UC-NRLF 24 314 FLAMES AND O INCANDESCENT SOLIDS LSON, THE ELECTRICAL PROPERTIES OF FLAMES AND OF INCANDESCENT SOLIDS THE ELECTRICAL PROPERTIES OF FLAMES AND OF INCANDESCENT SOLIDS BY HAROLD A. WILSON M D.SC. (LONDON), M.A., F.R.S., F.R.S.C. FORMERLY FELLOW OF TRINITY COLLEGE, CAMBRIDGE, AND PROFESSOR OF PHYSICS IN KING'S COLLEGE, UNIVERSITY OF LONDON, MACDONALD PROFESSOR OF PHYSICS IN M C GILL UNIVERSITY, MONTREAL Xonbon : IQnfteraitg of Xonbon pre06 PUBLISHED FOR THE UNIVERSITY OF LONDON PRESS, LTD. BY HODDER & STOUGHTON, WARWICK SQUARE, E.C. 1912 HODDER AND STOUGHTON PUBLISHERS TO THE UNIVERSITY OF LONDON PRESS ur. PREFACE THIS book is intended to give a concise but fairly complete account of recent researches on the electrical properties of incandescent bodies and of flames. I have attempted to present the mathematical theory required in as simple a form as possible, without loss of accuracy, and to make estimates of the reliability of some of the measure- ments described. Some matter not hitherto published is contained in the book. H. A. W. January 1912. CONTENTS / CHAP. PAGE I INTRODUCTION 1 II THE DISCHARGE OF NEGATIVE ELECTRICITY BY HOT PLATINUM IN A VACUUM ...... 4 III THE DISCHARGE OF NEGATIVE ELECTRICITY BY HOT PLATINUM IN HYDROGEN AND OTHER GASES . . 16 IV THE DISCHARGE OF NEGATIVE ELECTRICITY BY VARIOUS SUBSTANCES 28 V THE DISCHARGE OF POSITIVE ELECTRICITY BY HOT BODIES 33 VI THE CONDUCTIVITY OF THE BUNS EN FLAME . . .57 VII THE ELECTRICAL CONDUCTIVITY OF SALT VAPOURS . 70 VIII THE ELECTRICAL CONDUCTIVITY OF FLAMES FOR RAPIDLY ALTERNATING CURRENTS 100 IX FLAMES IN A MAGNETIC FIELD 112 ELECTRICAL PROPERTIES OF FLAMES CHAPTER I INTRODUCTION THAT flames conduct electricity and that hot bodies lose an electrical charge and various other associated facts have been known for more than a century, but it is only during the last twenty years that the electrical properties of bodies at high temperatures have been systematically investigated. The earlier observations are mostly of a purely qualitative character, and the conditions of the experiments described not sufficiently definite for them to be of much use for an accurate comparison between theory and experiment. The development of the ionic theory of the electrical pro- perties of gases by Sir J. J. Thomson led to numerous experi- mental investigations, which naturally included an examination of the electrical properties of flames and hot solids in the light of the new theory. In consequence a great increase in our knowledge of the relations between matter and electricity at high temperatures has taken place and the ionic theory has become firmly established in this field. The following pages contain an account of many of the more recent investigations on the electrical properties of hot bodies and flames, especially of such as are of a quantitative character giving results capable of accurate comparison with theory. Elster and Geitel l made a great many observations on the charge acquired by an insulated plate put near hot wires in different gases at various pressures. 1 Wied. Ann. 1882, 1883, 1884, 1885, 1887, 1889. B 1 2 ELECTRICAL PROPERTIES OF FLAMES Sir J. J. Thomson l measured the conductivity of many gases and vapours of salts and metals between platinum electrodes at a bright red heat. Gases and vapours which dissociate he found conduct very much better than those which do not. Sir J. J. Thomson 2 in 1899 determined the ratio of the charge e to the mass m of the negative ions emitted by an incandescent carbon filament in hydrogen at a low pressure, and found it equal to about 10 7 , which is the value of e/m for electrons. McClelland 3 examined gases which had been drawn past a hot platinum wire and showed that they contained positive and negative ions. The velocity of these ions due to an electric field he found was very small and smaller the hotter the wire. The writer 4 examined the variation of the current from hot platinum in air with the temperature, and from the rate of variation calculated the energy rendered latent by the formation of the ions at the surface of the platinum. Rutherford 5 measured the velocity of the ions emitted by hot platinum in air and found that the ions had a considerable range of velocities. The average velocity increased with the temperature. O. W. Richardson 6 examined the current from hot platinum in a vacuum and explained its variation with the temperature by supposing that the electrons in the metal, to which its conduc- tivity is due, escape at high temperatures. Richardson's theory is now well established as the result of many investigations by himself and others. Giese 7 investigated the electrical properties of the gases coming from flames and explained many of them on the ionic theory. McClelland 8 determined the velocities of the ions in gases drawn from flames and found them to vary from 0'23 cm. per 1 Phil. Mag. V. 29, pp. 358, 441, 1890. 2 Phil. Mag. V. 48, p. 547, 1899. 3 Proc. Camb. Phil. tioc. vol. x. p. 241, 1900. 4 Phil. Trans. A. vol. 197, p. 415, 1901. 5 Physical Review, vol. xiii., December 1901. 6 Proc. Camb. Phil. Soc. vol. xL p. 286, 1902. 7 Wied. Ann. vol. xvii. pp. 1, 236, 519, 1882 ; vol. xxxviii. p. 403, 1889. ^ 8 Phil. Mag. V. 46, p. 29, 1898. INTRODUCTION 3 sec. for one volt per cm. near the flame to 0'04 cm. per sec. some distance away. Arrhenius l in 1891 investigated the conductivity of flames containing salt vapours, and found that the conductivity due to salts of the alkali metals increases rapidly with the atomic weight of the metal. Arrhenius' results were confirmed and extended by Smithells, Dawson, and the writer. 2 The writer 3 measured the velocity of the ions in flames, and showed later 4 that Faraday's laws of electrolysis apply to alkali salt vapours at high temperatures. The investigations just mentioned are some of the first of those in which definite quantities were measured. Most of the above and subsequent researches are described more fully in the following chapters. A full account of the old experiments is given in Wiede- mann's Eleldricitat, Bd. IV. B. Sir J. J. Thomson, in Conduction of Mcdridty through Gases, gives a summary of the most important observations made by the earlier experimenters and references to their papers. I have not discussed the numerous observations which have been made on gases drawn from flames or from the neighbour- hood of hot wires. These observations show that ions are present in such gases and their velocities have been found. Also I have not given any account of the numerous observa- tions on the' deflection of flames by electric and magnetic fields. 1 Wied. Ann. vol. xliii. p. 18, 1891. 2 Phil Trans. A. vol. 193, p. 89, 1899.'' 3 Phil. Trans. A. vol. 192, p. 499, 1899. 4 Phil. Trans. A. vol. 197, p. 415, 1901. ^ B 2 CHAPTER II THE DISCHARGE OF NEGATIVE ELECTRICITY BY HOT PLATINUM IN A VACUUM WHEN a negatively charged clean wire of pure platinum is raised to a high temperature in a vacuum, it is found to lose its charge. If the negative terminal of a battery is connected to the hot wire, and the positive terminal to a conductor near the wire, a continuous current passes between the con- ductor and the wire through the vacuum, but if the connections of the battery are reversed little or no current is obtained. The current is only obtained when the wire is hot, so that it is clear that it consists of negative electricity emitted by the wire. The current obtained is about 10 ~ n to 10 ~ 7 of an ampere per sq. cm. of platinum surface, at a temperature of about 1600 C. Much larger currents than this may be obtained if impurities, such as hydrogen and alkali metal salts, are present in the platinum, even in minute quanti- ties. The current increases rapidly with the temperature of the wire. The above statements can be verified with the apparatus shown in Fig. 1. A loop of pure platinum wire PP is suspended inside a glass tube about 2 cms. in diameter and 12 cms. long. The ends of the loop are attached to two stout platinum wires DE sealed through the upper end of the tube. A cylinder of platinum foil AB sur- rounds the loop and is connected to wires sealed through the lower end of the tube at F. A side tube leads FIG. 1. DISCHARGE OF NEGATIVE ELECTRICITY 5 to a mercury pump capable of reducing the pressure below O'OOl mm. of mercury. The loop may be of wire 0'2 mm., and the wires DE about 1 mm. in diameter. Before sealing the side tube to the pump, the apparatus is washed with boiling nitric acid and distilled water. The loop is heated by passing a current through it, and its resistance is found by making it one of the arms of a Wheatstone's bridge. The temperature of the loop is obtained from its resist- ance. The current between the loop and the cylinder is measured with a galvanometer. To get rid of gases evolved by the apparatus when the wire is heated, it is best to admit air to atmospheric pressure and pump it out several times while the wire is kept at about 1600 C. If these precautions are taken and a good vacuum obtained, the current from the wire will be found to be of the order of magnitude stated, and will remain fairly constant. The use of charcoal and liquid air greatly facilitates the obtaining of a good vacuum. According to the ionic theory, we should expect the negative electricity emitted by the wire to be carried by charged atoms, or to consist simply of free electrons. The ratio of the charge (e) to the mass (in) of the negative ions emitted by a hot carbon filament was determined by Sir J. J. Thomson in 1899. l Two parallel aluminium plates were arranged in a vessel which could be ex- hausted. A small incandescent lamp filament was fixed between the plates and close to one of them. The plate near the filament was negatively charged, and the current carried by the negative ions from the filament to the other plate was measured. When a magnetic field was produced parallel to the plates, this current was diminished if the field was greater than a definite value depending on the potential difference and distance between the plates. From the values of these quantities the ratio e/m was calculated, and found to be about 9 X 10 6 , which agrees within the errors of experiment with the value of e/m for cathode rays, or negative electrons. For the negative electricity emitted by a glowing Nernst filament Owen 2 found e/m = 6 X 10 6 , and for that 1 Phil. Mag. V. 48, p. 547, 1899. 2 Owen, Phil Mag. VI. 8, p. 230, 1904. 6 ELECTRICAL PROPERTIES OF FLAMES emitted by hot lime Wehnelt 1 found e/m = 1*4 x 10 7 . O. W. Richardson 2 has recently measured e/m for the negative electricity emitted by hot platinum itself, and finds it equal to about 1*5 x <10 7 . Thus it is clear that the negative electricity is emitted as free negative electrons. The emission of these electrons by many quite different substances at high temperatures affords a convincing proof that they are a common constituent of all forms of matter. In discussing the discharge of electricity from hot bodies, it is convenient to adopt a special name for the current carried by the electrons or ions emitted. Following Prof. O. W. Richardson, I shall call this current the thermionic current, and the ions carrying it thermions. The thermionic current obtained in a good vacuum is indepen- dent of the potential difference, provided this is greater than a few volts. If the P.D. is very small, some of the electrons which escape diffuse back to the wire, so that the current is smaller. The maximum current is usually called the saturation current. The variation of the thermionic current from hot platinum in a vacuum with the temperature of the platinum was first investi- gated by O. W. Richardson, 3 who at the same time put for- ward an elegant theory to account for it, which is now firmly established. The variation of the thermionic current with the temperature is shown in Fig. 2, given by Richardson (loc. cit.). If i denotes the saturation thermionic current per sq. cm. of platinum surface, and 6 the absolute temperature, then Richardson found i = A0*e-Q< 2 *, where A and Q are constants. This formula represents the curves shown in Fig. 2 very well. The following table, taken from a paper by the writer, 4 shows the accuracy with which Richardson's formula represents the 1 Wehneldt, Ann. d. Phys. vol. xiv. p. 425, 1904. 2 Phil. Mag. (6) vol. xvi. p. 740, 1908. Ibid. (6) vol. xx. p. 545, 1910. 3 Proc. Camb. Phil. Soc. vol. xi. p. 286, 1902. Phil. Trans, vol. 201, p. 516, 1903. 4 H. A. Wilson, Phil Trans, vol. 202, p. 243, 1903. DISCHARGE OF NEGATIVE ELECTRICITY 7 thermionic current. The calculated currents are those given by the equation i = 6'9 X 10 7 0*- 1310002 '. Temperature. 1375 1408-5 1442 1476 1510-5 1545 1580 Current per sq. cm. found. Current calculated. 1-57 x 10-8 1-49 x 10-8 3-43 " 3-33 7-46 7'18 15-2 15-3 32-3 31-8 63-8 64-5 128 128-5 According to Richardson's theory the electrons which escape from hot bodies are those which are contemplated in the electron 1200 1250 1300 1350 WOO W-5j = volume of liquid. Neglect- ing v l and putting v 2 = R0/p, we get L = ^ Let the internal work done in evaporating the liquid be P, so that L = P -f T and p+at.-SfJ p dO Hence Now p = frtfiVN, where m is the mass of a molecule, V the square root of the mean square of the velocities of all the mole- 1 Phil Mag., November 1909. 2 H. A. Wilson, Phil Trans. A. vol. 202. pp. 243-275, 1903. DISCHARGE OF NEGATIVE ELECTRICITY 15 cules, and N the number leaving each sq. cm. of the liquid surface per second, and I a constant. But V 2 is proportional to 6, hence we may write p = b'N^O, where l f is a constant. Putting this in the above equation, we get 0i*N 9 = P/l But i = Ne and R = 2, so that OM 9 P/l which is equivalent to * = D#*e " p 2e . For pure platinum in a vacuum, or in air at low pressure, O. W, Richardson, H. A. Wilson, F. Horton, Deininger, 1 and others have all obtained values of Q differing little from 130,000. As to A, however, there is a good deal of doubt, for a small error in the currents leads to a large error in A, and traces of hydrogen or other impurities change A much more than Q. It is probable that A for pure platinum is not much less than 10 8 . 1 Ann. der Phys. IV. vol. xxv. p. 304, 1908. CHAPTER III THE DISCHARGE OF NEGATIVE ELECTRICITY BY HOT PLATINUM IN HYDROGEN AND OTHER GASES. WHEN platinum is heated in gases such as oxygen, nitrogen, or helium, which have little or no action on it, the negative thermionic current is not directly affected. 1 The potential difference required to give the saturation current is increased, as we should expect. If the electric field near the hot wire exceeds a certain value, proportional to the pressure of the gas, the electrons acquire sufficient energy to ionize the molecules with which they collide, 2 so that then the current is increased by the presence of the gas. This effect led some experimenters to suppose that the gas really increases the number of electrons emitted by the wire, but it was shown by the writer (loc. cit.) that ionization by collisions is sufficient to account for it. In hydrogen, however, the negative thermionic current is greatly increased, even when the hydrogen is only present in minute quantities. 3 The following table gives the currents observed when success- ive small quantities of pure hydrogen were admitted into an apparatus like that shown in Fig. 1. The temperature of the platinum wire loop was 1350 C. Pressure of Hydrogen (p) mms. of Mercury. Thermionic Current (c) Scale Divisions. (<1OJ5)-- 0-0006 10 2-65 0-0015 20 2-70 0-0033 40 3-01 0-0053 50 2-65 0-0080 75 2-92 0-0140 110 2-85 1 H. A. Wilson, Phil Trans. A. vol. 202, p. 243, 1903 ; F. Horton, Phil. Trans. A. vol. 207, p. 149, 1908. 2 J. S. Townsend, The Theory of Ionization of Gases by Collision. 3 H. A. Wilson, Phil. Trans. A. vol. 208, p. 247, 1908. 16 DISCHARGE OF NEGATIVE ELECTRICITY 17 The values of cp-' u given in the third column are nearly constant, showing that the current is proportional to y 74 at 1350 C. The current from a clean wire at 1350 C. in a good vacuum, when all traces of hydrogen have been removed by letting in air and pumping it out several times with the wire at a high temperature, is usually not more than 1/250 in the units used. It appears, therefore, that at a pressure of 0'014 mms. at 1350 C. the hydrogen increases the thermionic current about 25000 times. It is very difficult to get rid of traces of hydrogen in highly exhausted tubes, so that it often happens that comparatively large currents are obtained. When the wire is heated, hydrogen may be evolved by the surrounding electrode, by the wire itself, or even by the glass. Since oxygen does not appear to affect the negative thermionic current, a simple way of getting its true value in the absence of hydrogen is to let in a little pure oxygen or air. Any hydrogen present is then burnt up at the hot wire > and the water vapour formed can be absorbed by phosphorus peutoxide. The potential difference used must riot be sufficient to produce ionization of the oxygen by collisions. When the pressure of the hydrogen is changed the resulting change in the thermionic current does not all occur immediately, but takes time to become established. The current variation lags behind that of the pressure. The same thing happens when the temperature of the wire is altered in hydrogen at constant pressure. This clearly indicates that the increase in the current produced by the hydrogen is due to the presence of hydrogen in the surface of the platinum, and that it takes time for the equilibrium between the metal and the gas to be established after any change in the conditions. The time required for the current to become constant varies considerably with the temperature and pressure. Half an hour is usually more than sufficient, even after a large change. At constant pressure the variation of the equilibrium current with the temperature is represented approximately by the for- mula i = A0*e -Q /2d , which holds good in a vacuum. The following table contains values of A and Q found by the writer. 1 1 Phil. Trans. A. vol. 208, p. 249, 1908. 18 ELECTRICAL PROPERTIES OF FLAMES Gas. Pressure. Q. A. Aii- Small 145,000 1-14 x'10 s Air Small 131,000 6-9 x 10 7 H 0-0013 mm. 110,000 10 H 0-112 mm. 90,000 5 x 10 4 H 113-00 56,000 2 x 10- The second values in air are for a wire which had been boiled in nitric acid for one hour, and the first for one boiled in nitric acid for twenty-four hours. In both cases the wire was heated strongly while air was let in and pumped out several times. In the second case it seems likely that a minute trace of hydrogen still remained in the wire. It will be observed that the hydrogen diminishes both Q and A. At constant pressure we have i A0*e~ Q2 *, where A and Q are functions of p, and at constant temperature i = ~Bp n , where B and n are functions of 6 only. Let \ and i 2 be the currents at X and 2 when the pressure is p. Then Now let if and i 2 be the currents at 6 1 and 2 when the pressure is p'. Then a rv' / 1 1 \ where Q' is the value of Q at p'. Also let i t = B x p n \ if = B^/^, i. 2 = B 2 p* t and i 2 = B 2 # /n *. Hence = or !i.^_ = (P ", - n z _ Q' - Q In this equation the right-hand side is a function of p only, and the left one of only. Hence both sides must be equal to a constant a say. Consequently n = a6~ l c andQ = U 2alogp, where c and U are constants. If these values are put in the DISCHARGE OF NEGATIVE ELECTRICITY 19 equation Bp n = A.6?s~Q' 2e we easily see that A must be equal to Kp ' c , where K is a constant. If we take a = 2400, we get the following values of Q + 2a P 0-0013 0-112 133-0 Q 110,000 90,000 56,000 u 78,000 79,500 79,500 If we take C = 0'73 we get the following values of A.p c = K. p A K 0-0013 10 7,800 0-112 5 x 10 4 10,100 133-0 2 x 10 2 3,600 Thus, while p is increased 10 5 times, U remains practically unchanged and K only varies by a factor of 3. A small error in the observed currents produces a large one in A, so that this quantity cannot be found very exactly. It seems, therefore, that the values found for A and Q agree well with the assumption that the current is proportional to p n at constant temperature. The equations A = Kp~ c and Q = P 2a log p give 4(Q- p ) A = Ke 2a ....... (1) Putting U = 79000, a = 2400, K = 9000, and c = 073, and calculating Q from the values found for A, the following results are obtained : Q = 6580 log A + 19100. Gas. Pressure. A y (Calculated ) Q (Found.) Air Air H 2 1 Small Small 0-0013 0-112 133-0 1-14 x 10 s 7 x 10 7 10 5 x 10 4 2 x 10 142,000 138,000 110,000 90,300 54,000 145,000 131,000 110,000 90,000 56,000 It appears that this relation is satisfied by the values of A and Q for a wire in air, as well as by those for the wire in hydrogen. If we put p = in the equations Q = P 2a log p and A = Kp~ c we get Q = oo , and A = oo . These equations there - C 2 20 ELECTKICAL PROPERTIES OF FLAMES fore require modifying to enable them to represent all the values of A and Q. If we suppose A = A /(l -f ap c ) where a is a constant, then, when ap c is large compared with unity, this formula will agree with A = Kp~ c and when p = it gives A = A . We have A / 1-14 X 10 8 /K= 9X10* = 1 ' 27) When p = O'OOl, ap c = 100, so that even at this pressure the difference between the two formulae is only one per cent. Equation (1) gives A = A fi2i fQ ~ Qo) , so that Q = Q - 2CW- 1 log (1 + ap e ). This formula gives Q = Q when p == 0, and for all measurable values of p does not differ appreciably from Q = Qo 2a lg P %ac~ l log a. When^> = 1, Q = U, so that this is the same as Q = U 2a log p, which has been shown to agree with the values found for Q at different pressures. If we substitute the values found for A and Q in the equation i = A0*-Q/ 2 we get . i = A (l + ap c ) " * Q If p = 0, this gives i Q = A <9* - -/ 26^e~ p/2e is equal to ?^/v/R/2?rNm, so that it should be proportional to the number (n) of free electrons per c.c. in the platinum. We have seen that A in the experimental formula i = A0*e ~ Q/2fl may be diminished by hydrogen, from 10 8 to 10 2 . But the conductivity of the platinum is very little affected by the hydrogen, so that n must really be practically unchanged. At first sight, therefore, the diminution of A appears to be incompatible with the theory. Richardson l pointed out that if Q varies with the tempera- ture, the value of A deduced from the observed currents may 1 Phil Trans. A. vol. 201, p. 497, 1903. 22 ELECTEICAL PROPERTIES OF FLAMES differ greatly from the theoretical value D = Thus, suppose P = Q + aO. Then the equation i= becomes i = Ds - / 2 0*e - Q/ 2 ', so that the value of A calculated from the currents is De - a / 2 and the value of Q calculated is not equal to P. Equating the theoretical and experimental expressions for the thermionic current, we get or P = Q + 20 log D/A ...... (1) so that if P and D satisfy this equation, then the observed currents will agree with the formula i = A0*e " Q/2d , as is found to be the case. Consequently, P and D may be any functions of and p which satisfy (1), and yet the formula i = A0*~Q/ 20 , in which A and Q are constants, will agree with the observed currents. According to the electron theory of metallic conduction, it is probable that n does not vary very much with the temperature. The conductivity is roughly inversely proportional to the absolute temperature for most metals. According to the electron theory the conductivity is proportional to ne 2 h/mV, where h is the mean free path of the electrons. Now V is proportional to \f 6, so that if 1 is independent of the temperature, this requires n to be inversely proportional to >\/0 to make the conductivity inversely proportional to 0. In the measurements of the thermionic cur- rents the range of temperature is not very large usually, so that the variation of \/0 is comparatively small. Consequently, we may suppose n to be independent of without serious error. If we suppose that n and so D are independent of the temperature, then, according to the theory, P = Q + 20 log D/A must increase uniformly with 0. According to this view, the changes in A with the pressure of the hydrogen are to be ascribed to the variation of P with the temperature, and not to any change in D. Also it follows that the number of electrons per c.c. cannot be even roughly calculated from the value found for A. In order to get D and P it is necessary to make some hypothesis to explain the variation of P with the temperature. 1 i H. A. Wilson, Phil. Trans. A. vol. 208, p. 247, 1908. DISCHARGE OF NEGATIVE ELECTRICITY 23 To explain the energy necessary to enable an electron to escape from the platinum we supposed that an electrical double layer exists at the surface. Let this consist of an infinitely thin layer of electricity at a distance t from the platinum, having a charge o per sq. cm. If no electrons were present the difference of potential between the layer and the platinum would be 4>7iot ; but actually electrons will be present in between the layer and the platinum, and will increase the electric force. This effect will increase as the temperature rises, so that if P is due to such a layer, it will vary with the temperature. Let n denote the number of electrons per c.c. at a point at a distance x. from the platinum. Let p denote the gas pressure due to the electrons, and p denote the electric volume density so that p = ne. Then when there is equilibrium we have dpjdx -f- Fp = 0, where F denotes the electric force inside the double layer. Now, at the layer of electricity p is very small, since only a minute fraction of the electrons escape, consequently at x = t F = 4jra and dF/dx = 0. Let p = /3p, where /? is a constant at constant temperature, so that ft dx ~ dx ~ 4>n dx z ' Hence- * + F f = 0, r dx 2 dx yri which gives f} j- JF 2 = c. When x = t this becomes c = 8^ 2 o 2 , so that tifS- -f F 2 = 16jiV. ^ dx Integrating, this gives F = (F _+ a (F .+ where a = 4jra. At x = p = Po , so that 8jrft> + F 2 = a 2 . Now F will be nearly equal to a, so that this gives approximately 24 ELECTRICAL PROPERTIES OF FLAMES Hence- J_- = 87ro * * This gives V = -- fdx = - ft log (l + ~ e - ** + -$* , fi* V Pn/5 167T0 2 In this equation the terms R frat/fii = 10-14) f are quite negligible compared with -- f- 4 ^/^ = 10 14 ), so that PoP we get which gives, putting ft = ft 6, V = knot + 2ft log ^: P, the work in calories required for N electrons to escape, is equal to NeV/J, where J is the mechanical equivalent of heat ; also, since P = Q when 6 = 0, we can put Q = knotNejJ and so obtain 2 = Q - / 2 / 8 tf ^rfVN\ ~Q^ CompariDg this with P = Q + 20 log D/A we get . D N. Since j9 = pft Q 6 = ^^ w r e see that /? eN is equal to the gas constant, hence ft Q e~N/J = 2 calories. Hence If we take two values of Q, C^ and Q 2 , and the corresponding values A l and A 2 , we get _ DISCHARGE OF NEGATIVE ELECTRICITY 25 This equation, with the values found for A and Q, gives D = 3-7 x 10 8 . Having found D we can use it to calculate the value of ne. We have D = ne^ ^ . Here R = 8'4 x 10 7 ergs, N = 9644 E.M. units, and e/m = 1*7 X 10 7 in E.M. units as for cathode rays. Putting in these values and D = 3*7 x 10 8 , we get ne = 2'4 x 10 3 coulombs, or 7'2 X 10 12 E.S. units. Since e is equal to 4*9 x 10 - 10 E.S. units, this gives n = 1*5 x 10 22 free electrons in one c.c. of platinum. The number of atoms of platinum in one c.c. is 6 x 10 22 , so that there is one free electron for every four atoms. The expression for t then gives the following values : Q A t 145,000 131,000 110,000 90,000 56,000 1-14 x 10 8 6-9 x 10 7 10 6 5 x 10 4 2 x 10 2 9-6 x 10- 8 cm. 9-9 107 9-0 5-6 The five values of t agree as well as could be expected. It is interesting to apply the formula for t to platinum polarised with hydrogen in dilute sulphuric acid. The potential fall in this case is about 0'9 volt, which corresponds to a value of Q about 2-1 x 10 4 . If, then, we suppose A/D to be small, Q2g which is the case in hydrogen at high pressures, we get f 2 = ^ which gives at 6 =300, t = 4r8 X 10 ~ 8 . The thickness of the double layer in this case has been estimated by several observers from the polarisation capacity, and found to be about 2 x 10 ~ 8 cm. Thus the theory proposed leads to probable values of the thickness of the double layer and of the number of free electrons per c.c. in the platinum, so that it seems adequate to explain the facts. Substituting the values found for A, Q and D in the formula P = Q "4- 20 log D/A, we get the following values of P : 26 ELECTRICAL PROPERTIES OF FLAMES Gas. Pressure, P. Air 145,000+ 2-350 H 2 0-0013 110,000 + 11-830 H 2 0-112 90,000 + 17-820 H 2 133-0 56,000 + 28-860 Thus, in air P only varies very slowly with the temperature. It appears, therefore, that the thickness t of the double layer on the platinum is unchanged by the hydrogen, which, however, diminishes the fall of potential across it. This effect may be due to positively charged hydrogen atoms in the double layer, but the precise way in which the hydrogen acts is unknown. In some experiments Richardson l found that the leak from a hot platinum wire in hydrogen was independent of the pressure, even when this was reduced to a very small value. The writer 2 found that this is always the case after a wire has been heated in hydrogen at a comparatively high pressure for some time. After this treatment the properties of the wire are completely changed. The wire, then, gives a large thermionic current practically independent of the pressure of the hydrogen, from 760 mms. down to less than O'OOl mm. The following table gives the currents observed from a wire treated in this way, at a pressure of O'OOS mm. : Temperature. 1578 C. 1613 C. 1648 C. 1683 C. Amperes per sq. cm. 9-51 x 10- 5 19-26 38-7 723 These numbers give A = 1*67 x 10 10 , and Q = 135300. The value of Q is thus nearly the same as for a wire in air, but A is 100 times larger. If the wire is heated in air or oxygen the large thermionic current immediately disappears. It can also be made to disappear 1 Phil. Trans. A. vol. 207, p. 1, 1906. 2 Phil Trans. A. vol. 208, p. 247, 1908. DISCHARGE OF NEGATIVE ELECTRICITY 27 by heating above 1700 C. in a very high vacuum. These facts make it very probable that the hydrogen combines with the wire, forming a very stable compound. This compound must have a very small dissociation pressure. It must also be formed very slowly, unless the pressure of the hydrogen is high. After the wire has been heated in oxygen it gives the same thermionic currents as an ordinary wire in which the compound has never been formed. However, a permanent effect seems to remain, for the time lag of the current after changes of pressure seems much greater than before. Richardson found that increasing the potential difference from 19 volts to 286 volts caused the negative leak in hydrogen at 1-77 mms., at 1084 C. to diminish gradually from 147 x 10~ 8 to 26 x 10 ~ 8 ampere. This effect, he suggested, may be due to the bombardment of the wire by the positive ions produced by ionisa- tion by collisions due to the high potential. This bombardment may remove the hydrogen atoms in the double layer, and so make the negative current correspond with that due to hydrogen at a lower pressure. The writer found that a wire in hydrogen giving a negative current which was slowly increasing with the time, gave less current at high temperatures than at low. The current was saturated and rose when the temperature was diminished. These peculiar effects seem to take place only when the wire is not in equilibrium with the hydrogen. Further investigation is required to find out their cause. Other substances besides hydrogen have been found to increase the negative thermionic current. Thus the writer noticed a great increase due to phosphorus pentoxide. 1 A systematic examination of the effects of a large number of different substances might lead to interesting results. 1 Phil. Trans, vol. 202, p. 243. CHAPTER IV THE DISCHARGE OF NEGATIVE ELECTRICITY BY VARIOUS SUBSTANCES O. W. RICHARDSON 1 investigated the negative thermionic current from carbon and sodium, as well as from platinum. Both these substances gave very large currents. Sir J. J. Thomson 2 found the current from sodium to be greatly increased by the presence of hydrogen, so that it could be observed even at ordinary temperatures. Wehnelt 3 discovered that the oxides of the alkaline earths emit a copious supply of negative electrons when heated in a vacuum. Owen 4 measured the negative thermionic current from a Nernst lamp filament. In all these cases the formula i = A0*~ Q/2 * was found to represent the variation of the current with the temperature. The following table gives the values found for Q and A. Q is expressed in calories per gram molecule of electrons, and A so as to give the current in amperes per sq. cm. Substance. Q A Carbon 19-6 x 10* 10 15 Sodium 6-3 10 2 Baryta 9 7 x 10 7 Lime 8-6 5 x 10 7 Nernst filament 9-2 7 x 10 4 Owen (loc. cit.) examined the effect of a transverse magnetic field on the negative thermionic current, and found that a part of it was carried by heavy ions not easily deflected by the field. With platinum at 1300 C., 95 per cent, of the current could be deflected by a small field, and therefore was carried by electrons. 1 Phil Trans. A. vol. 201, p. 516, 1903. In these early experiments traces of hydrogen or other impurities were probably present and caused a very great increase in the thermionic currents. See Pring and Parker, Phil. Mag., Jan. 1912. 2 Conduction of Electricity through Gases, p. 203. 3 Ann. d. Phys. (4) vol. xiv. p. 425, 1904. 4 Proc. Camb. Phil Soc. vol. xii. p. 493, 1904. Phil. Mag. (6) 8, 230, 1904. 28 DISCHARGE OF NEGATIVE ELECTRICITY 29 With new wires the percentage of heavy ions was greater than with wires which had been heated for some time. Felix Jentzsch l measured the negative thermionic current from a number of metallic oxides in a vacuum. He found the following values of Q and A. The constant A gives the current per sq. cm. in electrostatic units. Substances. Q A BaO 83-2 x 10-' 5 141.x 1 Q15 SrO 89-8 , 152 , ) CaO 80-6 , 129 , I MgO 79-0 , 1 x 1 O io BeO 47-8 , 0-31 Y 9 3 72-6 , ' 5590 _ : La 2 6 3 75-8 , 207 A1 9 O 3 74-6 , j 2 ZrO 9 73-2 1970 ThO 9 71-2 10-5 CeOo 74-2 586 ZnO 70-2 0-092 Fe 2 0o 93-8 1076 Nil)' 102-4 8370 , i CoO 99-4 1595 , CdO 60-4 0-11 , ) CuO 45-0 , > O'OOl ) It will be observed that Q does not vary very much, whereas A varies very greatly. Jentzsch pointed out that the possible error in Q was two or three per cent., while that in A was as much as 500 per cent. Consequently, it is very difficult to get more than the order of magnitude of A. For lanthanum oxide he gives the following table : Absolute Temperature. Current (Calculated). Current (Found). Percentage difference. 1355 133 12-2 8 1405 367 35-5 3 1450 86-2 82-4 4 1470 124 132 6 1510 249 256 3 1570 662 692 4 1625 1525 1515 1 1680 3325 3065 8 1720 5700 7160 26 Inaugural Dissertation, Berlin, 1908 30 ELECTRICAL PROPERTIES OF FLAMES The calculated currents are those given by the equation i = 516 x lO^e- 75800 -' 2 ' Jentzsch found the currents in all cases to obey the same law. The copious emission of negative electrons by lime can be shown very clearly by means of a vacuum tube fitted with a " Wehnelt cathode." This consists of a strip of platinum foil which can be heated to incandescence by passing a current through it. On the foil is a small patch of lime, obtained by putting a drop of dilute calcium nitrate solution on it and then heating. The tube is provided with another electrode to serve as anode. If a moderate P.D. say 200 volts is maintained between the anode and cathode, then on heating the cathode, a narrow stream of cathode rays is emitted by the patch of lime. If the pressure is not too low, the path of this stream through the tube is visible as it emits a faint blue light. The deflection of the stream by magnetic and electric fields can be easily demonstrated owing to the low P.D., so that such a tube is very useful for showing the properties of cathode rays. Sir J. J. Thomson found that a good way of making the patch of lime is to put a very small bit of sealing-wax on the foil and then heat it. The wax contains lime, or baryta, and gives a firmly adherent patch. Hydrogen increases the current from lime in the same way as from platinum. Thus, G. H. Martyn * calculated the following negative thermionic currents at 1600 C. from observations at different temperatures : Platinum in air . . . . 5 x 10 ~ 7 ampere Lime in air. . . . . 5 x 10 ~ 2 Platinum in hydrogen . . . 10 -1 Lime in hydrogen . . . 10 3 F. Horton 2 gives the following values of the constants Q and A found in helium at a few mms. pressure : Platinum . . . T22 x 10 5 T6 X 10 6 Calcium .... 7'29 x 10 4 17 X 10 4 Lime . . . . 9'58 x 10 4 6'4 x 10 11 - * Phil. Mag., August 1907. 2 Phil. Trans. A. vol. 207, p. 149, 1908. DISCHARGE OF NEGATIVE ELECTRICITY 31 He observed that the current from lime is greatly increased by hydrogen. The conductivity of metallic oxides, like lime, is small at low temperatures, but increases rapidly with the temperature. The variation of the conductivity (a) with the temperature l is given at any rate roughly by the formula o Ke~ S2d , where K and S are constants. Hence, we have approximately D = Be~ s/2fl ; so that i = B0*e-< p + s > ;2 . It follows from this that the value of Q calculated from the currents observed at different temperatures with metallic oxides is not P but P -f- S. Also, the value found for A is equal to B = De~ s -' M . Thus, if n for metallic oxides is calculated from the values found for A, as was done by several observers, it must be wrong by the factor s'~ S2e , which usually amounts to many thousands. 2 O. W. Richardson 3 pointed out that the escape of negative electrons from hot bodies should be accompanied by an absorption of heat, just as in the analogous case of the evaporation of a liquid. ; - The calculation given at the end of Chap. I shows that the latent heat of emission of one gram molecule of electrons is P -f- R0, so that the determination of this latent heat affords a method of finding P not Q. Wehnelt and Jentzsch 4 found that the current required to keep a platinum wire coated with lime hot was greater when it was charged negatively and emitting electrons than when it was charged positively so that the electrons were prevented from escaping. From the difference between the two currents the heat rendered latent was calculated, and was compared with the theoretical amount calculated from the thermi- onic current and the known value of Q for lime. The observed values, however, came out several times larger than those calcu- lated. This is especially remarkable, because the value of P must be considerably smaller than the value of Q calculated from the thermionic currents, which, as we have seen, is equal to P -f- S. 1 F. Horton, Phil Mag., April 1906. 2 H. A. Wilson, Phil. Trans. A. vol. 208, p. 247, 1908. 3 Phil. Trans. A. vol. 201, p. 497, 1903. 4 Ann. d. P/iys. vol. 28, p. 537, 1909. 32 ELECTRICAL PROPERTIES OF FLAMES The reason for the discrepancy is not known. Possibly it is merely due to unavoidable errors in measuring such small quantities. Further experiments are desirable to clear up this question. When the electrons emitted by a hot body are absorbed by a cold electrode we should expect an evolution of heat. This effect was observed by Richardson and Cooke. 1 The cold electrode used by them was a strip of platinum, and the heat developed was estimated from its change of resistance due to the rise in tempera- ture. They measured the heat developed in the platinum strip when it had been treated with nitric acid to remove hydrogen, and also when it had been saturated with hydrogen. In the first case the mean value of P deduced from the observed heating effects was 128,000, and in the second case 105,000. The temperature of the cold electrode was probably not more than 500 Absolute, so that to compare the values found for P with those calculated from the thermionic currents we require the values at about 500 Abs. The value of P for pure platinum given by the expression P = 145000 + 2-35(9 at 500 Abs. is 146,000, which does not differ much from 128,000. Also, 145,000 is rather higher than the value of Q found by most observers, which is about 130,000, which would make P at 500 Abs. 131,000. For platinum in hydrogen at 133 mms. P = 56000 + 28'860. This makes P at 500 Abs. equal to 70,000, which is rather less than Richardson and Cooke's value 105,000. For hydrogen at 0112 mm. P at 500 Abs. comes out 99,000 and so agrees very well with 105,000. It seems likely that though the platinum strip was saturated with hydrogen, before putting it in the apparatus most of the hydrogen must have escaped when the pressure was reduced to a small value. Con- sequently, the amount remaining in the platinum may very likely have been about that corresponding to a pressure of 0*112 mm. It will be observed that since Q is only equal to P at Abs., it is not correct to compare the value of P deduced from the heating effect directly with Q. It is clear that Richardson and Cooke's experiments are in excellent agreement with the theory, which thus receives an interesting confirmation. 1 Phil Mag., July 1910. CHAPTER V THE DISCHARGE OF POSITIVE ELECTRICITY BY HOT BODIES. A POSITIVE charge escapes from hot bodies in air at a rate which increases rapidly as the temperature rises. The negative thermionic current is very little affected by the presence of air, and is much smaller than the positive current unless the pressure is very low or the temperature very high. The variation of the positive thermionic current from hot platinum in air at atmospheric pressure, with the temperature, was investi- gated by the writer in 1901 1 . The apparatus used consisted of a platinum tube 0'75 cm. in diameter, which was heated in a gas furnace. Along the axis of this tube a platinum electrode 12 cms. long and 0*3 cm. in diameter was supported, and the current between the electrode and tube through the air was measured. A constant current of air could be passed through the tube during the measurements. The temperatures of the tube and electrode were measured by means of thermo-couples. Fig. 4 shows the relation between the current and potential difference observed with this apparatus at 1080 C. without any current of air through the tube. When the inside electrode was positively charged the current was nearly saturated with 200 volts, but when the tube was positive it continued to increase up to 800 volts. When the inside electrode is positive, the ions start from it and move across to the tube, so that they start in the strong electric field close to the electrode, whereas when the current is reversed they start in the weaker field at the tube. Also, owing to the greater area of the surface of the tube, the current from it is larger and so more difficult to saturate. In this experiment with no air current the electrode was colder than the tube, which also helps to explain the larger current from the tube. The potential difference, about 1000 C., could not be raised much above 800 volts without an arc forming between the elec- 1 Phil. Trans. A. vol. 197, pp. 415-441, 1901. D 33 34 ELECTRICAL PROPERTIES OF FLAMES trodes. Thus the P.D. required to produce saturation is not very much less than that required to spark through the gas. It was found that on heating the tube and putting on the P.D. a large current was obtained at first, which rapidly fell off and settled down to a nearly constant value in one or two minutes. After 40O CeLLs. 800 Votts.) FIG. 4. standing cold for some hours this initial large current could always be obtained. The initial current was often ten times the steady current. The steady current was found to diminish gradually from day to day. The following numbers illustrate this effect : Date. Temperature 900 C. Temperature 1100 C. July 6 10 30 40 x 10 - 6 ampere 11 0-7 400 x 10 - 6 ampere 140 DISCHARGE OF POSITIVE ELECTRICITY 35 Fig. 5 shows the variation of the current with the temperature, using 240 volts with the inside electrode positive, so that the current was saturated. Fig. 6 shows the same thing with 40 volts, for which the current was nearly proportional to the voltage. In these experiments a rapid current of air was passed through the tube. This kept the inside tube hot, and also served to blow out 700 7,000 /,/00 . 7,200 7,300 C. Temperature* FIG. 5. the platinum dust which is emitted at high temperatures. If this dust is allowed to accumulate in the air near the platinum, the ions get stuck to it, which makes it more difficult to saturate the current. In a good vacuum there is practically no permanent positive thermionic current from hot platinum, so that we may D 2 36 ELECTRICAL PROPERTIES OF FLAMES conclude that the steady current obtained Is due to the presence of the' air. The fact that the positive current is very large compared with the negative current, unless the temperature is very high, shows that the ions are formed at the surface of the platinum. Ampe Temper&ture. FIG. The precise way in which the positive ions are formed is unknown, but if we regard the emission of positive ions as analogous to evaporation, then the calculation given at the end of Chap. I can be applied, so that we should expect the saturation current carried by the positive ions to be given by the equation i =* A.&E ~ Q ? 6 , where A is a constant and Q the apparent energy DISCHARGE OF POSITIVE ELECTRICITY 37 rendered latent by the production of one gram molecule of ions. This equation represents the variation of the current due to 240 volts with the temperature shown in Fig. 5 fairly well if Q is taken equal to 50,000. The variation of the; jeurrent due to 40 volts with the temperature shown in Fig. 6 gives values of Q which diminish as the temperature rises from 36,000 at $75 C- to 25,000 at 1300 C. The heat rendered latent by the production of ions at the surface of hot platinum was first calculated from the variation of the thermionic current in air with the temperature by the writer in 1901 (loc. cit.). It was then supposed that the air molecules dissociated into positive and negative ions at the surface of the platinum, and that there was an equilibrium between the ions and undissociated molecules. On this supposition the formula i = A0*e~ Q -' 4 *, where i is the current due to a small P.D., was deduced by the application of the thermodynamical theory of chemical equilibrium. The current due to a small P.D. was taken to be proportional to the concentration of the ions at the surface of the platinum. With this formula the currents in Fig. 6 give values of Q ranging from 71,000 at 975 C. to 49,000 at 1,300 C. It is clear now that the theory just mentioned is. inadequate, because according to it we should expect the air. to produce a negative thermionic current equal to the positive < one, which is not found to be the case. The analogy with evaporation enables the formula i DO^s ~ p 20 to be deduced without making any supposition as to the precise way in which the ions are produced, but this formula is only applicable to the saturation currents. Various suppositions can be made to explain the formation of the positive ions. We may suppose that the air molecules lose a negative electron to the hot platinum when they collide with it with a normal velocity greater than a definite value. In this way the formula i = D0*e - p / 2e can easily be obtained as for the negative electrons escaping from the platinum. Just as in the case of the negative electrons, the values of A and Q calculated from the observed currents are not necessarily equal to the values of D and P. According to the supposition just mentioned, D ought to be equal to ne^/R/ZnmN, where n is now 38 ELECTRICAL PROPERTIES OF FLAMES the number of molecules in one c.c. of the air, and m the mass of an air molecule. Another view which may be taken is that there is a layer of positively charged atoms, or molecules, of the gas on the surface of the platinum, held in position by the attraction due to their charges. These atoms, of course, tend to acquire the amount of kinetic energy corresponding to the temperature, and when one gets more than a certain amount we may suppose it escapes. According to this view we should expect the negative thermionic current to be increased by the presence of the gas, which is not the case, except with hydrogen. Another view, proposed by O. W. Richardson, is that the gas molecules dissociate to some extent into atoms which combine with the platinum. The compound formed dissociates into platinum and positively charged atoms of the gas. The pressure of the atoms, on this view, is proportional to the square root of the pressure of the undissociated gas. On this view, at low pressures the current should be nearly proportional to the square root of the pressure, and, at high pressures, nearly independent of the pressure, because then the combination between the platinum and oxygen is complete. If the dissociation into atoms were complete the current would be proportional to the pressure at low pressures. It will be convenient now to consider the relation between the current and the potential difference between the electrodes. In the case of two concentric cylinders, the electric force F is given by the equation 4- (Fr) = 4>nor dr where Q is the density of the electrification in the gas. The current c is equal to ZnrYqk, where k is the velocity of the ions due to unit field. Hence d ,, 4er so that (F s r s ) - (F.r^ = (r* - r,) where F 2 is the field at radius r 2 and F l that at r r This equation shows that the electric field will not be DISCHARGE OF POSITIVE ELECTRICITY 39 2c appreciably changed by the ions so long as ^- (V 2 2 r^) is small compared with Fr. If the field is only slightly altered by the ions we may write Yr = F^ + <5(Fr) where d(Fr) is a small quantity. Hence <5(Fr) - 27r 1 (r 2 - r i 2 ) = ^ F where p l is the density of electrification at r r If dV denotes the change in the P.D. due to the ions, we have, when the inside electrode is positive, dV =f" 2 dVdr = Wr/ - r* - 2r* logjj) J n ? i 7 taking r., to be the radius of the outer tube and i\ that of the inner. Hence In the same way, when the outside tube is positive, Tn Putting in r z = O375 and i\ = 0'15 cm., this becomes A7 0146c V = -- , h 0'436^ 2 . ^2/t The curve with the outside tube positive, shown in Fig. 4, can be represented very well from 200 to 800 volts by an equation of the form V = Ac + B, where A and B are constants. From this curve we get B = 0'436^ 2 = 0'5 E.S. units, so that g z = 1-15 E.S. units. Also, since = A = and = 10 ~ 5 in the straight dc JcQ 2 dc part of the curve, we get k = 1-3 X 10 4 in E.S. units or k = 43 cms. per sec. per volt per cm. The curve with the inside electrode positive can also be repre- sented by V = Ac + B between 20 and 100 volts, but B is too small to be estimated accurately. The current at the inside electrode when it is positive is equal to 2nr l Q l k r The relation between F and the current density i 40 ELECTRICAL PROPERTIES OF FLAMES was given by Sir J. J. Thomson. l If there are n ions per c.c. close to the electrode, the number striking it per sec. per sq. cm. is nV/^/6n, where V is the velocity of agitation of the ions, accord- ing to the kinetic theory of gases. If we suppose that when an ion strikes the platinum it gives up its charge, then we have neV I /== * x/w& where I denotes the saturation current per sq. cm. Also, i and k = l'4eA/mV, so that IF "\72 ;: is independent of the temperature, and A for a molecule of nitrogen at C. and 760 mms. is 9'5 X 10 ~ 6 cm. Also rnriV 2 3p , . ,, . . . - = --, where p is the pressure of a gas containing n molecules per c.c. For a gas at atmospheric pressure, p = 1*01 X 10, m V 2 and ne = 2'6 x 10 10 , so that - =- = 2 E.S. units. Hence IF I i i = =p-^_-g an d since i = Q-JeF^ we get Q = - -. If s denotes the saturation current per cm., then s = 2jrr 1 I, also c = Zytr^ and k = 1*3 x 10 4 . Substituting these values in the expression found for V and the values of i\ and r 9 we obtain which gives V in E.S. units. The saturation-current per cm. for the curve in Fig. 4 is 5'6 X 10 4 E.S. units. So that for this curve V = 0-275^- + (l - --) x 0-056. s c \ s / The following table gives values of V calculated by this equation, and also the observed values of c/s taken off the curve : 1 Conduction of Electricity through Gases, p. 208, 1906. DISCHARGE OF POSITIVE ELECTRICITY 41 c's V in volts (Calculated). c s (Found). o-i 24-3 0-12 0-2 34-2 0-22 0-3 47-1 0-30 0-4 65-1 0-40 0-5 91 0-63 0-6 131 0-68 0-7 197 0-82 0-8 333 0-86 0-9 744 0-9 Owing to the small scale of Fig. 4, the values of cl* could not be read off very exactly, so that the agreement between column one and column three is as good as could be expected, and provides an interesting confirmation of Sir J. J. Thomson's theory of the relation between the current and the electric force. It is plain that the value of k deduced from the currents with the outer electrode positive is consistent with the currents with the inside electrode positive. Since = value of F required to make i 90 per cent, of I is 18 E.S. units, or 5400 volts per cm. The value of F required to spark through air at 1000 C. is probably about 6500 volts. It was found that the potential difference could not be increased much above 800 volts without an arc forming, which agrees with this estimate. Thus, to completely saturate the current was impossible, although the electrodes were only two or three mms. apart, because the necessary field is greater than that required to spark through the gas. Neverthe- less, the current was 75 per cent, of the saturation current with only 200 volts, which is only one-quarter of the P.D. required to spark. IF According to the equation 'i = ---- =^7: - F + mV 2 /l ' of i/I is independent of the temperature, so that we should expect the variation of the current due to a small electric force with the temperature to be the same as for the saturation currents. Provided that the electric field is not appreciably the value 42 ELECTRICAL PROPERTIES OF FLAMES disturbed by the ions, we should, therefore, expect the current due to a small P.D. to be proportional to the saturation current. The current due to 40 volts increased less rapidly with the temperature than the current due to 240 volts, especially at the higher temperatures. This is probably due to the disturbance of the electric field by the ions, which, although small at 1000 C. y increases rapidly with the temperature. l'4e/l The formula k = ^- gives k = 65 cms. per sec. for one volt per cm. for a nitrogen molecule in air at atmospheric pressure at 1000 C. This agrees as well as could be expected with the value of k found above. That slow ions were not formed by the ions sticking to platinum dust from the electrodes, was due to the dust being blown out by the air current, and to the tube having been heated for long periods before the measurements described were made. Rutherford 1 measured the thermionic current from a sheet of platinum, heated by passing a current through it, to a parallel electrode in air at atmospheric pressure. He found the positive current diminished at high temperatures, and showed that this was due to the presence of slowly moving ions which were formed in increasing numbers as the temperature rose. He determined the velocity of the ions, and found it fell off with the distance from the hot plate. At several cms. distance it was about 1*9 cms. per sec. for one volt per cm. This is not far from the velocity of the ions produced in air by Rontgen rays, which are probably single molecules of oxygen or nitrogen. The very slow ions which were present at the higher temperatures are, no doubt, formed by gas ions sticking to platinum dust. Near the hot plate the ions had much larger velocities than 1'9. If X denotes the electric force in the air between the hot TAT platinum sheet and the parallel electrodes, then ^ = 4>nQ, where x is the distance from the sheet and Q the density of electrification in the air. The current per sq. cm. (i) is equal to 7^X, so that Physical Review, vol. xiii, p. 321, 1901. DISCHARGE OF POSITIVE ELECTRICITY 42 If we assume that k is independent of x and the same for all the ions, we get If I is the distance between the plate and electrode, and V the potential difference, then fti & I7 8 *^ , \*'* 3/2 l V= y^ =s ldAT- + V - C \ When x = 0, we have X = \/c. When the current is small compared with the saturation current we may take it to be proportional to X , so that i = X , where is a constant. Hence k [78m/. " 12mlA k . When i is so small that i 2 /fP and i s /f} B can be neglected, this gives approximately 3/2 so that the current is proportional to V 2 and inversely proportional to/ 3 . Rutherford found that this equation represented his experi- mental results fairly well when / was not less than two or three cms., so that his currents were extremely small compared with the saturation currents. When I is small, and i not too small, the equation (1) reduces to I . which is of the same form as we found for cylindrical electrodes when the electric field was not much affected by the ions. This equation obviously affords a simple method of finding 7c. TT According to the equation -y = ^ ~, which we have seen represents the variation of the current with the electric force at the surface of the platinum, F must be equal to 6 E.S. units for i to be 75 per cent, of I. To calculate the P.D. required to give about 75 per cent, of the saturation current, therefore, we may piit X = >v /c = 6; so that 44 ELECTRICAL PROPERTIES OF FLAMES If i = 10 - 6 ampere, or 3000 E.S. units, I = 5 cms., k = 3 x 10 s . This gives V = 14700 volts. If I = 4 2 cm., we get V = 336 volts. OO/' In this case the average electric force Q y^ - ^T O = 6*1 E.S. ' O X 0'2 units, is nearly equal to X 0> so that the electric field is practically unaffected by the presence of the ions. It is only when i is a small fraction of the saturation current that the electric field is appreciably disturbed by the charge in the gas. It has been suggested that in my experiments the current was always very far from saturation, so that the variation of the current with the temperature was due to the variation of the velocity of the ions, and not to the variation of the ionization. That this was not the case is obvious from the fact that the current was nearly saturated with 200 volts, and was proportional to the P.D. up to about 100 volts. Also the value of Q calculated from the saturation currents agrees with the result obtained by O. W. Richardson with entirely different apparatus. In Rutherford's experiments the variation of the current with temperature was largely due to the variation of the velocity of the ions, and was entirely different from the variation with temperature in my experiments.- The initial large positive thermionic current mentioned above was found by O. W. Richardson l to occur with a new platinum wire in a vacuum, and to be proportional to s~ af , where t denotes the time, and a is a constant. . The value of a depends on the temperature and other conditions. This suggests that this initial current is due to the presence of some substance which disappears at a rate proportional to the amount of it present. It disappears almost completely after heating a new platinum wire for a short time in a vacuum, but it can be made to reappear by allowing the 1 Phil. Mag., July 1903. DISCHARGE OF POSITIVE ELECTRICITY 45 platinum to be exposed to the air in a room. Richardson 1 found it reappeared if the wire was exposed to a luminous discharge or heated in any of the commoner gases. W. Wilson 2 found that heating the platinum in the presence of water, or dipping it in water, caused it to afterwards give a large positive current when heated in air at atmospheric pressure. He also found that the decay of the initial positive current only goes on while the current' is flowing and not while the hot platinum is surrounded by an insulated electrode. Sir J. J. Thomson 3 measured elm for the positive ions from hot platinum in air at a low pressure. A strip of platinum foil was arranged parallel to an insulated electrode, and 3 mms. from it. The strip could be heated by an alternating current and raised to any desired potential. The electrode and strip were contained in an exhausted tube contain- ing air at a low pressure. A magnetic field could be applied parallel to the surfaces of the strip and electrode and the current carried by the positive ions from the strip to the electrode was measured. It was found that a magnetic field of strength 19,000 completely stopped the current with a potential difference of 3 or 4 volts, but only diminished it by 75 per cent, with 10 volts. The effect of the magnetic field was not appreciable with a potential difference above 120 volts. If x is the distance of an ion from the hot strip, X the electric force parallel to x, and H the magnetic force parallel to the axis of z, then d?x v TT dy , 1N m d? = x - e+He Tt- ;- ; (1) d 2 y dx x dy or m-r- = ricx at since -j- when x = ; hence, from (1) ctt . FIG. 9. Fig. 9 shows the relation "between the current and P.D. obtained in this way, 1 the lower electrode being negatively charged and about 2 cms. above the burner. 1 H. A. Wilson, Phil. Trans. A. vol. 192, p. 499, 1899. 60 ELECTRICAL PROPERTIES OF FLAMES Fig. 10 shows the relation between the current and distance between the gauze electrodes. The current was almost independent of distance up to 3 cms. but then fell off rapidly. This was mainly due to the upper electrode getting cooler when near the top of the flame. If the upper electrode was kept at a nearly constant temperature, by passing a current through -it, the current was nearly independent of the distance, right up to the top of the flame. With horizontal gauze electrodes the current of gas carries up a continuous large supply of ions between the electrodes from below them, so that we should expect a large current to be obtained, even with the electrodes very close together. sou $200 1 * IX> S K 100 * u g 50 -*4 -* - *^* *sc \ X, \ \ \ Disl ance betwe ;n /?< i Etec \ trodei I* 'H r -. 1 ^ 3 4 5 6 7 d 9 Cms. FIG. 10. The variation of the potential along the flame from one electrode to the other was examined 1 by means of a fine platinum exploring wire, connected to an electrostatic voltmeter or quadrant electrometer. The voltmeter was connected to one of the electrodes and to the wire. The wire was perpendicular to the line joining the electrodes, and could be moved along the flame from one electrode to the other. Since the flame is a conductor and the wire insulated, it takes up the potential of the flame at the place where it is put in. Fig. 11 shows the variation of the potential obtained in this 1 H. A. Wilson, Phil. Trans. A. vol. 192, p., 499, 1899 ; Phil. Mag., October 1905. Marx, Ann. der Phys. vol. iv. p. 2, 1900. CONDUCTIVITY OF THE BUNSEN FLAME 61 way with the electrodes 17'7 cms. apart, and a P.D. of 550 volts, between them. It will be seen that there is a uniform potential gradient except near to the electrodes. Near the negative electrode there is a large fall of potential, and a small one close to the positive electrode. Such a variation of the potential is characteristic of conduction through flames, and always occurs when both the electrodes are hot. If one of the electrodes is moved near to the edge of the flame, so that it becomes cooler, the fall of potential near it increases. In this way nearly all the drop of potential can be concentrated at either the positive or negative electrode. 400 200 8 '0 FIG. 11. 12 14- 16 1 8 CMS. The uniform gradient between the electrodes is proportional to the current. This was shown by using two exploring wires, kept at a constant distance apart and connected to an insulated quadrant electrometer. The following numbers were obtained in this way. 1 Current (C) 1 = S-s x 10 -9 ampere. P.D. between exploring wires. P.D. -=- c. 270 54 18 4-0 volts 0-8 0'25 0-015 0-015 0-014 The exploring wires were O5 cm, apart. H. A. Wilson, Phil, Mag., October 1905. 62 ELECTRICAL PROPERTIES OF FLAMES Mr. E. Gold 1 found the uniform gradient proportional to the current between the limits 5 x 10 ~ 6 ampere and 260 X 10 ~ 6 ampere. In his experiments the current was increased by putting alkali salts, such as potassium carbonate, on the negative electrode, but the salt vapour did not extend into the part of the flame where the exploring wires were put in. It appears, therefore, that at a distance from the electrodes the flame obeys Ohm's law. In Mr. E. Gold's experiments, the ratio of the potential gradient in volts per centimetre to the current in amperes was 0'70 x 10 5 . The cross-section of the flame was about 2 sq. cms., so that the specific resistance of the flame was 1'4 x 10 5 ohms per c.c. In my experiments just mentioned the specific resist- ance was about 2 x 10 6 ohms per c.c. The specific resistance of a Bunsen flame varies greatly with the composition of the mixture of coal gas and air. The fall of potential in the uniform gradient between the electrodes is equal to Acd, where c is the current, d the distance between the electrodes, and A a constant. When d is small, Acd can be neglected compared with the total fall of potential (V), and then V = Be 2 approximately, as we have seen. In any case, therefore, the equation V = Acd + Be 2 represents the relation between the current, potential difference, and distance between the electrodes. The numbers given in the table supra are represented approximately by this equation with A = 0'03 and B = 0-0061. The term Be 2 is equal to the fall of potential near the electrodes. If H! denotes the number of positive ions per c.c. in the flame, x the charge on each ion, t^ the velocity with which they are moving in the direction from one electrode to the other, and n 2 , 2 and v z denote the corresponding quantities for the negative ions, then the current per sq. cm. (i) is given by the equation The velocity of an ion through a gas is proportional to the strength of the electrical field (X), so that if the gas is flowing 1 Proc. Roy. Soc. A. vol. 79, 1907. CONDUCTIVITY OF THE BUNSEN FLAME 63 towards the negative electrode with velocity u, we have l \ = ^i-^- ~^~ u V, 2 = 2 X - U where 7^ and & 2 denote the velocities of the ions relative to the gas in unit field. Hence i = ?i 1 e 1 (7t 1 X + u) + ^2 (^2-^- ~~ u \ Take the axis of x perpendicular to the surfaces of the electrodes, and suppose that everything is constant over planes parallel, to the electrodes, then / In the uniform gradient between the electrodes -, - = 0, so that n^ = n z e z , and therefore and is therefore independent of the velocity of the flame gases. Comparing this with the equation V = Adc -f Be 2 , we see that y x = y Aa = ^to +*i> " . where a is the cross-section of the flame. Thus, the fact that the flame at a distance from the electrodes obeys Ohm's law, shows that the velocities of the ions in it are proportional to the strength of the electric field. The theory of the relation between the current and the potential difference in an ionized gas is given by Sir J. J. Thomson in his book on The Conduction of Electricity through Gases, chap, iii, and I shall only give here a short discussion of some points which apply particularly to conduction through flames. In nearly all cases of the conduction of electricity through gases the charge on a positive ion is equal to the charge on a negative ion. If we assume that this is the case in flames, we obtain _ = ^(X - n 2 )e . ..... (1) and en^kJL + u) + en 2 (k 2 X u) = i ..... (2) where u is the velocity of the gas in the direction of x. 64 ELECTRICAL PROPERTIES OF FLAMES These equations give 1 ~ Let the positive electrode be at # = and the negative at x = 1. In the case where u = close to the positive electrode we have ?i x = 0, because the positive ions all move towards the negative electrode, while at the negative electrode n z = 0. Hence, from (3) and (4), in this case . = 8m dx J x = (5) These equations enable & x and k z to be easily calculated from tire variation of X near the electrodes ; but only rough estimates can be got in this way, because it is impossible to measure X very exactly close to the electrodes. The corresponding equations when u is not zero can, of course, be easily obtained, but are of no value. If the electrodes are made of horizontal wire gratings to allow the flame to flow through them, it is evident that u is not zero, and also that n^ and n z cannot be put equal to zero at the positive and negative electrodes, respectively, because the flame gases contain ions which are carried through such electrodes. The distribution of electric force near such electrodes will not be the same as near plane electrodes, except at distances from them greater than the distance between the wires forming the grating. Thus, the equations (5) ought not to be applied to results obtained with grating electrodes. In flames when both electrodes are hot the variation of the electric -force is much larger near the negative than near the positive electrode. This is shown clearly in Fig. 11. The equa- tions (5) show that this means that the velocity of the negative ions is much larger than the velocity of the positive ions. 1 Close to the negative electrode the current must be carried by 1 H. A. Wilson, Phil. Trans. A. vol. 192, p. 499, 1899. CONDUCTIVITY OF THE BUNSEN FLAME 65 the positive ions, so that the electric force is large there, owing to the small velocity of these ions. At the positive electrode the current is carried by negative ions having a high velocity, so that the force there is only slightly greater than in the uniform gradient. The variation of the potential shown in Fig. 1 1 is represented fairly well, except close to the positive electrode, by the equation y = 540 - 4-44^ - 462e - Using this equation to calculate ( ) we get by (5) \ doc / x i &]_ = 14 cms. per sec. for one volt per cm., which, of course, is subject to a large possible error. This appears to be the only estimate yet made of the velocity of the positive ions in a Bunsen flame free from salt vapours. The gases present in such a flame are N 2 , H 2 O, CO, CO 2 , etc. An ion consisting of OO 2 would prob- ably have a velocity of about 40 cms. per sec., 1 which is of the same order as that just found. There seems, therefore, no reason to doubt that the positive ions in a Bunsen flame free from salt consist simply of charged molecules of the gases present. The variation of the potential gradient near the positive electrode is too slight to enable k z to be estimated in this way, but it is clear that it must be of a much higher order of magnitude. Let q denote the number of fresh ions of either sign produced per c.c. per sec., and consider a layer of thickness dx perpendicular to the x axis. Inside one sq. cm. of this layer qdx fresh positive ions are produced per sec., and an^n^dx positive ions disappear by recombination, a being the coefficient of recombination. The number of positive ions entering the layer due to the electric field is 7v 1 X^ 1 , so that in a steady state, when ^- 0, we have (6) In the same way for the negative ions See p. 86. 66 ELECTRICAL PROPERTIES OF FLAMES (1), (6), and (7) give It follows from (1) and (8) that in the uniform potential gradient between the electrodes, n l = n 2 n and q an. 2 Hence + k z ) = Xc fa + />'.,) JI > a Equation (8) shows that ^ is positive when the ionization q is greater than the recombination a n^n^. In the layers near the electrodes there must be an excess of ionization over recombina- tion, because in the uniform gradient XQ-JI&J positive ions per sq. cm. flow past per sec., away from the positive electrode, and X 'W& 2 negative ions away from the negative electrode. Thus d 2 X 2 /cfe 2 must be positive near each electrode, so that the curve giving the relation between X 2 and x must be convex to the a? axis near the electrodes. Consequently, the electric force rises as either electrode is approached. Since & 2 is much greater than \ the excess of ionization over recombination is much greater near the negative electrode than near the positive, so the variation in X near the negative electrode is much greater than near the positive electrode. If & 2 is very large compared with k : then the current will be nearly equal to Xe?i 2 & 2 except close to the negative electrode, where n 2 = and the current is equal to 'K.enfa in any case. The theory of the distribution of the electric force between the electrodes can be greatly simplified 1 when k 2 is large compared with &]_ by assuming that the current is equal to Xe% 2 & 2 , but this assumption obviously fails close to the negative electrode. Equations (3), (4), and (5), when u = 0, give /dX*\ __ dX 2 & 2 ?i 2 \ dx )x = I dx \dx)x = " dx Since (-T ) is nearly zero, we have, approximately, \ CtOC / x = 1 J. J. Thomson, Conduction of Electricity through Gases, chap. iii. CONDUCTIVITY OF THE BUNSEN FLAME 67 k z n 2 _ \ dx, Jx = I ~dx With V = 540 4'44a; 462g- 1-87( ' " *> this gives the follow- ing numbers cms. 01 0-45 0-5 5-3 1-0 39 It appears, therefore, that in the case shown in Fig. 11 the current carried by the positive ions is half the total current one millimetre from the negative electrode, and one-fifth five milli- metres from it, but at one cm. away it is only 3 per cent. Most of the fall of potential occurs within one cm. of the negative electrode, so that it is clear that the variation of the potential near the negative electrode cannot be accurately calculated by assuming that i = X.enjc 2 . J. J. Thomson * found that the varia- tion of the potential' near the negative electrode, calculated on the assumption that i = Jienjt zt does not agree with that observed. We have seen that near the negative electrode the excess of ionization over recombination is equal to k z nK , where n is the number of negative or positive ions per c.c. in the uniform gradient, and X the electric force there. This number of negative ions is produced per sec. in a layer next to the negative electrode of thickness 1 2 , where ql% k z 'iiK . If, following J. J. Thomson, we assume that in this layer no recombination takes place, and that outside it the electric force is uniform and equal to X , then the fall of potential in the layer can be calculated. It comes out proportional to i 2 . Near the positive electrode we may imagine a similar layer of thickness ^ = - in which also the drop of potential is proportional to i 2 . In the uniform gradient the fall of potential is proportional to the current and to the distance between the electrodes, so that V = Ale + Be 2 , p 2 1 Conduction of Electricity through Gases, p. 235, 1906. 68 ELECTRICAL PROPERTIES OF FLAMES which is. the equation which we have seen represents the experimental results satisfactorily. The ratio of / x to A 2 is equal to kjky In the curve shown in Fig. 11 the potential gradient is uniform up to about 2 cms. from the cathode, and less than 1 mm. from the anode. If we suppose these distances to represent A., and Aj we see that & 2 must be at least twenty times k r This method of estimating kjk^ was used by Marx. 1 It is clearly too inaccurate to have any value for the assumption that recombina- tion does not take place inside the layers cannot be true in flames, and the width of the layers cannot be estimated at all accurately. FIG. 12. Inside the Bunsen flame the fall of potential between the electrodes always consists of large drops near the electrodes, with a small gradient between. If one of the electrodes is much colder than the other, the greater drop takes place at the colder electrode, whether it is positive or negative. Fig. 12, given by Marx, 2 shows how the shape of the potential curves for two horizontal electrodes depends on the temperature of the positive electrode. Its temperature was altered by raising the electrodes in the flame, keeping the distance between them constant. 1 Loc. cit. * Loc. cit. CONDUCTIVITY OF THE BUNSEN FLAME 69 In the uniform gradient q = an 2 , so that none of the ionization there contributes to the current. It is clear, therefore, that the current is always far from saturation when there is a uniform gradient in the middle and sudden drops of potential near the electrodes. On the layer theory (A x -f- A 2 )/7 is the ratio of the actual current to saturation current. The current between the two hot parallel plates in the flame does not diminish appreciably, even when the distance between them is altered from, say 2 cms. to 1 mm., which shows clearly that the current is very far from its saturation value at the larger distance. It would be interesting to make experiments on the variation of the current with the distance between the electrodes at very small distances. Hot electrodes in a Bunsen flame must emit ions which will help to carry the current at the surface of the electrodes. The fraction of the current carried by these ions is usually small. It is easy to see that if the negative electrode emitted & 2 7iX nega- tive ions per sec., the drop of potential near that electrode would disappear, and the uniform gradient would extend right up to it. Since this does not happen, even when very small currents are passed through the flame, 1 it is clear that the thermionic current is relatively very small. F. L. Tufts 2 found that coating the negative electrode with lime caused the potential drop there to nearly disappear. This is evidently due to the large emission of negative electrons by hot lime. 1 E. Gold, Proc. Eoy. Sac. A. vol. 79, 1907. 2 Phys. Zeitschr. vol. v. p. 76, 1904. CHAPTER VII THE ELECTRICAL CONDUCTIVITY OF SALT VAPOURS presence of the vapour of a metallic salt in a Bunsen flame increases its conductivity. Salts of the alkali metals of large atomic weight give a specially big effect. This effect can be conveniently studied qualitatively with the apparatus described at the beginning of the last chapter. If the two electrodes are placed about 1 cm. apart, and a bead of potassium carbonate on a platinum wire held below them so that the vapour from it fills up the flame between the electrodes, the current due to any P.D. is increased probably several thousand times. If the electrodes are placed further apart the effect of the salt vapour in different parts of the space between the electrodes can be easily tried. It is found that the current is not appreciably changed unless the salt vapour is put in close to the negative electrode. At the positive electrode, and anywhere between the electrodes, there is no effect, but if the salt vapour comes in contact with the negative electrode, a very large increase in the current is produced. If the electrodes are connected to an alternating P.D. and some potassium carbonate placed on one of them, a galvanometer in the circuit will indicate a current in the direction from the electrode without salt to the other, for the flame will practically allow no current to flow in the opposite direction. 1 If salt is put on the negative electrode, so that a large current is obtained, then on putting in a bead of potassium carbonate in some other part of the flame between the electrodes, it is found that the current is increased, and that the current is nearly inversely proportional to the length of the flame left free from salt. Thus, if two-thirds of the distance between the electrodes is filled with salt vapour, the current is about trebled. 1 H. A. Wilson, R.L Lecture, February 1909. 70 CONDUCTIVITY OF SALT VAPOURS 71 With K 2 CO 3 on the negative electrode, the current diminishes as the distance between the electrodes is increased. This is shown in Fig. 13. Roughly speaking, the current is inversely proportional to the distance between the electrodes so long as the positive electrode does not come into contact with the salt vapour from the negative electrode. Coating the negative electrode with lime acts in the same way as putting salt on it, which was discovered by Tufts 1 before the similar effect due to salt was observed. 2 8 FIG. 13. MS. Fig. 14 shows the distribution of potential between the electrodes with potassium carbonate on the negative electrode. Comparing this with Fig. 11, it will be seen that the drop of potential at the negative electrode is much diminished, and the uniform gradient correspondingly increased. If the two exploring wires are placed in the uniform potential gradient in the flame, and connected to an insulated quadrant electrometer, the gradient, as we have seen in the previous chapter, is proportional to the current, showing that the flame 1 F. L. Tufts, Phys. Zeitschr. vol. v. p. 76, 1904. 3 H. A. Wilson, Phil. Mag., October 1905. 72 ELECTRICAL PROPERTIES OF FLAMES away from the electrodes, when free from salt, obeys Ohm's law. If a bead of salt is put just below the two wires, so that they are both in the salt vapour, the P.D. between them becomes practically zero, although without salt on the negative electrode the current is not appreciably affected. This shows clearly that the salt vapour is a much better conductor than the flame by itself. In one experiment of this kind the principal electrodes were 18 cms. apart, and the uniform gradient, as indicated by the explor- ing wires and electrometer, was 1*6 volts per cm. with a P.D. of 700 volts between the main electrodes. The current gave a galvano- meter deflection of 200 mms. with no salt on the negative ouu OLTS: 400 200 < ^ |S, ^ u> x^ * S^ "N <^ X \ \ 8 FIG. 10 14. ia 14 16 electrode. On putting a bead of potassium carbonate below the exploring wires the electrometer deflection became zero, while the current was unchanged. In the equation V = Me + Be 2 the term Be 2 represents the fall of potential at the electrodes, and Adc the fall in uniform gradient. In this experiment Adc = 18 x 1-6 volts, so that Be 2 = 700 - 29 = 671 volts. Now, the salt vapour occupied about 2 cms. of the flame, so that when it was put in the fall in the uniform gradient was diminished by 2 x 1;6 = 3*2 volts. Be 2 must, therefore, have been increased by 3'2 volts ; that is, by one in two hundred. The current c, there- fore, ought to have been increased by one in four hundred, or from 200 to 200'5. But in these experiments the flame is never CONDUCTIVITY OF SALT VAPOURS 73 perfectly steady, so that the galvanometer deflection always oscillates slightly, so that so small an increase could not have been detected. In this way it is easy to explain the fact that although the salt vapour is a much better conductor than the flame, yet it has no effect on the current, except at the negative electrode. The reason is that since nearly all the fall of potential takes place close to the negative electrode, that is, that practically all the resistance to the passage of the current is close to this electrode, increasing the conductivity of the rest of the flame is practically without effect. When salt is put on the negative electrode the drop of potential there is greatly diminished, so that the distribution of en 30 20 10 o Cu rre tit 2 x io~) 6 A up. E.M.F o-; rVc Id i, m^ ***. 12345 cms. FIG. 15. potential is changed to a nearly uniform potential gradient from one electrode to the other; that is, the resistance is nearly uniformly distributed. In this case, if a part of the flame is filled with salt vapour, the total resistance is nearly proportional to the length left free from salt, so that the current is nearly inversely proportional to this length. If the positive electrode is moved to the end of the flame, so that it becomes much cooler than the negative electrode, the fall of potential takes place mainly at the positive electrode, and then, as we should expect, the current is increased when salt is put on the positive electrode, but not when it is put on the negative electrode. Fig. 15 shows the distribution of potential with potassium carbonate on the negative electrode for a total P.D. of 07 volt, 74 ELECTRICAL PROPERTIES OF FLAMES and Fig. 16 that with potassium carbonate on both electrodes, but not in the space between the electrodes. These two figures are taken from a paper by E. Gold. 1 When the flame is completely filled with salt vapour the distribution of potential between the electrodes becomes again similar to that in a flame free from salt, the current being, however, much greater for a given potential difference. For experiments on flames filled with salt vapour, it is best to use a method devised by Gouy. 2 A salt solution is sprayed by means of compressed air, and the air and spray are mixed with coal gas, so that the mixture gives a Bunsen flame uniformly 10 FIG. 16. filled with salt vapour. Fig. 17 shows the apparatus used by the writer 3 in one series of experiments. Carefully regulated supplies of coal gas and air were mixed together, along with spray of salt solution, and the mixture burnt from a brass tube 0*7 cm. in diameter. The air supplied by the water pump P partly escapes by bubbling through mercury in B, and then passes into a carboy A. From A the air passes through a flask W containing water, to the sprayer S, and its pressure is measured by the water manometer M. The air supply is regulated by means of a pinch-cock K, and by altering the water supply to the pump. The coal gas was passed through a regulator R into a gasometer H, from which it passed through a constriction L into the globe 1 Proc. Roy. Soc. A. vol. 79, 1907. 2 Ann. de Ghimie et de Phys. [5], t. xviii. p. 25. :{ Phil Trans. Roy. Soc. A. vol. 192, pp. 499-528, 1899. CONDUCTIVITY OF SALT VAPOURS 75 Gr, where it mixed with the air and spray. The gas pressure was indicated by a manometer M'. The mixture passed into a globe G', where the coarser spray settled, and then to the flame F. With an apparatus of this kind a very steady flame containing a definite amount of salt vapour can be obtained. The amount of salt in the flame is proportional to the strength of the solution used. The relation between the current and potential difference has been examined in flames filled with alkali salt vapours by Arrhenius; 1 Smithells, 2 Dawson and the writer, and by the writer. 3 Arrhenius measured the current between two vertical parallel FIG. 1-7. platinum electrodes. He found that the relation between the current and P.I), could be expressed approximately in all cases by the equation C = A^/K/(V), where A is constant, depending on the metal, but the same for all salts of any one metal, K the concentration in gram molecules per litre of the solution sprayed, and /(V) denotes a function of the P.D. between the electrodes, which has the same values for all salts. Thus, with a constant P.D., the current was proportional to the square root of ' the amount of salt in the flame. Arrhenius' electrodes were 0'56 c.m. apart, so that we should 1 Wied. Ann. vol. xlii. 1891. 2 Phil. Trans. A. vol. 193, p. 89, 1899. 3 Phil. Trans. A. vol. 192, p. 499, 1899. 76 ELECTRICAL PROPERTIES OF FLAMES expect the term Keel in the equation V = Acd + Be 2 to be small compared with Be 2 when c is not too small. Consequently for large values of V we should expect /(V) to be proportional to , so that c = A^/KV. The following table contains Arrhenius' results for potassium iodide, the unit of current being 10- 8 ampere. The currents are the difference between the current with salt and that without any. Concentration of Solution. E M F. in Clark's Cell. Normal = 1. i 4 TV eV *** T0^2T nfW 1 540 248 120 52-2 20 6-9 2-7 2 616 284 139 59-9 23 7-9 2-9 5 734 360 174 75-8 29-1 10-1 3'7 10 1009 464 225 99-7 37-4 13-0 47 20 1340 616 298 130 49-6 17-2 6-3 40 1920 811 427 186 71-2 24-8 9-0 An examination of these numbers shows that the current varies rather more rapidly than ^/K, and that it is nearly proportional to ^/V when V is greater than that due to two cells. Arrhenius found that the conductivity of the alkali salt vapours in the flame increased rapidly with the atomic weight of the metal. The fact that all salts of any one metal gave equal currents was explained by Arrhenius by supposing that they were all converted into hydroxides by the water vapour present in the flame. Arrhenius' results were confirmed and extended by Smithells, Dawson, and the writer (loc. cit.). The current was measured between two concentric cylinders with their axis vertical in a Bunsen flame containing salt vapour. The inside cylinder was hotter than the outside one, and a current was always obtained when the electrodes were connected to the galvanometer without any battery in the circuit. Fig. 18 shows the relation between the current, from the inside to the outside cylinder, and P.D. when a ^ normal solution of potassium nitrate was sprayed. It will be seen that the current is much greater when the CONDUCTIVITY OF SALT VAPOURS 77 outside cylinder is negative than when it is positive. Since V = Ei 2 approximately, where i is the current density at the negative electrode, we get V = Bc 1 2 /(2^r 1 /) 2 and V = Bc 2 z /(2nrJ) z , where I is the length of the cylinders, i\ the radius of the outside one, r. 2 that of the inside one, and c x the current with the outside cylinder negative, and c 9 that with the inside cylinder negative. Hence e 1 /c 2 = rjr z . For the cylinders used, rjr 2 was about 2, whereas in the above diagram c- 1 /c 2 for 5 volts is about 3, but the calculation assumes the two cylinders to be at the same temperature. 150 -3 -* SO FIG. 18. When the P.D. was zero, there was a current from the inside cylinder to the outside one. This shows, of course, that the equation V = Adc -f- Be 2 cannot be true in this case, when V is very small. The explanation of this current is probably as follows. The negative ions in the flame have a much higher velocity than the positive ions, so that they diffuse more quickly. Consequently, an insulated electrode immersed in the flame acquires a small negative potential sufficient to make the rate at which negative ions fall on it equal to the rate at which positive ions fall on it. This potential is greater the higher the temperature. Con- sequently the outside cylinder tends to take up a higher potential 78 ELECTRICAL PROPERTIES OF FLAMES than the inside one. The hot electrodes in the flame emit ions, and this emission is probably increased by the salt vapour. If an electrode is emitting negative ions it will tend to acquire a positive charge, so that there may be an effect due to this cause in the opposite direction to that due to diffusion. These effects, how- ever, are small, and can usually be neglected when the potential difference between the electrodes is above two or three volts. The relation between the current and P.D. for small P.D.'s is Upper Electrode Positive o 5 $ S Lorfer Electrode Negative. FIG. 19. complicated by such effects as those just mentioned, which are difficult to allow for accurately. The distribution of potential between the electrodes L in a flame containing rubidium chloride is shown in Fig. 19. The electrodes were horizontal wire gratings. It will be seen that the uniform gradient is very small, although the current with 120 volts was about 2 x 10 ~ 4 ampere. The lower electrode consisted of a gauze with wires 3 mms. apart, while the upper one had wires about 1 mm. apart. The upper electrode was cooler than the lower one. 1 H. A. Wilson, Phil. Trans. A. vol. 192, p. 507, 1899. CONDUCTIVITY OF SALT VAPOURS 79 cms. Fig. 20 shows the change in the distribution of potential when the upper electrode is changed from positive to negative. With the lower one positive, there is no drop near to it. The lower electrode, which was very hot in these experiments, therefore must have emitted a thermionic positive current, for otherwise there ought to have been a small drop at it. In these experiments the upward current of the flame gases carries a continuous supply of ions up through the lower electrode. Con- sequently, if the lower electrode is positively charged it will attract the negative ions from the gas as they pass through it, so that the gas will acquire a positive charge. The theory of the variation of the potential near the elec- trodes is complicated by this supply of ions from below. Marx l made estimates of the order of magnitude of the ionic velocities in flames containing salt vapours, by applying the theory of the variation of the potential near, plane electrodes in a gas at rest to his observations with horizontal coarse grating electrodes in the flame. He made use of J. J. Thomson's layer theory, described in a previous chapter. The results are of little value, owing to the theory used not applying when the ionized gas is streaming through grating electrodes. Moreover, the method is of little use, even in cases to which the theory does apply. Marx's lower grating had wires 3 mms. apart, and he used measure- ments of the potential taken up by a wire parallel to the grating, made at distances from the grating as small as O35 mm. At such distances from the grating the lines of flow of the current must have been nearly normal to the surface of the grating wires, and so not perpendicular to the exploring wire. Also the effective area of the electrodes must have been more nearly equal to the area of the surface of the wires than to the area of the grating. In view of these considerations, I do not think Marx's experiments Ann. d. Phys. vol. iv. p. 2, 1900. 80 ELECTRICAL PROPERTIES OF FLAMES can be regarded as giving even the order of magnitude of the ionic velocities. All that can be deduced from the distribution of potential between the horizontal grating electrodes is that when both are equally hot the velocity of the negative ions is probably con- siderably larger than that of the positive ions, for the variation of the potential near the negative electrode is more rapid than near the positive electrode. THE VELOCITY OF THE IONS OF SALT VAPOURS IN FLAMES The velocity of the positive ions of alkali salt vapours in flames was estimated by the writer 1 by finding the potential gradient required to make them move down the flame against the upward stream of gases. The apparatus used is shown in Fig. 21. FIG. 21. F Flame inside glass cylinder, resting on wooden block W. and covered with metal plate T. EE Grating electrodes. PP Screen above lower electrode. AA Bead of salt and support. CC' Commutators. B Battery. G Galvanometer. 1 Phil. Trans. A. vol. 192, p. 499, 1899. CONDUCTIVITY OF SALT VAPOURS 81 A bead of salt was put in the flame just below the upper electrode, and the current from the lower electrode measured. It was found that when the upper electrode was positive, introducing the bead caused no increase in the current unless the potential difference between the electrode was greater than 100 volts, when the electrodes were 5 cms. apart. When the upper electrode was negative, other conditions being the same, the current was increased on introducing the bead, even with one or two volts. To prevent any ions reaching the lower electrode by passing down the sides of the flame, where the velocity of the gases is small, a screen was placed above the lower electrode. This was of platinum gauze, with a hole in the middle 2 cms. in diameter. This hole was filled up by the flame, which also passed through the gauze around the hole. The lower electrode was bent up so that it was only 2 or 3 mms. below the screen. The screen was connected to the battery, so that the galvanometer only received the current going through the hole in it to the lower electrode. Fig. 22 shows the results obtained with a bead of potassium carbonate. It will be seen that the bead did not appreciably increase the current when the upper electrode was positive, unless the P.D. was above about 100 volts. The P.D. required to increase the current with the upper electrode positive was found to be about 100 volts for all salts of caesium, rubidium, potassium, sodium, and lithium. The possible error in the necessary P.D. was rather large, especially in the case of sodium and lithium, 82 ELECTRICAL PROPERTIES OF FLAMES which only gave a small increase, even with large potentials. The value 100 volts was probably correct within 20 per cent. The potential gradient in the upper part of the space between the electrodes was found to be 3'3 volts per cm. without any salt, when the P.D. was 100 volts. The introduction of the salt lowers the potential gradient in the part of the flame filled with salt vapour to practically zero, so that it increases the fall of potential in the rest of the flame. In the present case, if the salt vapour occupied 2 cms. of the flame it would increase the fall of potential at the negative electrode by 6'6 volts. The drop at the negative electrode was 84 volts, so that since the current is proportional to the square root of the drop, the current ought to have been increased by 3'3 in 84, or 4 per cent. The current was eight scale divisions, so that this increase could not be detected. Since the uniform gradient in the absence of salt is proportional to the current, it must have been increased by 4 per cent, to 3*31 volts per cm. Obviously, the gradient which is required is that just below the salt vapour, and not that in it, which is very small. The average velocity of the gases in the burner tube was found to be 206 cms. per second from the volume passing through. The diameter of the flame was about 2*5 cms., which indicates a cross- section about thirteen times that of the tube. Owing to the rise of temperature, an expansion of about eight times might be expected, but gas enters the flame along its sides. Since the pressure of the gas in the tube is very nearly equal to atmospheric pressure, it seems clear that the velocity in the flame must be practically the same as that in the tube, in spite of the change of volume, because there is no pressure difference available to change the velocity. Hence we get for the apparent velocity of the positive ions of any alkali salt due to one volt per cm. 206 cms. 3-3 : 2 sec. It has been assumed so far that if the positive ions move down the flame they will increase the current, and the fact that an increase is observed above a definite P.D. was supposed to justify this assumption. The precise way in which the current is increased remains to be considered. CONDUCTIVITY OF SALT VAPOURS 83 In the uniform gradient the current, as we have seen, 1 is independent of the velocity of the gases, and given by i = Xe9t(j -f- ^2)- When the salt is put in the uniform gradient in the salt vapour is given by where X' is very small compared with X and n large compared with n ; k^ and k z ' are probably of the same order as 7^ and k. 2 . Hence, at the critical P.D. Xrc^ + k 2 ) = XV(/,V + V)- At the edge of the salt vapour X changes to X', so that there will be a layer of charge in the gas there. The positive ions of the salt do not move down at the critical P.D., so that below the salt X must be practically unaltered, as we have seen. If now the P.D. is slightly increased, the positive salt ions move down slowly. As they go down they will continually re- combine with the negative flame ions present, and continually be reionized. Thus the conductivity of the flame below the salt will now be increased, and when the salt ions get to the negative electrode they will accumulate there and diminish the fall of potential. The increase of the current, it will be observed, is almost entirely due to the effect of the positive ions on the drop of potential at the negative electrode, and not to the increase in the conductivity in the uniform gradient. The maximum possible increase of the conductivity in the uniform gradient below the salt vapour can be easily calculated. Suppose the current without salt is i , and with salt i, and let X be the minimum gradient required to make the positive ions move down. Then, below the salt the gradient cannot be less than X , so that the conductivity below the salt cannot be increased more than in the ratio i/i , for X is the gradient when the ions just do not move down, and therefore is equal to the gradient in the free flarne corresponding to i . Consequently, just above the critical P.D., the concentration of the salt ions moving down must be extremely small, but they accumulate at the negative electrode, and so produce an appreciable effect there. 1 See p. 63. G 2 84 ELECTRICAL PROPERTIES OF FLAMES It appears, therefore, that the salt ions which move down are not charged ions all the time, but must be continually recombining and reionizing. Since they produce an effect when they get to the lower electrode, it is clear that they must differ from the flame ions, so they cannot be hydrogen ions. It is natural to suppose that they are atoms of the alkali metal as in salt solutions. Suppose that a particular metal atom is ionized for a fraction / of the time, then if it just moves down the flame this means that /(^X u) = (1 f)u or /A^X = , where u is the velocity of the flame gases, for while the atom is not charged it will be carried upwards with velocity u. It appears, therefore, that the quantity determined in the experiment described is fk^ and not k r It is convenient to call/A^ the apparent velocity of the positive salt ions. This experiment has been repeated by Mr. Lusby. 1 He found that the critical P.D. was 62 volts for all salts of alkali and akaline earth metals. The distance between his electrodes was only 3 cms., which, unfortunately, was not enough to allow the uniform gradient to be well developed in the absence of salt, for the space occupied by the negative drop was over 2 cms. With the salt in, he observed a very small gradient for nearly 2 cms. below the upper electrode, which was evidently due to this part of the flame containing salt vapour. He found the uniform gradient without salt to be 6*5 volts per cm., and the velocity of the flame to be 206 cms. per sec. This gives " l4/ " 6'5 "sec. which agrees as well as could be expected with the value of 62 ' I found, for his uniform gradient was too short (0'2 cm.) sec. to be measured at all exactly. He used the value of the gradient found with salt vapour 2 to calculate ^/, but this is obviously incorrect. What is required is the gradient just below the salt vapour, which, since the current is the same, should be the same as without salt. Moreau 3 estimated the apparent velocity of the positive ions 1 Proc. Camb. Phil Soc. vol. xvi. part i. 1910. 2 Lusby got k, f = 300 cms> by using the gradient found with salt in. A sec. very minute trace of salt vapour is enough to greatly diminish the gradient. 3 Journal de Physique (4), vol. ii. p. 558. CONDUCTIVITY OF SALT VAPOURS 85 of sodium and potassium salts by finding the potential gradient required to make them move across the flame from the bottom of one vertical electrode to the top of another. In this way he found fcj/ = 80 cms. per sec., which agrees well with 62 cms. per sec. Marx's estimate of the order of magnitude of 7j lt /has already been discussed. He found k^f to be about 250 cms. per sec., which is of the same order as 60. OTY1S The mean of 32, 62, and 80 is 58 ', which may be taken to sec. be the most probable value of Tc^f and is probably correct within 50 per cent. ; Js^f, of course, must vary in different flames, and in different parts of the same flame. If the positive ions consist of atoms of the metal, we should expect fcj to be nearly inversely proportional to the square root of the atomic weight of the metal. Now, the conductivity due to a definite amount of salt increases rapidly with the atomic weight, so that / must be much smaller for lithium than for caesium. If we suppose that when the concentration of the salt vapour is very small / is proportional to the square root of the atomic weight of the metal, and & x inversely proportional, then the product & lt / would be constant, as is found to be the case. It is probable l that for caesium / is nearly unity, 2 so that, assuming this, we get the following values of ^ : Atomic Weight. 1* Caesium . . .. "..' . _ Rubidium ""'_ Potassium - . . " . . . Sodium . .-..' .- Lithium . . . . ' . 133 85-4 39-2 23-1 7-0 58 72 107 139 i 253 I think it is more probable that these numbers are too large than too small. The value of k : to be expected on the kinetic theory can only be estimated very roughly, because the necessary data as to the free path of the ion, etc., have to be guessed at, in the flame. 1 H. A. Wilson, Phil. Mag., June 1911. 2 If / for caesium is less than unity then the values of fcj will be corre- spondingly greater. (See page 110.) 86 ELECTRICAL PROPERTIES OF FLAMES The temperature of a Bunsen flame is above the melting-point of platinum, because very thin wires will melt in it, so that it cannot be much below 2000 C. Estimates made by putting in thermocouples are, of course, too low, because the couple radiates, and so does not take up the true temperature. According to the kinetic theory, we have Jc, = 2 A /,r r ? , where e is the charge on \ 27i mV the ion, A its mean free path, w its mass, and V the square root of the mean square of its velocity of agitation. The flame contains N 2 , H 2 O, CO, H 2 , etc. Of these N 2 is present in the largest quantity. The free path of a nitrogen molecule in nitrogen at and 760 mms. is 9'5 X 10 ~ 6 cm. 1 At 2000 C. this gives 7'9 X 10~ 5 cm. The free path of an atom of caesium is probably smaller than that of a molecule of nitrogen, so that I shall take the free path of a caesium atom in the flame to be 4 x 10 ~ 5 cm. The velocity of agitation of a hydrogen molecule at C. is 1'84 x 10 5 cms. per sec., so that for a caesium atom at 2000 C. we get V = 1-84 x W X , = 6-5 x 10.. Also e/m for a caesium atom carrying the same charge as a hydrogen atom in solutions is equal to 7 2 '5 in electromagnetic units. . el 1-4 x 72-5 x 4 x 10~ 5 x 10 8 Hence, we get k, = 1 = _ 6 ___ = 6'3 - for one volt per cm. This is nearly ten times smaller sec. than the value 58 found for caesium on the assumption that / is unity for this metal, but the data used in the calculation of k v and also the formula employed are so doubtful that no weight can be attached to the discrepancy. The experimental result and the theoretical value are of the same order of magnitude, which is all that could be expected. I think, therefore, that there is no reason to doubt that the positive ions of alkali salt vapours in flames are atoms of the metal, as in solutions. This view is powerfully supported by the fact discovered by Lenard that the yellow coloration of the 1 Meyer's Kinetic Theory of Gases, p. 192. CONDUCTIVITY OF SALT VAPOURS 87 flame by sodium salts is attracted by a negatively charged electrode in the flame. If two platinum wires are put in a Bunsen flame, one above the other, and some sodium carbonate is put on the upper one, then if the wires are connected to a battery giving a few hundred volts, or to an induction coil, sodium light appears at the lower wire when it is the negative pole, but not when it is positive. 1 This clearly shows that the positive ions contain the metal, and effectually disposes of the suggestion that the positive ions of salt vapours in flames consist of hydrogen atoms. If they were hydrogen atoms it would be difficult to explain the increase in the current above the critical P.D., for hydrogen atoms going down would not increase the conductivity at the negative electrode. Moreover, salt vapours enormously increase the conductivity of the cyanogen flame, which contains no hydrogen. 2 The velocities of the ions of salt vapours in air at about 1000 C. was estimated by the writer, 3 using a method similar to that used in the flame. A mixture of air and spray of salt solution was passed through a platinum tube heated to a bright red heat in a gas furnace. The P.D. required to make the ions of the salt vapour move against the stream of hot air on emerging from the tube was found in the same way as in the flame. In this case there was practically no current until the critical P.D. was reached, so that the potential gradient could be taken to be uniform without serious error. The critical P.D. was found to be 25 volts for the positive ions of all the alkali salts, and 48 volts for salts of Ca, Sr, and Ba. For the negative ions of all salts of alkali metals and alkaline earth metals the critical P.D. was 7 volts. The velocity of the air current was 160 cms. per sec., so that the apparent ionic velocities were (1) Negative ions . ... .."..*. . . 26 (2) Positive ions of alkali metals 7*2 sec cms. sec. (3) Positive ions of alkaline earth metals . . 3*8 sec. 1 H. A. Wilson, KL Lecture, February 12, 1909. a Smithells, Dawson and Wilson (loc. cit.). 3 Loc. cit. 88 ELECTRICAL PROPERTIES OF FLAMES The possible error in these experiments was large, and the values obtained can only be regarded as giving the order of magnitude of the velocities. The free path of an air molecule in air at C. and 760 mms. is 9'6 x 10- 6 cms. At 1000 C. this becomes 4*5 x 10~ 5 cms. For a caesium atom carrying the same charge as a monovalent ion in solutions e/m = 72'5, and VI 97^ v 9 = 4 ' 9 x 104 - If we assume that the free path of the caesium atom is one- half that of an air molecule, we get , 1-4 x 72-5 x 2-3 x 1Q- 5 x 10 8 *> = 4-9 x 10* t-8 cms> P er sec - for one volt per cm. This agrees as well as could be expected with the value 7*2 found if we assume that for caesium / is about unity. For the lighter metals we may suppose that / is smaller than unity, as in flames. The distribution of the electric force in flames shows that the velocity of the negative ions must be much larger than that of the positive ions. The writer and others 1 attempted to find the velocity of the negative ions by the same method as was used for the positive ions, and results varying from 1000 to more than 10,000 were obtained. When the upper electrode is negatively charged, putting in the salt increases the current, even with small potential differences. Fig. 23 shows the results obtained by the writer. 2 It will be observed that the current with salt increases rapidly at about one volt, and it was supposed, therefore, that this was the critical P.D. The current, however, is very considerably increased by the salt, even with zero P.D. When the upper electrode is negatively charged there is a large potential drop at it, and a uniform gradient between the electrodes, which is proportional to the current and independent of the velocity of the gas. When salt is put in near the upper electrode the large drop there is diminished, and so the uni- form gradient and the current must be increased, whether the 1 Moreau and E. Gold. 2 Phil Trans. A. vol. 192, 1899. CONDUCTIVITY OF SALT VAPOURS 89 negative ions move down the flame or not. Thus the method used for the positive ions is not applicable to the negative ions, and the supposed determinations of the velocity of the negative ions made by it are of no value. Indirect determinations, which will be discussed in later chapters, show that the velocity of the I negative ions is about 10,000 cms. per sec. for 1 volt per cm. This is about what we should expect if the negative ions were free electrons. The free path of an electron in nitrogen at 2000 C. may be FIG. 23. taken to be about 31*6 X 10 ~ 5 cm.; that is, four times the free path of a nitrogen molecule. The velocity of agitation is V = 1-84 x 10 5 x /2273 x 2 x 1-8 x JO 3 = 3 . 2 x 1Q7 V 273 Taking e/m = 1'75 x 10 7 , we get _ 1-4 x 175 x 10 7 x 31-6 x 10~ 5 x lO 8 3-2 x 10 7 = 24,400 cms. per sec. for 1 volt per cm. Probably the actual free path is shorter than 31*6 X 10 ~ 5 cm., on account of the attraction between the electron and the molecules If we take & 2 = A -^ instead of 1-4 TT we get Jc 9 = 8700. - raV mV If the positive ions of alkali salts in flames consist of metal 90 ELECTRICAL PROPERTIES OF FLAMES atoms, and the negative ions of free electrons, as seems probable, then the ionization most likely consists in the expulsion of an electron from an uncharged atom of the metal. Or a molecule of the hydrate, like KOH, may combine with an atom of hydrogen, forming water and K, which at the moment of its liberation emits an electron. The precise way in which the ions are formed can only be guessed at. e"k Note. The theoretical formula k = ^ =- T - was first obtained mv by Sir J. J. Thomson. Langevin, by allowing for the variation of 2, got k = cA/wiV. The writer, 1 allowing also for the variation of V, got !'4 These results are typical of the behaviour of most alkali salts. Fig. 26 shows the variation of the current with the temperature in several cases. It was found that above 800 volts the current was nearly saturated in nearly all cases, and also that above 1400 C. the current was nearly independent of the temperature. It appeared, therefore, that there was a maximum possible current which could not be increased by raising either the P.D. or the temperature. The table on p. 97 gives the values found for this maximum possible current. It is clear that the maximum current is proportional to the strength of the solution sprayed, and inversely proportional to the electro-chemical equivalent of the salt. Let M denote the mass of salt entering the tube per sec. and Q the total charge on all the positive or negative ions formed from this amount of salt. Then it appears from the above results that Q = A M E where A is a constant and E denotes the electro-chemical equivalent of the salt. According to Faraday's laws of electrolysis, one gram-equivalent of any salt in the liquid state is electrolysed by the passage of 96,440 coulombs, or Q _ 96,440 M E CONDUCTIVITY OF SALT VAPOURS 97 Salt. Grams per litre. Electro- chemical Equivalent. E. Current. C. EC. CsCl . . . 10 168 15-1x10-4 2-54x10-1 Rbl . . . . 10 212 13-5 2-86 KI . . . . 10 166 16-4 2-72 Nal . 10 150 16'4 2-46 CsCl . . . 1 168 1-61 2-70x10-2 CsgCOg . . . 1 163 1-61 2-62 Rbl .... 1 212 1-25 2-65 RbCL . . . 1 121 2-24 2-71 Rb 2 C0 3 . . . 1 115 2'44 2-80 KI 1 166 1-66 2-75 KBr. . . . 1 119 2-13 2-53 KF . . . . 1 58 4-42 2-57 K 2 C0 3 . Nal .... 69 150 4-00 1-82 2-76 2-73 NaBr . . . 103 2-44 2-52 NaCl . . . 59 4-73 279 Na 2 CO.,. . . Lil .... 1 53 134 4-73 2-03 2-51 2-72 LiBr. . . 1 87 3-12 2-72 LiCl. . . . 1 43 6-25 2-69 Li 9 C0 3 . . . 1 37 7-48 2-77 where Q is the quantity of electricity required to electrolyse a mass M of the salt. The amount of salt entering the tube was estimated by burning the air and spray along with coal gas, so as to give a Bunsen flame. An equal flame was arranged near the first one, in which a bead of salt on a platinum wire could be placed. By adjusting the position of the bead it was possible to arrange so that the two- flames were equally brightly coloured by the salt. The loss of weight of the bead in a known time then gave the amount of salt passing through the tube. This method was first used by Arrhenius. 1 In this way it was found that when a solution containing one gram per litre was sprayed, 27 x 10 ~ r grams of salt entered the tube per second. 1 Wied. Ann. vol. xlii. p. 18, 1891. 98 ELECTRICAL PROPERTIES OF FLAMES Hence we get EQ _ 2-63 X IP' 2 " " "M" 2-70 x 10-' This agrees as well as could be expected with the value 96,440 found for solutions. It appears, therefore, that Faraday's laws of electrolysis of liquids apply also to salts in the state of vapour. In other words, Q/M is the same in salt vapours at 1400 C. as in solutions at the ordinary temperature. Since equivalent weights of the alkali salts contain equal numbers of metal atoms, it follows that the charge carried by the salt vapours per atom of metal is the same a*s the charge on one monovalent ion in solutions. The ratio of the charge e to the mass m for the positive ions of alkali sulphates has recently been determined by O. W. Richard- son, 1 by observing their deflection in a magnetic field. The method used was the same as that described in Chap. V for the positive ions emitted by a hot strip of platinum. The hot strip was coated with the alkali sulphate. The following table gives the mean values of e/m found by Richardson. Since in the electrolysis of solutions one gram of hydrogen is deposited by the passage of 9644 electromagnetic units of electricity, we have e/m for a hydrogen atom in solutions equal to 9644. If we divide 9644 by the values of e/m found for the positive ions, we get their equivalent weights. Substance. e/m. Equivalent weights of + ions. (H = 1). Atomic weights of metals. Li 2 S0 4 .... 1600 6-0 7-0 Na 2 SO 4 .... 430 22*5 23-1 K 2 S0 4 .... 265 36-4 39-2 Kb 2 SO 4 .... 101 96 85-4 Cs 2 SO 4 .... 73 132 133 It is clear from these results that the positive ions emitted by the alkali sulphates at high temperatures contain the metal only, 1 Phil. Mag., December 1910. CONDUCTIVITY OF SALT VAPOURS 99 and that the charge per atom of metal is the same as in solutions. These experiments, however, give no information as to the number of atoms of the metal in each ion. As we have seen, the positive ions in flames are probably single atoms, so that most likely the same is true in the present case. Davisson 1 has made a series of measurements of e/m for the positive ions emitted by salts of the alkaline earths. He found they were single atoms of the metal with single ionic charges in most cases. APPENDIX. Since all alkali salts give positive ions having equal apparent velocities, Langevin 2 suggested that these ions consist of hydrogen atoms. The formula k = eh/mv gives about 300 for a hydrogen atom in a flame at 2000 C. This view is supported by Lusby (loc. cit.), who finds 7^ = 300. I think Lusby 's value is too high and prefer the explanation of the equality of the velocities given above. However, the question must be regarded as an open one, and further experiments are required before a, 'definite conclusion can be arrived at. 1 Phil Mag., January 1912. 2 Comptes rendus, t. CXL., 1905, p. 35. H 2 CHAPTER VIII THE ELECTRICAL CONDUCTIVITY OF FLAMES FOR RAPIDLY ALTERNATING CURRENTS THE conductivity of flames for rapidly alternating currents was investigated by E. Gold and the writer. 1 The apparatus used is shown in Fig. 27. A mixture of coal gas and air containing spray was burnt as a non -luminous flame, with a sharply denned inner cone. The FIG. 27. electrodes used were concentric platinum cylinders 5 cms. high and 2'4 and 1'2 cms. in diameter. The conductivity between the electrodes was determined by means of a Wheatstone-bridge arrangement, of which the electrodes formed one arm, and the other three arms consisted of small air condensers, the capacity of one of which was adjustable with a micrometer screw. An induction-coil, I, charged two Leyden jars J\, J 2 , and these 1 Phil. Mag., April 1906. 100 ELECTRICAL CONIJ^OTJVTTY 7ipx + C cix and V = 27CQX 2 -f- Cx + D, where C and D are constants to be determined. When x = 0, V = D = 0, and when x = t t Hence V l = In the same way in FB we have V = - 2npx 2 + C'x + D'. 104 ELECTRICAL PROPERTIES OF FLAMES ^7V When x = D - t 2 ^ = - X and V = V, + V 8 ; so that we get for V at x = D Now ^ + t 2 = d, so that V = - X D + Znpdtft! -d) ..... (1) The force acting on a negative ion is X e A^, 1 , where A is a constant representing the viscous resistance to motion with unit velocity. Let m be the mass of a negative ion ; then its equation of motion is v dH i , \ dt i -X e=m^ + A^ ....... (2) The current density inside the slab is given by the equation dL K dX where K is the specific inductive capacity of the medium between the plates in the absence of ions. Thus, K is unity, and Now, in a flame containing a salt vapour, the fall of potential nearly all takes place near the electrodes, so that X is probably very small, even when rapidly alternating currents are used. Con- sequently, since Q is large, -- -^- may be neglected in comparison with Q -^ Hence (3) becomes i = Q ~~ approximately. Substituting in (1) the value of X got from (2), we get V = Y oS in^ = D(^5 + ^f) This gives mD d\ AD d\ ~ -D , But -TT = --- Hence dt Q mD d z i , AD di ^ ^ + jt ELECTRICAL CONDUCTIVITY OF FLAMES 105 The solution of this equation is i = _ w -pp- .... (5) 1 \ p 2 mT)/ m 2 J where / tana = A If a P.D. V = V sin^ is applied to a condenser of capacity C, the current is given by the equation i = CV p cospt. For the flame, if A and m are both negligible, (5) becomes 4>nd so that the apparent capacity is - per unit area. Now is the amplitude of vibration of the negative ions, so that qd must be the amount of electricity flowing during a half vibration. Let i = -- t so that Q = ^~ sin^. Then we have, integrat- ing from to n, y Q d = ^ or ^ = so that the apparent capacity per unit area is 1 / g If Q = this makes the capacity zero, whereas it should T 1 ^J"V v~-ri * This is due to the omission of - 7 ,, which would not In!) 4>n at be negligible if were small. If, however, we take A/ ^ to be the increase in the apparent capacity due to the presence of the ions, then no error will be made, even if Q be small. According to the theory, therefore, we should expect the apparent capacity to be independent of the number of alternations per second, and of the distance between the electrodes, and to be inversely proportional to the square root of the potential difference 106 ELECTRICAL PROPERTIES OF FLAMES between the electrodes, which agrees exactly with the experimental results. The expression ^J ^, has been obtained by neglecting the mass of the negative ions, and the resistance to their motion, so that it appears that the alternating current through the flame is determined merely by the density of the layer of positive charge left in the gas near the electrodes when the negative ions move under the action of the alternating electric field. KtV JO 50 60 70 FIG. 29. If a steady P.D. is applied to two electrodes immersed in an ionized gas, and if the positive ions cannot move, it is easy to see that a current will only pass for the short time required for the accumulation of a positive charge near the negative electrode to become sufficient to make the electric force near the positive electrode zero. Thus the two electrodes will behave like a con- denser when the P.D. is applied. When a rapidly alternating P.D. is applied it is easy to see that even if the positive ions move, pro- vided their velocity is small compared with that of the negative ions, the arrangement will behave like a condenser if the number of ions per c.c. is very large, and the mass of the negative ions very small. ELECTRICAL CONDUCTIVITY OF FLAMES 107 The following table gives the values found for d 2 ~ l d^ 1 with a number of salt solutions sprayed into the flame : Salt. Grams per litre. du (in tenths of an inch). i i (2 di CsCl . 50 0'08 12-2 10 0-18 5-26 55 1 0-34 2-64 0-333 0-48 1-78 O'l 1-10 0-61 Cs 2 C0 3 .... 25-5 0-13 7'40 ?? 2-55 0-30 3-03 5) 0-26 0-59 1-40 35 0-026 1-90 0-23 RbCl 48-1 0'22 4'24 9'6 0'29 3'15 ,, . . . . 1-92 0'41 2-14 Rb 2 C0 3 .... 50-4 0-19 4-96 10 0-25 3-70 >} - 1 0-50 1-70 K 2 C0 3 . ;;"':.. 100 0-062 15-8 3) . 10 0-297 3-07 KC1 . . , . . 100 0-20 4-70 20'8 0'30 3 -03 1 0-50 1-70 NaCl 100 0'47 1*83 LiCl 102-5 1-3 0-47 In Fig. 29 the above values of d 2 ~ l d^ 1 are shown graphically. Fig. 30 shows the steady currents due to an E.M.F. of 0*227 volt, between cylindrical electrodes in a flame, taken from the paper by Smit hells, Dawson and the writer (see p. 92). The amount of salt entering the flame per second was nearly the same in the two sets of experiments. The following table gives the values of d. 2 ~ 1 d^ 1 for decinormal solutions obtained from the curves in Fig. 29, and also the steady currents due to 0'227 volt : 108 ELECTRICAL PROPERTIES OF FLAMES Salt. i i V 1 Salt. Steady Current. (1 = 10 -7 ampere). Ratios. V*' " k ' CsCl . . . 6-7 CsCl . . . 22-2 3'3 0-70 Cs 2 C0 3 . . 5-9 CsN0 3 36-6 6'2 1-03 iRb 2 C0 3 . . 3-7 RbN0 3 . . 25-9 7 1-37 RbCl . . . 3-2 RbCl . . 11-3 3-5 1-05 K 2 C0 3 . . 2-9 |K 2 C0 3 . . 11-2 3-9 1-15 KC1 . . . 2-6 KC1 . . . 5-75 2-2 0-92 In the work with steady currents the conductivities of caesium and rubidium carbonates were not measured ; so the values for nitrates are given, since the conductivities of all oxysalts of the same metal were found to be nearly equal for steady currents. 40 30 rii ^o I 6 10 TGPt 10 20 C,?/)MS Pft LtTffZ FIG. 30. The last column contains the square root of the conductivity for steady currents divided by d 2 ~ l d^ ~ l . The numbers in this column do not vary much, which shows that the conductivity for rapidly alternating currents varies nearly as the square root of the conductivity for steady currents. The conductivities of potassium chloride and rubidium chloride were found to vary nearly as the square root of the concentration ELECTRICAL CONDUCTIVITY OF FLAMES 109 for steady currents ; so that we should expect them to vary as the fourth root of the concentration for rapidly alternating currents and this was found to be approximately true. 1 The steady currents due to 0'227 volt are probably proportional to the number of ions present per c.c. in the flame, so that the comparison of the conductivities for steady and alternating P.D.'s shows that for the latter the conductivities as measured by d 2 ~ l 6? 1 " 1 are proportional to the square root of the number of ions present per c.c. This is what we should expect from the formula A/, ^ , for Q = ne. It appears, therefore, that the theory considered agrees very well with the facts. If c denotes the increase in the apparent capacity per unit area, we have ~V K-l where K is the apparent specific inductive, capacity of the salt V (K I) 2 vapour. Hence Q = -^ ,^ ' With air between the electrodes instead of flame, d was equal to 6'66, while with the flame free (*.($(* from salt, it was 3'33. Hence K = - j very nearly. a 2 The table on p. 110 gives a few values of K. K, of course, has no relation to the true specific inductive capacity of the salt vapours, which must be little different from unity. The third column contains the values of the number of ions per c.c given by V (K I) 2 the equation ne = ^ ,-. 2 V was about 1'2 E.S. units, and D was 0*6 cm. e was taken to be 5 x 10 ~ 10 E.S. units, so that n = 1-06 x 10 9 (K - I) 2 . The amount of salt entering the flame per minute when a solution containing one gram per litre was sprayed was 0'053 milligram. The velocity of the flame gases was about 200 cms. per sec., and the diameter of the flame about 3 cms., so that the 1 H. A. Wilson and E. Gold (loc. cib.\ 110 ELECTRICAL PROPERTIES OF FLAMES Salt. Grams per litre. K. n. N. 08,06, 25-5 51 2-7 x 10 12 5-5 x 10 13 2-55 22 - 4-7 x 10 11 5-5 x 10 12 ij 0-26 11 1-1 x 10 11 5-6 x 10 11 CsCl 0-026 50 3-5 83 6-7 x 10 9 7-2 x 10 1 - 5-6 x 10 10 10 1 * 10 37 1-4 x 10 12 2 x 10 13 ) 1 20 3-9 x 10 11 2 x 10 12 RbCl 01 48-1 6 30 2-7 x 10 10 9 x 10 11 2 x 10 11 1-4 x 10 14 ?> 1-92 16 2-4 x 10 11 5-6 x 10 12 K 2 C0 3 100 107 1-3 x 10 13 5-1 x 10 14 10 22 4-7 x 10 11 5-1 x 10 KC1 100 33 1-1 x 10 12 4-7 x 10 14 20-8 22 4-7 x 10 11 9-7 x 10 13 >j 1 12 1-3 x 10 11 4-7 x 10 12 NaCl 100 14 1-8 x 10 11 5-9 x 10 14 LiCl 102-5 5 1-7 x 10 10 8-4 x 10 14 Free flame 2 1-1 x 10 9 amount of salt per c.c. in the flame was about G x 6 x 10~ 7 milligram with a solution containing G grams per litre. Let N denote the number of metal atoms per c.c., and E the chemical equivalent of the salt. Then G x 9644 x 3 x 10 10 x 6 x 1Q- 10 G E 9644 N = = ~ x 3-5 x 10 14 5 x 10- 10 x E for ~w~ is the number of metal atoms in one gram of the salt. The last column in the above table contains the values of N given by this formula. It will be seen that with the dilute solutions of caesium salts the number of ions is about one-tenth the number of metal atoms present. With salts of the other metals the proportion of ions is less. The values of n and N, of course, are subject to a large possible error. For caesium salts at very small concentrations it seems probable that n and N do not really differ very much. We can get a rough estimate of the velocity of the negative ions * in the flame without salt by using the value of n(= 1*1 X 10 9 ) and the known conductivity of the flame for steady currents. We 1 E. Gold, Proc. Ray. Soc. A. vol. 79, p. 43, 1907. ELECTRICAL CONDUCTIVITY OF FLAMES 111 have i = JLne(k 1 +k z )&nd = 10' 15 E.M. units, 1 e = 17 X 1Q - 20 Hence 7^ + k 2 = 5'3 X 10 ~ 5 . But 7^ is small compared with k z , so that for one volt per cm. we get 7,\ 2 = 5300. This agrees as well as could be expected with the theoretical value for a negative electron. 1 See p. 62. CHAPTER IX FLAMES IN A MAGNETIC FIELD IT will be convenient to begin by considering the theory of the effect of a magnetic field on a flame. Suppose that a thin plane vertical sheet of flame moving upwards with velocity V is acted on by a magnetic force of strength H perpendicular to the sheet. Let there be a vertical uniform electric field of strength Y upwards in the flame. Since the velocity of the negative ions is very large compared with that of the positive ions, only the former need be considered. The equations of motion of a negative ion describing a free path are d 2 x dy m-Td = Xe He~~ dt 2 dt d 2 y TT dx m :dr= ^ + He-r- dt 2 dt d 2 z m df*=* where y is measured vertically upwards, and x horizontally at right angles to the magnetic field. If we regard the gas as a viscous medium, exerting a force on the ions proportional to their velocity, the equations of motion become d 2 x v TT <% e dx m-r^ = Xe He - 77- -TT dt 2 dt k z dt dt 2 dt k't\dt d 2 z e dz m

| txO gj 2 C 1 o 1 / /x < J/ V X / /x \ V X V oo -5,0 30 -4,0 jo-ao 30 -Zp **^ min 30 -U 5? ID X) 2X 00 3^ Mdgi >00 40QO 5,000 6fH ietic field <) X \ FIG. 31. magnet, which gave a nearly uniform field over the entire area of the flame between the exploring wires. Some potassium carbonate was put on the negative electrode to diminish the drop of potential there, and so increase the cur- rent. There was no salt in the part of the flame between the poles of the magnet. The ratio of the potential difference between the exploring wires to the current was taken as a measure of the resistance of the flame. Fig. 31 shows the results obtained. FLAMES IN A MAGNETIC FIELD 117 The curve drawn is that given by the equation 100*5=3-1 X 10- 7 H 2 + r5 x 10- 3 H K where R denotes the resistance and H the magnetic field. It appears, therefore, that the effect of the magnetic field is made up of two parts, one proportional to the square of the field, and the other proportional to the field. The lack of symmetry is evidently connected with the upward motion of the flame. We have seen that when the top and bottom of the flame are insulated the horizontal velocity of the negative ions is given by u = k z (X HV), so that the conductivity is given by v = nek z (l ^), where C denotes the current. A. \ A. / In the absence of a magnetic field the current C is given by C = nek z X Q . Putting a = C /X , a = C/X, k z k z = dk z , and a a = do, we obtain, approximately, do = d\ __ HY ~~ = k z " X eh We have k z = 1'4 -a,*o that to get the change in k z it is mil necessary to calculate the change in A, the mean free path, due to the magnetic field. Consider a particular free path making an angle 6 with H. There are three forces acting on the electron (1) Xe (2) Ye = - e& 2 H(X - HV) (3) ReU sin 6. The electric force X was about 10 volts per cm., or 10 9 , / 2 HX was therefore about 10 8 , while HU is about 10 10 , since IT = 3 x 10 7 . Consequently, the force Ye can be neglected, so that the effect of the magnetic field is due to the force HeU sin 6. This force causes the electron to describe an arc of a circle of radius Q given by mil* TT TT /a - HeU sin 6. Q If / is the length of the straight line between the ends of the free path, and I' the length along the arc, we have, therefore, 1 = 2 e sin ( 118 ELECTRICAL PROPERTIES OF FLAMES Hence, since =- is small, Q 24m 2 U 2 The mean value of sin 2 6 is f , that of / 2 is 2A 2 , and that of IT' 2 H 2 e 2 /l 2 is 3U~ 2 , so that the mean value of (l f 1) /I' is equal to - 1 ^-- m 2 U 2 Hence, since - ^=- = k 2 2 , -^ = - T V H V for the time of describing the free paths is increased in the ratio of /' to I. Sir J. J. Thomson, who first calculated the effect of a magnetic field on conductivity, on the electron theory, got JH 2 & 2 2 , but he did not take into account the variations of A and U. The equation which was found to represent the experimental results was ^5 = 3-1 x 10~ 9 H 2 + 1-5 X 10- 5 H. If we assume that the term in H 2 is equal to T VH 2 & 2 2 we get A 2 = 1-8 x 10~ 4 or & 2 = 18,000 for one volt per cm. This agrees as well as could be expected with the theoretical value of 7^ 2 for an electron. y The term in H gives v = To X 10 ~ 5 , so that since X was about A. 10 9 , V = 1'5 X 10 4 , which is about one hundred times too large. It is clear, therefore, that the part of the effect proportional to H is much greater than that to be expected theoretically. The reason for this discrepancy is not known, and further experiments are desirable to elucidate it. It was found that when the electrodes at each end of the flame were remo\ 7 ed, then the exploring wires took up a potential difference proportional to the magnetic field, and about equal to 200Hrf, where d is their distance apart. This indicates that the induced E.M.F. in the flame due to its upward motion has nearly the value VH per cm., as was to be expected. NAME INDEX ARRHENIUS, 3, 75, 76, 90, 97 Beattie, 56 Brown, 11, 12, 48 Cooke, 32 Davisson, 54, 99 Dawson, 3, 75, 76, 87, 90 Deininger, 15 Elster, 1 Garrett, 53, 56 Geitel, 1 Giese, 2 Gold, 62, 74, 88, 100, 109, 110 Horton, 15, 30, 53, 54 Hulbirt, 48 Jeans, 90 Jentzsch, 29, 31 Langevin, 90, 99 Lenard, 86 Lusby, 84, 89 Martyn, 20, 30 Marx, 60, 68, 79, 85, 114, 115 McClelland, 2 Moreau, 84, 88 Owen, 5, 28, 55 Parker, 28 Pring, 8 Richardson, 2, 6, 7, 11, 12, 13, 20, 21, 26, 28, 31, 32, 38, 44, 47, 48, 50, 51, 52, 54, 98 Rutherford, 2, 42, 43, 44 Smithells, 3, 75, 76, 87, 90 Thomson, J. J., 1, 2, 3, 5, 28, 30, 40, 41, 45, 46, 53, 54, 63, 67, 79, 90, 118 Tufts, 69, 71 Townsend, 16 Wehnelt, 6, 28, 30, 31 Wellisch, 90 Willows, 56 Wilson, W., 45 PRINTED FOR THE UNIVERSITY OF LONDON PRESS. LTD., BY RICHARD CLAY & SONS, LIMITED, LONDON AND BUNGAY. 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