in diameter 
 is shown in Fig. 144. The terminals for curves A and B were 
 aluminium wires, for G they were aluminium discs. 
 
249] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 465 
 
 By comparing these results with those for the thickness of the 
 cathode dark space we see that under similar conditions as to 
 
 pressure and current the distance between the striae is considerably 
 greater than the thickness of the dark space. 
 
 248. Influence of the size of the discharge tube. The wider the 
 tube the greater the distance between the striae. According to 
 Willows (/. c.) this distance is never greater than the diameter 
 of the tube. When the striae reach to the sides of the tube 
 Goldstein showed that the ratio of the distances between the 
 striae for two given pressures is independent of the diameter of 
 the tube. Another way of stating Goldstein's law is that the 
 constant m which occurs in the equation 
 
 d. p 
 
 (see Art. 247) is independent of the size of the tube. 
 
 249. Influence of the nature of the gas. According to Willows 
 the distances between the striae in different gases under the same 
 conditions as to pressure and current are not very different. At 
 pressures between 1 mm. and '5 they are somewhat further apart 
 in hydrogen than in air or nitrogen. The rate of alteration of the 
 T. a. 30 
 
466 DISCHARGE THROUGH GASES AT LOW PRESSURES. [250 
 
 distance with the pressure is however greater in the denser gases 
 than in hydrogen. The range of pressure over which striations can 
 be obtained is much greater in hydrogen than in air. 
 
 250. The striae are most readily developed at the negative 
 end of the positive column. Thus if the pressure be gradually 
 reduced to that at which striation occurs, the first appearance of 
 striation is the formation of a single stria at the end of the 
 positive column. Successive striations are then formed until 
 the whole of the positive column is striated. The stria at the 
 negative end of the positive column always retains some indi- 
 viduality; thus its distance from its next neighbour is greater 
 than the average distance ; it is also often brighter than the other 
 striaB. 
 
 251. Effect of a sudden contraction in the discharge 
 Goldstein* found that in a tube with a constriction, such as that 
 in Fig. 145, the end of the constriction next the anode behaved 
 
 Fig. 145. 
 
 like a cathode, i.e. that there was a dark space, negative glow, and 
 Faraday dark space close to a ; and that these were affected by a 
 magnetic field in just the same way as if they had been produced 
 by a metallic cathode. Lehmannf made a series of experiments 
 with perforated diaphragms stretching across the discharge tube. 
 He found on the side of the diaphragm next the anode the 
 
 Fig. 146. 
 
 negative glow and the Faraday dark space ; the cathode dark 
 space was however absent. In the experiment represented in Fig. 
 146 the diaphragm was a porcelain sieve. He made other experi- 
 ments with tubes having several perforated metallic diaphragms 
 
 * Goldstein, Wied. Ann. xi. p. 832, 1880. 
 f Lehmann, Drud^s Ann. vii. p. 1, 1902. 
 
252] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 467 
 
 stretching across them. These diaphragms were connected with 
 wires fused through the tube so that they could be connected up 
 in various ways. If the diaphragms were all insulated the appear- 
 ance of the discharge was as represented in Fig. 146. On the 
 
 t 
 
 r 
 4- 
 
 c h c 
 
 Fig. 147. 
 
 anode side of each diaphragm there was the negative glow and 
 the Faraday dark space, but no cathode dark space. If however 
 two of the diaphragms were connected together by a metallic wire 
 outside the tube, as Fig. 147, there was negative light but no dark 
 space on the right of the diaphragms a and c ; there was however 
 a well defined dark space on the right of b. In this case some of 
 the current instead of passing through the tube might pass through 
 the wire outside, and at b would have ; as at the cathode k, to pass 
 from the metal to the gas. At the other diaphragms we may 
 suppose the current went through the holes in the diaphragm. 
 
 252. Alternations in the luminosity of the discharge, similar 
 
 Fig. 148. 
 
 in appearance to those observed in the striated positive column 
 
 302 
 
 at 
 
468 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [253 
 
 low pressures, occur in certain cases in the discharge through gas 
 at atmospheric pressure. Thus Topler* found that if several 
 large Leyden jars were discharged across a spark gap, a plate of 
 semi-insulating material such as basalt being inserted between 
 the terminals, the portion of the discharge between the negative 
 electrode and the plate showed distinct striations. Fig. 148 is 
 copied from a figure given by Topler. The discharge of an in- 
 duction coil through the flame of a candle gives a bright discharge 
 traversed by dark spaces as in Fig. 149. 
 
 Fig. 149. 
 
 253. Distribution of temperature along the line of discharge. 
 The average temperature of the gas in a discharge tube through 
 which a luminous discharge is passing is often less than 100 C. 
 Thus E. Wiedemannf proved that the average temperature of 
 air at a pressure of 3 mm. in a tube conveying a luminous dis- 
 charge was less than 100 C. Hittorf J measured the temperature 
 in a discharge tube at three places, (1) in "the positive column, 
 
 * Topler, Wied. Ann. Ixiii. p. 109, 1897. 
 
 f E. Wiedemann, Wied. Ann. vi. p. 298, 1879. 
 
 J Hittorf, Wied. Ann. xxi. p. 128, 1884. 
 
253] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 469 
 
 (2) in the negative glow and (3) in the Crookes dark space, and 
 found that it was highest in (3) and lowest in (1). E. Wiede- 
 mann* showed that the distribution of temperature along the 
 tube depended materially upon the pressure, and that while at 
 low pressures the temperature of the cathode was higher than 
 that of the anode, the reverse was true at pressures greater 
 than 26 mm. Woodf made a very complete survey of the tem- 
 perature in a discharge tube by means of a bolometer, which, 
 floating on a barometer column of mercury, could be placed in 
 any position in the tube. He found that in the unstriated dis- 
 charge .the temperature is constant in the positive column, 
 diminishes in the Faraday dark space until it reaches a minimum 
 just on the anode side of the negative glow, and then rapidly 
 increases in the dark space next the cathode. In the striated 
 discharge the temperature is greater in the luminous parts than 
 in the dark. In no case did the bolometer indicate a temperature 
 of more than 100 C. The bolometer temperature is of course 
 the average temperature of .all the molecules in a considerable 
 space, and the fact that the average temperature is low does 
 not preclude a few of the molecules possessing an amount of 
 kinetic energy very much greater than that corresponding to the 
 
 m- 
 
 Fig. 150. 
 
 temperature indicated by the bolometer. The distribution of tem- 
 perature along the tube in a striated and an unstriated discharge 
 is indicated by the curves in Fig. 150. It will be seen on com- 
 
 * E. Wiedemann, Wied. Ann. x. p. 202, 1880. 
 t Wood, Wied. Ann. lix. p. 238, 1896. 
 
470 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 [254 
 
 paring these with the curves given for the distribution of electric 
 force along the tube that the two curves are very similar. As 
 the rate of work done by the current at any point of its path is 
 proportional to the product of the current and the electric force, 
 or since the current is constant, to the electric force, if all the 
 work were converted into heat the curves for temperature would 
 be similar to those for electric force. As this is very approximately 
 the case we conclude that in tubes of moderate pressure the greater 
 part of the electrical work appears as heat in the gas at places 
 not very distant from where the work is done. 
 
 254. Action of a magnetic field on the discharge. It is con- 
 venient to consider separately the action of the magnetic force 
 on the various parts of the discharge. We shall begin with the 
 negative glow. Pliicker* showed that under a magnetic field the 
 glow distributed itself in just the same way as a collection of iron 
 filings, having perfect freedom of motion ; thus the bright boundary 
 of the negative glow coincides with the lines of magnetic force 
 passing through the end of the negative electrode. This effect is 
 illustrated in Figs. 151 and 152, which are taken from Pliicker's 
 
 Fig. 151. 
 
 paper. In Fig. 151 the lines of magnetic force are transverse 
 to the current, while in Fig. 152 they are more or less along it. 
 The negative glow in, fact behaves as if its luminosity were 
 
 * Pliicker, Pogg. Ann. ciii. p. 88, 1858. 
 
 
254] 
 
 DISCHARGE THROUGH GASES AT LOW PRESSURES. 
 
 471 
 
 produced by something moving along the lines of magnetic 
 force. If the direction of the magnetic force is along the line 
 
 Fig. 152. 
 of discharge the negative glow spreads further down the tube 
 
 Fig. 153. 
 
 and the positive column is driven back; if the magnetic force 
 
 Fig. 154. 
 
 is at right angles to the tube, the negative glow follows the lines 
 of force across the tube and does not extend so far down as when 
 
472 DISCHARGE THROUGH GASES AT LOW PRESSURES. [255 
 
 there is no magnetic field ; the positive column now comes further 
 down the tube towards the cathode, and if it is striated new stria- 
 tions appear. These effects are illustrated by Figs. 154 and 155, 
 
 Fig. 155. 
 
 which are due to Lehmann*. Fig. 154 represents the case when 
 the magnetic force is along, Fig. 155 when it is across the tube. 
 
 255. Magnetic force affects the disposition of the glow over 
 the surface of the cathode as well as its course through the gas. 
 Thus Hittorff found that when the negative electrode is a flat 
 vertical disc and the discharge tube is placed so that the disc lies 
 axially between the poles of a strong electromagnet, the disc is 
 cleared of glow except on the highest point on the side most 
 remote from the anode or the lowest point on the side nearest to 
 it, according to the direction of the magnetic force. In another 
 experiment Hittorf, using as cathode a metal tube about 1 cm. in 
 diameter, found that when the axis of the cathode was at right 
 angles to the line joining the poles of an electromagnet the cathode 
 was cleared of glow in the neighbourhood of the places where the 
 normals are at right angles to the lines of magnetic force. Both 
 these results are what we should expect if the glow were due to 
 charged particles projected normally from the cathode. The effect 
 of a magnetic field on the disposition of the glow over the cathode 
 has also been investigated by Schuster J. 
 
 256. The positive column is also affected by the magnetic 
 field, the general effect being that the column is bent into a curve 
 
 * Lehmann, Drude's Ann. vii. p. 1, 1902. 
 f Hittorf, Pogg. Ann. cxxxvi. p. 221, 1869. 
 Schuster, Proc. Roy. Soc. xxxvii. p. 317, 1884. 
 
257] DISCHARGE THROUGH GASES AT LOW PRESSURES. 473 
 
 resembling the path of a positive particle under the action of 
 the magnetic field and the electric force in the tube (see Art. 
 40). When the negative glow is deflected the positive column 
 bends towards the place where the negative glow reaches the 
 walls of the tube ; this effect is shown in Fig. 156, which is due 
 to Lehmann. There is often a dark space separating the ends of 
 the negative glow and the positive column, as if the area of contact 
 of the former with the glass acted like a secondary cathode. 
 
 Fig. 156. 
 
 257. Effect of magnetic force on the striations. The influence 
 of the magnetic field on the striations has been carefully studied 
 by Spottiswoode and Moulton*, and by Goldstein f; the conclu- 
 sion they arrived at was that the bright parts of the striations, 
 like the negative glow, set themselves along the lines of magnetic 
 force, each bright part setting along the line of magnetic force 
 passing through it and being separated by a dark space from its 
 neighbour. As very important deductions have been made from 
 this behaviour of the striae, we quote the description of this effect 
 given by Spottiswoode and Moulton and by Goldstein. The 
 former say : " If a magnet be applied to a striated column it will 
 be found that the column is not simply thrown up or down as a 
 whole, as would be the case if the discharge passed in direct lines 
 from terminal to terminal threading the striae in its passage. On 
 the contrary, each stria is subjected to a rotation or deformation of 
 exactly the same character as would be caused if the stria marked 
 the termination of flexible currents, radiating from the bright head 
 of the stria behind it and terminating in the hazy inner surface 
 of the stria in question. An examination of several cases has led 
 the authors of this paper to conclude that the currents do thus 
 radiate from the bright head of a stria to the inner surface of the 
 next, and that there is no direct passage from one terminal of the 
 
 * Spottiswoode and Moulton, Phil. Trans. Part i. p. 205, 1879. 
 t Goldstein, Wied. Ann. xi. p. 850, 1880. 
 
474 DISCHARGE THROUGH GASES AT LOW PRESSURES. [258 
 
 tube to the other." Goldstein gives the following description of 
 the behaviour of the striated column under magnetic force : " The 
 appearance is very characteristic when in the unmagnetized con- 
 dition, the negative glow penetrates beyond the first striation into 
 the positive column. The end of the negative glow is then further 
 from the cathode than the first striation or even, if the rarefaction 
 is suitable, than the second or third. Nevertheless the end of the 
 negative glow rolls itself under the magnetic action up to the 
 cathode in the negative curve which passes through the cathode. 
 Then separated from this by a dark space follows on the side of 
 the anode a curve in which all the rays of the first striation are 
 rolled up, then a similar curve for the second striation, and so on." 
 We shall have occasion to refer to this point again when we 
 consider the theory of the discharge. 
 
 258. Paalzow and Neesen *, who investigated the effect of a 
 magnetic field in helping or retarding the discharge, found that 
 when the lines of force are parallel to the line of discharge, the 
 nature of the effect depends upon pressure ; if p is the pressure 
 at which the discharge first begins, p m the pressure when the 
 current through the tube is a maximum, and p n the lowest 
 pressure at which the discharge passes, then for pressures be- 
 tween p and p m the magnetic force retards the discharge, while 
 if the pressure is between p m and p n it helps it ; thus the 
 magnetic field produces in this case the same effect as an 
 increase in pressure. The same results are true if the anode 
 alone is exposed to the magnetic force; if only the cathode is 
 exposed to this force the preceding results hold if the field is 
 weak ; if the field is very strong, however, the effects produced are 
 just the opposite, the magnetic field producing the same effect as 
 a diminution in pressure. 
 
 When the lines of magnetic force are at right angles to the 
 discharge the magnetic field at all pressures retards the discharge- 
 They found that the effect of the magnetic field was not instan- 
 taneous, often taking several seconds before producing its normal 
 effect. This lag is a very frequent phenomenon in the discharge 
 tube ; it generally can be explained by the effects produced by 
 previous sparks ; thus as it is easier for one discharge to .follow 
 
 * Paalzow and Neesen, Wied. Ann. Ixiii. p. 209, 1897. 
 
259] DISCHARGE THROUGH GASES AT LOW PRESSURES. 475 
 
 another than to be the first to pass through the tube, the magnetic 
 field might not be able at once to stop the discharge if a strong 
 discharge had just previously passed through the tube, though it- 
 might be able to prevent a discharge starting in the tube. 
 
 The author showed many years ago that the passage of the 
 electrodeless discharge was hampered by a transverse magnetic 
 field and facilitated by a longitudinal one. 
 
 259. Willows*, who also investigated the effect of a transverse 
 magnetic field on the potential difference between the terminals 
 of a discharge tube containing gas at a low pressure, found that 
 when the magnetic force is confined to the neighbourhood of the 
 cathode the potential difference is diminished by the magnetic 
 field when the pressure is low and increased when it is high. 
 The effect is represented in the curves in Fig. 157, the scale of 
 
 60 
 
 (,^0 
 
 4io 
 600 
 580 
 56o 
 
 540 
 520 
 5"0o 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 \ 
 
 
 
 A./ 
 
 1AGW 
 
 :r o> 
 
 /. 
 
 
 
 
 
 
 A 
 
 
 
 B. A 
 
 IHGNt 
 
 T Of 
 
 F 
 
 
 
 
 
 
 V 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 \ 
 
 
 
 
 
 
 A^ 
 
 * 
 
 
 
 
 
 V 
 
 s 
 
 
 
 ^ 
 
 ""' 
 
 
 
 
 
 
 
 \ 
 
 
 ^^ 
 
 *~ 
 
 ***" 
 ^ ^^ 
 
 a * 
 
 
 
 Ji-J 
 
 
 20 40 (.0 80 100 1*0 140 'kO 'SO 700 MO 
 
 Pressure. 
 Fig. 157. 
 
 pressures is such that a pressure of 1 mm. of mercury is repre- 
 sented by 223. The pressure at which the curve for the magnet 
 on intersects that for the magnet off, increases as the magnetic 
 force increases and decreases when the current through the tube 
 decreases. When the magnetic force is concentrated at any 
 part of the tube except the cathode it always increases the 
 potential difference. 
 
 * Willows, Phil. Mag. vi. 1, p. 250, 1901. 
 
476 DISCHARGE THROUGH GASES AT LOW PRESSURES. [260 
 
 Willows also investigated the effect of a uniform transverse 
 magnetic field on the distribution of electric force between the 
 terminals, the results of his experiments are represented by the 
 curves in Fig. 158 ; the magnetic field diminishes to a considerable 
 extent the great drop in the electric force which occurs in the 
 negative glow. 
 
 = 2'///nm. 
 
 I 
 
 Cathode 
 
 Fig. 158. 
 
 Anode 
 
 260. Birkeland* has shown that in a tube containing gas at a 
 very low pressure a strong magnetic force parallel to the line of dis- 
 charge produces an enormous diminution in the potential difference 
 required to spark through the tube ; the potential difference when 
 the magnetic force at the cathode reaches a critical value falling 
 to less than one-tenth of its previous value. Almyf has shown 
 
 * Birkeland, Comptes Rendus, cxxvi. p. 586, 1898. 
 t Almy, Proc. Camb. Phil. Soc. xi. p. 183, 1901. 
 
262] DISCHARGE THROUGH GASES AT LOW PRESSURES. 477 
 
 that this effect can be produced by a transverse magnetic force as 
 well as by a longitudinal one, and that the sudden diminution in 
 potential is accompanied by a change in the appearance of the 
 discharge, the magnet causing the discharge to change from a form 
 in which it passes from the whole of the cathode to one where 
 it is concentrated in one or more bright streams. This change in 
 the appearance of the discharge, and also the diminution in the 
 potential difference between the terminals, can be produced 
 without the aid of the magnet by covering the outside of the 
 tube in the neighbourhood of the cathode with tinfoil connected 
 with the cathode. Almy showed that the effect of the magnet did 
 not arise from the charges of statical electricity which accumulate 
 on the glass of the tube, by showing that it took place when the 
 cathode was placed inside a metal cylinder which was used as the 
 anode. 
 
 261. We have already (see p. 358) described the appearance 
 presented by the discharge when the terminals are placed very 
 near together, an interesting modification of such an experiment 
 is shown in Fig. 159, which represents an experiment made by 
 
 Fig. 159. 
 
 E. Wiedemann* in which the anode was enclosed in a narrow 
 glass tube which dipped into the cathode dark space ; it will be 
 noticed that the positive light turns round after leaving the tube 
 and joins the negative glow. 
 
 262. Discharge produced by very rapidly alternating electro- 
 motive forces. E. Wiedemann and Ebertf and HimstedtJ have 
 made some very interesting experiments when the discharge was 
 sent through the tube by the very rapidly alternating forces 
 produced by discharging a condenser; in Wiedemann and Ebert's 
 experiments the terminals were connected with the terminals in 
 a Lecher's bridge arrangement producing electrical oscillations 
 
 * E. Wiedemann, Wied. Ann. Ixiii. p. 242, 1897. 
 
 t E. Wiedemann and Ebert, Wied. Ann. 1. pp. 1, 221, 1893. 
 
 $ Himstedt, Wied. Ann. lii. p. 473, 1894. 
 
478 DISCHARGE THROUGH GASES AT LOW PRESSURES. [262 
 
 whose time of swing was only about 10~ 8 seconds. In Himstedt's 
 experiments the alternating forces were produced by a Tesla 
 transformer. The appearance presented by the tube is shown 
 in Fig. 160 ; it will be seen that both electrodes show only 
 the phenomena associated with a cathode, i.e. we have the dark 
 space, the negative glow, and the Faraday dark space, but no 
 
 Fig. 160. 
 
 positive light ; the latter is represented by the luminosity in the 
 middle of the tube ; this disappears at very low pressures. The 
 thickness of the dark space next the electrode diminishes as the 
 rapidity of the oscillations increases. 
 
CHAPTER XVI. 
 
 THEORY OF THE DISCHARGE THROUGH VACUUM TUBES. 
 
 263. WE shall now proceed to apply the theory given on 
 p. 376 of the spark discharge to explain some of the phenomena 
 observed when the discharge passes through a vacuum tube con- 
 taining gas at a low pressure. We have regarded the spark 
 discharge as originating in the ionisation of the gas by moving 
 ions, the small negative ions the corpuscles being more efficient 
 ionisers than the positive ones, which have a greater mass. If, 
 however, the ionisation in an electric field not exposed to external 
 ionising agents, such as Rontgen rays, were solely due to the 
 collisions of corpuscles with the molecules of the gas we could not 
 have a continuous current through the gas. For suppose, to begin 
 with, there were a few corpuscles between the electrodes, then 
 if the negative electrode is on the right the electric field will set 
 the corpuscles moving to the left, and if it were strong enough 
 ionisation would occur between the positive electrode and the 
 place from which the original corpuscles started. The new cor- 
 puscles produced by the collisions of the original ones with the 
 molecules of the gas would themselves produce new ions, but all 
 these would be formed to the left of the birth-place of the ions 
 which produced them, there would thus be a gradual exodus of 
 corpuscles towards the positive electrode while the gas round 
 the negative electrode would in time be deprived of corpuscles 
 and would cease to conduct, and by hypothesis it could no longer be 
 ionised as all the negative ions would have been driven to the 
 positive electrode. 
 
480 THEORY OF THE DISCHARGE [263 
 
 We have seen that in every gas 'spontaneous' ionisation is 
 continually taking place, and it might be urged that this process 
 would furnish a supply of negative ions which would rapidly 
 multiply by collisions with the molecules of the gas, and so 
 furnish a supply of carriers sufficient for the current through 
 the tube. If this were the case however the potential difference 
 between the electrodes would vary rapidly with the current, in 
 reality however the variation is very slight. 
 
 Again, the current under a given difference of potential would 
 depend upon the amount of the spontaneous ionisation, i.e. the 
 ionisation independent of the electric field ; we can however increase 
 the latter a hundredfold by exposing the gas in the discharge 
 tube to the action of Rontgen rays without producing any appre- 
 ciable increase in the current passing through the gas. To account 
 for the phenomena of the discharge we must have ionisation 
 produced by the electric field itself close to the cathode; we 
 shall suppose that this ionisation is produced by the positive, 
 ions, and although these require a much greater amount of energy 
 before they can act as ionisers than do the corpuscles, yet the very 
 intense electric field which exists close to the cathode is sufficient 
 to give them, when under its influence they have come up to 
 the cathode, all the energy they require. 
 
 There are several ways in which these rapidly moving positive 
 ions might produce fresh negative ions ; the two that most 
 naturally suggest themselves are, (1) that the positive ions by 
 collision ionise the molecules of the gas near the cathode, (2) that 
 the positive ions by striking against the surface of the cathode 
 communicate so much energy to the corpuscles contained in the 
 layer of metal close to the surface of the cathode that they are 
 able to escape from the metal, just as they are able to escape from 
 a metal when it is raised to incandescence. 
 
 The consequences will be very much the same whichever of 
 these views we take ; for the strength of the electric field increases 
 so quickly near the surface of the cathode that the kinetic energy 
 possessed by the positive ions, when they arrive quite close to the 
 surface, will be enormously greater than when they are just a 
 little further off, so that any ionisation produced by the collision 
 of these positive ions with the molecules of the gas will be 
 practically confined to the layer of gas close to the surface of the 
 
264] THROUGH VACUUM TUBbiS. 481 
 
 cathode. It is possible that the luminous glow which spreads 
 over the cathode marks the seat of this ionisation. Thus whether 
 we suppose the positive ions to act according to the method (1) or 
 (2) we have negative ions starting from close to the surface of the 
 cathode ; these are driven from it by the electric field and soon 
 acquire such velocities that they ionise the gas through which 
 they pass, producing a supply of positive ions which are attracted 
 by the electric field up to the cathode, there to produce a fresh 
 supply of negative ions. 
 
 Thus the positive and negative ions in the space close to the 
 cathode are on this view mutually dependent; if the supply of 
 either is stopped, that of the other at once fails. This is very well 
 illustrated by the experiment represented in Fig. 110, p. 384, in 
 which an obstacle placed in the dark space throws a shadow as it 
 were backwards and forwards ; the obstacle stops the supply of 
 positive ions to a portion of the cathode (the portion in shadow); 
 this portion is no longer able to send out negative ions, in fact 
 it ceases to act as an electrode. 
 
 Origin of the dark space. 
 
 264. Let us now consider in more detail the ionisation pro- 
 duced by the negative ions coming from the cathode. The primary 
 ones which start from or near the surface will in consequence of 
 the very intense electric field which exists close to the cathode be 
 shot out with very great velocity, they will therefore be cathode 
 rays of a very penetrating kind ; such rays in a given length of 
 path do not produce so much ionisation as those moving with a 
 smaller velocity. Let us now consider the case of a corpuscle 
 produced by the collision of one of the primary ones with a 
 molecule some little distance in front of the cathode ; this 
 ' secondary ' corpuscle will start from a field much less intense 
 than that from which the primary corpuscle started, it will therefore 
 not acquire nearly so great a velocity; it will correspond to a 
 much more easily absorbed kind of cathode ray, and will therefore 
 in a given length of path produce many more ions. Again, the 
 corpuscles produced by the ' secondary ' corpuscles or by the 
 primary ones at a greater distance from the cathode will in 
 consequence of their smaller velocity be still more easily absorbed, 
 T. G. 31 
 
482 
 
 THEORY OF THE DISCHARGE 
 
 [265 
 
 and therefore produce still more ions per unit of path. Thus the 
 amount of ionisation will be small in the strong parts of the field 
 near the cathode, but will increase with great rapidity when we 
 get to the weaker parts. Thus if ionisation were accompanied by 
 luminosity the places close to the cathode where the electric field 
 is strong would be dark, while the luminosity would increase with 
 very great rapidity in the places more remote from the cathode 
 where the electric field is weaker : the increase would be so rapid 
 that the contrast and line of demarcation between the light and 
 dark places would be sharply marked. 
 
 265. The scarcity of the negative ions in the strong field close 
 to the cathode and their rapid increase in the weaker parts of the 
 field towards the negative glow are strikingly shown in some 
 
 cathode 
 
 Fig. 161. 
 
 experiments made by the writer*. In these a discharge tube was 
 used similar to that shown in Fig. 161, G is a floating cathode 
 which can be raised or lowered in the tube, A is the anode, and B 
 
 J. J. Thomson, Phil. Mag. vi. 1, p. 361, 1901. 
 
265] 
 
 THROUGH VACUUM TUBES. 
 
 483 
 
 a closed metal vessel provided with a window covered with very 
 thin aluminium foil. The impact of negative ions on this 
 window was found to generate rays which penetrated the tinfoil 
 and ionised the gas in the closed vessel. This gas therefore 
 conducted electricity, and if the electrode D was charged and 
 connected with an electrometer, the charge leaked from it, the 
 rate of leaking indicating the amount of ionisation in the gas, 
 care being taken to charge up the electrode to a sufficiently high 
 potential to produce the saturation current through the gas. The 
 rays are very easily absorbed, this is clearly shown by diminishing 
 the pressure of the gas in the closed vessel B and observing the rate 
 of leak at different pressures. As long as the rays are entirely 
 absorbed in passing through the gas in the vessel, the number of 
 ions in the vessel, and therefore the saturation current, will be 
 independent of the pressure of the gas ; as soon however as the 
 pressure gets so low that the rays pass through the gas without 
 much absorption, the saturation current becomes proportional to 
 the pressure. The following table, which gives the variation of 
 the saturation current with the pressure, shows that it is not 
 until the pressure gets low that the saturation current is affected 
 by the pressure, hence we conclude that the radiation produced 
 by the impact of the negative ions against the window can 
 only penetrate through a few millimetres of air at atmospheric 
 pressure : 
 
 Pressure in vessel D 
 (thickness of vessel 1 cm. ) 
 
 Saturation current 
 
 770 mm. 
 
 87 
 
 270 
 
 90 
 
 100 
 
 64 
 
 45 
 
 37 
 
 10 
 
 11 
 
 5 
 
 3 
 
 The intensity of the rays produced by these negative ions 
 depends very much upon the distance of the window from the 
 cathode. This is clearly shown by the following table, the results 
 of which are represented by the curve in Fig. 162, in which the 
 ordinates represent the amount of ionisation in the vessel and the 
 abscissae the distance from the cathode. 
 
 312 
 
484 THEORY OF THE DISCHARGE [265 
 
 Pressure in discharge tube 6 m. Width of dark space 6 mm. 
 
 Distance of window from 
 
 lonisation in vessel I) 
 
 surface of cathode 
 
 (arbitrary units) 
 
 3 
 
 21 
 
 4 
 
 54 
 
 5 
 
 105 
 
 6 
 
 195 
 
 8 
 
 150? 
 
 10 
 
 180 
 
 20 
 
 66 
 
 30 
 
 40 
 
 40 
 
 25 
 
 It will be seen that the effect of the rays produced by the impact 
 is small close to the cathode, increases very rapidly as we approach 
 the negative glow, attains a maximum in the glow, and then 
 
 Fig. 162. 
 
 quickly drops down to a very small value ; in fact the effect 
 produced by the collision 'of the negative ions against the window 
 varies in the way that we have described for the amount of 
 ionisation produced by the collision of the corpuscles with the- 
 molecules of the gas. 
 
267] THROUGH VACUUM TUBES. 485 
 
 266. The fact that the ionisation inside the vessel D increases 
 and decreases with the luminosity in the discharge might lead to 
 the suspicion that the ionisation inside D was not due to rays 
 generated by the impact of negative ions against the window, but 
 to the light coming from the gas ; that it is in reality due to the 
 former and not to the latter cause is shown by the following experi- 
 ment. The tube was placed in a field of magnetic force, the lines of 
 magnetic force being parallel to the window in the box D; the 
 magnetic field concentrates the negative glow and increases its 
 luminosity, so that if the ionisation in the box were due to the 
 luminosity and not to the impact it should be increased by the 
 magnetic field ; on the other hand, since the negative ions move 
 parallel to the lines of magnetic force, and therefore parallel to 
 the window, the impact of the ions against the window is stopped, 
 so that if this is the cause of the ionisation inside the box it 
 should be very much diminished by the field ; on trying the 
 experiment it was found that the magnetic field almost entirely 
 stopped the ionisation. 
 
 267. On the theory we are discussing the negative glow is 
 due to the ionisation brought about by collisions between mole- 
 cules of the gas and corpuscles which have started some distance 
 from the cathode, such corpuscles being the descendants, so to 
 speak, of the corpuscles which started from close to the cathode 
 and which move with very much greater velocity than the glow- 
 producing corpuscles which have started in a much weaker 
 electric field. The thickness of the dark space will evidently be 
 greater than the mean free path of a corpuscle, for this would be 
 the approximate magnitude of the dark space if the negative 
 glow were produced by collisions with the corpuscles from the 
 cathode; the greater the mean free path the further will the 
 negative glow be from the cathode, and we should expect from 
 the preceding theory a linear relation between the thickness of the 
 dark space and the mean free path. 
 
 The corpuscles which start from close to the cathode being 
 but little absorbed may sometimes pass right through the negative 
 glow, as in the case of the discharge studied by E. Wiedemann 
 and represented in Fig. 124, p. 432. These corpuscles are the 
 cathode rays which we shall discuss in the next chapter. 
 
486 THEORY OF THE DISCHARGE [268 
 
 268. When ionisation takes place in the region round the 
 cathode the positive ions move towards the cathode, while the 
 negative ones move away from it ; this produces an excess of 
 positive electricity in the gas near the cathode. In consequence of 
 this positive charge the electric force diminishes as we recede from 
 the cathode. When the electric field sinks below a certain value 
 it can no longer communicate to the corpuscles sufficient energy 
 to make them act as ionisers, so that after the field has sunk to 
 this value the ionisation will cease ; it would be more accurate to 
 say that the ionisation will cease soon after the field has reached 
 this value, for the corpuscles may retain for some little distance 
 the energy they acquired in stronger parts of the field and so 
 continue to act as ionisers for a short distance in the weak field. 
 The limit of the negative glow, furthest from the cathode, marks 
 on our view the place where ionisation ceases. 
 
 269. Let us now consider what would happen in the gas 
 between the anode and the negative glow g. Let us suppose for 
 a moment that there is no ionisation taking place between g and 
 the anode. Then as the current will be carried by ions dragged 
 by the electric field from the region of ionisation between g and 
 the cathode, all the ions between g and the anode will be negative 
 ions, so that there will be a negative charge in the gas to the 
 left of g ; but a negative charge involves an increase in the electric 
 force as we go from g towards the anode, and if the anode is far 
 enough away the electric field may increase to such an extent 
 that it is again able to give to the negative corpuscles sufficient 
 kinetic energy to make them ionisers. When this happens the 
 gas again becomes luminous, and we have in fact a repetition of 
 the process occurring in the negative glow. The increased ionisa- 
 tion in the luminous part of the discharge will diminish the 
 strength of the electric field until this gets so weak that no further 
 ionisation takes place, the luminosity again ceases and the current 
 will again, as in the Faraday dark space, be carried by ions pro- 
 duced elsewhere; there will also, as in that space, be an excess of 
 negative ions, this will cause the electric force again to increase, 
 ionisation accompanied by luminosity will recur, and the process 
 will be repeated right up to the anode ; we thus get bright and 
 dark patches as in the striated positive column. On this view the 
 luminous portions of the striations correspond to the negative 
 
270] THROUGH VACUUM TUBES. 487 
 
 glow, the intervening dark spaces to the Faraday dark space, the 
 process taking place along the positive column being a repetition 
 of that taking place near the cathode. The similarity between 
 the striated positive column and the phenomena at the cathode has 
 been insisted on by several observers, notably by Spottiswoode and 
 Moulton*, Goldstein -f- 5 and LehmannJ. Goldstein's statement is 
 very clear and explicit, he says, " Jede einzelne Schicht des posi- 
 tiven Lichtes ist ein dem frtiher sogenannten negativen oder 
 Kathodenlichte entsprechendes Gebilde, und das geschichtete 
 positive Licht besteht eigentlich aus einer Aufeinanderfolge von 
 Komplexen negativen Lichtes ." Several observers have regarded 
 the behaviour of the positive column as necessarily implying a 
 discontinuity in the discharge. Thus Spottiswoode and Moulton 
 from the behaviour of the striated column liken the transmission 
 of electricity along the positive column "to an action consisting 
 of an independent discharge from one stria to the next, and the 
 idea of this action can perhaps be best illustrated by that of a line 
 of boys crossing a brook on stepping stones, each boy stepping on 
 to the stone the boy in front of him has left." On the view we 
 have indicated above a striated discharge need not necessarily be 
 discontinuous. 
 
 270. We saw in Art. 35 that when the velocity of the ions 
 is proportional to the electric force the curve representing the 
 relation between the electric force at a point and the distance of 
 that point from one of the electrodes is convex to the axis when 
 the ionisation in the gas is greater than the recombination of the 
 ions, and concave when it is less. The curve representing the 
 distribution of electric force along the striated positive column is 
 however (see Fig. 129) concave at the bright parts of the striae 
 where we have supposed the ionisation to be greatest, and convex 
 at the dark parts where the ionisation is least. In a case, however, 
 like that of a striated discharge where the pressure of the gas is 
 low, and the free path of a corpuscle therefore considerable, the 
 velocity of a corpuscle at a point will depend not only upon 
 the magnitude of the electric force at that point, but also upon 
 the forces which acted upon it before it reached the point : thus 
 
 * Spottiswoode and Moulton, Phil. Trans. Part i. p. 205, 1879. 
 
 t Goldstein, Wied. Ann. xi. p. 831, 1880; xii. pp. 90, 249, 1881. 
 
 Lehmann, Die Elektrischen Entladungen. 
 
 Goldstein, Berlin. Monatsber. May 4, 1876. 
 
488 THEORY OF THE DISCHARGE [271 
 
 the conditions upon which the investigation in Art. 35 is based 
 need not apply in this case. 
 
 271. Case when the discharge is not striated and the positive 
 column is of uniform intensity. The corpuscles are continually re- 
 combining, so that unless there is fresh ionisation their number is 
 continually diminishing : if the rate of ionisation is equal to that 
 of recombination the number of corpuscles will remain constant. 
 Thus if, when the ionisation begins at the anode end of the Faraday 
 dark space, the strength of the field is such that the number of 
 ions produced by it in unit time is just equal to the number which 
 recombine in that time, the number of ions, the strength of the 
 field, the amount of ionisation, and therefore the luminosity will 
 be constant all along the line of discharge, and we shall have the 
 case of the uniform positive column. 
 
 272. Anode fall of potential. Let us consider a point P close 
 to the anode A, then the current at P is carried by negative 
 corpuscles produced further from the anode than P and by positive 
 ions either coming out of the anode or produced from the gas 
 between P and A. That a considerable supply of positive ions 
 is produced within a short distance of the anode is proved by the 
 fact that in the uniform positive column the electric force is 
 constant within a short distance of the anode, and when this is the 
 case there are as many positive as negative ions per unit volume' 
 of the gas. Thus if the ions are produced in the gas the ionisation 
 in the gas near the anode must be so intense that in an exceed- 
 ingly thin layer of gas there are sufficient positive ions produced 
 to neutralise the electrostatic effect of the negative ones moving 
 up to the anode. Now under these conditions, if i is the current, 
 R l} R 2 the velocities of the positive and negative ions respectively, 
 the number of positive ions which cross unit area of the uniform 
 positive column in unit time is R l il(R l + R 2 ) e, where e is the 
 charge on an ion. Suppose w is the work required to ionise a 
 molecule of the gas, then in the thin layer referred to an amount 
 of work equal to wR l i/(R l + R 2 )e must be done by the electrical 
 field in unit time ; but if V is the difference of potential between 
 the two sides of this layer (one of these sides is the anode), the 
 electrical work done in unit time is VR 2 i/(Rj + R. 2 ), since the 
 quantity of negative electricity entering this layer in unit time 
 
273] THROUGH VACUUM TUBES. 489 
 
 is R. 2 i/(R l + R. 2 ); hence supposing all the electrical work is spent 
 in ionising the gas, we have 
 
 VR 2 i R,wi 
 
 or e -^w] 
 
 M z 
 
 this is an inferior limit to F, since it is obtained on the assumption 
 that all the work is spent in ionising the gas : we have thus a 
 finite drop in the potential at the anode. If we proceed on the 
 other supposition, that the positive ions come from the anode, just 
 as we have seen positive ions do come out of metal or out of the 
 gases absorbed by metal when the temperature is above a dull 
 red heat, the preceding investigation will still apply, if 10 stands 
 for the energy required to eject an ion from the metal, so that 
 in this case again there is a finite drop of potential at the 
 anode. 
 
 273. Action of magnetic force upon tJie discharge. We have 
 seen (see Art. 40) that when a charged particle moving through a 
 gas is acted upon by both electric and magnetic forces, it will follow 
 the lines of magnetic and not of electric force, provided RH is a 
 large quantity ; here H is the magnetic force, and R the velocity 
 acquired by an ion under unit electric force. Another way of ex- 
 pressing the same result is to say that a charged particle, moving 
 with the velocity v, will follow the lines of magnetic force if mv/eH, 
 the radius of the circle into which the path of a free particle 
 is bent when moving at right angles to the magnetic force, is 
 small compared with the mean free path of the particle. The 
 result when put in this form is obvious, since (see p. 82) the free 
 paths of the particles are spirals round the lines of magnetic 
 force, and as the radii of these spirals are small compared with 
 the length of the mean free path the only direction in which 
 the particles make any appreciable progress is that of the mag- 
 netic force. The negative particles will be much more likely than 
 the positive to follow the lines of magnetic force ; for in the first 
 place, the mean free path of the negative particles is greater than 
 that of the positive, and secondly, the value of m/e is much less 
 for the negative than for the positive particles. Thus we may 
 expect the negative particles to follow the lines of magnetic force, 
 
490 THEORY OF THE DISCHARGE [274 
 
 even when the motion of the positive ones is but little affected 
 by the magnetic field. The tendency of the negative particles 
 to follow the lines of magnetic force is strikingly shown by the 
 behaviour of the negative glow in a strong magnetic field, when, 
 as Pllicker has shown (see p. 470), the boundary of the glow 
 coincides with a line of magnetic force. 
 
 274. Since the negative particles are much more affected 
 than the positive by a magnetic field, if the proportion of the 
 current carried by the negative ions varies at different points in its 
 course the current will be much more deflected by the magnetic 
 field in some places than in others. This is exactly what happens 
 in the striated discharge; for "suppose A and B are 'the bright 
 parts of two consecutive striae, then since by hypothesis there is 
 ionisation in A, many more negative particles will leave A from the 
 anode side than enter it from the cathode side ; thus the proportion 
 of the current carried by the negative ions will be much greater 
 on the anode side of the bright patches than on the cathode 
 side ; the portion of the current on the anode side of a bright 
 patch will therefore be much more affected by the magnetic field 
 than that on the cathode side : the general effect of this will 
 be much the same as if the current were discontinuous, and 
 this, as we have seen (see p. 473), corresponds to the behaviour 
 of the striated column in the magnetic field. 
 
 275. Effect of a constriction in the tube. Goldstein (see p. 466) 
 has shown that on the anode side of a constriction we get negative 
 glow ; this is what we should expect on the preceding theory, for 
 the electric force in the constriction will be greater than in the 
 wider parts of the tube : there are several lines of reasoning by 
 which we may show that this must be the case ; in the first place 
 the current density in the constriction is greater than in the rest 
 of the tube ; thus if there are in the constricted part the same 
 number of ions per cubic centimetre as elsewhere, the velocity of 
 the ions must be greater ; for this to be the case the electric force 
 must be greater also : or again, if the density of the ions is greater 
 in the constriction than in the wide parts of the tube, then since 
 the ions are produced by the electric field the larger number of 
 ions will involve a more intense electric field. Thus, as the force 
 in the constriction is greater than in the rest of the tube the 
 
277] THROUGH VACUUM TUBES. 491 
 
 corpuscles which emerge from the constriction on the anode side 
 will in the constriction have acquired a large amount of kinetic 
 energy, and will therefore, like the corpuscles in the negative glow, 
 produce great ionisation with its attendant luminosity. 
 
 276. Effect of pressure upon the electric force. We shall 
 consider the case of a continuous positive column : in this case 
 the reasoning given in Art. 193 applies, where it is shown that if 
 X is the mean free path of a corpuscle and X the electric force, 
 then X\ is constant ; in an unlimited gas X is inversely pro- 
 portional to the pressure ; hence in this case we should have X 
 proportional to the pressure. In the case of a gas contained in a 
 tube the mean free path will be somewhat diminished by the 
 restraint imposed by the tube ; this diminution will be specially 
 marked when the pressure of the gas is low and the tube narrow, 
 If X' is the mean free path of the corpuscle in the tube and X the 
 free path in an unlimited gas at the same pressure, then since A/ is 
 less than X, X, the electric force in the tube, will be greater than 
 that in the free gas. This agrees with experience, as we find the 
 potential gradient greater in small tubes than in large ones. 
 Without calculating the expression for the mean free path by 
 a rigorous method we can easily in a general way see how the 
 tube will affect the potential gradient. For if d is the diameter 
 of the tube, then when d is large compared with X, X' is very 
 approximately equal to X ; while when d is small compared with 
 X, X' is comparable with d ; this condition will be satisfied if 
 
 I a I 
 \ d \' 
 
 where a is a constant. Since X\' is constant, we have X pro- 
 portional to , or since 1/X is proportional to p the pressure, we 
 X x 
 
 have X = A + Bp, where A and B are constants. 
 
 277. We have hitherto supposed that the ionisation in the 
 discharge tube was entirely due to the collisions of the ions with 
 the molecules of the gas: there is, however, another source of 
 ionisation. E. Wiedemann* discovered that an electric spark 
 emits something which is propagated in straight lines, is stopped 
 
 * E. Wiedemann, Zeitschr. /. Electrochemie, p. 159, 1895. 
 
492 DISCHARGE THROUGH VACUUM TUBES. [278 
 
 by all solids and liquids, and which possesses the power of 
 exciting thermoluminescence (see p. 496) in suitable bodies; 
 he called this radiation from the spark ' Entladungstrahlen.' 
 Hoffmann*, who subsequently investigated this question, showed 
 that 'Entladungstrahlen' are emitted by discharges through 
 vacuum tubes as well as by sparks, and that this radiation is 
 not deflected by a magnet ; he found that the radiation is 
 absorbed by carbonic acid gas to a much greater extent than 
 by oxygen. The writer f showed that these 'Entladungstrahlen' 
 possess the power of ionising the gas through which they pass, 
 so that a part, though often only a small part, of the ionisation in 
 the tube is due to these rays. The rays are given out by the 
 luminous parts of the discharge, i.e. by the luminous positive 
 column and especially by the luminous parts of the discharge 
 near the cathode ; they are not, however, given out by the Faraday 
 dark space. As these rays help to ionise the gas the whole of the 
 ionisation has not to be done by the collisions ; so that the strength 
 of the field required to produce discharge will be a little less 
 than that calculated on the collision hypothesis ; the difference 
 will increase with the strength of the current, so that the 
 Entladungstrahlen would tend to make the potential .gradients 
 in the tube diminish as the strength of the current through the 
 tube increases. 
 
 278. We shall see that when the motion of a charged ion is 
 accelerated the ion emits radiation analogous to Rontgen rays, 
 the energy emitted per unit time being e*f*l%V, where e is the 
 charge on the ion, f its acceleration, and V the velocity of light. 
 As the ions carrying the current in the discharge tube are con- 
 tinually being accelerated by the electric force, and frequently, 
 in addition, have their velocities suddenly altered by the collisions 
 they make with the molecules of the gas, during which time their 
 accelerations are very great, they will emit radiation, which will be 
 most intense where the electric force is greatest ; this radiation is, 
 I think, Wiedemann's Entladungstrahlen. 
 
 * Hoffmann, Wied. Ann. Ix. p. 269, 1897. 
 
 t J. J. Thomson, Proc. Camb. Phil. Soc. x. p. 74, 1899. 
 
CHAPTER XVII. 
 
 CATHODE RAYS. 
 
 279. So many observations have been made on these rays, - 
 and such important conclusions drawn from them, that it is con- 
 venient to devote a separate chapter to their consideration. 
 
 The cathode 'rays were discovered by Plticker* in 1859 ; he 
 observed on the glass of a highly exhausted tube in the neighbour- 
 hood of the cathode a bright phosphorescence of a greenish-yellow 
 colour. He found that these patches of phosphorescence changed 
 their position when a magnet was brought near to them, but 
 that their deflection was not of the same nature as that of the rest 
 of the discharge which we have seen he had carefully studied. 
 Plucker ascribed the phosphorescence to currents of electricity 
 which went from the cathode to the walls of the tube and then 
 retraced, for some reason or another, their steps. 
 
 The subject was next taken up by Pliicker's pupil Hittorf*f% 
 to whom we owe the discovery that a solid body placed between 
 a pointed cathode and the walls of the tube casts a well-defined 
 shadow, and the shape^f the shadow only depending upon that of 
 the body, and not upon whether the latter be opaque or trans- 
 parent, an insulator or a conductor. This observation was con- 
 firmed and extended by Goldstein J, who found that a well-marked, 
 though not a very sharply defined shadow was cast by a small 
 body near the cathode, whose area was much greater than that of 
 the body: this was a very important observation, for it showed 
 that the rays producing the phosphorescence came in a definite 
 direction from the cathode. If the cathode were replaced by a 
 
 * Pliicker, Pogg. Ann. 107, p. 77, 1859; 116, p. 45, 1862. 
 f Hittorf, Pogg. Ann. 136, p. 8, 1869. 
 J Goldstein, Berl. Monat. p. 284, 1876. 
 
494 CATHODE RAYS. [280 
 
 luminous disc of the same size no shadow would be cast by a 
 small object placed near it, for though the object might intercept 
 the rays which came normally from the disc, yet enough light 
 would be given out sideways by other parts of the disc to prevent 
 the shadow being well marked. Goldstein, who introduced the 
 term ' Kathodenstrahlen ' for these rays, regarded them as waves 
 in the ether, a view which received much support in Germany. 
 A very different opinion as to the origin of the rays was expressed 
 by Varley*, and later by Crookesf, who advanced many and 
 weighty arguments in support of the view that the cathode rays 
 were electrified particles shot out from the cathode at right angles 
 to its surface with great velocity, causing phosphorescence and 
 heat by their impact with the walls of the tube, and 'suffering a 
 deflection when exposed to a magnetic field by virtue of the 
 charge they carried. The particles in this theory were supposed 
 to be of the dimensions of ordinary molecules ; the discovery 
 made by Hertzj that the cathode rays could penetrate thin gold- 
 leaf or aluminium was difficult to reconcile w r ith this view of the 
 cathode rays; although it was possible that the metal when exposed 
 to a torrent of negatively electrified particles acted itself like a 
 cathode and produced phosphorescence on the glass behind. 
 The measurements described in Chapter V. of the mass of the 
 particles carrying the charge show that though the cathode rays 
 do consist of negatively electrified particles, the particles are not 
 of the dimensions of even the smallest molecules, having a mass 
 only about one-thousandth part of .that of a molecule of hydrogen. 
 We shall now proceed to describe the properties of the cathode 
 rays in detail, beginning with that which led to their discovery, 
 viz. the phosphorescence they produce when they fall on solids. 
 
 i 
 
 280. The colour of the phosphorescent light they produce 
 when they fall on glass depends upon the nature of the glass; 
 thus with soda glass the light is yellowish-green, with lead glass it 
 is blue. A very large number of bodies become phosphorescent 
 when exposed to these rays; indeed, this phosphorescence often 
 affords a convenient means for detecting the rays : as phosphor- 
 escence is very easily excited in potassium platino-cyanide a 
 
 * Varley, Proc. Roy. Soc. xix. p. 236, 1871. 
 
 t Crookes, Phil. Trans. Pt. i. 1879, p. 135 ; Pt. n. 1879, p. 641. 
 
 Hertz, Wied. Ann. xlv. p. 28, 1892. 
 
281] CATHODE RAYS. 495 
 
 screen of this substance is often used to detect the rays. The 
 spectrum of the light given out by bodies when phosphorescing 
 under bombardment by these rays is generally a continuous one. 
 Sir William Crookes* has shown that when the cathode rays fall 
 on some of the rare earths, such as yttrium, the substance gives 
 out a spectrum with bright bands ; he has founded on this obser- 
 vation a spectroscopic method which is of the greatest importance 
 in the study of the rare earths f) These earths are luminous 
 when raised to a high temperature as in the mantles of Welsbach 
 burners ; there is, however, a marked difference between the 
 incandescence produced in this way and that produced by cathode 
 rays ; thus in the Welsbach burner the addition of 1 per cent, of 
 ceria to thoria increases the luminosity* elevenfold as compared 
 with that of pure thoria. Campbell S win ton J has shown, however, 
 that it produces no appreciable change in the luminosity under 
 cathode rays : again, in the flame pure ceria gives about as much 
 light as pure thoria, while under cathode rays pure thoria gives 
 a brilliant light, and pure ceria practically no light at all. 
 
 281. The impact of the cathode rays produces in some cases 
 very definite chemical changes ; thus Goldstein has shown that 
 the haloid salts of the alkali metals change colour when exposed 
 to the rays ; thus for example, crystals of rock-salt acquire under 
 the rays a beautiful violet tint ; this tint is not permanent, 
 though under certain circumstances the rate of decay is exceed- 
 ingly slow : thus there are at the Cavendish Laboratory some of 
 these crystals, which, corked up in a test-tube but not kept in the 
 dark, have retained a strong coloration for more than five years: 
 exposure to moisture causes the colour to fade away rapidly. 
 Lithium chloride is especially easily coloured ; if a beam of cathode 
 rays is slowly moved over the salt by a magnet the path of the 
 beam traces out a coloured band over the surface of the salt. 
 Similar changes in colour can be produced by chemical means ; 
 thus if sodium chloride is heated up with -sodium vapour it gets 
 coloured in much the same way as if it were exposed to cathode 
 rays ; the coloured salt is also produced at the cathode in the 
 
 * Crookes, Phil. Trans. Pt. n. 1879, p. 661. 
 
 t Ibid. Pt. in. 1883; Pt. n. 1885. 
 
 J Campbell Swinton, Proc. Roy. Soc. Ixv. p. 115, 1900. 
 
 Goldstein, Wied. Ann. liv. p. 371, 1899^ y 
 
496 CATHODE RAYS. [282 
 
 electrolysis of haloid salts. The coloured salt also occurs native. 
 According to E. Wiedemann and Schmidt* the coloration is 
 due to the formation of a sub-chloride. Elster and Geitelf 
 discovered that these coloured salts are very photo-electric, dis- 
 charging negative electricity when exposed to light ; behaving, in 
 fact, as if they contained traces of the free metal. The glass of a 
 vacuum tube also acquires a violet tint after long use. 
 
 282. The power of the glass to phosphoresce is deadened by 
 long exposure to cathode rays : this is very beautifully shown in 
 an experiment made by Crookes J ; the shadow of a mica cross 
 was thrown upon the walls of the tube ; after the discharge had 
 been running for some time the cross was shaken down or a new 
 cathode in a different part of the tube was used ; the pattern of 
 the cross could still be traced on the glass, but it was now brighter 
 than the rest of the glass instead of darker as before. The 
 portions outside the original pattern got tired by the bombard- 
 ment, and so in the second part of the experiment phosphoresced 
 less brightly than the portions inside the original shadow which 
 were now bombarded for the first time. Crookes found that this 
 change in the phosphorescence of the glass persisted even after 
 the glass had been fused and again allowed to cool. 
 
 283. Villard found that cathode rays exert a reducing action ; 
 thus if they fall upon an oxidised copper plate, the part exposed to 
 the rays becomes bright. In considering the chemical effects pro- 
 duced by the rays we ought not to forget that the incidence of 
 the rays is often accompanied by a great increase in temperature, 
 and that some of the chemical changes may be secondary effects 
 due to the heat produced by the rays. Platinum after long 
 exposure to the rays gets covered with platinum black. 
 
 284. Tliermoluminescence. In some cases, even when no 
 visible coloration is produced, the behaviour of the body after 
 exposure to the rays shows that it has been changed. A very 
 striking instance is the case called by E. Wiedemann || 'Tliermo- 
 luminescence.' Some bodies, after exposure to cathode rays, 
 
 * Wiederaann and Schmidt, Wied. Ann. liv. p. 262, 1895 ; Ixiv. p. 78, 1898. 
 
 t Elster and Geitel, Wied. Ann. lix. p. 487, 1896. 
 
 t Crookes, Phil. Trans. Pt. n. p. 645. 1879. 
 
 Villard, Journal de Physique, 3 me Serie, t. viii. p. 140, 1899. 
 
 II E. Wiedemanu and Schmidt, Wied. Ann. liv. p. 604, 1895. 
 
284] 
 
 CATHODE RAYS. 
 
 497 
 
 are found to 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 when in their normal state ; 
 they retain this property for weeks, and even months, after ex- 
 posure to the rays. The substances in which this property is 
 most highly developed belong to the class of bodies called by 
 Van 't Hoff* solid solutions; these are formed by precipitating 
 simultaneously from a solution two salts, one greatly in excess 
 of the other. The influence of a slight trace of a second substance 
 
 Substance 
 
 Cathode 
 phosphorescence 
 
 After-glow 
 
 Thermo- 
 luminescence 
 
 CaS0 4 
 
 faint yellowish 
 
 none 
 
 none 
 
 CaS0 4 -f^MnS0 4 . ... 
 
 red 
 
 intense green 
 
 strong green 
 
 intense green 
 
 SrS0 4 
 
 none 
 
 
 
 SrS0 4 + #MnS0 4 
 
 bright red 
 
 perceptible 
 
 perceptible 
 
 BaS0 4 
 
 faint dark violet 
 
 
 
 BaS0 4 + x MnS0 4 
 
 dark blue 
 
 faint 
 
 very faint 
 
 MgSCX.. 
 
 red 
 
 perceptible 
 
 feeble 
 
 MgS0 4 + l/ MnS0 4 ... 
 ZnSO,.. 
 
 intense dark red 
 bright, white 
 
 persistent 
 persistent 
 
 intense red 
 white 
 
 ZnS0 4 +l%MnS0 4 ... 
 Na 2 S0 4 
 
 intense red 
 bluish 
 
 very persistent 
 faint 
 
 very strong red 
 bright 
 
 Na 2 S0 4 + 0'5%MnS0 4 
 CdS0 4 
 
 intense brown- 
 ish yellow 
 yellow 
 
 strong 
 persistent 
 
 bright yellow 
 bright yellow 
 
 CdS0 4 + l%MnS0 4 ... 
 CaFl 2 
 
 intense yellow 
 faint bluish 
 
 very persistent 
 very faint 
 
 intense yellow 
 faint 
 
 CaFl 2 + #MnFl 2 
 
 intense green 
 
 persistent 
 
 intense green 
 
 
 
 
 
 on the phosphorescence produced while the rays are playing on 
 the substance ; the after-glow, which lingers for a time after the 
 rays are stopped; and the thermoluminescence is shown by the 
 
 * Van 't Hoff, Zeitschr. /. physik. Chem. v. p. 322, 1890. 
 T. G. 32 
 
498 CATHODE RAYS. [285 
 
 preceding table, due to E. Wiedemann and Schmidt*. By the 
 symbol CaSO 4 + #MnSO 4 is meant a 'solid solution' of a trace 
 of MnS0 4 in a matrix of CaS0 4 . 
 
 The ' Entladungstrahlen ' (see p. 491) also give rise to thermo- 
 luminescence, as Wiedemann found that any of the preceding 
 substances showed thermoluminosity if sparks were produced 
 close to them. 
 
 285. We may compare the after-glow observed with these 
 solids with that which is observed when the electric discharge 
 passes through certain gases which are found to remain luminous 
 for a considerable time after the discharge has passed through 
 them. It is not necessary that the discharge should consist of 
 cathode rays; most kinds of discharges will produce this after- 
 glow if the pressure is suitable ; it is exceptionally conspicuous 
 in electrodeless discharges and is especially well developed in 
 oxygen and cyanogen, gases which polymerise with great ease. 
 I think there are strong reasons for believing that the after-glow 
 is very closely connected with the power some gases possess of 
 polymerising and forming complex molecules; and that the gradual 
 return of the gas from its polymerised to its normal form is accom- 
 panied by the emission of light. 
 
 286. Like the thermoluminescence of solids, the after-glow in 
 gases seems to be increased by the presence of small quantities of 
 impurities; thus it is brighter in oxygen with a little nitrogen 
 than in pure oxygen. Newallf discovered a very remarkable 
 effect connected with the after-glow in oxygen ; he found that with 
 the electrodeless discharge the after-glow was only developed when 
 the pressure was between the limits '6 mm. and "01 mm. If the 
 discharge is sent through the gas at a pressure not between these 
 limits, there is no glow, but if after the discharge has ceased the 
 pressure is altered so as to come within the limits the gas at once 
 begins to glow, suggesting that the polymerised form is stable, i>e. 
 does not go back into the normal form except between the limits 
 C mm. and '01 mm. It may be mentioned that this is the region 
 of pressure in which some observers, though not all, have observed 
 large departures from Boyle's law. 
 
 * Wiedemann and Schmidt, Wied. Ann. Ivi. p. 201, 1895. 
 t Newall, Proc. Camb. Phil. Soc. ix. p. 295, 1897. 
 
288] CATHODE RAYS. 499 
 
 In the case of phosphorescent solids and liquids we may regard 
 the phosphorescence as arising in the following way. The cathode 
 rays or Entladungstrahlen will ionise the substance, causing 
 complex substances to be formed which phosphoresce as they 
 break up into their original constituents ; some of these complex 
 molecules are unstable at the temperature of the room and at 
 once begin to decompose, giving rise to the after phosphorescence 
 of the glass, etc. ; others are stable at ordinary temperatures, but 
 are unstable and decompose at high temperatures ; these produce 
 thermoluminescence. 
 
 287. M c Clennan* has shown that some salts, especially the 
 sulphates of potassium, barium, strontium and calcium, after ex- 
 posure to cathode rays, or to the radiation from a spark, possess 
 the power of discharging a positively electrified body placed 
 near them in a gas at low pressure, behaving in fact as if 
 they were photo-electric bodies exposed to the action of ultra- 
 violet light, i.e. they emit slowly moving negatively electrified 
 corpuscles. M c Clennan made experiments to show that there 
 was no emission of ultra-violet light from the heated salts. There 
 does not seem to be any connection between the powers of salts to 
 produce the effect discovered by M c Clennan and their power of 
 producing thermoluminescence: as M c Clennan found that many 
 salts which glowed strongly when heated did not give his effect, 
 which was given by some salts which hardly showed any thermo- 
 luminescence. 
 
 288. Thermal effects produced by the rays. The cathode 
 rays heat bodies on which they fall, and if the rays are concen- 
 trated by using a portion of a hollow cylinder or spherical shell 
 as a cathode, platinum may be raised to incandescence, thin pieces 
 of glass fused, and the surface of a diamond charred. 
 
 Measurements of the amount of heat developed by the rays 
 have been made by E. Wiedemann and Ebertf, E. Wiedemann J, 
 and Ewers . A simple example will give some idea of the 
 amount of energy carried by the rays. If n is the number 
 
 * M'Clennan, Phil Mag. vi. 3, p. 195, 1902. 
 
 t Wiedemann and Ebert, Sitz. der phys. med. Soc. Erlangen, Dec. 1891. 
 
 I E. Wiedemann, Wied. Ann. Ixvi. p. 61, 1898. 
 
 Ewers, Wied. Ann. Ixix. p. 167, 1899. 
 
 322 
 
500 CATHODE RAYS. [289 
 
 of corpuscles striking a body in unit time, m the mass of a 
 corpuscle, and v its velocity, then E the energy possessed by the 
 corpuscles striking the body in unit time is ^nmv* '; if all the 
 corpuscles coming from the cathode are caught by the body and 
 e is the charge on a corpuscle, then ne = I, the current carried 
 
 by the corpuscles; thus E=^I v*: now 10~ 5 amperes is not an 
 
 exceptionally high value for /, and if v - o x 10 9 cm./sec. we get, 
 since m/e=W~ 7 , E 12'5 x 10 5 ; thus the energy possessed by 
 the corpuscles striking the body per minute would be nearly 
 2 calories. 
 
 289. The impact of the corpuscles does more than heat the 
 body, it makes it phosphoresce, it produces Rontgen rays, and 
 causes the body to emit cathode rays. Interesting information is 
 afforded by measuring the heat produced by the cathode rays, 
 and also the charge of electricity brought to the body by the 
 rays; such measurements have been made by the author*, and 
 later in greater detail by Cadyf. Cady's method was to measure 
 (1) the heat produced in a bolometer strip against which the rays 
 struck, and (2) the negative charge acquired by the bolometer 
 per second ; the latter, it is important to notice, need not be 
 the same as the charge carried by the corpuscles striking the 
 body in one second, for some of the corpuscles may rebound from 
 the body without giving up a charge, or the impact of the rays 
 may cause the body to give out cathode rays, carrying from it 
 a negative charge, or positively electrified atoms, giving to it an 
 additional negative charge ; thus if / is the charge carried by the 
 corpuscles, i that acquired by the bolometer per second, then / is 
 not necessarily the same as i. If V is the potential difference 
 between the electrodes in the tube, then the energy carried by 
 the corpuscles is VI. Cady measured the ratio of Vi to Q the 
 mechanical equivalent of the heat developed in unit time ; he 
 found that this ratio depends greatly upon the value of i ; as long 
 as i is large it is greater than unity, diminishing as i diminishes ; 
 when i gets very small (less than 10~ 7 amperes), the ratio becomes 
 constant and equal to '83 ; as the ratio is less than unity it follows 
 that there is an emission of negative electricity from the bolometer, 
 
 * J. J. Thomson, Phil. Mag. v. 44, p. 293, 1893. 
 t Cady, Drude's Ann. i. p. 678, 1900. 
 
290] CATHODE RAYS. 501 
 
 either by the reflection of the cathode rays, or by the emission of 
 secondary cathode rays from its surface. We have seen that the 
 measurement of i and V does not give the energy reaching the 
 surface through the cathode rays ; a slight modification of the ex- 
 periment would, however, give the data by which this energy could 
 be determined; all that is necessary would be to surround the 
 bolometer by an insulated Faraday cylinder, into which the rays 
 were admitted through a small opening, and then to measure the 
 charge received by this cylinder in unit time. 
 
 E. Wiedemann* has shown that the energy spent in pro- 
 ducing phosphorescence is but a small fraction of the incident 
 energy. 
 
 290. Mechanical effects produced by the rays. A secondary 
 result of the thermal effects produced by the rays are the very 
 interesting mechanical effects which have been especially studied 
 by Crookes I" and Puluzj. A typical example of these is afforded 
 by the well-known experiment due to Crookes represented in 
 Fig. 163, where the axle of a very light mill with a series of vanes 
 
 Fig. 163. 
 
 is mounted on glass rails, in a vacuum tube ; when the discharge 
 passes through the tube the cathode rays strike against the upper 
 vanes and the wheel rotates and travels from the negative to the 
 positive end of the tube. 
 
 A simple calculation will show that we cannot ascribe the 
 rotation to the momentum communicated to the vanes by the 
 impact of the corpuscles against them ; for, take the case when 
 the rays are so powerful that they carry the very large current of 
 10~ 5 amperes, and that they move with the very high velocity of 
 10 10 cm./sec. : if N is the number of corpuscles striking a surface 
 in unit time, m the mass of the corpuscles ; then supposing the 
 
 * E. Wiedemann, Wied. Aim. Ixvi. p. 61, 1898. 
 
 t Crookes, Phil. Trans. 1879, pt. i. p. 152. 
 
 Puluz, Radiant Electrode Matter. Physical Society's Bepriut of Memoirs, p. 275. 
 
502 CATHODE RAYS. [291 
 
 corpuscles to rebound from the surface with a velocity equal to 
 that with which they impinge against it, the momentum commu- 
 nicated to the surface in unit time is 2NmW w ; if e is the charge 
 carried by a corpuscle, then Ne is the current carried by the rays, 
 in our case 10" 6 in absolute measure ; hence the momentum 
 
 7?? 
 
 communicated to the surface per second is equal to 2 10 4 dynes, 
 
 & 
 
 or as m/e = 10~ 7 to 2 x 10~ 3 dynes : this is equivalent to a differ- 
 ence of pressure on the two sides of a vane 1 sq. cm. in area of one- 
 five-hundred-millionth part of an atmosphere ; an effect altogether 
 too small to explain the movement of a body such as that repre- 
 sented in Fig. 163. This movement is probably due to an 
 effect similar to that observed in a radiometer, as the impact 
 of the cathode rays, will make one side of the vanes much 
 hotter than the other. Starke* has shown that when the vanes 
 are arranged so that the radiometer effect is eliminated, the 
 mechanical effect is exceedingly small in his experiments, where 
 the current carfied by the cathode rays was 10~ 7 amperes and the 
 potential difference 10,000 volts certainly less than 10~ 4 dynes. 
 
 291. Electric charge carried by the cathode rays. The fact 
 that the cathode rays carry a negative charge of electricity was 
 proved in a very direct way by Perrin-f-. Fig. 164 represents 
 a modification of his experiment. The rays start from the 
 
 Fig. 164. 
 
 cathode A and pass through a slit in a brass rod B, which fits 
 lightly into the neck of the tube ; this rod is connected with the 
 
 * Starke, Drude's Ann. iii. p. 101, 1900. 
 
 t Perrin, Comptes Rendus, cxxi. p. 1130, 1895. 
 
292] CATHODE RAYS. 503 
 
 earth and used as an anode ; the rays after passing through the 
 slit enter the spherical vessel C. In this vessel there are two 
 coaxial metal cylinders, the outer one D connected with the 
 earth, the inner one E carefully insulated and connected with an 
 electrometer. The cylinders are placed so as to be out of the 
 direct line of fire of the rays. When the discharge passed 
 through the tube and the cathode rays passed horizontally through 
 the vessel C, the inner cylinder E received a small, but only small, 
 negative charge. The cathode rays /were then deflected by a 
 magnet; their path could be inferred from the position of the 
 phosphorescent patch on the walls of (7; when the deflection was 
 increased, so that the position of the path showed that the rays 
 had fallen on fhe opening of the cylinders, there was a very great 
 increase in the negative charge received by E ; when the rays had 
 been so much deflected that the phosphorescent patch fell below 
 the slit the negative charge in the cylinder E again disappeared. 
 This experiment shows that the rays carry a negative charge, 
 as it proves that the negative electrification follows exactly the 
 same course as the rays producing the phosphorescence on the 
 glass. 
 
 This experiment also shows that the cathode rays make the 
 gas through which they j3ass__a conductor of electricity ; for if in 
 the experiment the discharge is kept continuously passing through 
 the tube and the cathode rays deflected until they pass into the 
 cylinder, the negative charge on the cylinder will rise to a certain 
 value, beyond which it will not increase however long the discharge 
 may be kept running ; this shows that the gas around the cylinder 
 is a conductor, and the steady state of the cylinder is reached when 
 it loses as much electricity by conduction through the gas as it 
 gains from the cathode rays. The same thing is shown when the 
 cylinder is given a negative charge before the discharge through 
 the gas begins : if this charge is less than a certain value the 
 cathode rays will increase the charge ; if however it is greater than 
 this value, the cathode rays will diminish the charge until it 
 falls to this critical value. 
 
 292. Reflection of cathode rays. When cathode rays strike 
 the surface of either a conductor or an insulator cathode rays 
 start from the surface in all directions ; this phenomenon is called 
 the diffuse reflection of the cathode rays: we must be careful 
 
504 CATHODE RAYS. [293 
 
 however to remember that reflection is used in a different sense 
 from that which is usual in optics, where for example we should 
 not speak of the phosphorescent light given out by such a sub- 
 stance as quinine when struck by ultra-violet light as reflected 
 rays; in the case of the cathode rays all the cathode rays pro-y 
 ceeding from a surface struck by cathode rays are called reflected 
 rays. The existence of such rays is easily shown by an experi- 
 ment due to Goldstein*. The cathode rays from the cathode G 
 
 Fig. 165. 
 
 fall on the plate A which can be rotated by a handle passing 
 through a stuffing-box. The half of the tube AB on the illu- 
 minated side of A becomes phosphorescent from the cathode 
 rays diffusely reflected from A. The reflection occurs even when 
 the plate does not itself become phosphorescent under cathode 
 rays. 
 
 293. Measurements of the amount of ' reflection ' experienced 
 by cathode rays when incident upon different substances and at 
 different angles of incidence have been made by Campbell 
 Swintonf, by StarkeJ, and by Austin and Starke. Campbell 
 S win ton's experiments, which had for their object the measure- 
 ment of the variation of the ' reflected ' rays at various angles of 
 incidence and emergence, were arranged as represented in Fig. 1G6. 
 C is the cathode ; A the reflecting surface, a flat piece of platinum 
 which could be rotated about its axis ; F a Faraday cylinder which 
 receives the rays emitted by the surface ; this could be set so that 
 the opening made any required angle with the direction of the 
 incident rays ; the charge received by this cylinder was taken as 
 the measure of the amount of reflection. Campbell Swinton 
 
 * Goldstein, Wied. Ann. xv. p. 254, 1882. 
 
 + Campbell Swinton, Proc. Roy. Soc. Ixiv. p. 377, 1899. 
 
 Starke, Wied. Ann. Ixvi. p. 49, 1898 ; Drude's Ann. iii. p. 75, 1900. 
 
 Austin and Starke, Drude's Ann. ix. p. 271, 1902. 
 
293] 
 
 CATHODE RAYS. 
 
 505 
 
 came to the conclusion that although the 'reflection' was very 
 diffuse there was appreciably more in the direction in which the 
 angle of emergence was equal to the angle of incidence than in 
 
 Fig. 166. 
 
 any other direction ; he found that the total amount of emission 
 was slightly greater at oblique than at normal incidence ; he 
 measured also the charge received by the reflector and found 
 that though with normal incidence it received a large negative 
 charge, the charge diminished as the incidence became more 
 oblique, vanished, and finally with very oblique incidence became 
 positive. The positive charge received by the reflector has also 
 been observed by Austin and Starke (I.e.). 
 
 Starke determined the proportion between the incident and 
 receding rays, or rather the ratio of the negative charge acquired 
 by the reflector to that carried by the receding rays. 
 
 The principle of the method used by Starke is as follows. The 
 cathode rays enter through a hole in the cylinder and strike the 
 reflector ; the cylinder and reflector are each connected to earth 
 through high-resistance galvanometers ; when the rays strike 
 against the reflector currents pass through these galvanometers ; 
 
506 
 
 CATHODE RAYS. 
 
 [293 
 
 let i*!, i 2 be the currents through the galvanometers connected with 
 the reflector and cylinder respectively; let N be the number of 
 corpuscles striking the reflector in unit time, n the number leaving 
 
 B 
 
 Fig. 167. 
 
 it in the same time, e the charge on a corpuscle ; then, if there is 
 no ionisation in the gas of the cylinder, no escape of the receding 
 rays through the hole, and no diffusion of the incident rays in the 
 cylinder causing some of the incident rays to strike the walls of 
 the cylinder instead of the reflector, we have 
 
 (N n} e = ii ; ne i 2 ; 
 
 or 
 
 hence if we measure ^ and i z we can determine the value of n/N ; 
 in practice some corrections are necessary, for which we must 
 refer to Starke's paper (/.c.); the value of n/N depends upon the 
 metal ; the following are Starke's values for this quantity : 
 
 Metal 
 
 Density 
 
 njN 
 
 Metal 
 
 Density 
 
 njN 
 
 Pt .. 
 
 21-5 
 
 72 
 
 Brass . . . 
 
 8-1 
 
 43 
 
 Pb 
 
 11-3 
 
 63 
 
 Fe 
 
 7-7 
 
 40 
 
 Ag 
 
 10-5 
 
 59 
 
 Zn 
 
 7-1 
 
 40 
 
 Bi .. 
 
 9-9 
 
 58 
 
 Al 
 
 2-6 
 
 25 
 
 Ni 
 
 8-9 
 
 48 
 
 Mg 
 
 1-7 
 
 25 
 
 Cu... . 
 
 8'5 
 
 45 
 
 
 
 
 
 
 
 
 
 
 Thus the value of n/N increases with the density of the metal ; 
 the numbers given above are roughly proportional to the square 
 root of the density ; we see that even for the lightest metals the 
 number of corpuscles receding from the surface is as much as 
 one quarter of the number of those approaching it. The pre- 
 ceding values of n/N are when the incidence of the cathode rays 
 is normal; in this case n/N does not depend upon the velocity of 
 the incident rays. 
 
295] CATHODE RAYS. 507 
 
 294. The fact observed by Campbell Swinton (I. c.) that when 
 the incidence is very oblique the reflector acquires a positive 
 instead of a negative charge, has been carefully studied by Starke 
 and Austin*, who have measured the charge received by the 
 reflector for cathode rays incident at various angles; they find 
 that the angle of incidence at which the charge received by the 
 reflector changes from to + depends on the material of which 
 the reflector is made and the velocity of the rays. With denser 
 reflectors the change from to 4- takes place at a smaller angle 
 of incidence than it does with lighter reflectors ; and, again, the 
 smaller the velocity of the rays the smaller the critical angle. 
 The amount of influence exerted by the nature of the metal, 
 and the velocity of the rays, may be illustrated by the following 
 numbers due to Austin and Starke. With a platinum reflector, 
 and with cathode rays produced by a potential difference of 
 9000 volts, the critical angle of incidence was 60 ; with a copper 
 reflector, and a potential difference of 8700 volts, the critical angle 
 was 80, and with a potential difference of 5000 volts, 70. 
 
 295. Since, in some cases, the reflector receives a positive 
 charge from the impact of the negatively electrified corpuscles, 
 more corpuscles must leave the surface than arrive at it ; it follows 
 that the velocity of the receding corpuscles must, on the average, 
 be less than that of the approaching ones, otherwise the energy 
 emitted by the reflector would be greater than the energy re- 
 ceived. Measurements of the velocity of the ' reflected ' rays, by 
 means of the deflection they experience in a magnetic field, have 
 been made by Merritt f, Austin and Starke (I.e.), and Gehrckej; 
 both Merritt and Austin and Starke came to the conclusion that 
 the velocity of the reflected rays was much the same as that of 
 the incident; Gehrcke, however, by a very ingenious method 
 showed that among the 'reflected' rays there were a large number 
 whose velocities were considerably less than that of the incident 
 rays. Gehrcke's method is represented in Fig. 168; K t and K 2 are 
 two cathodes connected together and with the negative pole of 
 an electrical machine; the rays from K^ went straight from the 
 cathode on to a fluorescent screen FF\ while those from K 2 fell on 
 
 * Austin and Starke, Drude's Ann., ix. p. 271, 1902. 
 t Merritt, Physical Review, vii. p. 217, 1898. 
 J Gehrcke, Drude's Ann., viii. p. 81, 1902. 
 
508 
 
 CATHODE KAYS. 
 
 [295 
 
 a magnesium reflector, the ' reflected' rays from which fell on the 
 same screen. J" a and 7~ 2 are the coils for producing the magnetic 
 
 Fig. 168. 
 
 field. The appearance of the phosphorescence on the screen be- 
 fore and after the magnetic field was started is shown in Fig. 169. 
 
 LAHHHHH 
 
 Fig. 169. 
 
 The middle patches F, F' represent the phosphorescence without 
 a magnetic field due to the direct and reflected rays respectively; 
 the patches above and below these represent the phosphorescence 
 when the magnetic field was on, the upper and lower patches 
 corresponding to fields in opposite directions. It will be noticed 
 that while the patch of phosphorescence, due to the direct rays, 
 
296] CATHODE RAYS. 509 
 
 has not been sensibly broadened by the magnetic field, the narrow 
 patch due to the 'reflected' rays has become a broad band, showing 
 the presence of some rays much more easily deflected, and there- 
 fore moving more slowly than the incident rays. Since one of the 
 boundaries of the reflected patch keeps in line with one of the 
 direct patch, there must be some of the reflected rays which move 
 with approximately the same velocity as the incident rays. 
 
 We conclude from this experiment that a surface struck by 
 cathode rays emits secondary rays which on the average move 
 more slowly than the primary ones. The ratio of the number 
 of secondary to the number of primary rays is greater at oblique 
 than at normal incidence. The 'reflection' of cathode rays at 
 the surface of a solid seems in many respects analogous to the 
 emission of corpuscles from a body illuminated by ultra-violet 
 light. The corpuscles in the primary rays penetrate some little 
 distance below the surface, ionising the molecules against which 
 they strike ; the secondary corpuscles produced in this way, and 
 perhaps also some of the primary ones whose motion has been 
 reversed by the collision they have made with the molecules 
 of the reflector, escape from the reflector and form the reflected 
 cathode rays. 
 
 The path of a corpuscle which strikes the reflector obliquely 
 will be nearer the surface than if it strikes the reflector normally, 
 arid thus the corpuscles liberated by it will have a shorter 
 distance to travel before reaching the surface of the reflector and 
 emerging from it, we should therefore expect the oblique rays 
 to produce more reflected rays. 
 
 296. Transmission of Cathode Rays. It was for a long time 
 believed that even the thinnest slice of a solid was impervious 
 to cathode rays. Thus Goldstein and Crookes had shown that 
 bodies as thin as a film of collodion or glass blown as thin as 
 possible cast intensely black shadows when interposed between 
 the cathode and the walls of the tube. In 1892, however, Hertz* 
 found that behind a piece of gold-leaf or thin aluminium foil 
 there was appreciable phosphorescence, and that the phosphor- 
 escence was deflected by a magnet. 
 
 * Hertz, Wied. Ann. xlv. p. 28, 1892. 
 
510 
 
 CATHODE RAYS. 
 
 [297 
 
 297. Lenard' s Experiments. Lenard* made a series of most 
 interesting experiments on the passage of cathode rays through 
 very thin films. The rays were produced in a tube like that 
 represented in Fig. 170. 
 
 Fig. 170. 
 
 K, the cathode, is an aluminium disc fastened to a stiff wire 
 which is surrounded by a glass tube ; the anode is a brass tube 
 surrounding part of the wire carrying the cathode. The end of 
 the tube opposite the cathode is closed by a metal cap fastened 
 to the tube by marine-glue ; a hole 17 mm. in diameter is bored 
 through this cap and covered with a piece of thin aluminium 
 foil, about '00265 mm. thick. This window is in metallic contact 
 with the cap, and was together with the anode connected with 
 earth. The tube is exhausted until the difference of potential 
 between the cathode and anode is very great, and strong cathode 
 rays reach the window. In a dark room a diffuse light spreads 
 from the window into the air outside ; this light is brightest 
 close to the window, its outline is very indefinite ; with a strong 
 discharge in the tube the light can be traced to some centi- 
 metres away from the tube. Phosphorescent bodies placed in 
 the neighbourhood of the window phosphoresce. In air at 
 ordinary pressures the rays proceeding from the window diffuse 
 * Lenard, Wied, Ann. li. p. 225, 1894. 
 
 \ 
 
298] CATHODE RAYS. 511 
 
 out very rapidly, and shadows cast by solid bodies placed in their 
 path are ill defined and many times larger than the bodies casting 
 them. These rays are much more easily studied if the window, 
 instead of opening on to the air, opens on to another tube from 
 which the air can be exhausted : when the air in this tube is 
 at a low pressure, the rays travel a well-defined path and can 
 easily be studied. The rays are deflected by a magnet, by an 
 electric field, and carry a negative charge of electricity ; the ratio 
 of the charge to the mass of the carrier has been determined 
 by Lenard (see p. 95) and found to have the same value as for 
 cathode rays. These facts show that these rays are cathode rays ; 
 it is often, however, convenient to distinguish between cathode 
 rays inside and outside the tube producing them ; it is thus 
 desirable to keep the term Lenard rays for the latter and use 
 cathode rays for those inside the tube. 
 
 Lenard measured the absorption of these rays by various 
 substances, and arrived at the simple law connecting absorption 
 with density, already discussed on p. 310. Lenard measured the 
 intensity of his rays by the phosphorescence they produced in 
 a solution of pentadekylparatoleketone. Seitz*, who has made 
 similar measurements, measured the total charge of electricity 
 carried by the rays. We must remember that unless all the rays 
 are moving with the same velocity the two methods may give 
 different results ; in the electrical method all the corpuscles count 
 equally, whatever their velocity may be; in the optical method, 
 however, this is no longer the case, the more rapidly moving 
 corpuscles producing much more phosphorescence than the same 
 number of corpuscles with smaller velocity. 
 
 298. We have, when considering the reflection of the cathode 
 rays, supposed that the incident rays gave by means of collisions 
 sufficient energy to some of the corpuscles in the metal to enaole 
 them to escape from it. In the case of reflection we have to 
 deal with the corpuscles which emerge from the face of the metal 
 first struck by the rays; when, however, the metal is very thin, 
 some of the corpuscles travelling in the same direction as the 
 incident rays may come out on the far side of the metal and 
 form part of the bundle of transmitted rays; many of these 
 secondary rays will be moving with smaller velocities than the 
 * Seitz, Drude's Ann. iv. p. 1, 1901. 
 
512 CATHODE RAYS. [299 
 
 primary rays, and thus the transmitted rays will not be homo- 
 geneous, and the electrical and optical methods of estimating 
 their intensity may, as explained above, give different results. 
 
 299. A loss of velocity in the rays emerging from thin plates 
 of metal has been observed by Leithausers* and Des Coudres f % ; 
 the latter has shown also that the patch of phosphorescence due to 
 these rays is under the action of a magnetic field drawn out into 
 a broad patch, showing that the transmitted rays are not homo- 
 geneous (compare the corresponding result found by Gehrcke for 
 the reflected rays, see p. 508). Des Coudres showed also that the 
 rays which emerge obliquely from the metal have smaller velocities 
 than those emerging normally. 
 
 300. Scattering of Cathode Rays inside the tube. Measure- 
 ments of the scattering of cathode rays inside the discharge tube 
 have been made by Kaufmann j, who employed the electrical 
 method. The greatest potential differences employed was only 
 about 7500 volts, so that the velocity of the rays in Kaufmann's 
 experiments was very much less than in those of Lenard. The prin- 
 ciple of the method used by Kaufmann was as follows. Consider 
 a bundle of rays originally horizontal pfassing through the gas, then 
 if NQ is the number of corpuscles crossing a vertical plane AB in 
 unit time, the number crossing a parallel plane CD at a distance x 
 from AB will be J\T e~ to , where b is by definition the coefficient 
 of absorption ; if e is the charge carried by a corpuscle the 
 quantity of negative electricity entering the space between AB 
 and CD in unit time is N Q e, the amount leaving it is N ee~ bx ; 
 hence if ABCD is surrounded by a metallic cylinder the 
 quantity of electricity received by the cylinder in unit time 
 is N e (1 e~ bx ) ; hence, if we compare the charge received by 
 the cylinder with that which passes through the end CD, we 
 shall find (1 e"^)^" 6 *, from which we can deduce the value 
 of b. Kaufmann in this way determined 6 for nitrogen, car- 
 bonic oxide, carbonic acid and hydrogen, at pressures ranging 
 from about 1/50 to 1/28 of a millimetre of mercury and 
 with potential differences from about 2500 to 7500 volts ; he 
 
 * Leithausers, Site. Berlin. Akad. d. Wissensch. Mar. 13, 1902. 
 t Des Coudres, Phys. Zeits. iv. p. 140, 1902. 
 Kaufmann, Wied. Ann. Ixix. p. 95, 1899. 
 
301] CATHODE RAYS. 513 
 
 found that if V is the potential difference in the discharge tube 
 in volts, p the pressure in millimetres of mercury, then for the 
 same gas, within the limits of pressure and potential difference 
 indicated, bV/p was constant; i.e. the absorption coefficient is 
 proportional to the pressure and inversely proportional to the 
 kinetic energy of the corpuscle. The values for the different 
 gases are indicated in the following table : 
 
 Gas bV/p Molecular weight 
 
 H 2 730 2 
 
 N 2 5650 28 
 
 CO 6380 28 
 
 C0 2 6830 44 
 
 The values of b do not follow those of the molecular weight 
 as closely as the values determined by Lenard ; one reason for this 
 may be the greater velocities of the rays investigated by Lenard ; 
 we have seen (p. 315) that it is only for very rapidly moving 
 cathode rays that we could expect Lenard's law to be strictly true ; 
 another reason may be that in the method used by Kaufmann 
 the positive and negative ions produced by the primary rays 
 by collision with the molecules of the gas might diffuse with 
 different velocities to the conductors in the tube, so that part 
 of the current measured in these experiments may be due to 
 secondary ionisation. 
 
 301. Magnetic Spectrum of Cathode Eays. Birkeland * found 
 that when the cathode rays are produced by means of an in- 
 duction coil, a patch of cathodic phosphorescence is not merely 
 displaced by a magnetic field, but is broken up into several 
 distinct patches; thus, for example, if there is originally a 
 narrow straight band of phosphorescence, then under the magnetic 
 field several parallel bright bands of phosphorescence separat -d 
 by comparatively dark spaces are observed. This is called the 
 magnetic spectrum. I have obtained similar effects by deflecting 
 the rays by electric instead of magnetic forces. This splitting 
 up of the rays shows that the original bundle of cathode rays 
 is not homogeneous, but is made up of groups moving with 
 different, and finitely different, velocities; each group being 
 differently deflected, the slower ones more than the faster. 
 
 * Birkeland, Comptes Rendus, cxxiii. p. 92, 1897. 
 T. G. 33 
 
514 CATHODE RAYS. [302 
 
 Strutt* has shown that the magnetic spectrum is due to the 
 want of uniformity necessarily associated with the use of an 
 induction coil, which produces a discontinuous discharge, and that 
 if the cathode rays are produced by a large electrostatic machine, 
 or a large number of storage cells, either of which gives a con- 
 tinuous discharge, the phosphorescence is not broken up into 
 separate patches by a magnetic or an electric field. 
 
 302. Path of the Cathode Rays in the Discharge Tube. The 
 cathode rays are deflected by an electric force; thus, as the 
 electric field is very intense in the Crookes dark space, the rays 
 as they pass through this space will, unless the lines of force in 
 it are straight (this is approximately the case when the cathode 
 is a large plane disc), be deflected and their paths will not 
 coincide with the normals to the cathode at their point of 
 projection. The amount of deflection of the path from this 
 normal will depend mainly upon the rate at which the intensity 
 of the electric field diminishes as we recede from the cathode : 
 if, as in the case when the pressure is not very low, the field 
 close to the cathode is very much more intense than that at 
 some distance away from it, the corpuscles will acquire so much 
 energy while still close to the cathode that they will not be 
 much deflected by the comparatively feeble fields traversed by 
 J-hein during the rest of the journey; in this case the paths of 
 the rays will be approximately the normals to the cathode, so 
 that if the cathode is a hollow spherical bowl the rays will travel 
 along the radii of the sphere and will be brought to a focus at 
 its centre. If however the strength of the field only changes 
 slowly as we recede from the cathode, we shall get much 
 greater deviation than in the last case, for not only will the 
 velocity they acquire while still close to the cathode be smaller, 
 but also the deflecting force when they get away from the 
 cathode will be greater. The paths of the rays will now be no 
 longer along the normals because of the deflecting force, nor will 
 they, owing to the inertia of the corpuscles, be along the lines 
 of force unless these are straight. The paths of the corpuscles 
 will be between the normal and the lines of force ; thus, for 
 example, in the case of the hollow bowl, the path will be between 
 the normal CP and the line of force PQ (Fig. 171); thus, if the 
 
 * Strutt, Phil. Mag. v. 48, p. 478, 1899. 
 
304] CATHODE RAYS. 515 
 
 paths cross the axis of the bowl at all, they will do so at points 
 on the far side of the centre. It is well known that when, as in 
 
 Fig. 171. 
 
 the bulbs used for producing Rontgen rays, a cathode of this kind 
 is used, the ' focus' gets further from the cathode as the ex- 
 haustion is increased. Goldstein*, who made a series of beautiful 
 experiments on the phosphorescent patterns produced by curved 
 cathodes of different shapes, showed, by using an unsymmetrical 
 cathode, that the rays crossed when the pressure was com- 
 paratively high, but did not do so at very high exhaustions. 
 The appearance of the cathode rays from a curved cathode is 
 shown by the diagrams in Fig. 173 taken from a paper by 
 Campbell Swintonf; it will be seen that this is very different 
 from that which would result if the rays travelled along the 
 normals to the cathode. 
 
 303. The motion of the corpuscles in a vacuum tube offers a 
 fine field for the application of Hamilton's Principle of Varying; 
 Action : for since the cathode is an equipotential surface, and the 
 corpuscles leave that surface normally and with equal amounts of 
 energy, their paths will, by the Principle of Varying Action, be 
 the orthogonal trajectories of a system of surfaces. 
 
 304. We have regarded the cathocle rays^ as originating from 
 positive ions which were formed by the cathode rays themselves 
 
 * Goldstein, Wied. Ann. xv. p. 254, 1882. 
 
 t Campbell Swinton, Proc. Roy. Soc. Ixi. p. 79, 1897. 
 
 332 
 
516 CATHODE RAYS. [304 
 
 at a distance from the cathode. If however the path PQ of the 
 cathode ray is curved (Fig. 172), and if the positive ion is pro- 
 duced at Q, then, in consequence of the difference in mass between 
 
 Fig. 172. 
 
 the positive and negative ions, the path of the positive ion up 
 to the cathode will not be QP, but some other path such as QP' ; 
 thus the cathode rays produced at P will, when the paths are 
 not straight lines, give rise to positive ions which will help to 
 make cathode rays which start not from P but from some other 
 point P'. 
 
 The distance between the places where the positive ions 
 strike the cathode and the origin of the cathode ray producing 
 these ions will be greatest for the rays which start from near 
 the boundary of the cathode, as these travel through the part 
 of the electric field where the lines of force are most curved; 
 there will thus not be many positive ions striking against the 
 outer parts of the cathode, on this account the rate of emission 
 of the cathode rays increases as we approach the centre of the 
 cathode ; on the other hand, if the cathode is curved the electric 
 force close to the cathode will be a minimum at the centre, so 
 that on this account the rays would be fewer along the axis; 
 taking both these effects into consideration we should expect 
 there would be a tendency for the rays to attain a maximum 
 at some place intermediate between the centre and edge of the 
 cathode. 
 
305] CATHODE RAYS. 517 
 
 The observations of Campbell Swinton* establish the existence 
 of such an effect; he found that with concave cathodes, when 
 the pressure of the gas is within certain limits, the cathode rays 
 do not form a solid pencil but are condensed into a hollow conical 
 shell. He proved this by means of the phosphorescence produced 
 by these rays on a carbon plate whose plane was at right angles 
 to the cathode : the phosphorescent patch was a circular ring 
 with in some cases a bright spot at the centre. The appearance 
 of the phosphorescence is represented in Fig. 173. 
 
 T T T 
 
 Fig. 173. 
 
 This hollowness of the bundle of cathode rays was found by 
 Campbell Swinton to depend on the curvature of the cathode, it 
 did not occur when this was plane. 
 
 305. Repulsion of Cathodic Streams. Goldstein f found that 
 when in a discharge tube there are two cathodes connected 
 together, the cathodic rays from one cathode are deflected when 
 they pass through the dark space surrounding the other cathode. 
 
 One of Goldstein's experiments was as follows: one of the 
 cathodes was a hollow metal cylinder a, from which a pencil of 
 cathode rays issued, producing luminosity in the gas through 
 
 * Campbell Swinton, Proc. Roy. Soc. Ixi. p. 79, 1897. 
 t Goldstein, Eine neue Form der elektrischen Abstossung. 
 
518 CATHODE RAYS. [305 
 
 which they travelled ; the other cathode (b) was a wire at right 
 angles to the axis of the bundle of rays proceeding from a ; when 
 
 Fig. 174. 
 
 6 was disconnected from a the path of the rays from a was 
 straight, but when a and b were connected the cathode rays 
 from a were bent sharply away when they approached b. Gold- 
 stein found that the amount of deflection did not depend on 
 the material of which the cathodes were made, nor on the nature 
 of the gas through which the rays passed. The deflection ceased 
 if the deflecting cathode was surrounded by a screen of some 
 solid substance. 
 
 Another example of the deflection of two cathode streams is 
 afforded by an experiment made by Crookes*; a and b (Fig. 175) 
 are two metal discs, either or both of which can be made into 
 
 Fig. 175. 
 
 cathodes, a diaphragm with two holes cut in it is placed in front 
 of these discs, and the path of the rays through the tube is 
 marked out by the phosphorescence they excite in a chalked 
 plate inclined at a small angle to their path. When a is the 
 cathode and 6 is idle the rays travel along the path df, while when 
 a is idle and b the cathode they travel along ef. When, however, 
 * Sir W. Crookes, Phil. Trans. 1879, part ii. p. 652. 
 
306] CATHODE RAYS. 519 
 
 a and b are cathodes simultaneously the paths of the rays are 
 dg and eh respectively, the two streams having apparently re- 
 pelled each other. Crookes attributed the divergence of the rays 
 to the repulsion between the negative charges of electricity 
 travelling along with them. E. Wiedemann and Ebert*, however, 
 by a modification of this experiment, have shown that this is 
 not the cause of the repulsion ; they provided the holes d and e 
 with shutters, and found that when a and b were simultaneously 
 cathodes eh was the path of the rays through e, whether the 
 window at d was open or shut, although when it was shut there 
 were of course no cathode rays travelling along dg to deflect those 
 passing through d, showing that the deflection of the rays has 
 its origin in the space between a and d. 
 
 The effects we have been describing can all be explained by 
 the electrostatic repulsion of the negative electricity travelling 
 along the cathode rays, by the strong electric field which sur- 
 rounds a cathode; this repulsion is appreciable only when the 
 rays from one cathode pass through the dark space of the de- 
 flecting cathode, because, as we have seen, the intensity of the 
 electric field is very much greater in the dark space than it is 
 at any other part of the discharge ; we have, on page 435, 
 discussed a method of using this deflection of the cathode rays 
 for measuring the strength of the electric field in the tube. 
 
 306. Canalstrahlen or Positive Rays. When a perforated 
 cathode is used, there may, if the pressure is between certain 
 limits, be observed luminous streams passing through the holes in 
 
 the cathode, emerging on the side of the cathode remote from the 
 
 anode, and travelling in straight lines, as in Fig. 176; these were 
 
 * Wiedemann and Ebert, Wied. Ann. xlvi. p. 158, 1891. 
 
520 CATHODE RAYS. [306 
 
 first observed by Goldstein*, and called by him Canal strahlen. 
 They excite phosphorescence on the part of the glass against which 
 they strike, and if this glass is soda glass the places struck by these 
 rays show, when observed through the spectroscope, the sodium 
 lines. Wehnelt-f- has shown that when these rays strike against 
 a copper plate they oxidise it ; the cathode rays, as we have seen 
 (p. 496), reduce an oxidised plate. Schmidt J has shown that the 
 oxidation of metals by the Canalstrahlen is not due to the impact 
 of the rays but is an indirect effect due to the rays producing 
 active oxygen when they pass through the gas ; he showed this by 
 casting a shadow on the copper plate by interposing between it 
 and the rays a solid obstacle, the part of the plate in shadow was 
 as much oxidised as that exposed to the direct impact of the rays. 
 In hydrogen Schmidt observed that the Canalstrahlen exert a 
 reducing effect. 
 
 Though these rays are much less deflected than the cathode 
 rays by electric and magnetic fields, they do suffer appreciable 
 deflection, and W. Wien has shown (see p. 117) that the direction 
 of these deflections indicates that the Canalstrahlen consist of posi- 
 tively charged particles ; he has measured, by the method indicated 
 in Chap. V., the ratio of the charge to the mass, and finds for the 
 maximum value of this quantity 10 4 , which is the ratio of the 
 charge to the mass for the hydrogen ion in the electrolysis of 
 solutions. Wien found that, in addition to the rays which give 
 this limiting value to e/m, there were always other rays present 
 which gave smaller values for e/m, and that there was no evidence 
 that the change in this quantity was discontinuous, which it 
 would be if the charge could only change by multiples of e 
 and the mass by multiples of ra. I have observed similar 
 variations in the value of e/m for the positive ions given off 
 from incandescent wires ; I think this variation is probably due 
 to the positive ions losing their charges before they reach the 
 glass where they produce phosphorescence ; what is measured in 
 these determinations is ratio of the mean value of e^to m ; if 
 now the positive ion gets neutralised by a negative charge before 
 it reaches the glass, then the mean value of e would be smalleK 
 
 * Goldstein, Berlin Sitz. xxxix. p. 691, 1886 ; Wied. Arm. Ixiv. p. 45, 1898. 
 t Wehnelt, Wied. Ann. Ixvii. p. 421, 1899. 
 t Schmidt, Drude's Ann. ix. p. 703, 1902. 
 
307] CATHODE RAYS. 521 
 
 than if it retained its charge up to the moment of impact. We 
 must remember that the gas through which the Canalstrahlen 
 move is ionised, and that there are plenty of corpuscles about 
 to neutralise the positive charge. It may be urged that if the 
 ions had lost their charge before striking the glass, they would 
 not be able to produce phosphorescence, since, as far as our 
 knowledge extends, phosphorescence is not produced by the im- 
 pact of uncharged molecules; but, according to Wien's deter- 
 mination, the positive ions in the Canalstrahlen are moving with 
 a velocity of more than 10 8 cm./sec.: we have no experience of 
 molecules moving with anything like this velocity; the shock of 
 the collision might be sufficient to ionise the molecule afresh, 
 and thus produce in the neighbourhood of the place of impact 
 effects analogous to those produced by the collision of charged ions. 
 
 307. Several experiments have been made by W. Wien*, 
 Ewers "f and Villardj; to detect the positive charge carried by the 
 Canalstrahlen by catching, as in Perrin's experiment on the 
 negative charge carried by the cathode rays (see p. 502), the 
 Canalstrahlen in a Faraday cylinder, and observing the charge 
 acquired by that cylinder. The aforesaid physicists differ in their 
 interpretation of the results they obtain; all agree that under 
 certain circumstances the Faraday cylinder, placed behind a per- 
 forated cathode, receives a positive charge of electricity, but 
 while Wien and Ewers think that this charge is carried by the 
 Canalstrahlen, Villard is of opinion that it is a secondary effect 
 due to the slow diffusion into the cylinder of ions from other 
 parts of the tube. In his experiments he found that the 
 Canalstrahlen were able to penetrate into the cylinder for some 
 time before it gave any indication of a positive charge, indeed 
 if the charge only lasted a short time, the positive charge in 
 the cylinder first appeared some little time after the discharge 
 had stopped. It seems possible that while the discharge is 
 passing the gas in the tube is too good a conductor to allow 
 the charge on the cylinder to accumulate; just as in Perrin's 
 experiment the conductivity of the gas prevents the negative 
 charge on the cylinder rising above a certain value, however 
 
 * W. Wien, Wied. Ann. Ixv. p. 445, 1898. 
 
 t Ewers, Wied. Ann. Ixix. p. 167, 1899. 
 
 J Villard, Journal de Physique, [3], t. viii. pp. 5 and 140, 1899. 
 
522 CATHODE RAYS. [307 
 
 long the cathode rays are kept playing on the cylinder; when 
 the discharge stops, the gas recovers its insulating power, and 
 the cylinder can retain any charge that diffuses into it ; if this 
 view is correct, the positive charge observed in the cylinder is 
 due mainly, at any rate, to diffusion and not to convection by the 
 Canalstrahleri. 
 
 In spite of the indecisive results obtained by this experi- 
 ment, the magnetic and electric deflections obtained by W. Wien 
 seem conclusive evidence that the Canalstrahlen carry a positive 
 charge. 
 
 On the view of the discharge given in Chap. XVI. there is 
 a stream of positively charged molecules moving towards the 
 cathode, causing this to emit cathode rays ; if the cathode is 
 perforated, part of this stream may pass through the holes, 
 producing in the gas behind the cathode luminosity, forming 
 in fact the Canalstrahlen, or positive rays as we may call them, 
 if we think this view of their constitution sufficiently established. 
 
CHAPTER XVIII. 
 
 EONTGEN RAYS. 
 
 308. RONTGEN found in 1895 that when the pressure in a 
 discharge tube is so low that the walls of the tube are vividly phos- 
 phorescent, rays which are propagated in straight lines come from 
 the tube ; these rays illuminate a screen made of phosphorescent 
 substance, and affect a photographic plate placed in their path. 
 Rontgen showed too that these rays were not entirely stopped 
 even by substances opaque to ordinary light, such as the flesh 
 of the hand, and that if the hand is placed between the bulb 
 and a phosphorescent screen, the shadow cast by the flesh is not 
 so dark as that cast by the bones, and thus the shape of the 
 latter can be distinguished. The rays which produce these effects 
 are now called Rontgen rays. The character of the rays de- 
 pends greatly upon the state of the tube in which they are 
 produced ; if the pressure in the tube is very low, so that the 
 potential difference between its terminals is very large, the rays 
 are much more penetrating than when the pressure of the gas 
 is higher, and the potential difference between its electrodes 
 smaller; very penetrating rays are sometimes called hard rays, 
 the more easily absorbable rays, soft ones. We have already seen 
 that even the rays emitted at any one time by the same \,abe 
 are not all of one type (see p. 246). 
 
 We have already discussed a good many of the properties 
 of the Rontgen rays in connection with the power they possess 
 of ionising a gas through which they pass ; we shall now consider 
 the other properties of these rays. 
 
 Rontgen showed, and the observation has been confirmed by 
 very many subsequent experimenters, that the rays are not bent 
 
524 RONTGEN RAYS. [309 
 
 when going from one medium to another, and therefore that they 
 suffer no deviation after passing through a solid prism. 
 
 We have seen (p. 258) that Rontgen rays when they strike 
 against a solid, a liquid, or even a gas, generate secondary rays 
 which in the case of impact against a solid or a liquid are 
 of a much less penetrating character than the incident ones ; 
 the incidence of Rontgen rays on the surface of a solid will 
 therefore give rise to radiation proceeding from the surface ; by 
 far the greater part of this 'reflected' radiation is diffuse, i.e. 
 though the incident rays are all travelling in one direction, the 
 ' reflected' rays will spread out in all directions. The question 
 as to whether this 'diffuse return' of the rays, -as Sir George 
 Stokes called it, is accompanied by specular reflection, in 
 other words, whether there is an excess of the reflected rays 
 in the direction in which the angle of reflection is equal to the 
 angle of incidence, is one on which observers disagree. Lord 
 Blythswood* and Rood'f have obtained photographs in which 
 there is evidence of this effect ; other observers have, however, 
 been unable to detect it. The specular reflection must in any 
 case be small, since the transparency of a powder is the same 
 as that of the same bulk of material when solid, and the defini- 
 tion through it as good. 
 
 No evidence of any polarisation of the rays has been obtained ; 
 the opacity of two crystals of tourmaline or of herapathite, placed 
 one on the top of the other, is the same when the axes of the 
 crystals are crossed as when they are parallel. 
 
 The Rontgen rays increase the electrical conductivity of badly 
 conducting liquids as well as of gases J, they increase also the 
 electric absorption of solids. Curie has lately shown that the 
 rays from radium also produce the same effect on liquids. 
 
 309. Source of the Rays. By taking photographs of a card 
 pierced with pinholes, and drawing the lines joining the photo- 
 graph of a hole with the hole itself, and finding their points of 
 intersection, it has been shown that the spot struck by the 
 cathode rays is the place from which the 'Rontgen rays originate. 
 
 * Lord Blythswood, Proc. Roy. Soc. lix. p. 330, 1896. 
 t Eood, Silliman's Journal, [4], ii. p. 173, 1896. 
 J J. J. Thomson, Nature, Iv. p. 606, 1897. 
 Curie, Comptes Rendus, cxxxiv. p. 420, 1902. 
 
310] RONTGEN RAYS. 525 
 
 Thus when the rays strike the walls of the tube, the phosphor- 
 escent part of the glass is the origin of the rays ; when a ' focus 
 tube,' i.e. one with a hollow cathode, and a plate of some infusible 
 substance placed where the cathode rays converge, the part of the 
 plate struck by the cathode rays is the source of the Rontgen rays. 
 Campbell Swinton* has shown that cathode rays impinging 
 normally on the plate are more effective in producing Rontgen , 
 rays than those which strike obliquely against the plate. The ' 
 Rontgen rays produced when the cathode rays strike against 
 a plane area come off approximately uniformly in all directions. 
 This is shown by the folio wing experiment: a hemispherical photo- 
 graphic film is placed so that its centre is at G, a point on a metal 
 plate struck by cathode rays travelling in any direction ; the 
 Rontgen rays starting from the f)late affect the film, and when 
 the photograph is developed its intensity is found to be approxi- 
 mately uniform until we approach quite close to the line where 
 the plane of the plate intersects the film. When the rays are 
 produced by the impact of the cathode rays against the glass 
 walls of the tube more rays appear to come out from any place 
 normally than obliquely ; this is, however, a secondary effect due 
 to the absorption of the rays by the glass through which they 
 have to pass ; as the rays which come out obliquely have to pass 
 through a greater thickness of glass than those which emerge 
 normally they are more enfeebled by the absorption due to the 
 glass. 
 
 310. Velocity of Propagation of Rontgen Rays. Experiments 
 to determine the velocity of the Rontgen rays have been made 
 by Brunhesf and Blondlotj. The property used in each distance 
 to detect the rays was the effect these rays have in facilitating 
 the passage of a spark. This property, it must be confessed, 
 does not seem well fitted for the purpose; for since the effect 
 of the rays on the spark is due to the ionisation of the gas 
 close to the spark gap, and as the gas when once ionised would 
 remain so for an appreciable time, the effect of the rays on the 
 spark might persist for some time after the rays had stopped, 
 and thus the brightening of the spark by the rays is not 
 
 * Campbell Swinton, Proc. Roy. Soc. Ixiii. p. 432, 1898. 
 f Brunhes, Comptes Eendus, cxxx. p. 169, 1900. 
 J Blondlot, Comptes Rendus, cxxxv. p. 666, 1902. 
 
.526 RONTGEN RAYS. [310 
 
 conclusive evidence that the rays fall on the spark gap 
 simultaneously with the passage of the spark. The method 
 adopted by Blondlot, in his experiments which have just 
 
 H' 
 
 A' 
 
 B' 
 
 7 
 c 
 
 D\ 
 
 I 
 
 
 A "" 
 Fig. 177. 
 
 B 
 
 been published, is indicated by the diagram in Fig. 177. B, B' 
 are the terminals of the secondary of an induction coil, these 
 are connected with the plates A and A' of a Hertz radiator, and 
 to the terminals H and H f of a tube exhausted sufficiently to 
 emit Rontgen rays. A resonator made of copper wire folded into 
 a triangle ODD' is placed beneath the radiator. The spark gap 
 C of the resonator is placed so that it receives Rontgen rays from 
 the tube HH', but is protected from all other radiation by 
 screens of black paper and an aluminium plate. The radiator 
 AA' consists of two horizontal brass cylinders immersed in vase- 
 line oil. The view taken by Blondlot of the action of this 
 apparatus is as follows : when the current in the primary of the 
 induction coil is broken the difference of potential between H 
 and H' increases until it is sufficient to send a discharge through 
 the tube and cause it to emit Rontgen rays ; when the potential 
 difference increases a little further a spark passes between A and 
 A, short circuiting, as it were, this circuit and extinguishing the 
 discharge through the tube HH'. The length of the gap between 
 A and A was adjusted so that the potential required to produce 
 the spark was only slightly greater than that required to send 
 a discharge through the tube, so that the tube was extinguished 
 very soon after the spark commenced and the radiator commenced 
 to vibrate. The ' electromotive force round the resonator will be 
 still longer in rising to a value great enough to spark across (7, 
 so that, if the tube is close to C, the Rontgen rays will have 
 left C long before the spark passes, and thus if the effect of the 
 rays on the spark is confined to the time when the rays are 
 actually falling on the spark gap the rays will have no influence 
 upon the spark. Blondlot found that in this case the sparks are 
 
310] RONTGEN RAYS. 527 
 
 not affected by placing a lead plate between the tube HH' and 
 the spark gap G. If now long wires are inserted between A and H 
 and A 1 and H', the extinction of the rays in the tube HH' will 
 take place at a longer interval after the commencement of the 
 spark between A and A', and if the wires are sufficiently long 
 the delay may be so great that the spark may have commenced at 
 C before the rays have ceased to fall upon the spark gap, so that 
 the rays may increase the brilliancy of the spark; in this case 
 Blondlot found that the interposition of a lead plate diminished 
 the brightness of the spark. The arrival of the rays at the spark 
 gap can also be delayed by moving the tube HH' away, keeping 
 the lengths of wire between A and H and A' and H' constant, 
 but uncoiling the wire so as to allow of the motion of HH'. 
 Blondlot found that moving the tube away increases the bright- 
 ness of the sparks when the Rontgen rays fall on the spark gap, 
 but when the rays are stopped by a lead plate the motion of 
 the tube has no effect upon the sparks. When the tube is just 
 so far away from the gap that the rays pass through the gap 
 during the whole of the time the sparks are passing across (7, 
 the effect of the rays will be a maximum, for increasing the 
 distance of the tube from the gap will dimmish the intensity 
 of the rays at the spark gap without increasing the time during 
 which they and the electric field act together at the gap : pushing 
 the tube nearer the gap diminishes the time of conjoint action 
 of the rays and field at the spark gap. Let us suppose that the 
 tube is in such a position that the sparks are at their brightest, 
 and suppose now that the length of the wires between A and H 
 and also between A' and H' is shortened by a length I ; let V 
 be the velocity of propagation of an electrical disturbance along 
 a wire, then if we suppose that the extinction of the bulb HH' 
 is due to the propagation of the drop of potential at A A' pro- 
 duced by the short circuiting of this circuit by the spark, ;he 
 rays will terminate at the time l/V earlier than they did before ; 
 if they were just contemporaneous with the force at the gap 
 before, they can be made so again by moving the tube a distance 
 I' further from the gap without altering the length of the wires, 
 provided I'/V'l/V, where V is the velocity of Rontgen rays 
 through air; provided also that the lengthening of the wires 
 and the displacement of the tube does not affect the magnitude 
 and duration of the forces acting on the spark gap. Blondlot's 
 
528 . BONTGEN KAYS. [311 
 
 method is then to start with the bulb in the position in which 
 the sparks are brightest, shorten or lengthen the wires AH and 
 A'H' by I, and then measure the distance I' through which he 
 has to displace the tube until the brightness of the sparks is 
 again a maximum ; then we have, on the preceding theory, 
 V'/V=l'/l. Blondlot found, as the result of a large number of 
 experiments, that I' is equal to I ; hence he concludes that the 
 velocity of propagation of Rontgen rays through the air is equal 
 to the velocity of propagation of an electrical disturbance along 
 a metal wire, and this is known to be equal to the velocity of 
 light ; so that he regards the experiments as proving that the 
 velocity of Rontgen rays is the same as_ that of light. 
 
 I do not see how Blondlot's explanation of the effects could 
 apply unless the effects produced by the rays on the spark gap 
 ceased simultaneously with the rays, and if this effect is due to 
 the ionisation of the gas round the air gap we should expect 
 the effect to last some time after the rays cease. 
 
 311. Diffraction of Rontgen Rays. Many experiments have 
 been made to test whether, as in the case of light, there are 
 both inside and outside the boundary of the shadows cast by 
 very small objects, variations in the intensity of the rays corre- 
 sponding to the well-known diffraction fringes. Rontgen*, who 
 investigated this point, was never able to satisfy himself that 
 the effects he obtained were undoubtedly due to diffraction. 
 Fommf observed in the photograph of a narrow slit light and 
 dark bands which looked like diffraction bands, but observations 
 with different sized slits showed that this could not be their 
 origin, and Haga and WindJ have explained them as contrast 
 effects. These observers, who have made long-continued re- 
 searches on this subject, have obtained with a narrow V-shaped 
 slit, only a few thousandths of a millimetre broad at its widest 
 point and made of platinum plates about half a millimetre thick, 
 effects which would be produced by diffraction, and which have 
 not been explained in any other way. The image of such a slit 
 is shown on a greatly magnified scale in Fig. 178 : this diagram 
 
 * Bontgen, Wied. Ann. Ixiv. p. 18, 1898. 
 
 t Fomm, Wied. Ann. lix. p. 350, 1896. 
 
 $ Haga and Wind, Wied. Ann. Ixviii. p. 884, 1899. 
 
 Wind, Physikalische Zeitschrift, ii. p. 292, 1901. 
 
312] RONTGEN RAYS. 529 
 
 represents one of the photographs with its vertical dimensions 
 magnified two hundred times, while the horizontal dimensions are 
 
 Fig. 178. 
 
 only doubled. The broadening of the narrow part of the shadow 
 is the effect relied upon for showing the diffraction. To obtain 
 a similar amount of broadening with light of a definite wave 
 length, the length of the wave would have to be of the order 
 2 x 10~ 8 cm. If we regard the Rontgen rays as due to discon- 
 tinuous pulses, this will be the order of the thickness of the 
 pulse for the particular rays under consideration. 
 
 312. We have no evidence that the Rontgen rays suffer any 
 deflection when passing through magnetic fields strong enough to 
 produce very large deflections of cathode rays. 
 
 T. G. 34 
 
CHAPTER XIX. 
 
 PROPERTIES OF MOVING ELECTRIFIED BODIES. 
 
 313. As Rontgen rays are produced when the cathode rays 
 strike against an obstacle, and as the cathode rays consist of 
 negatively charged particles, it is of interest to examine the 
 effects which are produced when the motion of a charged particle 
 is suddenly stopped. 
 
 When a particle with a charge e of electricity is moving 
 
 uniformly parallel to the axis of z with a velocity w, it produces 
 
 at a point whose coordinates relative to the particle are x, y, z, a 
 radial electric polarization equal to 
 
 a? + y 2 4- z' 2 U 
 
 4ir(F*-ii#./ , 2a _ F a V 
 \f + y '\V*=&*}\ 
 
 and a magnetic force whose components a, /3, y parallel to the 
 axes of a?, y, z respectively are given by the equations 
 
 TT- 
 
 Vw 
 
 a = 
 
 
 7 = 0, 
 
 V being the velocity of propagation of electrodynamic dis- 
 turbances through the medium surrounding the sphere (see 
 Recent Researches in Electricity and Magnetism, pp. 18 19). 
 
314] PROPERTIES OF MOVING ELECTRIFIED BODIES. 531 
 
 When w the velocity with which the particle is moving is small 
 compared with V, the radial electric polarization becomes 
 
 e 1 
 
 the same as when the particle is at rest ; and the components of 
 
 the magnetic force are given by 
 
 11 
 
 y 
 ew y 
 
 x 
 
 7 = 0. 
 
 314. In an electric field in which the components of the electric 
 polarization are f, g, h, those of the magnetic induction a, b, c, 
 there is mechanical momentum, the components U, V, W of 
 which per unit volume are given by the equations 
 
 U=cg-bh, 
 V=ah-cf, 
 W=bf-ag 
 (see Recent Researches, p. 13). 
 
 Substituting the expressions we have given for the polarization 
 and magnetic force due to the moving charged particle and in- 
 tegrating throughout the space outside a small sphere of radius a 
 described round the electrified point we find if P, Q, R are the 
 components of the resultant momentum of the medium outside 
 the sphere in this direction 
 
 ......... (i), 
 
 where p is the magnetic permeability of the medium and 
 
 sin ^ -T7- 
 
 (see Recent Researches, p. 21) ; when w is small compared with V, 
 the value of R reduces to 
 
 2 ue 2 
 
 342 
 
532 PROPERTIES OF MOVING ELECTRIFIED BODIES. [315 
 
 Thus if m is the mass of the particle the momentum due to 
 its motion is not m'w but in virtue of the momentum in the 
 electromagnetic field 
 
 m'w 4- R, 
 or when w is small 
 
 a 
 Thus the particle will in this case behave as if its mass were 
 
 , , 2yue 2 
 increased by - . 
 
 315. In the general case when w is not small, let % denote 
 m'w + R and suppose the particle is acted on by 'a magnetic force 
 H at right angles to its direction of motion, the mechanical force 
 acting upon the particle is Hew, hence if in the time Bt the 
 direction of motion is deflected through an angle &6 we have 
 
 if 8s be an element of the path, p its radius of curvature, then 
 
 ~a Ss wSt 
 ou = ------ , 
 
 P P 
 hence p = ~- ; 
 
 but if elm is the ratio of the charge to the effective mass then 
 
 mw 
 ^He* 
 
 hence m = ^ = m' H . 
 
 w w 
 
 Now from the expression (1) for R we see that when w 
 approaches F, R/w increases rapidly, hence if what we may call 
 the electrical mass is comparable with the mechanical, we should 
 expect m/e would vary with the velocity of the particle, increasing 
 as the velocity increases. From the expression given for R we 
 see that it is only with particles moving with velocities com- 
 parable with that of light that we could expect to get measurable 
 variations in the value of m/e ; happily particles travelling with 
 these speeds are furnished by radium and the value of m/e 
 for these rapidly moving molecules has been made the subject of 
 a most interesting research by Kaufmann*. 
 
 * Kaufmann, Gottingen Nach., Nov. 8, 1901. 
 
316] PROPERTIES OF MOVING ELECTRIFIED BODIES. 533 
 
 316. The method used by Kaufmann is illustrated in Fig. 179. 
 
 Fig. 179. 
 
 A small piece of radium was placed at C in a vessel from 
 which the air was extracted, the radiations from the radium passed 
 through a strong electric field in the space between the parallel 
 plates P l} P 2 which were '1525 cm. apart and maintained at a 
 potential difference of 6750 volts, they then passed through a 
 small hole D in a diaphragm and then on to a photographic 
 plate E\ during the whole of their journey from C to E the rays 
 were under the influence of a magnetic field produced by the 
 electromagnet NS ; the deflection due to the magnetic field was 
 at right angles to that due to the electric. If the electric and 
 magnetic fields were not in action all the rays from the radium 
 would strike the photographic plate at the same point, when 
 however the rays are exposed to the electric and magnetic fields 
 the deflection will depend upon the velocity, so that the rays of 
 different velocities will now strike the plate at different points 
 and the impression produced by the radium on a plate will be a 
 curved line ; by measuring the photograph the-deflection due to the 
 magnetic field and also that due to the electric field can be found, 
 and from these deflections (see Chap. V.) the values of v the velocity 
 of the particles and the corresponding value of e/m can be found. 
 Kaufmann found that when his plates were exposed for several 
 
534 
 
 PROPERTIES OF MOVING ELECTRIFIED BODIES. 
 
 [316 
 
 days he got a clearly defined curve from which he deduced the 
 following values of e/m and v. 
 
 v x 10- 10 
 
 e/m x 10~ 7 
 
 2-83 
 
 63 
 
 2-72 
 
 77 ' 
 
 2-59 
 
 975 
 
 2-48 
 
 1-17 
 
 2-36 
 
 1-31 
 
 It is clear from these numbers that e/m diminishes as the 
 velocity of the particle increases, so that if e remains the same 
 the value of ra increases with the velocity. As this increase must 
 be due to the ' electrical mass ' it follows that the electrical mass 
 must be comparable with the mechanical mass. To find the 
 proportion between the two, we must make some assumption as 
 to the distribution of electricity on the corpuscle. Kaufmann 
 assumed that the distribution was the same as if the corpuscle 
 were a conducting sphere ; the electrical field due to a moving 
 conducting sphere has been solved in great detail by Searle*. 
 On this supposition Kaufmann calculated from his experiments 
 that the electrical mass of a slowly moving corpuscle was about J 
 of the mechanical mass. He points out that the proportion will 
 depend upon the assumption made as to the distribution of 
 electricity over the corpuscle, and in a later paper he shows that 
 his experiments are consistent with the view that the whole of the 
 mass is electrical. 
 
 There does not seem to me any reason for attributing electrical 
 conductivity to the corpuscle itself, and I prefer to take another 
 view of the electric field due to a corpuscle and to assume that it 
 coincides with that part of the field due to a point charge which 
 is outside a small sphere of radius a having the point charge for 
 centre. On this supposition the electrical mass is R/w where R 
 is given by equation (1). Using this formula I have calculated, 
 on the supposition that the whole of the mass is electrical, the 
 ratios of the masses of the corpuscles moving with the velocities 
 occurring in Kaufmann's experiments to the mass of. a corpuscle 
 
 Searle, Phil. Mag. v. 44, p. 340, 1897. 
 
317] 
 
 PROPERTIES OF MOVING ELECTRIFIED BODIES. 
 
 535 
 
 moving with an exceedingly small velocity; the values of this 
 ratio (p) are given in the following table, p are the values ob- 
 served by Kaufmann. 
 
 1 
 
 v x 10- 10 
 
 p' 
 
 P 
 
 2-85 
 
 3-1 
 
 3-09 
 
 2-72 
 
 2-42 
 
 2-43 
 
 2-59 
 
 2-0 
 
 2-04 
 
 2-48 
 
 1-66 
 
 1-83 
 
 2-36 
 
 1-5 
 
 1-65 
 
 Thus the observed and calculated values of p do not differ 
 by more than 10 per cent., suggesting that all the mass of the 
 corpuscles is electrical in its origin. On this supposition the mass 
 
 of a slowly moving corpuscle is - -or m/e = -r pe/a, from the 
 
 o a o 
 
 known values of m/e and e we find a to be about 10~ 13 cm. As 
 the mass of a corpuscle has been seen to have an electrical origin 
 the question naturally suggests itself whether the masses of all 
 bodies may not have the same origin. 
 
 317. The phenomena we have described in the earlier part of 
 the book show that corpuscles are a constituent of all bodies, so that 
 part of the mass of these bodies is due to the corpuscles and is 
 therefore electrical : it is easy to imagine a form of atom for which 
 the whole mass would be electrical. For suppose that the atoms 
 are made up of a large number of negatively electrified corpuscles 
 each corpuscle being associated with its corresponding positive 
 charge, and suppose that these positive charges are spread over a 
 much greater volume than the corpuscles, the aggregation thus 
 formed would consist of a distribution of positive electricity through 
 a sphere, the corpuscles being distributed through the sphere in 
 such a way as to be in equilibrium under their own repulsions 
 and the attractive force to the centre of the sphere arising from 
 the positive electrification, in fact we should get an atom similar 
 to that described by Lord Kelvin in his paper "^Epinus Atomized" 
 (Phil. Mag. Mar. 1902). If the radius of the sphere occupied by 
 the positive electrification is large compared with the radius of a 
 corpuscle, it 'is easy to show that the mass of the atom will only 
 differ slightly from the sum of the masses of the individual 
 
536 PROPERTIES OF MOVING ELECTRIFIED BODIES. [318 
 
 corpuscles considered as discrete systems. Thus in any aggrega- 
 tion or dissociation of a system of atoms the changes in the mass 
 would, since the number of corpuscles remains unaltered, be 
 exceedingly small in comparison with the whole mass of the 
 atoms in any particular state. 
 
 318. There is another point of view from which we may regard 
 the question of electrical mass which may perhaps be most easily 
 explained by considering the simple case of a moving charged 
 particle. If a, b, c are the components of the magnetic in- 
 duction, /, g, h those of the polarization, i.e. the number of 
 Faraday tubes passing through unit area at right angles to their 
 length, then (see Recent Researches, p. 13) the components of 
 the momentum in the field are 
 
 eg bh, ah cf, bf ag. 
 
 The magnetic field is due to the motion of the Faraday tubes, 
 and if the charged point is moving parallel to the axis of z 
 with a velocity w we have (see Recent Researches, p. 8) 
 
 a = 4i7r^wg, 
 
 b = 4>7TfJLWf, 
 
 c = 0, 
 
 where p is the magnetic permeability of the medium through 
 which the Faraday tubes are moving. Substituting these values 
 for a, b, c in the expressions for the components of the momentum 
 we find that these become 
 
 - 4,-jr/jLwfh, ^-jriJLwgh, 4>7r/ji (/ 2 + (f + h-) w 4 TT^W. 
 Thus the resultant momentum is at right angles to the direction 
 of the Faraday tube and is in the plane through the tube and the 
 direction of motion of the particle, the magnitude of the resultant 
 momentum is 
 
 4,7TfjL (/ 2 + g 2 + A 2 ) w sin 6, 
 
 where 6 is the angle between the Faraday tube and its direction 
 of motion, thus w sin is the velocity of the tube at right angles 
 to its length. Hence we see that the momentum in the field is 
 the same as would exist if the Faraday tubes carry with them when 
 they move at right angles to themselves a mass of the ether equal 
 per unit volume to 47r//, (/ 2 + # 2 + A 2 ), while when the tubes move 
 parallel to their length they do not drag any ether along with 
 
319] PROPERTIES OF MOVING ELECTRIFIED BODIES. 537 
 
 them. The momentum in the field is the momentum of this 
 bound ether. Thus on this view the electrical mass of a charged 
 body represents the mass of the ether dragged along or imprisoned 
 by the Faraday tubes associated \vith that body, and thus on the 
 hypothesis mentioned above that all mass is electrical in its origin 
 it would follow that the mass of all bodies has its origin in the 
 ether dragged along by the Faraday tubes associated with the 
 body (see Proceedings of Cambridge Philosophical Society, Mar. 
 1903); the author hopes shortly to publish a more detailed account 
 of the consequences which result from this point of view. 
 
 Effect of suddenly stopping a moving charged particle. 
 
 319. The author gave an analytical investigation of this 
 question in the Philosophical Magazine for Feb. 1897 ; the follow- 
 ing geometrical treatment of the same problem is based upon the 
 method of Faraday tubes. Let us consider the case of a charged 
 point moving so slowly that the Faraday tubes are uniformly 
 distributed, and suppose the point to be suddenly stopped, the 
 effect of stopping the point will be that a pulse travels outwards 
 from it with the velocity V, but as the Faraday tubes have inertia 
 they will until the pulse reaches them go on moving uniformly 
 
 Fig. 180. 
 
 with a velocity w parallel to the axis of z, i.e. they will continue 
 in the same state of motion as before the stoppage of the point. 
 
538 PROPERTIES OF MOVING ELECTRIFIED BODIES. [319 
 
 Let us consider the behaviour of a tube which at the moment of 
 stopping the charge had the position PQ, and consider the state 
 of things after an interval t from the stoppage ; a pulse whose 
 thickness S depends on the time taken to stop the particle will 
 have travelled out to a distance Vt. In front of this pulse the 
 motion of the tubes will not have been affected, i.e. they have 
 travelled parallel to themselves through a distance wt parallel to 
 the axis of z ; behind the pulse the tube will have been brought 
 to rest along the line it occupied when the point was stopped, 
 thus the portions behind and in front of the pulse will be repre- 
 sented by ON, P'Q' in Fig. 180. Hence to preserve the continuity 
 
 I0*t 0' 0" 0'" 
 
 Fig. 181. 
 
 of the tube it must bend sharply round in the pulse itself, so that 
 now the tube has a considerable tangential component. The 
 stoppage of the point will thus produce a tangential component 
 in the electric force which we proceed to calculate, supposing that 
 the pulse is very thin so that the tube in it may be regarded as 
 approximately straight. Then 
 
 tangential electric polarization P'N wsindt 
 normal electric polarization NN' 8 
 
 where t is the time which has elapsed since the stoppage of the 
 particle and S is the thickness of the pulse. 
 
 The left-hand diagram in Fig. 181 shows the configuration of 
 the tube at the times when, if the particle had not been stopped, 
 it would have been at o, o", o". 
 
 Since the normal electric polarization at a distance r from the 
 
319] PROPERTIES OF MOVING ELECTRIFIED BODIES. 539 
 
 particle is equal to e/4>7rr 2 and if V is the velocity of propagation 
 of the disturbance Vt = r, we have from (1) 
 
 . i i 4. 1-4.- e 
 
 tangential electric polarization = . - ^ = 
 
 as this electric polarization is moving at right angles to itself 
 with a velocity V it produces a magnetic force at right angles 
 to the polarization and to its direction of motion, i.e. parallel to, 
 but in the opposite direction to the magnetic force before the 
 particle was stopped and equal to 4<7rV times the polarization, 
 
 a 
 
 i.e. to ., w sin 6 ; hence in the pulse we have (1) a tangential 
 
 electric polarization equal to ew sin #/47rrSF, and (2) a magnetic 
 force equal to ew sin 0/rS ; as these only vary inversely as the 
 distance from the particle while the polarization and magnetic 
 force before the particle was stopped varied inversely as the 
 square of the distance, their magnitudes in the pulse will except 
 in the immediate neighbourhood of the particle be very great 
 compared with their values outside the pulse. Thus the stoppage 
 of the charged particle is accompanied by the propagation out- 
 wards of a thin pulse of very intense electric and magnetic force ; 
 pulses produced in this way constitute I believe the Rb'ntgen 
 rays. It will be seen that on the Electromagnetic Theory of 
 Light the pulses which we suppose to constitute the Rontgen 
 rays are in many respects identical with waves of visible light ; 
 both consist of electric and magnetic forces at right angles to 
 each other and to the direction of propagation ; the difference 
 between the Rontgen rays and a beam of sodium light is that 
 the thickness of the Rontgen ray pulse is very small compared 
 with the wave-length of sodium light, and that in the Rontgen 
 rays there is not that regular periodic character occurring in a 
 train of waves of constant wave-length. Sir George Stoker in 
 the Wilde Lecture given before the Manchester Philosophical 
 Society showed that many of the differences between Rontgen 
 rays and ordinary light, such for example as the absence of 
 refraction, could be explained by the theory that the Rontgen 
 rays consisted of pulses whose thickness was very small compared 
 with the wave-length of visible light. 
 
 A very complete investigation of the diffraction of Rontgen 
 rays from this point of view has been given by Sommerfeld*. 
 * Sommerfeld, Phyrik. Zeit. (1) p. 105, (2) p. 55, 1900. 
 
540 
 
 PROPERTIES OF MOVING ELECTRIFIED BODIES. 
 
 [320 
 
 320. If H is the magnetic force in the pulse the energy per unit 
 volume of the pulse is -- H 2 (half of this is due to the magnetic 
 
 and half to the electric field), substituting the value given for H 
 and integrating throughout the volume of the pulse we find that 
 the energy in the pulse is 
 
 3 
 
 Thus the amount of energy radiated away in the pulse varies 
 inversely as the thickness of the pulse, and the thickness of the 
 pulse depends upon the abruptness with which the particle is 
 stopped ; if the stoppage is very abrupt the pulse, is thin, if it is 
 gradual it is wide. The amount of energy radiated away in 
 Rontgen rays bears to the energy in the field the ratio of 2a 
 to 8, where a is the radius of the corpuscle ; see p. 532. If 8 is 
 equal to 2a then all the energy (assuming that the mass of the 
 particle arises wholly from electrical causes) will be radiated away; 
 with thicker pulses only a portion of the energy is radiated, the rest 
 is absorbed where the particle is stopped. 
 
 321. In the preceding investigation we have supposed that 
 the velocity of the particle is small compared with the velocity of 
 light, the same method will however apply when this limitation 
 is removed. 
 
 When the particle moves with the velocity of light the electric 
 and magnetic forces before the stoppage are confined to a plane 
 through the centre of the sphere at right angles to its direction of 
 motion. To find the effect at a time t after the stoppage of such a 
 
322] PROPERTIES OF MOVING ELECTRIFIED BODIES. 541 
 
 particle we apply the same principle as before, that outside a pulse 
 whose radius is Vt the field is the same as if the particle had gone 
 on moving uniformly with the velocity it had when stopped, and 
 that between the charged particle and the pulse the distribution 
 of Faraday tubes is uniform. Thus we shall find a deformation 
 of the Faraday tubes such as is shown in Fig. 183 ; the plane of 
 magnetic and electric force travels on as if the particle had not 
 been stopped, since it always keeps just outside the sphere of 
 radius Vt and there is in addition a spherical pulse formed by 
 the parts joining the Faraday tubes inside the sphere to those 
 outside. 
 
 Q 
 
 Fig. 183. 
 
 322. To find the magnitude of the tangential polarization T 
 we may proceed as follows. Consider an element of the pulse 
 ABCDEFGH formed by the intersection of two meridian planes 
 ABFE, DCGH inclined at an angle $$ and two cones BCGF, 
 ADHE whose semi-vertical angles are and + dO with the 
 outer and inner spheres bounding the pulse, then since there 
 is no free electricity inside this element the number of lines 
 of force which leave the face BCGF must equal the sum of the 
 numbers entering the faces AD EH and EFGH, hence if 8 is the 
 thickness of the pulse, T the tangential polarization, we have 
 
 ~ (TSr sin d<f>) dO = -*- 2 rdO r sin 6 d<f>, 
 
 du 
 
 or ~<TSrsin<9) = .- sin 
 
 CiU 47T 
 
542 PROPERTIES OF MOVING ELECTRIFIED BODIES. [323 
 
 * ~ CQS 
 
 
 T- 
 
 ~ 
 
 sin 6 
 
 and H the magnetic force in the spherical pulse is given by the 
 equation 
 
 ._ eV\ cos 6 
 = rB ""sin 6 ' 
 
 Magnetic and Electric Forces due to the acceleration of 
 charged particles. 
 
 323. In the investigation in Art. 319 we supposed that the 
 particle was reduced to rest ; exactly the same method will however 
 give us the effects produced when smaller changes in the velocity 
 of the particle occur and when the velocity of the particle is altered 
 without being destroyed. We saw in Art. 319 that when a 
 particle moving with a velocity w is reduced to rest, i.e. when 
 a change w is produced in the velocity, a tangential electric 
 polarization T and a tangential magnetic force H are produced 
 which, at a distance r from the particle, are at the time r/ V after 
 stopping the particle given by the equations 
 
 _ ew sin 6 _ ew sin 
 
 J- . tTV> i -tl s \ 
 
 if r is the time taken to stop the particle, 8 (the thickness of the 
 pulse) is equal to FT, hence we may write 
 
 ~ _ ew sin 6 Tr_ew sin 6 
 ^4VFVT' ' rVr 
 
 If now the velocity of the particle instead of being diminished 
 by w in the time r is increased by &w in the same time, we can 
 prove by exactly the same method that there will be a tangential 
 electric polarization T' and a magnetic force H' given by the 
 equations 
 
 m, _ e&w sin 6 rr> _ eBw sin 6 
 " ' ' 
 
 rVr "' 
 
 since &w is the increase in the velocity in the time T, Sw=fr, 
 where /is the acceleration of the particle; hence substituting this 
 value for Sw, we have 
 
 y , = e/sin d jy, = _e/sm0 
 4?r7V ' rV ' 
 
324] PROPERTIES OF MOVING ELECTRIFIED BODIES. 543 
 
 thus an accelerated charged particle produces in the surrounding 
 field tangential, magnetic, and electric forces which vary inversely 
 as the distance from the particle. 
 
 By Poynting's theorem the rate at which energy is flowing 
 radially through unit area of surface is V*T'H'\ integrating this 
 expression over the surface of a sphere having its centre at the 
 particle, we find that the rate at which energy crosses the surface 
 
 2 e 2 /" 2 
 is - Jy , a result given by Larmor (Phil. Mag. v. 44, p. 503, 1897). 
 
 324. The radiation of energy from the moving charged particle 
 will modify its motion; thus supposing the particle to have the 
 mass m and to be acted upon by a uniform force X, then if v is the 
 velocity of the particle the kinetic energy is ^mv 2 and the accele- 
 
 CM t) 
 
 ration is -r ; suppose that in time $t the particle moves over a 
 ctt 
 
 distance S#, the work done on the particle by the external force 
 is XeBx, this work must equal the increase in the kinetic energy 
 plus the energy radiated away in time St, hence 
 
 v * */i ox 2 e* 
 Xetx = 3 (Jrnt? 2 ) + g y 
 
 dv 2 e 2 dv 
 
 we see from this equation that if the particle starts from rest its 
 acceleration is initially zero instead of Xejm. 
 
 Solving equation (1), we find 
 
 m dv 
 Xe 
 
 (2). 
 
 Thus if T is the time required for the acceleration to reach half 
 its final value Xe/m, we have 
 
 Thus, until a time comparable with e z /Vm has elapsed, the 
 acceleration of th$ particle and therefore the rate at which it is 
 losing energy by radiation will be small compared with their 
 
544 PROPERTIES OF MOVING ELECTRIFIED BODIES. [324 
 
 final values ; thus if a pulse of electric force passes over a charged 
 particle a much smaller proportion of the energy in the pulse 
 will be radiated away if the pulse is so thin that the time taken 
 for it to pass over the particle is comparable with T than will be 
 radiated from the thick pulses whose time of transit is much 
 longer, for then the thin pulses will have much greater penetrating 
 power than the thick ones. The expression given in Art. 138 for 
 the coefficient of absorption of a Kontgen ray only applies to the 
 case when the pulse is so thick that the time taken for it to pass 
 over a charged particle is large compared with e 2 /m V, the coefficient 
 of absorption for thinner pulses is much smaller. 
 
SUPPLEMENTARY NOTES. 
 
 CHAPTER I. 
 
 EXPERIMENTS made by McClemian (American Physical Society, Dec. 
 1902), Rutherford and Cooke (ibid.), Sfcrutt (Nature, Feb. 19, 1903) 
 have shown that the leak through air in a closed vessel depends upon 
 the material of which the walls of the vessel are made; the variations 
 with different substances are very considerable, thus Strutt found that 
 with one specimen of platinum for the walls of the vessel, the current 
 through the vessel was three times that when the walls were made of 
 glass. This shows that part of the ionisation is due to radiation given 
 out by the walls. The same conclusion had previously been arrived at 
 by Patterson (Proc. Camb. Phil Soc. xn. p. 44); as the result of his 
 experiments on the variation of the current through a large vessel with 
 the pressure : he found that starting from atmospheric pressure the first 
 diminution of pressure produced little or no effect upon the leak, it was 
 not until the pressure had been considerably reduced that diminution in 
 pressure produced a proportionate diminution in the rate of leak, this is 
 precisely what would occur if the ionisation were due to easily absorbed 
 rays given out by the sides of the vessel which at high pressures got 
 absorbed before they reached the opposite sides of the vessel, for in this 
 case as long as the pressure is high enough to make the gas absorb all 
 the rays before they travel across the vessel, the number of ions pro- 
 duced and therefore the saturation current will be independent of the 
 pressure; when however the pressure is reduced so low that the rays 
 given out by the walls are able to travel across the vessel without being 
 absorbed a diminution of the pressure will diminish the ionization and 
 therefore the saturation current. Strutt (loc. cit.) has observed similar 
 effects. 
 
 Part of the ionization in a closed vessel seems to be due to a veijy 
 penetrating radiation which traverses the walls of the vessel, for 
 McClennan (loc. cit) and Rutherford have shown that if the vessel be 
 shielded by an envelope of lead or a thick layer of water the satura- 
 tion current is reduced by about 20 / o . We do not know yet whether 
 T. G. 35 
 
546 SUPPLEMENTARY NOTES. 
 
 the ionisation due to these very penetrating rays is direct]} 7 due to 
 their passage through the gas or whether it arises mainly from a more 
 absorbable secondary radiation excited in the walls of the vessel by the 
 passage through them of the more penetrating rays. Patterson's 
 experiments seem to point to the latter as the more probable. These 
 penetrating rays may possibly come from the constituent of the 
 atmosphere which produces the induced radio-activity on a negatively- 
 electrified rod (see page 328). Rutherford has shown that this gives 
 out penetrating rays; the same substance seems to be the origin of the 
 radio-activity which C. T. R. Wilson has observed in freshly fallen 
 rain, as the rate at which this dies away is about the same as that on 
 a negatively electrified wire. The substance apparently deposits on the 
 drops as they fall through the air. 
 
 The radiation from the walls seems most probably due to a trace of 
 a very radio-active substance present in the material, as walls made of 
 different samples of the same substances such as lead, platinum or tin- 
 foil give very different ionisations. 
 
 Elster and Geitel (Physikalische Zeitschrift, in. p. 574) show that air 
 absorbed in the soil possesses very much greater conductivity than 
 atmospheric air. It is shown (p. 553) that water from deep wells 
 contains a radio-active gas very similar in its properties to the emana- 
 tion of radium. The diffusion of these gases from the soil and water 
 into the air must increase its conductivity; they cannot however 
 explain the conductivity of a gas shut up in a closed vessel, as the 
 activity of the gas derived from water dies away to half its value in 
 a few days. Thus after the gas had been shut up for a week or two 
 this course of radio-activity would disappear, and we must look to 
 other causes to explain the conductivity of gases confined in closed 
 vessels; the experiments described above indicate that the ionisation 
 may be due to radiation from the sides of the vessel and to rays from 
 outside penetrating the walls. 
 
 With reference to meteorological observations on the state of ionisa- 
 tion of the air it may be well to point out that observations on the rate 
 of escape from an electrified body in the open air are of little value as 
 the current is not saturated and the leak depends upon the velocity as 
 well as upon the number of the ions. We can test the number of ions 
 present in the air when in a steady state by drawing it rapidly through 
 a tube and measuring the saturation current between an axial wire 
 and the tube. To determine the rate at which ions are being produced 
 in the free air is very difficult, as to get the current saturated we must 
 enclose the air in a vessel and then we get the additional ionisation 
 due to the walls of the vessel. 
 
SUPPLEMENTARY NOTES. 547 
 
 CHAPTER II. 
 
 Since this work was in type M. Langevin has published in his re- 
 markably able thesis, Recherches sur les gaz ionises, University of Paris, 
 1902, some very important investigations on the law of the recombina- 
 tion of ions and the velocities of the ions in the electric field. He 
 shows by a simple calculation that the recombination of the positive 
 and negative ions is brought about by the approach of the ions caused 
 by the electrical attraction between them ; if it were not for this 
 attraction the rate of recombination of the ions would be ver^ small 
 compared with that which actually exists. The number of collisions 
 between the positive and negative ions caused by their mutual attrac- 
 tion can easily be shown to equal 4?r (k^ + k 2 ) ePN, when k l and k 2 
 are the velocities of the positive and negative ions under unit electric 
 force P and N respectively, the number of positive and negative ions 
 in unit volume, if every collision resulted in recombination, then a, the 
 coefficient of recombination as defined on p. 15, would equal 
 
 4?r (k } + k. 2 ) e, 
 
 only a fraction of the collisions will however result in recombination, 
 in the other cases the kinetic energy acquired ,by the ions in their 
 approach to each other will cause them to separate again after collision, 
 and at low pressure when the velocities of the ions under electric forces 
 are large, this fraction should be less than at high pressures when the 
 velocities are small, if e is the fraction of the number of collisions which 
 result in recombination 
 
 a = 47T6 (k-L + & 2 ) e. 
 
 Langevin determines the value of e by the following method: if the 
 gas between two parallel metal plates maintained at a constant 
 difference of potential is exposed to Rontgen rays for the exceedingly 
 small time during which a single discharge from an induction coil lasts, 
 the ions produced in the space between the plates will begin to move 
 towards the plates, the positive ions moving towards the negative plate, 
 and the negative towards the positive ; as the ions move past each other 
 some of them will recombine, so that Q the number of negative ions 
 coming up to the positive plate will be less than Q , the number of 
 negative ions produced by the Rontgen rays between the plates, the 
 stronger the electric field between the plates the faster will the ions 
 move up to the plates and the less time will there be for them to 
 recombine and in consequence the less the difference between Q and Q . 
 Langevin shows that if a- is the density of the electricity on the 
 electrified plates 
 
 352. 
 
548 
 
 SUPPLEMENTARY NOTES. 
 
 From this expression it is possible to calculate c ; the results of 
 Langevin's experiments are shown in the following table : 
 
 Ail- 
 
 CO, 
 
 Pressure in mm. 
 
 6 
 
 Pressure in mm. 
 
 e 
 
 152 
 
 o-oi 
 
 135 
 
 o-oi 
 
 375 
 
 0-06 
 
 352 
 
 0-13 
 
 760 
 
 0-27 
 
 550 
 
 0-27 
 
 1550 
 
 0-62 
 
 758 
 
 0-51 
 
 2320 
 
 0-80 
 
 1560 0-95 
 
 5 aim. 
 
 0-90 
 
 2380 p-97 
 
 The effect of pressure on the chance of collision resulting in re- 
 combination is very clearly seen; thus at the pressure of 152 mm. only 
 one collision in one hundred results in recombination, at the atmo- 
 spheric pressure the number has increased to one in four and at the 
 pressure of 5 atm. to nine out of ten. 
 
 From the equation 
 
 tt = 4:TT (kj_ + & 2 ) 6, 
 
 a/e can be deduced when c is known. 
 
 The values got by Langevin, McClung, and Townsend are in close 
 agreement, they are given in the following table : 
 
 Air... 
 C0 2 
 
 aje 
 
 LANGEVIN 
 
 Me CLUNG 
 
 TOWNSEND 
 
 3200 
 3400 
 
 3384 
 
 3492 
 
 3400 
 3500 
 
 Method of determining the velocity of the ions under an electric field. 
 
 Langevin has determined ^ and & 2 by the following method ; 
 suppose the region between the parallel plates A, CD is exposed for 
 a very short space of time to Rontgen rays, if there is such a strong 
 electric field between the plates that the recombination of the ions can 
 be neglected, then if the field were kept in one direction all the 
 negative ions would go to the positive plate and all the positive ones to 
 
SUPPLEMENTARY NOTES. 
 
 549 
 
 the negative ; if however the field were reversed before all the ions 
 got across, then the charge received by a plate would be less than in 
 the previous case, the difference would evidently depend upon the 
 velocities of the ions; if we make a series of measurements of the 
 charge received by the plate when the field is reversed at different 
 intervals after the ionisation we shall evidently have the means of 
 determining k^ and k. 2 . 
 
 The numbers obtained by Langevin by this method are at atmo- 
 spheric pressure. 
 
 Air 
 
 C0 2 
 
 *, 
 
 * 2 
 
 
 1 1 I 
 
 420 
 
 510 
 
 1-22 
 
 I 
 
 257 270 1-05 
 
 1 
 
 Langevin also investigated the variation of the velocity with the 
 pressure; as explained in the text the velocity of an ion should vary 
 inversely as the pressure as long as the nature of the ion does not 
 change, as however the negative ion at very low pressures is the 
 corpuscle, while at atmospheric pressures it is the corpuscle attached 
 to several molecules of the gas, we must as we reduce the pressure 
 arrive at a stage where the negative ion begins to get simpler and 
 when therefore the velocity will increase more rapidly than the re- 
 ciprocal of the pressure, this effect is clearly shown by the results of 
 Langevin's experiments, which are given in the following table : 
 
 Negative ions 
 
 Positive ions 
 
 P 
 
 /,-, 
 
 pk 2 !76 
 
 P 
 
 *i 
 
 j>*,/76 
 
 7-5 (cm.) 
 
 6560 
 
 647 
 
 7'5 (cm.) 
 
 4430 
 
 437 
 
 20-0 
 
 2204 
 
 580 
 
 20-0 
 
 1634 
 
 430 
 
 41-5 
 
 994 
 
 530 
 
 41-5 
 
 782 
 
 427 
 
 76-0 
 
 510 
 
 510 
 
 76-0 
 
 420 
 
 420 
 
 142-0 
 
 270 
 
 505 
 
 142-0 
 
 225 
 
 425 
 
 
 
 
 
 
 
 The velocities &, and k s are under unit electrostatic force, i.e. 300 
 volts per cm. 
 
550 SUPPLEMENTARY NOTES. 
 
 The increase in the value of pk^ with diminished pressure for pressures 
 below 20 cm. is clearly marked. There is a rise but a much smaller 
 one in the value of pk l . 
 
 Page 19. McClung has lately investigated at the Cavendish 
 Laboratory the effect of temperature upon a, and finds that a increases 
 rapidly as the temperature increases. 
 
 CHAPTER VI., p. 130. 
 
 H. A. Wilson has determined (Phil Mag. [6] v., p. 429, 1903) e the 
 charge on an iori as follows : he produces a cloud in the ionised gas, 
 using an expansion which will produce condensation on the negative 
 but not on the positive ions, thus all the drops are negatively electrified; 
 he then observes the rate of fall of these drops in an electric field, the 
 electric force being vertical; if X is the value of the force, acting so as 
 to make the drop move upwards, e the charge on the drop, and a its 
 radius, the downward force on the drop is g^-rrd 3 - Xe\ hence by Stokes's 
 rule the velocity v with which the drop falls will be given by the equal 
 
 3ATe\ or 
 
 thus by measuring v for different values of A" we can get a and e; by 
 this method Wilson finds 
 
 e= 3-1 x 10- 10 (c. G.s. electrostatic units). 
 
 CHAPTER VII., p. 144. 
 
 C. T. R. Wilson has recently shown by using a very large vessel for 
 the expansion that the few nuclei which act as centres of condensation 
 in a gas not exposed to external ionising influences such as Rontgen 
 rays carry charges and can, like those due to the Rontgen rays, be 
 removed by an electric field. He shows that the reason that the 
 external field produced no effect with smaller vessels is that in this 
 case the few ions in the vessel could be so easily removed by a small 
 electric force that differences of potential accidentally present in the 
 vessel were sufficient to remove the nuclei without the help of an 
 additional electric field. 
 
 CHAPTER VIIL, p. 160. 
 
 H. A. Wilson has recently shown that the presence of even a very 
 small quantity of hydrogen enormously increases the leak of negative 
 electricity from an incandescent platinum wire. The part of the leak 
 
SUPPLEMENTARY NOTES. 551 
 
 which depends on the hydrogen increases less rapidly with the tem- 
 perature than the part independent of the hydrogen, so that at very 
 high temperatures the latter is the more important. 
 
 CHAPTER XI., p. 255. 
 
 The more recent determinations of the work required to ionise 
 a molecule indicate a higher value than that given in the text. Thus 
 Langevin (Recherches sur les yaz ionises) from the results of some 
 experiments of Townsend's comes to the conclusion that the work done 
 on the ionic charge in falling through a potential difference of 60 volts 
 is a superior limit to the work required to ionise a molecule. Stark 
 (Drudes Ann. iv. p. 411, 1901; vii. p. 421, 1902) obtains values 
 ranging from 20 to 50 volts for the same quantity. 
 
 The effect of temperature on the ionisation of a gas by Rontgen 
 rays has been lately investigated by McClung at the Cavendish 
 Laboratory; he finds as the result of experiments made on gases at 
 constant pressure and at constant density, that the amount of ionisa- 
 tion in a given number of molecules of a gas exposed to Rontgen rays 
 is independent of the temperature, and is not, as Perrin thought, pro- 
 portional to the absolute temperature. He finds also that the absorp- 
 tion of the rays by a given number of molecules is independent of the 
 temperature of the molecules. 
 
 CHAPTER XL, p. 258. 
 
 The fact that ionisation obeys the additive law points to the con- 
 clusion that it is an atomic property, so that the likelihood of an atom 
 being ionised will depend upon the internal kinetic energy possessed 
 by the atom ; there are good reasons for thinking that the amount of 
 this energy possessed by an atom as well as the number of atoms 
 possessing a given amount of internal kinetic energy are to a very 
 large extent independent of the temperature of the gas; if we take this 
 view we can understand why the very small proportion of molecules 
 ionised does not increase rapidly with the temperature. 
 
 CHAPTER XL, p. 260. 
 
 Barkla (Phil. Mag. [6] v., p. 685, 1903) has made a very careful 
 examination of the secondary Rontgen rays produced when the 
 primary rays pass through a gas; he has shown that when the primary 
 rays pass through different gases at the same pressure the intensity of 
 the secondary radiation is proportional to the density of the gas. Thus 
 
552 SUPPLEMENTARY NOTES 
 
 for example the intensity of the secondary radiation due to oxygen is 
 to that from CO 2 as 32 is to 44. He finds too that the penetrating 
 power of secondary radiation differs little, if at all, from that of the 
 primary, so that the effect produced by the gas may be described as 
 a scattering of the primary rays. Langevin (Recherches sur les gaz 
 ionises) has investigated the secondary radiation produced when the 
 primary rays fall upon a metallic surface, and has shown that the 
 denser the metal the smaller the penetration of the secondary rays, 
 and also that the penetrating power of the secondary rays increases 
 with that of the primary. 
 
 CHAPTER XII., p. 290. 
 
 Rutherford and Soddy (Phil. Mag. [6] v., p. 576, 1903) give strong 
 reasons for supposing that radio-activity is the result of the breaking 
 up of the atom; thus the radium atom breaks up at first into the 
 positively electrified particles which constitute the a rays, the emana- 
 tion, and possibly other substances; the emanation breaks up one of 
 the products, being the substance which gives rise to induced radio- 
 activity, this, as it is radio-active, breaks down again into products 
 which, since they are not radio-active, have not been detected. 
 
 W. B. Hardy has recently shown that the rays from radium as well 
 as Eontgen rays produced very marked reddish-brown coloration in 
 a solution of iodoform in chloroform. 
 
 CHAPTER XII., p. 302. 
 
 A very interesting account of the properties of radium will be 
 found in the theses entitled Recherches sur les substances radio-actives, 
 lately published by Mme. Curie. 
 
 Mme. Curie and Laborde have recently shown (Comptes Rendus, 
 Mar. 16, 1903) that the salts of. radium are the seat of a continuous 
 development of heat which maintains them at a temperature con- 
 siderably in their experiments (1*5 C.) above that of the surrounding 
 heat. They found that the heat produced by 1 gramme of radium 
 per hour is about 100 calories. 
 
 The existence of the a radiation has been beautifully shown by 
 Sir William Crookes by the following method : a small piece of a salt 
 of radium is placed close to a screen of zinc blende ; on examining the 
 screen in a dark room by a lens it is seen to be dotted over with 
 scintillating phosphorescent patches which are continually changing 
 their places, these patches mark the spots where the screen is struck by 
 the positively electrified a rays. 
 
SUPPLEMENTARY NOTES. 553 
 
 CHAPTER XII., p. 322. 
 
 More recent experiments made by Debierne indicate that actinium 
 is a distinct substance, as it has been found to give out an emanation 
 whose activity lasts only for a few seconds ; the induced radio-activity 
 due to actinium is said to die away rather more slowly than that due 
 to radium. 
 
 As the duration of the activity of a radio-active substance is the 
 property by which it is most easily recognised it may be useful to give 
 a table of the time taken for the activity to fall to half its value for 
 those cases in which it has been determined. 
 
 Time taken for activity to fall to half its value. 
 
 Thorium emanation, 1 minute. 
 
 Induced activity due to thorium, 1 1 hours. 
 
 Radium emanation, 4 days. 
 
 Induced activity due to radium, 28 minutes. 
 
 Actinium emanation, a few seconds. 
 
 Induced activity due to actinium, rather less than 28 minutes. 
 
 Radio-active gas from water, 4 days. 
 
 Induced radio-activity due to this gas, about 40 minutes. 
 
 Induced radio-activity on a negatively 
 
 electrified wire in the open air, about 40 minutes. 
 
 The Curies have found that when bodies have been exposed for 
 a long time to the radium emanation there is in addition to the radio- 
 activity which disappears in 28 minutes a small residual activity 
 which takes months to disappear. 
 
 CHAPTER XII., p. 326*. 
 
 Experiments recently made at the Cavendish Laboratory have 
 shown that by far the greater part of the conductivity produced, by 
 bubbling air through water is due to the presence in the water of 
 a radio-active gas. The amount of this gas varies much in different 
 samples of water, in fresh deep well water from many parts of 
 England I have found it in considerable .quantity, while there is very 
 little in surface or rain water. This gas is liberated when air is 
 bubbled through the water, it can also be obtained by boiling the 
 water, the gas expelled from water by boiling having very high 
 conductivity. When once the gas has been drawn out of the water, 
 subsequent boiling or bubbling produces very little conducting gas. 
 
 355 
 
554 SUPPLEMENTARY NOTES. 
 
 Mr Adams in some experiments made at the Cavendish Laboratory 
 found that water after a rest of about a week recovered to some 
 extent its power of giving off a radio-active gas, the maximum 
 recovery amounting to about 10/ of the gas initially present. The 
 independent existence of this gas was shown in the following way: 
 a large quantity of highly conducting gas was liquefied at the Royal 
 Institution by Professor Dewar, the liquid so obtained was allowed 
 to evaporate and the gas coming off at the beginning of the evapora- 
 tion and also at the very end when it was nearly completed collected 
 and tested, the gas coming off at the beginning was found to have 
 far less conductivity than the gas had before liquefaction while the 
 gas left over at the end had about 30 times the original conductivity. 
 The conductivity can also be taken out of the gas by passing it slowly 
 through a tube immersed in liquid air. The radio-active gas resembles 
 very closely the emanation from radium; its activity has been shown 
 by Mr Adams to fall to one-half its original value in four days, the 
 time taken for the same process in the radium emanation, the induced 
 radio-activity due to the gas from water dies away to half its value 
 in about 42 minutes, the same as that of a negatively electrified wire 
 in air; according to Curie the time taken for the induced activity 
 due to the radium emanation to fall to half its value is 28 minutes. 
 I have also found that if to water from which the gas has been 
 expelled, certain substances, notably finely powdered bricks, the blue 
 clay from the Cambridge gault, or garden soil, are added, radio-active 
 gas is again obtained by boiling or bubbling. I have not however by 
 such means been able to get anything like the quantity of gas there is 
 in Cambridge tap-water. 
 
 CHAPTER XVIIL, p. 525. 
 
 Blondlot has shown that the rays which affect the sparks in the 
 experiment described on p. 525 are not Rontgen rays but a new type 
 of ray which he calls N rays, these rays are emitted by incandescent 
 burners as well as by sparks, they are refracted and are apparently of- 
 very long wave, some measured by Sagnac had a wave-length of ]- of a 
 millimetre. The rays when they fall upon incandescent platinum 
 increase its brightness without apparently increasing appreciably the 
 average temperature of the glowing wire. 
 
INDEX. 
 
 The numbers refer to the pages. 
 
 a rays 275 
 
 Absorption of cathode rays 310 
 of polonium rays 321 
 of radium rays 307, 311 
 of Eontgen rays 249, 253 
 of light, connection between and 
 
 photoelectric effects 217, 218 
 Actinium 294, 322 
 Additive property, absorption of Rdnt- 
 
 gen rays an 253 
 ionization produced by Eontgen 
 
 rays an 248 
 
 cathode fall of potential an 442 
 minimum spark potential an 443 
 After-glow in gases 498 
 Aitken, effect of dust on clouds 135, 179 
 Alkali metals, conductivity of salts of 199 
 effect of cathode rays on salts of 495 
 photoelectric effects of 212 
 Allen, H. S., ions produced by secondary 
 
 Eontgen radiation 265 
 Allen and Eutherford, rate of escape of 
 
 electricity through air 5 
 decay of induced radio-activity 323 
 Almy, discharge from fine wire 408, 410 
 effect of magnetic force on discharge 
 
 476 
 Alternating current, discharge of from 
 
 point 405 
 
 through gas at very low pressures 477 
 Anode fall of potential 458 
 Arc, electric 416 et seq. 
 appearance of 417 
 distribution of potential difference 
 
 between terminals 422 
 exploring electrodes in 423 
 effect of pressure on potential dif- 
 ference 420 
 hissing 430 
 intermittence of 419 
 magnetic field effect on 431 
 potential difference in different gases 
 
 421 
 potential difference at anode and 
 
 cathode 422 
 relation between potential difference 
 
 Arc, electric, current and length of arc 
 
 417 et seq. 
 temperature of 416 
 theory of 424 
 with terminals of different metals 
 
 419 
 Arons, potential difference of arc in 
 
 different gases 421 
 relation between potential difference 
 
 and current in arc 418 
 Arrhenius, conductivity of flames 197, 
 
 200 
 
 electrical wind 403 
 Aurora Borealis 165 
 Atmospheric electricity 3 
 Atomic weight of radium 306 
 Aurora Borealis 165 
 Austin and Starke, reflection of cathode 
 
 rays 504 
 velocity of reflected cathode rays 
 
 507 
 Ayrton, Mrs, appearance of electric arc 
 
 417 
 
 hissing arc 430 
 potential drop at anode 422 
 Ayrton, W. E., relation between current 
 and potential difference in arc 
 418 
 
 /S rays 275 
 
 Bailie, spark potential 352 
 
 discharge in a non-uniform field 
 
 387 
 Baker, effect of moisture on chemical 
 
 combination 142 
 Baly, striated discharge 463 
 Baly and Eamsay, critical pressure in 
 
 oxygen 447 
 
 Barkla, secondary Rontgen rays 551 
 Barus, electrification of a steam jet 133 
 electrical conductivity due to phos- 
 phorus 324 
 
 Battelli, critical pressure in oxygen 447 
 Becquerel, conductivity of hot air 155 
 electric deflection of rays from ra- 
 dium 111, 308 
 
556 
 
 INDEX. 
 
 Becquerel, magnetic deflection of rays 
 from radium 307 
 
 uranium 282 
 rays 274 et seq. 
 radiation from uranium 274 
 ratio of charge to mass for negative 
 
 ions from radium 111 
 separation of radio-active consti- 
 tuent from uranium 284 
 Bedwell, electricity conductivity due to 
 
 phosphorus 324 
 
 Bemont, discovery of radium 304 
 Benoist, ionisation of gas by Kontgen 
 
 rays 246 
 
 absorption of Kontgen rays 251 
 Berliner, gases from incandescent solids 
 
 179 
 Birkeland, effect of magnetic force on 
 
 discharge 476 
 magnetic spectrum of cathode rays 
 
 513 
 Bloudel, arc with terminals of different 
 
 metals 419 
 
 Blondlot, conductivity of hot air 155 
 velocity of propagation of Kontgen 
 
 rays 525 
 N rays 554 
 Blythe, distribution of potential in spark 
 
 discharge 390 
 
 Blythswood (Lord), reflection of Kont- 
 gen rays 524 
 
 Bohr, critical pressure in oxygen 447 
 Bouty, spark potential 352 
 
 connection between electric strength 
 
 and pressure 372 
 
 Boys, leakage of electricity through air 2 
 Branly, electrification by incandescent 
 
 solids 158, 181 
 
 Braun, electrification by flames 196 ' 
 ionization in explosive wave 194 
 Breisig, photoelectric effects in different 
 
 gases 230 
 
 Brooks (Miss), heat produced in sparks 396 
 and Kutherford, molecular weight 
 
 of radium emanation 318 
 Brunhes, velocity of Kontgen rays 525 
 Bubbling through water, electrification 
 
 due to 334 
 Buisson, effect of ultra-violet light on 
 
 air 140 
 
 photoelectric effect in gases 214 
 velocity of negative ions due to 
 ultra-violet light 221 
 
 Cady, thermal effects due to cathode 
 
 rays 500 
 Campbell- Swinton, hollowness of pencil 
 
 of cathode rays 517 
 path of cathode rays 515 
 production of Bontgen rays 525 
 phosphorescence under cathode rays 
 
 495 
 reflection of cathode rays 504 
 
 Canalstrahlen 117, 519 
 
 magnetic deflection of 520 
 positive charge carried by 521 
 oxidation by 520 
 
 Cantor, relation of oxidation to photo- 
 electric effects 242 
 
 Capstick, cathode fall of potential 441 
 Carey-Foster and Pryson, connection 
 between spark potential and spark 
 length 356 
 
 Carr, spark potential 352, 357, 360, 361 
 effect of material of electrodes on 
 
 spark 353 
 
 Cathode, current density at 443 
 disintegration of 451 
 distribution of potential near 444 
 fall of potential 439 
 
 depends on nature of cathode 
 
 440, 442. 
 
 effect of current on 446 
 Cathode rays 493 et seq. 
 absorption of 310 
 from uranium 282 
 ionisation due to 312 
 effect on salts of alkali metals 495 
 reducing action of 496 
 mechanical effects due to 501 
 thermal effects due to 499 
 electric charge carried by 502 
 mass of corpuscles in 91 et seq. 
 reflection of 503 
 magnetic spectrum of 513 
 scattering of 512 
 transmission of 510 
 velocity of reflected 507 
 velocity after? transmission 512 
 repulsion of streams of 517 
 determination of e/m for 91 et seq. 
 Cavallo, ionisation by incandescent 
 
 solids 155 . 
 
 Charge, electric, carried by an ion, de- 
 termination of 121 et seq. 
 electric, on ions 56 
 determination of ratio of charge 
 to mass of negative ion at low 
 pressures 91 et seq. 
 
 for corpuscles emitted by ra- 
 dium 111 
 Chattock, velocities of ions from point 
 
 discharge 53, 399 
 
 Chemical action, effect of on steam jet 134 
 electrification due to 336 
 effects produced by radium 320 
 Canalstrahlen 520 
 cathode rays 496 
 Child, potential gradient in ionized 
 
 gas 61 
 
 Chrystal, connection between spark po- 
 tential and spark length 356 
 Clouds produced by chemical action 134 
 formed round ions 124 
 relative efficiency of positive and 
 negative in producing 145 
 
INDEX. 
 
 557 
 
 Clouds produced by gases liberated by 
 
 electrolysis 337 
 Collie and Kara say, discharge through 
 
 helium 365 
 
 Collision, ionisation by 230 
 Cohesion dielcctrique 372 
 Coloration of salts of alkali metals 
 
 produced by cathode rays 495 
 Colson, nuclei from metals 142 
 Condensation round negative ion 124 
 Condensation round ions 136 
 Conduction of electricity through air 1 
 
 et seq. 
 
 Conductivity of gases, properties of 9 
 removed by filtering 10 
 
 electric field 11 
 various ways of producing 8 
 relation between current and 
 potential differences 12, 64 
 et seq. 
 
 air 1 et seq. 
 
 air in caves and cellars 7 
 air increases with time at first 
 
 in a closed vessel 6' 
 Conductivity of flames 197 
 
 produced by bubbling through water 
 
 326 
 
 Constitution of sparks 396 
 Constriction in tube, effect of on dis- 
 charge 466, 490 
 
 Cook, actinic power of spark discharge 411 
 Corpuscles 131 
 
 from hot wires 164 
 
 given out by metals exposed to 
 
 ultra-violet light 241 
 given out by radium 309 
 in motion ionise a gas 339 
 Coulier, effect of dust on clouds 135 
 Coulomb, leakage of electricity through 
 
 air 1 
 Critical spark length 356 
 
 pressure for spark discharge 361 
 Crookes (Sir W.), insulation of a good 
 
 vacuum 5 
 
 radiation from uranium 283 
 dark space 377, 432, 444 
 disintegration of cathode 451 
 striations 463 
 cathode rays 494 
 phosphorescence under cathode rays 
 
 495 
 mechanical effects due to cathode 
 
 rays 501 
 
 repulsion of cathodic streams 518 
 radiation from radium 552 
 Curie, M. and Mme, discovery of radium 
 
 303 
 
 atomic weight of radium 306 
 activity of radium 306 
 character of radium radiation 307 
 negative corpuscles given out by 
 
 radium 111, 308 
 radio-active gas from radium 318 
 
 Curie, M. and Mme, induced radio- 
 activity due to radium 316 
 ionisation due to uranium ionisa- 
 tion 281 
 
 Curie, Mme, discovers polonium 320 
 absorption of rays from polonium 
 
 320 
 Curie, Mme and Laborde, temperature 
 
 of radium in air 552 
 Curie, effect of radium rays on con- 
 ductivity of liquids 524^ 
 Curie and Sagnac, negative electricity 
 given out by plates exposed to 
 Kontgen rays 266 
 
 Current, connection with potential 
 difference for discharge through 
 a gas 12, 72 
 saturation 12 
 
 Current, variation of, with potential 
 difference for leak due to ultra- 
 violet light 219 
 
 connection between, and spark po- 
 tential for point discharge 401 
 current density at cathode 443 
 effect of, on cathode, fall of 
 
 potential 446 
 Currents, air caused by motion of ions 58 
 
 Dark space, Crookes' 377, 432, 444 
 thickness of 446 
 
 connection with mean free path 
 of molecules of the gas 450 
 relation of to current 450 
 theory of 481 
 Faraday's 433 
 
 Debierne, actinium 294, 322 
 Demarcay, spectrum of radium 305 
 Des Coudres, velocity of cathode rays 
 103 
 
 after transmission through 
 
 metal plates 512 
 
 Dewar, heat produced by spark 395 
 Diffraction of Rontgen rays 528 
 Diffusion of ions 20 
 coefficients of 27 
 of gases 30 
 
 Discharge from points 399 
 Discharge, electric, through gas at low 
 
 pressure 432 et seq. 
 theory of 479 et seq. 
 Discharge, striations in 463 
 Disintegration of cathode 451 
 Distance between striations 463 
 Dorn, negative ions given out by plate 
 
 exposed to Kontgen rays 266 
 velocity of corpuscles in secondary 
 
 Rontgen radiation 268 
 effect of moisture on thorium 289 
 persistence of radiation from ra- 
 dium 317 
 
 Drops, electrification of 143 
 Duddell and Marchant, arc with termi- 
 nals of different metals 419 
 
558 
 
 INDEX. 
 
 Dufay, ionisation by incandescent solids 
 
 155 
 Duncan, Bowland, and Todd, effect of 
 
 pressure on potential difference 
 
 in the arc 420 
 Durack, ionisation by rapidly moving 
 
 corpuscles 343 
 
 Duration of conductivity of gases 9, 16, 18 
 Dust, effect of on rate of leak through 
 
 on rate of recombination of ions 18 
 on clouds 135 
 
 Du Tour, ionisation by incandescent 
 solids 155 
 
 Earhart, spark potential for very short 
 
 sparks 352, 384 
 
 Ebert, thickness of dark space 446 
 Ebert and E. Wiedemann, effect of 
 ultra-violet light on sparks 348 
 thermal effects due to cathode rays 
 
 499 
 discharge at low pressures by rapidly 
 
 alternating currents 477 
 repulsion of cathode streams 519 
 Edison effect 162 
 
 Edlund, relation between potential dif- 
 ference and current in arc dis- 
 charge 418 
 Eichberg and Kallir, arc with terminals 
 
 of different metals 419 
 Electric field, effect of on conductivity 
 
 of gases 11 
 
 force, distribution of, in discharge 
 434 
 
 in Faraday dark space 453 
 
 positive column 455 
 Electric discharge through gases at low 
 
 pressures 432 
 theory of 479 et seq. 
 Electrical wind, 403 
 Electricity, one fluid theory of 131 
 effect of on steam jet 133, 134 
 Electrification of gases liberated by 
 
 electrolysis 337 
 due to bubbling through water 334 
 
 chemical action 336 
 effect of on induced radio-activity 
 
 322 
 effect of on condensation of drops 
 
 149 
 
 Electrodeless discharge used to find con- 
 ductivity of flames 173 
 glow produced by 447 
 effect of magnetic force on 475 
 Electrolysis, charge on gas liberated by 
 
 337 
 
 Electrolytic gas, clouds produced by 337 
 Elster and Geitel, leakage of electricity 
 through open air 3 
 
 air in caves and cellars 7 
 ionic theory of atmospheric elec- 
 tricity 149 
 
 Elster and Geitel, ionisation by incan- 
 descent solids 156 et seq. 
 gases from incandescent solids 179 
 effect of magnet on leak from hot 
 
 wire 186 
 photoelectric effects 211, 218 
 
 effect of plane of polarisation 
 on 234 
 
 temperature on 238 
 induced radio-activity on negatively 
 
 electrified wire 322, 328 
 radio-activity of air absorbed in the 
 
 ground 546 
 Emanation from thorium 285 
 
 source of 290 
 Emanation from radium 316 
 
 density of 318 
 
 Energy in Rontgen rays 280 
 Enright, electrification from chemical 
 
 action 336 
 
 Entladungstrahlen 491 
 Erman, electrification by flames 196 
 Ewers, thermal effects due to cathode 
 
 rays 499 
 positive charge carried by Canal- 
 
 strahlen 521 
 
 Exner and Haschek, pressure in sparks 
 394 
 
 Faraday, influence of successive sparks 
 
 347 
 
 dissymmetry of discharge 391 
 dark space 433, 453 
 Filtering, effect of on conduction through 
 
 gases 10 
 
 Flames, source of ionisation in 172 
 conductivity of 193 
 velocity of ions in 203 
 ionisation in gases from 193 
 distribution of electrification in 191 
 effect of electric field on 195 
 Fleming, Edison effect 162 
 
 exploding electrode in arc 423 
 theory of arc 423 
 Fluid theory of electricity 131 
 Fluorescence, connection of with photo- 
 electric effects 242 
 
 Fomm, diffraction of Kontgen rays 528 
 Force, electric distribution of in dis- 
 charge tube 434 
 
 in positive column 455 
 in Faraday dark space 453 
 Foster, Carey-, connection between spark 
 
 potential and spark length 356 
 Free-path, connection of with critical 
 
 spark length 372, 374 
 with electric force in discharge 379, 
 
 383 
 
 thickness of dark space 450 
 Frohlich, relation between potential 
 difference and current in arc 417 
 
 Gait, electrification due to bubbling 335 
 
INDEX. 
 
 559 
 
 Gases, rates of normal leak through 
 
 different gases 6 
 
 given out by incandescent solids 179 
 photoelectric properties of 213 
 Gehrcke, velocity of reflected cathode 
 
 rays 507 
 Geitel, rate of leak from a charged body 
 
 in air 4 
 
 Geitel and Elster, see Elster and Geitel 
 Giese, electrification by flames, 193, 
 
 197 
 Giesel, luminosity of radium, 306 
 
 magnetic deflection of radium rays 
 
 307 
 Goldstein, effect of temperature on 
 
 cathode fall of potential 440 
 distance between striations 463 
 effect of constriction in tube on 
 discharge 466 
 
 magnetic force on striations 473 
 similarity between striations and 
 
 effects at cathode 487 
 cathode rays 493 
 
 effect of on salts of alkali 
 
 metals 495 
 reflection of 504 
 phosphorescent patterns pro- 
 duced by 515 
 
 repulsion of cathodic streams 517 
 Canalstrahlen 520 
 
 Graham, distribution of electric force 
 in discharge tube 434 
 near cathode 445 
 in Faraday dark space 453 
 positive column 455 
 Granqvist, disintegration of cathode 451 
 Grier and Rutherford, radiation from 
 
 uranium 283 
 
 Gross and Shephard, relation between 
 potential difference and current 
 in arc 418 
 
 Guthrie, ionisation by incandescent 
 solids 155 
 
 Haga and Wind, diffraction of Bontgen 
 rays 528 
 
 Hall-effect in gases 205 et seq. 
 in discharge tube 461 
 
 Hallwachs, photoelectric effects 210, 217 
 
 Hankel, electrification by flames 196 
 
 Hardy, chemical effects due to Kontgen 
 rays 552 
 
 Harmuzescu, ionisation of gases by 
 Eontgen rays 246 
 
 Harvey and Hird, discharge of alter- 
 nating current from a point 405 
 
 Haschek and Mache, pressure in spark 
 
 394 
 and Exner, pressure in spark 394 
 
 Heat produced by spark 395 
 
 Heat, effect of on cathode fall of potential 
 440 
 
 Helium, spark potential in 364 
 
 Helium, discharge through 365 
 
 viscosity of 366 
 Helmholtz (K. von), effect of electricity 
 
 on a steam jet 133 
 and Eicharz, electrification of steam 
 jet 134 
 
 formation of clouds by chemi- 
 cal action 134 
 Hemsalech and Schuster, constitution 
 
 of sparks 396 
 Henry, phosphorescence of sulphide of 
 
 zinc 274 
 Henry (J.), photoelectric effect of gases 
 
 214 
 Hertz, photoelectric effects 211 
 
 effect of ultra-violet light on spark 
 
 348 
 
 explosive wave in spark 394 
 penetration of thin metal by cathode 
 
 rays 494, 509 
 
 Herwig, electrification by flames 196 
 Herz, distribution of electric force in 
 
 discharge 434 
 
 in the positive column 455 
 Heydwiller, heat produced by sparks 395 
 Himstedt, discharge of alternating cur- 
 rent from a point 405 
 alternating currents through gases 
 
 at low pressures 477 
 Hird and Harvey, discharge of alter- 
 nating current from a point 405 
 Hissing arc 430 
 Hittorf, leakage of electricity through 
 
 air 2 
 effect of salts on conductivity of 
 
 flames 177 
 
 electrification by flames 196 
 difficulty of producing short sparks 
 
 359 
 distribution of electric force in arc 
 
 434 
 
 cathode full of potential 439, 440 
 electric force in Faraday dark space 
 453 
 
 positive column 455 
 temperature in discharge tube 468 
 action of magnet on distribution of 
 
 glow over cathode 472 
 cathode rays 493 
 
 Hoffmann, Entladungstrahlen 49 
 Holmgren, electrification by shaking 
 
 wet cloth 143 
 
 Holtz, electrification by flames 195 
 Hoor, photoelectric effects 211 
 
 influence of temperature on 238 
 Humphreys, effect of pressure on spec- 
 trum 395 
 
 Impurities in gas, effect of on point dis- 
 charge 402 
 
 Incandescent solids, ratio of charge to 
 mass of corpuscles produced by 
 111 
 
560 
 
 INDEX. 
 
 Incandescent solids, ratio of charge to 
 mass for positive ions produced 
 by 119 
 
 ionisation by 155 et seq. 
 corpuscles emitted by 164 
 positive ions produced by 171 
 gases given out by 179 
 Induced radio-activity from thorium 
 emanation 294 
 
 duration of 296 
 time taken to produce 297 
 penetrating power of 299 
 due to radium 316 
 on negatively electrified wires in air 
 322, 328 
 
 rate of decay of 323 
 Intermittence of arc discharge '419 
 Ionisation by incandescent solids 155 
 
 et seq. 
 
 by collision 230,' 339 et seq. 
 by Eontgen rays 246 
 
 variation of with temperature 
 255 
 
 pressure 246 
 in different gases 247 
 
 an additive property 248 
 by cathode rays 312, 339 
 by Lenard rays 340 
 by uranium rays in different 
 
 gas 278, 281 
 by radium rays in different gas 
 
 312 
 by polonium rays in different 
 
 gas 312 
 
 by ultra-violet light 312 
 in explosive wave 214 
 Ions 11 
 
 explain conductivity of gases 13 
 theory of conduction through air 
 
 by 15 
 
 rate of recombination of 18 
 rate of diffusion of 20 
 velocity of 32-56 
 difference of velocities of positive 
 
 and negative 37 et seq. 
 velocity of in flames 49, 176 
 salt vapours 203 
 point discharge 53 
 charge on 56, 121 et seq. 
 mathematical theory of conduction 
 
 by 64 
 
 motion of in magnetic field 79-90 
 motion of under both electric and 
 
 magnetic forces 86 
 ratio of mass to charge for negative 
 in cathode rays 91, 95, 99, 100, 102 
 ratio of mass to charge for negative 
 produced by ultra-violet light 107 
 incandescent wire 111 
 radio-active substances 111, 112 
 positive ratio of charge to mass 117 
 
 given out by radium 282 
 positive produced by hot wire 171 
 
 Ions, work required to produce 189, 190, 
 255 
 
 condensation round 125 
 
 number of, produced by secondary 
 Eontgen radiation 265 
 
 negative given out by metals ex- 
 posed to Eontgen rays 266 
 
 number of in various parts of dis- 
 charge 460 
 
 Jaumann, effect of rapid variations in 
 potential on spark 350 
 
 Johnson, effect of rapid variations in 
 potential on spark 352 
 
 Kallir and Eichberg, arc with terminals 
 
 of different metals 419 
 Kaufmann, ratio of mass to charge of 
 
 ion 100 
 
 heat produced by discharge 395 
 scattering of cathode rays 512 
 effect of velocity on mass of cor- 
 puscle 533 
 Kelvin (Lord), electrification by shaking 
 
 mercury 143 
 
 effect of surface tension on forma- 
 tion of clouds 149 
 negative electrification due to bub- 
 bling 217, 334, 335 
 spark potential 352 
 Kiessling, effect of dust on clouds 135 
 Kirby and Townsend, ionisation by 
 
 collision 341 
 
 Knoblauch, photoelectric effects 213 
 relation of oxidation to 242 
 Koch, ionisation produced by hot wires 
 
 172 
 Kosters, electrification due to bubbling 
 
 335, 337 
 
 Kreusler, photoelectric current through 
 gases 223 
 
 Lag of electric spark 348 et seq. 
 Lang, v., relation between potential dif- 
 ference and current in arc 418 
 Langevin, recombination of ions 547 
 velocity of ions 548 
 work required to ionise a gas 551 
 secondary Eontgen rays 551 
 Laplace, electrification due to chemical 
 
 action 336 
 
 Larmor, radiation from an ion 543 
 Lavoiser, electrification due to chemical 
 
 action 336 
 Leakage of electricity through air 1 et seq. 
 
 in closed vessels 6 
 Lecher, intermittence of arc 419 
 Lehmann, appearance of short sparks 358 
 effect of constriction on discharge 
 
 466 
 
 action of magnet on discharge 472 
 similarity between striations and 
 effects at the cathode 487 
 
INDEX. 
 
 561 
 
 Leithausers, velocity of cathode rays 
 after transmission through metals 
 512 
 
 Lenard, ratio of mass to charge of ion 
 in Lenard rays 95, 96 
 
 when produced by ultra-violet 
 
 light 109 
 effect of ultra-violet light on oases 
 
 140 
 
 electrification by splashing 143, 334 
 photoelectric effects in gases 214 
 effect of pressure on photoelectric 
 
 leak 224 
 
 absorption of Lenard rays 310 
 transmission of cathode rays 510 
 rays 510 
 Lenard and Wolff, clouds formed by 
 
 ultra-violet light 135 
 Length of spark, relation of to spark 
 
 potential 354 
 
 Liebig, spark potential, 352, 355 
 Linss, leakage of electricity through 
 
 air 3 
 
 Luggin, relation between potential dif- 
 ference and current in arc 419 
 potential drop at anode and cathode 
 
 in arc discharge 422 
 Lyman, cathode fall of potential 440 
 
 McClean, electrification due to bubbling 
 
 through water 335 
 McClelland, velocity of ions in flames 
 
 49, 194 
 ions produced by incandescent wires 
 
 158 
 
 current through hot gases 185 
 McClelland and J. J. Thomson, absorp- 
 tion of Eontgen rays 245 
 McClennan, ionisation produced by cath- 
 ode rays 312 
 discharge produced by bodies after 
 
 exposure to cathode rays 499 
 effect of walls of vessel on leak 545 
 existence of penetrating radiation 
 
 545 
 McClung, effect of pressure on rate of 
 
 recombination of ions 19 
 effect of temperature on the rate of 
 
 recombination of ions 550 
 effect of temperature on the ionisa- 
 tion of a gas 551 
 McCluug and Rutherford, absorption of 
 
 Rontgen rays 251 
 energy in Eontgen rays 280 
 Mache and Haschek, pressure in spark 
 
 394 
 
 Magna, heat produced by electric dis- 
 charge 395 
 
 Magnetic deflection of rays from ura- 
 nium 282 
 
 radium 307 
 
 Magnetic field, effect of on leak from 
 hot wire 186 
 
 Magnetic field, effect of on lag of spark 
 350 
 
 spark 397 
 
 arc 431 
 
 discharge in vacuum tubes 
 
 4V70 
 on distribution of glow on 
 
 cathode 472 
 on negative glow 470 
 on striations 473 
 motion of ions 79 
 theory of effect on discharge 489 
 spectrum of cathode rays 513 
 Marchant and Duddell, arc with termi- 
 nals of different metals 419 
 Marx, distribution of temperature in 
 discharge through hot gases 205 
 transverse velocity of ions in 
 
 magnetic field 205 
 Mass of a corpuscle 131 
 
 effect of velocity on 532 
 Matteucci, leakage of electricity through 
 
 air 2 
 
 conductivity due to phosphorus 324 
 Meissner, formation of clouds 134, 338 
 
 pressure in spark 393 
 Merritt, velocity of reflected cathode 
 
 rays 507 
 Metals, nuclei from 142 
 
 non-arcing 420 
 
 Mey, cathode fall of potential 440, 442 
 Meyer and Schweidler, magnetic de- 
 flection of radium rays 307 
 Minimum potential for point discharge 
 399 
 
 spark discharge 366 
 Mohler, pressure in spark 394 
 Moisture, effect of, on thorium radiation 
 289 
 
 sparks 347 
 lag of sparks 350 
 cathode fall 440 
 Molecular weight of radium emanation 
 
 318 
 
 Molecules, number of in cubic centi- 
 metre of gas 57, 130 
 Motion of ion under magnetic force 79 
 
 and electric forces 86 
 Moulton and Spottiswoode, effect of 
 magnetic force on striatiom 473 
 similarity between effects at cathode 
 
 and striations 487 
 
 Miiller and De la Eue, effect of nature 
 of electrodes on spark potential 
 353 
 discharge between pointed electrodes 
 
 389 
 
 dissymmetry of discharge 391 
 pressure in spark 393 
 striated discharge 433, 463 
 
 Nabl, effect of pressure on rate of re- 
 combination of ions 19 
 
562 
 
 INDEX. 
 
 Naccari, conductivity due to phosphorus 
 
 324 
 heat produced by sparks 395 
 
 Naccari and Bellati, heat produced by 
 sparks 395 
 
 Nahrwold, leakage of electricity through 
 
 air 2 
 gases from incandescent solids 179 
 
 Narr, leakage of electricity through air 2 
 
 Natterer, spark length in different gases 
 375 
 
 Nebel, relation between potential differ- 
 ence and current in arc 418 
 
 Neesen and Paalzow, effect of magnetic 
 field on discharge 474 
 
 Negative electrification, induced radio- 
 activity caused by 322 
 
 Negative ions, velocity of 37 
 
 condensation round 121-125, 129 
 
 Negative glow 433 
 
 action of magnet on 470 
 
 Neureneuf, electrification in flames 195 
 
 Newall, electrodeless discharge 447 
 after-glow in gases 498 
 
 Nitrogen, spark potential in 364 
 
 Non-arcing metals 420 
 
 Number of molecules in a cubic centi- 
 metre of gas 57, 130 
 
 Obermayer, discharge from a point 411 
 Orgler, spark potential 352 
 Owen, formation of clouds 180 
 Owens, radio-activity of thorium 284 
 Oxidation by Canalstrahlen 520 
 
 connection of with photoelectric 
 effects 242 
 
 Paalzow, heat produced by spark 395 
 Paalzow and Neesen, effect of magnetic 
 
 force on discharge 474 
 Paschen, spark potential 352 
 
 discharge in a non-uniform field 387 
 Paschen's law 367 et seq. 
 Patterson, variation of leak in a closed 
 
 vessel with pressure 545 
 Peace, potential required to produce 
 
 sparks 352 
 effect of material of electrode on 
 
 spark potential 353 
 
 Perrin, effect of pressure on ionisation 
 by Rontgen rays 246 
 
 temperature on ionisation by 
 
 Kontgen rays 255 
 ionisation of different gases by 
 
 Kontgen rays 247 
 secondary Kontgen radiation 259 
 electric charge carried by cathode 
 
 rays 502 
 Pettinelli and Marolli, discharge from 
 
 hot electrodes 192 
 
 Peukert, relation between potential dif- 
 ference and current in the arc 
 418 
 
 Phosphorescence 274 
 
 caused by cathode rays 494 
 Phosphorus, conductivity due to 324 
 Photoelectric effects 211 et seq. 
 duration of 242 
 influence of temperature on 238 
 influence of plane of polarisa- 
 tion on 234 
 
 connection with phosphores- 
 cence and ionisation 242 
 connection with oxidation 242 
 properties of gases 213 
 Pliicker, action of magnet on discharge 
 
 470 
 Poggendorff, heat produced by spark 
 
 395 
 Point discharge, velocity of ions from 
 
 53, 399 
 connection between spark potential 
 
 and current 401, 408 
 effect of impurities on 402 
 with alternating currents 405 
 theory of 406 
 Polarisation of light, effect of plane of 
 
 on photoelectric effects 234 
 Polonium 304, 320 
 
 absorption of radiation from 321 
 Positive column 433 
 
 effect of magnet on 472 
 Positive ions, velocity of 37 
 
 ratio of charge to mass 117 
 near hot wire 171 
 from ultra-violet light 214 
 from radium 282 
 rays 519 
 
 Potential, distribution of in spark dis- 
 charge 390 
 
 minimum spark potential 366 
 cathode fall of 439 
 anode fall of 458 
 Pouillet, electrification by flames 195 
 
 chemical action 336 
 Precht, effect of magnetic force on spark 
 
 398 
 point discharge 400 
 
 with alternating current 405 
 Precht and Runge, atomic weight of ra- 
 dium 306 
 
 Preece (Sir W.), Edison effect 162 
 Pressure, effect of, on leak through air 5 
 on rate of recombination of ions 
 
 19 
 
 ultra-violet light discharge 226 
 spark potential 360 et seq. 
 potential difference in arc 420 
 potential gradient in positive 
 
 column 456 
 in spark 392 
 Priestley, ionisation by incandescent 
 
 solids 155 
 
 Pringsheim, relation between current 
 and potential difference in an 
 ionised gas 75 
 
INDEX. 
 
 563 
 
 Pringsheim, effect of moisture on chemi- 
 cal combination 142 
 discharge through hot gases 178 
 
 Radiation a and ft from radio-active 
 
 substance 275 
 Radiation from an ion 543 
 Radio-active emanations 285, 316, 318 
 Radio-active gas in water 553 
 Radio-activity of uranium 275 
 thorium 284 
 radium 303 
 polonium 304 
 actinium 304 
 induced 294 
 duration of 296 
 time taken to develop 297 
 penetrating power of 299 
 Radium, positive ions given out by 282 
 discovery of 303 et seq. 
 spectrum of 305 
 atomic weight of 306 
 types of radiation given out by 307, 
 
 308 
 
 radiation, absorption of 311 
 persistence of emanation 316 
 effect of heat on 317 
 chemical effects produced by 320 
 radiation, effect of on liquids 524 
 temperature of in air 552 
 Rain, radio-activity of 546 
 Ramsay and Baly, critical pressure of 
 
 oxygen 447 
 Ramsay and Collie, discharge through 
 
 helium 365 
 
 Ratio of charge to mass for corpuscles 
 91 et seq. 
 
 positive ions 117, 119 
 Ratio of velocities of positive and nega- 
 tive ions 37-41 
 Rayleigh (Lord), viscosity of helium 366 
 
 critical pressure of oxygen 447 
 Recombination of ions 14 
 rate of 16, 547 
 
 affected by dust 18 
 Reflection of cathode rays 503 
 
 Rontgen rays 524 
 Reinold and Riicker on surface tension 
 
 152 
 
 Reiss, heat produced by sparks 395 
 Repulsion of cathode rays 517 
 Richardson, ionisation from incandes- 
 cent solids 161 
 
 Richarz and Helmholtz, effect of elec- 
 trification and chemical action on 
 a steam jet 133, 134 
 Righi, photoelectric effects 211 
 
 effect of temperature on 238 
 ionisation of gases by Rontgen 
 
 rays 246 
 effect of material of electrode on 
 
 spark potential 353 
 Rollman, heat produced by spark 395 
 
 Rontgen rays 244, 523 et seq. 
 absorption of 245,~249, 253 
 ionisation of gases by 246 
 
 effects of pressure and tem- 
 perature on 246, 255 
 effect on steam jet 135 
 
 clouds 135 
 secondary 258 et seq. 
 
 in air 260 
 tertiary 273 
 reflection of 524 
 source of 524 
 theory of 
 velocity of 525 
 diffraction of 528 
 effect on solids and liquids 524 
 Rontgen, v., connection between electric 
 strength and mean free path 374 
 point discharge 399 
 Rood, reflection of Rontgen rays 324 
 Rowland, Duncan, and Todd, effect of 
 pressure on potential difference 
 in arc discharge 420 ts 
 Rue, De la and Miiller, effect of material 
 of electrode on spark potential 353 
 sparks between pointed electrodes 
 
 389 
 dissymmetry of electric discharge 
 
 391 
 
 pressure in sparks 393 
 striated discharge 433, 463 
 Runge and Precht, atomic weight of 
 
 radium 306 
 
 Russell, nuclei from metals 142 
 Rutherford, velocity of ions 32, 36, 47, 50 
 current from incandescent wire 
 
 175, 185 
 ionisation of different gases by 
 
 Rontgen rays 247 
 absorption of Rontgen rays 249 
 on uranium radiation 275 
 ionisation due to uranium radia- 
 tion 281 
 positive ions given out by radium 
 
 282 
 
 radio-activity of thorium 284 
 emanation from thorium 285 
 effect of temperature on radiation 
 
 from thorium 288 
 induced radio-activity from thox um 
 294 
 
 properties of 297 
 penetrating power of 297 
 velocity of positive ions producing 
 
 induced radio-activity 300 
 persistence of radiation from radium 
 
 317 
 effect of heat on radium radiation 
 
 317 
 existence of penetrating radiation 
 
 545 
 
 Rutherford and Allen, rate of leak of 
 electricity through air 5 
 
564 
 
 INDEX. 
 
 Kutkerford and Miss Brooks, molecular 
 
 weight of radium emanation 318 
 
 Eutherford and Cooke, effect of walls 
 
 of vessel on leak 545 
 Eutherford and Grier, uranium radia- 
 tion 283 
 
 Butherford and McClung, absorption 
 of Bontgen rays 251 
 
 energy in Etmtgen rays 280 
 Eutherford and Soddy, effect of moisture 
 
 on thorium emanation 289 
 source of thorium radiation 290 
 origin of ratio-activity 552 
 
 Sagnac, secondary Eontgen rays 259 
 
 tertiary Eontgen rays 273 
 Sagnac and Curie, negative ions given 
 out by plate exposed to Eontgen 
 rays 266 
 Salt vapours, conductivity of 200 et seq. 
 
 maximum current carried by 210 
 Saturation current 12 
 Scattering of cathode rays 512 
 Schmidt, photoelectric effects 213 
 
 relation of fluorescence and ionisa- 
 tion to photoelectric effects 242 
 radio-activity of thorium 284 
 oxidation by Canalstrahlen 520 
 Schmidt and E. Wiedemann, coloration 
 
 produced by cathode rays 496 
 Schuster, ratio of charge to mass of an 
 
 ion 99 
 
 shadow thrown on cathode 383 
 discharge in a non-uniform field 387 
 thickness of Crookes dark space 433 
 distribution of potential near cath- 
 ode 444 
 
 influence of current on dark space 450 
 action of magnet on distribution of 
 
 glow over cathode 472 
 Schuster and Hemsalech, constitution 
 
 of sparks 396 
 
 Schweidler, v. , current and potential dif- 
 ference curve 12 
 
 discharge by ultra-violet light 221 
 effect of pressure on 224, 233 
 Schweidler and Meyer, magnetic de- 
 flection of radium radiation 307 
 Secondary Eontgen rays 258 
 
 theory of 268 
 
 Seitz, transmission of cathode rays 511 
 Shadow on cathode 383 
 Shephard and Gross, relation between 
 potential difference and current 
 in arc 418 
 
 Sieveking, point discharge 401 
 Simon, ratio of charge to mass of cor- 
 puscle 100 
 
 Skinner, distribution of electric force 
 along discharge 434 
 near cathode 445 
 in Faraday dark space 453 
 anode fall of potential 458 
 
 Smithells, Dawson, and Wilson, con- 
 ductivity of salt vapours 200 
 Soddy and Eutherford, effect of tem- 
 perature on thorium radiation 289 
 source of radio-activity 290 
 Sommerfeld, diffraction of Eontgen rays 
 
 539 
 
 Source of Eontgen rays 524 
 Spark discharge 346 et seq. 
 effect of moisture of 347 
 lag of 348 
 
 influence of ultra-violet light on 348 
 effect of rapid changes in potential 
 
 on 351 
 
 theory of 376 
 Spark length, critical 356 
 Spark potential 352 et seq. 
 
 effect of material of electrode on 353 
 connection with spark length 354 
 et seq. 
 
 pressure 360 et seq. 
 minimum 366 
 in a non-uniform field 387 
 tables of 412 
 Sparks, pressure in 392 
 heat produced by 395 
 constitution of 396 
 very short. 384 
 
 effect of magnetic field on 397 
 Spectrum of radium 305 
 Spottiswoode and Moulton, effect of 
 
 magnetic force on striation 473 
 similarity between striations and 
 
 effects at cathode 487 
 Stark, cathode fall of potential 446 
 
 work required to ionise a gas 551 
 Starke, reflection of cathode rays 504 
 Starke and Austin, reflection of cathode 
 
 rays 504 
 
 Steam jet, effect of electricity on 133 
 incandescent wire on 134 
 chemical action on 134 
 Eontgen rays on 135 
 Stewart, gases from incandescent solids 
 
 179 
 Stokes (Sir G. G.), motion of an ion in 
 
 magnetic field 82 
 velocity of falling drop 121 
 theory of Eontgen rays 539 
 Stoletow, photoelectric effects 211, 217 
 connection between current and 
 potential difference for leak caused 
 by ultra-violet light 219 
 effect of pressure on photoelectric 
 leak 225, 232 
 
 temperature on photoelectric 
 
 leak 238 
 Strachan, distribution of electric force 
 
 in discharge 436 
 
 Straight line radiations from radio- 
 active bodies 289 
 Striations 433, 463 
 
 distance between 463 
 
INDEX. 
 
 565 
 
 Striations, effect of size of discharge tube 
 and pressure on distance between 
 465 
 effect of nature of gas on 465 
 
 magnetic force on 473 
 in gas at high pressures 468 
 Strutt (Hon. E. J.), absorption of radium 
 
 rays 311 
 spark potential 352 
 
 in different gases 364 
 cathode fall of potential 441 
 magnetic spectrum of cathode rays 
 
 514 
 
 effect of walls of vessel on leak 545 
 Surface tension, Remold and Eiicker on 
 
 152 
 Swyngedauw, effect of ultra-violet light 
 
 on sparks 348 
 
 effect of rate of variation of po- 
 tential on spark discharge 352 
 
 Tables of spark potential 412 
 Tamm, point discharge 400-401 
 Temperature, influence of on photo- 
 electric effects 238 
 
 iouisation by Eontgen rays 255, 
 
 551 
 
 thorium radiation 288 
 of terminals in arc 416 
 distribution of along line of dis- 
 charge through gas at low pres- 
 sures 468 
 
 Tertiary Eontgen radiation 273 
 Theory of discharge by ultra-violet 
 
 light 228 
 
 secondary radiation 268 
 spark discharge 376 
 point discharge 406 
 arc discharge 424 
 discharge through gas at low pres- 
 sures 479 et seq. 
 Thermoluminescence 496 
 Thorium, radio-activity of 284 
 
 radiation, effect of temperature on 288 
 
 moisture on 289 
 source of 290 
 
 Todd, Eowland, and Duncan, effect of 
 pressure on potential difference 
 in arc discharge 420 
 Topler, striations at high pressures 468 
 Townsend, current and potential dif- 
 ference curve 12 
 rate of recombination of ions 19 
 
 diffusion of ions 25 
 formation of clouds 134 
 secondary Eontgen radiation 261 
 electrification due to chemical action 
 
 336 
 
 charge on gas liberated by electro- 
 lysis 337 
 
 velocity of ions produced by chemi- 
 cal action 338 
 ionisation by collision 341 
 
 Transparency to Eontgen rays, coeffi- 
 cients of 252 
 cathode rays 313 
 radium rays 313 
 
 Ultra-violet light, ratio of charge to mass 
 
 for corpuscle produced by 107 
 effect of on condensation of clouds 
 139, 216 
 
 on air 140 
 
 positive ions produced by 214 
 theory of discharge due to 228 
 
 et seq. 
 
 effect of, on lag of spark 349 
 Uranium, radiation from 275 
 ionisation produced by 281 
 radio-active constituent of 283 
 
 Vacuum, insulation of 5 
 Varley, relation between potential dif- 
 ference and current for conduc- 
 tion caused by ultra-violet light 
 226 
 
 Varley, Cromwell, cathode rays 494 
 Velocity of ions 31 et seq. 
 
 methods of measuring 34 
 difference between positive and 
 
 negative ions 37 
 ratio of 73 
 table of 60 
 in point discharge 53 
 in salt vapours 176/ 
 in Games 192 ^f 
 cathode rays 103j|<^ 
 Eontgen rays 525 
 secondary Eontgen rays 268 
 rays from uranium 282 
 positive ions producing induced 
 
 ratio- activity 300 
 corpuscles, effect of on ionizing 
 
 power 344 
 Villard, reducing action of cathode rays 
 
 496 
 electrification due to Canalstrahleu 
 
 521 
 
 Villari, heat produced by discharge 395 
 Violle, temperature of arc 416 
 
 Walter, discharge before passage of 
 
 spark 350 
 Warburg, leakage of electricity through 
 
 air 2 
 lag of the spark 348 
 
 effect of ultra-violet light on 
 349 
 
 moisture on 350 
 magnetic force on 350 
 effect of impurities on point dis- 
 charge 403 
 
 cathode fall of potential 439, 440 
 Water, conductivity due to 326 
 electrification due to 334 
 radio-active gas in 553 
 
566 
 
 INDEX. 
 
 Watson, ionisation by incandescent 
 
 solids 155 
 
 Waves in air produced by sparks 393 
 Wehnelt, shadow cast on cathode 118 
 discharge from cathode 443 
 distribution of potential near cath- 
 ode 445 
 influence of current on thickness 
 
 of dark space 451 
 Wesendonck, dissymmetry of discharge 
 
 391 
 Wiechert, ratio of charge to mass of 
 
 an ion 102 
 
 Wiedemann (E.), temperature of gas 
 conveying electric discharge 468 
 constricted discharge 477 
 Entladungstrahlen 491 
 thermoluminescence 496 
 thermal effects due to cathode rays 
 
 499 
 
 energy required to produce phos- 
 phorescence 501 
 
 Wiedemann (E.) and Ebert, discharge 
 at low pressures by rapidly alter- 
 nating current 477 
 thermal effects due to cathode 
 
 rays. 499 
 
 repulsion of cathode streams 519 
 effect of ultra-violet light on spark 
 
 348 
 
 Wiedemann (E.), and Schmidt, color- 
 ation produced by cathode rays 
 496 
 Wiedemann (G.), heat produced by 
 
 sparks 395 
 Wien, ratio of charge to mass for 
 
 positive ion 117 
 Canalstrahlen 520 
 
 Willows, distance between striations 463 
 effect of size of discharge tube on 
 
 stria 465 
 influence of nature of gas on striae 
 
 465 
 effect of magnetic field on discharge 
 
 475 
 
 Wilson, C. T. E., leakage of electricity 
 
 through air and other gases 4, 6 
 
 condensation of clouds round ions 
 
 121, 125, 136 
 nuclei from metals 142 
 
 Wilson, C. T. E., relative efficiency of 
 positive and negative ions in pro- 
 ducing clouds 145 
 ions produced by point discharge 
 
 411 
 
 radio-activity of rain 546 
 Wilson, H. A., ratio of mass to charge 
 
 on corpuscle 102 
 
 effect of dissolved salt on forma- 
 tion of clouds 141, 337 
 source of ionisation in flames 172 
 velocity of ions in salt vapours 176 
 discharge through flame gases 178 
 work required to ionise a gas 190 
 distribution of potential in hot gases 
 
 191 
 
 velocity of ions in flames*192, 202 
 conductivity of flames 197 
 current through salt vapours 201, 
 
 210 
 
 distribution of electric force in dis- 
 charge 434 
 
 current density at cathode 443 
 electric force in Faraday dark space 
 453 
 
 positive column 455 
 distribution of ions along discharge 
 
 459 
 
 Hall effect in gases 461 
 charge on the ion 550 
 effect of hydrogen on leak from hot 
 
 wires 550 
 
 Wind, electrical 403 
 Wind and Haga, diffraction of Eontgen 
 
 rays 528 
 Wolf, relation of spark potential to 
 
 pressure 371 
 Wood,"distribution of temperature along 
 
 line of discharge 469 
 Work required to ionise a gas 190, 255, 
 
 551 
 Wurtz, non-arcing metals 420 
 
 Zeleny, velocity of positive and negative 
 
 ions 37-47 ^- 
 currents in gas caused by motion 
 
 of ions 59 
 
 potential gradient in ionised gas 61 
 effect of temperature on photo- 
 electric effects 238 
 
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