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diff --git a/32063.txt b/32063.txt new file mode 100644 index 0000000..2f85b97 --- /dev/null +++ b/32063.txt @@ -0,0 +1,6178 @@ +The Project Gutenberg EBook of Encyclopaedia Britannica, 11th Edition, +Volume 6, Slice 8, by Various + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 8 + "Conduction, Electric" + +Author: Various + +Release Date: April 19, 2010 [EBook #32063] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK ENCYC. BRITANNICA, VOL 6, SL 8 *** + + + + +Produced by Marius Masi, Don Kretz, Juliet Sutherland, and +the Online Distributed Proofreading Team at +https://www.pgdp.net + + + + + + + + + +Transcriber's notes: + +(1) Numbers following letters (without space) like C2 were originally + printed in subscript. When letters are subscripted, they are + preceded by an underscore, like C_n. + +(2) Characters following a carat (^) were originally printed in + superscript. + +(3) Letters topped by Macron are represented as [=x]. + +(4) [oo] stands for infinity; [int] for integral; [alpha], [beta], etc. + for greek letters. + +(5) The following typographical errors have been corrected: + + Page 871: "an equation which is very useful, because it enables us, + if we know the distribution." 'because' amended from 'becaus'. + + Page 890: "The colour of the luminosity due to positive rays is not + in general the same as that due to anode rays." 'positive' amended + from 'postive'. + + Page 890: "Anode Rays.--Gehrcke and Reichenhein (Ann. der Phys. 25, + p. 861) have found that when the anode consists of a mixture of + sodium and lithium chloride." 'mixture' amended from 'mixure'. + + + + + ENCYCLOPAEDIA BRITANNICA + + A DICTIONARY OF ARTS, SCIENCES, LITERATURE + AND GENERAL INFORMATION + + ELEVENTH EDITION + + + VOLUME VI, SLICE VIII + + Conduction, Electric + + + + +Article in This Slice: + + CONDUCTION, ELECTRIC + + + + +CONDUCTION, ELECTRIC. The electric conductivity of a substance is that +property in virtue of which all its parts come spontaneously to the same +electric potential if the substance is kept free from the operation of +electric force. Accordingly, the reciprocal quality, electric +resistivity, may be defined as a quality of a substance in virtue of +which a difference of potential can exist between different portions of +the body when these are in contact with some constant source of +electromotive force, in such a manner as to form part of an electric +circuit. + +All material substances possess in some degree, large or small, electric +conductivity, and may for the sake of convenience be broadly divided +into five classes in this respect. Between these, however, there is no +sharply-marked dividing line, and the classification must therefore be +accepted as a more or less arbitrary one. These divisions are: (1) +metallic conductors, (2) non-metallic conductors, (3) dielectric +conductors, (4) electrolytic conductors, (5) gaseous conductors. The +first class comprises all metallic substances, and those mixtures or +combinations of metallic substances known as alloys. The second includes +such non-metallic bodies as carbon, silicon, many of the oxides and +peroxides of the metals, and probably also some oxides of the +non-metals, sulphides and selenides. Many of these substances, for +instance carbon and silicon, are well-known to have the property of +existing in several allotropic forms, and in some of these conditions, +so far from being fairly good conductors, they may be almost perfect +non-conductors. An example of this is seen in the case of carbon in its +three allotropic conditions--charcoal, graphite and diamond. As charcoal +it possesses a fairly well-marked but not very high conductivity in +comparison with metals; as graphite, a conductivity about +one-four-hundredth of that of iron; but as diamond so little +conductivity that the substance is included amongst insulators or +non-conductors. The third class includes those substances which are +generally called insulators or non-conductors, but which are better +denominated dielectric conductors; it comprises such solid substances as +mica, ebonite, shellac, india-rubber, gutta-percha, paraffin, and a +large number of liquids, chiefly hydrocarbons. These substances differ +greatly in insulating power, and according as the conductivity is more +or less marked, they are spoken of as bad or good insulators. Amongst +the latter many of the liquid gases hold a high position. Thus, liquid +oxygen and liquid air have been shown by Sir James Dewar to be almost +perfect non-conductors of electricity. + +The behaviour of substances which fall into these three classes is +discussed below in section I., dealing with metallic conduction. + +The fourth class, namely the electrolytic conductors comprises all those +substances which undergo chemical decomposition when they form part of +an electric circuit traversed by an electric current. They are discussed +in section II., dealing with electrolytic conduction. + +The fifth and last class of conductors includes the gases. The +conditions under which this class of substance becomes possessed of +electric conductivity are considered in section III., on conduction in +gases. + +In connexion with metallic conductors, it is a fact of great interest +and considerable practical importance, that, although the majority of +metals when in a finely divided or powdered condition are practically +non-conductors, a mass of metallic powder or filings may be made to pass +suddenly into a conductive condition by being exposed to the influence +of an electric wave. The same is true of the loose contact of two +metallic conductors. Thus if a steel point, such as a needle, presses +very lightly against a metallic plate, say of aluminium, it is found +that this metallic contact, if carefully adjusted, is non-conductive, +but that if an electric wave is created anywhere in the neighbourhood, +this non-conducting contact passes into a conductive state. This fact, +investigated and discovered independently by D. E. Hughes, C. Onesti, E. +Branly, O. J. Lodge and others, is applied in the construction of the +"coherer," or sensitive tube employed as a detector or receiver in that +form of "wireless telegraphy" chiefly developed by Marconi. Further +references to it are made in the articles ELECTRIC WAVES and TELEGRAPHY: +_Wireless_. + + _International Ohm._--The practical unit of electrical resistance was + legally defined in Great Britain by the authority of the queen in + council in 1894, as the "resistance offered to an invariable electric + current by a column of mercury at the temperature of melting ice, + 14.4521 grammes in mass, of a constant cross-sectional area, and a + length 106.3 centimetres." The same unit has been also legalized as a + standard in France, Germany and the United States, and is denominated + the "International or Standard Ohm." It is intended to represent as + nearly as possible a resistance equal to 10 deg. absolute C.G.S. units + of electric resistance. Convenient multiples and subdivisions of the + ohm are the microhm and the megohm, the former being a millionth part + of an ohm, and the latter a million ohms. The resistivity of + substances is then numerically expressed by stating the resistance of + one cubic centimetre of the substance taken between opposed faces, and + expressed in ohms, microhms or megohms, as may be most convenient. The + reciprocal of the ohm is called the mho, which is the unit of + conductivity, and is defined as the conductivity of a substance whose + resistance is one ohm. The absolute unit of conductivity is the + conductivity of a substance whose resistivity is one absolute C.G.S. + unit, or one-thousandth-millionth part of an ohm. Resistivity is a + quality in which material substances differ very widely. The metals + and alloys, broadly speaking, are good conductors, and their + resistivity is conveniently expressed in microhms per cubic + centimetre, or in absolute C.G.S. units. Very small differences in + density and in chemical purity make, however, immense differences in + electric resistivity; hence the values given by different + experimentalists for the resistivity of known metals differ to a + considerable extent. + + +I. CONDUCTION IN SOLIDS + +It is found convenient to express the resistivity of metals in two +different ways: (1) We may state the resistivity of one cubic centimetre +of the material in microhms or absolute units taken between opposed +faces. This is called the _volume-resistivity_; (2) we may express the +resistivity by stating the resistance in ohms offered by a wire of the +material in question of uniform cross-section one metre in length, and +one gramme in weight. This numerical measure of the resistivity is +called the _mass-resistivity_. The mass-resistivity of a body is +connected with its volume-resistivity and the density of the material in +the following manner:--The mass-resistivity, expressed in microhms per +metre-gramme, divided by 10 times the density is numerically equal to +the volume-resistivity per centimetre-cube in absolute C.G.S. units. The +mass-resistivity per metre-gramme can always be obtained by measuring +the resistance and the mass of any wire of uniform cross-section of +which the length is known, and if the density of the substance is then +measured, the volume-resistivity can be immediately calculated. + + If R is the resistance in ohms of a wire of length l, uniform + cross-section s, and density d, then taking [rho] for the + volume-resistivity we have 10^9R = [rho]l/s; but lsd = M, where M is + the mass of the wire. Hence 10^9R = [rho]dl^2/M. If l = 100 and M = 1, + then R = [rho]'= resistivity in ohms per metre-gramme, and 10^9[rho]' + = 10,000d[rho], or [rho] = 10^5[rho]'/d, and [rho]' = 10,000MR/l^2. + + The following rules, therefore, are useful in connexion with these + measurements. To obtain the mass-resistivity per metre-gramme of a + substance in the form of a uniform metallic wire:--Multiply together + 10,000 times the mass in grammes and the total resistance in ohms, and + then divide by the square of the length in centimetres. Again, to + obtain the volume-resistivity in C.G.S. units per centimetre-cube, the + rule is to multiply the mass-resistivity in ohms by 100,000 and divide + by the density. These rules, of course, apply only to wires of uniform + cross-section. In the following Tables I., II. and III. are given the + mass and volume resistivity of ordinary metals and certain alloys + expressed in terms of the international ohm or the absolute C.G.S. + unit of resistance, the values being calculated from the experiments + of A. Matthiessen (1831-1870) between 1860 and 1865, and from later + results obtained by J. A. Fleming and Sir James Dewar in 1893. + + TABLE I.--_Electric Mass-Resistivity of Various Metals at 0 deg. C., + or Resistance per Metre-gramme in International Ohms at 0 deg. C._ + (Matthiessen.) + + +---------------------+---------------------+-------------+ + | | Resistance at 0 deg.| | + | | C. in International | Approximate | + | Metal. | Ohms of a Wire | Temperature | + | | 1 Metre long and | Coefficient | + | | Weighing | near 20 | + | | 1 Gramme. | deg. C. | + +---------------------+---------------------+-------------+ + |Silver (annealed) | .1523 | 0.00377 | + |Silver (hard-drawn) | .1657 | .. | + |Copper (annealed) | .1421 | 0.00388 | + |Copper (hard-drawn) | .1449 (Matthiessen's Standard) | + |Gold (annealed) | .4025 | 0.00365 | + |Gold (hard-drawn) | .4094 | .. | + |Aluminium (annealed) | .0757 | .. | + |Zinc (pressed) | .4013 | .. | + |Platinum (annealed) | 1.9337 | .. | + |Iron (annealed) | .765 | .. | + |Nickel (annealed) | 1.058[1] | .. | + |Tin (pressed) | .9618 | 0.00365 | + |Lead (pressed) | 2.2268 | 0.00387 | + |Antimony (pressed) | 2.3787 | 0.00389 | + |Bismuth (pressed) | 12.8554[1] | 0.00354 | + |Mercury (liquid) | 12.885[2] | 0.00072 | + +---------------------+---------------------+-------------+ + + The data commonly used for calculating metallic resistivities were + obtained by A. Matthiessen, and his results are set out in the Table + II. which is taken from Cantor lectures given by Fleeming Jenkin in + 1866 at or about the date when the researches were made. The figures + given by Jenkin have, however, been reduced to international ohms and + C.G.S. units by multiplying by ([pi]/4) X 0.9866 X 10^5 = 77,485. + + Subsequently numerous determinations of the resistivity of various + pure metals were made by Fleming and Dewar, whose results are set out + in Table III. + + TABLE II.--_Electric Volume-Resistivity of Various Metals at 0 deg. + C., or Resistance per Centimetre-cube in C.G.S. Units at 0 deg. C._ + + +---------------------+---------------------+ + | | Volume-Resistivity. | + | Metal. | at 0 deg. C. in | + | | C.G.S. Units | + +---------------------+---------------------+ + |Silver (annealed) | 1,502 | + |Silver (hard-drawn) | 1,629 | + |Copper (annealed) | 1,594 | + |Copper (hard-drawn) | 1,630[3] | + |Gold (annealed) | 2,052 | + |Gold (hard-drawn) | 2,090 | + |Aluminium (annealed) | 3,006 | + |Zinc (pressed) | 5,621 | + |Platinum (annealed) | 9,035 | + |Iron (annealed) | 10,568 | + |Nickel (annealed) | 12,429[4] | + |Tin (pressed) | 13,178 | + |Lead (pressed) | 19,580 | + |Antimony (pressed) | 35,418 | + |Bismuth (pressed) | 130,872 | + |Mercury (liquid) | 94,896[5] | + +---------------------+---------------------+ + + TABLE III.--_Electric Volume-Resistivity of Various Metals at 0 deg. + C., or Resistance per Centimetre-cube at 0 deg. C. in C.G.S. Units._ + (Fleming and Dewar, _Phil. Mag._, September 1893.) + + +--------------------------+------------------+------------------+ + | | Resistance | Mean Temperature | + | Metal. | at 0 deg. C. per | Coefficient | + | | Centimetre-cube | between 0 deg. C.| + | | in C.G.S. Units. | and 100 deg. C. | + +--------------------------+------------------+------------------+ + |Silver (electrolytic and | | | + | well annealed)[6] | 1,468 | 0.00400 | + |Copper (electrolytic and | | | + | well annealed)[6] | 1,561 | 0.00428 | + |Gold (annealed) | 2,197 | 0.00377 | + |Aluminium (annealed) | 2,665 | 0.00435 | + |Magnesium (pressed) | 4,355 | 0.00381 | + |Zinc | 5,751 | 0.00406 | + |Nickel (electrolytic)[6] | 6,935 | 0.00618 | + |Iron (annealed) | 9,065 | 0.00625 | + |Cadmium | 10,023 | 0.00419 | + |Palladium | 10,219 | 0.00354 | + |Platinum (annealed) | 10,917 | 0.003669 | + |Tin (pressed) | 13,048 | 0.00440 | + |Thallium (pressed) | 17,633 | 0.00398 | + |Lead (pressed) | 20,380 | 0.00411 | + |Bismuth (electrolytic)[7] | 110,000 | 0.00433 | + +--------------------------+------------------+------------------+ + + _Resistivity of Mercury._--The volume-resistivity of pure mercury is a + very important electric constant, and since 1880 many of the most + competent experimentalists have directed their attention to the + determination of its value. The experimental process has usually been + to fill a glass tube of known dimensions, having large cup-like + extensions at the ends, with pure mercury, and determine the absolute + resistance of this column of metal. For the practical details of this + method the following references may be consulted:--"The Specific + Resistance of Mercury," Lord Rayleigh and Mrs Sidgwick, _Phil. + Trans._, 1883, part i. p. 173, and R. T. Glazebrook, _Phil. Mag._, + 1885, p. 20; "On the Specific Resistance of Mercury," R. T. Glazebrook + and T. C. Fitzpatrick, _Phil. Trans._, 1888, p. 179, or _Proc. Roy. + Soc._, 1888, p. 44, or _Electrician_, 1888, 21, p. 538; "Recent + Determinations of the Absolute Resistance of Mercury," R. T. + Glazebrook, _Electrician_, 1890, 25, pp. 543 and 588. Also see J. V. + Jones, "On the Determination of the Specific Resistance of Mercury in + Absolute Measure," _Phil. Trans._, 1891, A, p. 2. Table IV. gives the + values of the volume-resistivity of mercury as determined by various + observers, the constant being expressed (a) in terms of the resistance + in ohms of a column of mercury one millimetre in cross-section and 100 + centimetres in length, taken at 0 deg. C.; and (b) in terms of the + length in centimetres of a column of mercury one square millimetre in + cross-section taken at 0 deg. C. The result of all the most careful + determinations has been to show that the resistivity of pure mercury + at 0 deg. C. is about 94,070 C.G.S. electromagnetic units of + resistance, and that a column of mercury 106.3 centimetres in length + having a cross-sectional area of one square millimetre would have a + resistance at 0 deg. C. of one international ohm. These values have + accordingly been accepted as the official and recognized values for + the specific resistance of mercury, and the definition of the ohm. The + table also states the methods which have been adopted by the different + observers for obtaining the absolute value of the resistance of a + known column of mercury, or of a resistance coil afterwards compared + with a known column of mercury. A column of figures is added showing + the value in fractions of an international ohm of the British + Association Unit (B.A.U.), formerly supposed to represent the true + ohm. The real value of the B.A.U. is now taken as .9866 of an + international ohm. + + TABLE IV.--_Determinations of the Absolute Value of the + Volume-Resistivity of Mercury and the Mercury Equivalent of the + Ohm._ + + +-----------------+------+----------------------+--------+----------+---------+ + | | | | |Value of |Value of | + | | | |Value of|100 Centi-|Ohm in | + | Observer. | Date.| Method. |B.A.U. |metres of |Centi- | + | | | |in Ohms.|Mercury |metres of| + | | | | |in Ohms. |Mercury. | + +-----------------+------+----------------------+--------+----------+---------+ + |Lord Rayleigh | 1882 | Rotating coil | .98651 | .94133 | 106.31 | + |Lord Rayleigh | 1883 | Lorenz method | .98677 | .. | 106.27 | + |G. Wiedemann | 1884 | Rotation through 180 | .. | .. | 106.19 | + | | | deg. | | | | + |E. E. N. Mascart | 1884 | Induced current | .98611 | .94096 | 106.33 | + |H. A. Rowland | 1887 | Mean of several | .98644 | .94071 | 106.32 | + | | | methods | | | | + |F. Kohlrausch | 1887 | Damping of magnets | .98660 | .94061 | 106.32 | + |R. T. Glazebrook | 1882 | Induced currents | .98665 | .94074 | 106.29 | + | | 1888 | | | | | + |Wuilleumeier | 1890 | | .98686 | .94077 | 106.31 | + |Duncan and Wilkes| 1890 | Lorenz | .98634 | .94067 | 106.34 | + |J. V. Jones | 1891 | Lorenz | .. | .94067 | 106.31 | + | | | +--------+----------+---------+ + | | | Mean value .98653 | | | + | | | | | | + |Streker | 1885 | An absolute determin-| | .94056 | 106.32 | + |Hutchinson | 1888 | ation of resistance| | .94074 | 106.30 | + |E. Salvioni | 1890 | was not made. The | | .94054 | 106.33 | + |E. Salvioni | .. | value .98656 has | | .94076 | 106.30 | + | | | been used | | | | + | | | | +----------+---------+ + | | | Mean value .94076 | 106.31 | + | | | | | + |H. F. Weber | 1884 | Induced current | Absolute measure- | 105.37 | + |H. F. Weber | .. | Rotating coil | ments compared | 106.16 | + |A. Roiti | 1884 | Mean effect of | with German silver| 105.89 | + | | | induced current | wire coils issued | | + |F. Himstedt | 1885 | | by Siemens and | 105.98 | + | | | | Streker | | + |F. E. Dorn | 1889 | Damping of a magnet | | 106.24 | + |Wild | 1883 | Damping of a magnet | | 106.03 | + |L. V. Lorenz | 1885 | Lorenz method | | 105.93 | + +-----------------+------+----------------------+-------------------+---------+ + + For a critical discussion of the methods which have been adopted in + the absolute determination of the resistivity of mercury, and the + value of the British Association unit of resistance, the reader may be + referred to the _British Association Reports_ for 1890 and 1892 + (_Report of Electrical Standards Committee_), and to the + _Electrician_, 25, p. 456, and 29, p. 462. A discussion of the + relative value of the results obtained between 1882 and 1890 was given + by R. T. Glazebrook in a paper presented to the British Association at + Leeds, 1890. + + _Resistivity of Copper._--In connexion with electro-technical work the + determination of the conductivity or resistivity values of annealed + and hard-drawn copper wire at standard temperatures is a very + important matter. Matthiessen devoted considerable attention to this + subject between the years 1860 and 1864 (see _Phil. Trans._, 1860, p. + 150), and since that time much additional work has been carried out. + Matthiessen's value, known as _Matthiessen's Standard_, for the + mass-resistivity of pure hard-drawn copper wire, is the resistance of + a wire of pure hard-drawn copper one metre long and weighing one + gramme, and this is equal to 0.14493 international ohms at 0 deg. C. + For many purposes it is more convenient to express temperature in + Fahrenheit degrees, and the recommendation of the 1899 committee on + copper conductors[8] is as follows:--"Matthiessen's standard for + hard-drawn conductivity commercial copper shall be considered to be + the resistance of a wire of pure hard-drawn copper one metre long, + weighing one gramme which at 60 deg. F. is 0.153858 international + ohms." Matthiessen also measured the mass-resistivity of annealed + copper, and found that its conductivity is greater than that of + hard-drawn copper by about 2.25% to 2.5% As annealed copper may vary + considerably in its state of annealing, and is always somewhat + hardened by bending and winding, it is found in practice that the + resistivity of commercial annealed copper is about 1-1/4% less than + that of hard-drawn copper. The standard now accepted for such copper, + on the recommendation of the 1899 Committee, is a wire of pure + annealed copper one metre long, weighing one gramme, whose resistance + at 0 deg. C. is 0.1421 international ohms, or at 60 deg. F., 0.150822 + international ohms. The specific gravity of copper varies from about + 8.89 to 8.95, and the standard value accepted for high conductivity + commercial copper is 8.912, corresponding to a weight of 555 lb per + cubic foot at 60 deg. F. Hence the volume-resistivity of pure annealed + copper at 0 deg. C. is 1.594 microhms per c.c., or 1594 C.G.S. units, + and that of pure hard-drawn copper at 0 deg. C. is 1.626 microhms per + c.c., or 1626 C.G.S. units. Since Matthiessen's researches, the most + careful scientific investigation on the conductivity of copper is that + of T. C. Fitzpatrick, carried out in 1890. (_Brit. Assoc. Report_, + 1890, Appendix 3, p. 120.) Fitzpatrick confirmed Matthiessen's chief + result, and obtained values for the resistivity of hard-drawn copper + which, when corrected for temperature variation, are in entire + agreement with those of Matthiessen at the same temperature. + +The volume resistivity of alloys is, generally speaking, much higher +than that of pure metals. Table V. shows the volume resistivity at 0 +deg. C. of a number of well-known alloys, with their chemical +composition. + + TABLE V.--_Volume-Resistivity of Alloys of known Composition at 0 deg. + C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coefficients + taken at 15 deg. C._ (Fleming and Dewar.) + + +-----------------------+-----------+-------------+-------------------+ + | |Resistivity| Temperature |Composition in per | + | Alloys. | at 0 | Coefficient | cents. | + | | deg. C. |at 15 deg. C.| | + +-----------------------+-----------+-------------+-------------------+ + |Platinum-silver | 31,582 | .000243 |Pt 33%, Ag 66% | + |Platinum-iridium | 30,896 | .000822 |Pt 80%, Ir 20% | + |Platinum-rhodium | 21,142 | .00143 |Pt 90%, Rd 10% | + |Gold-silver | 6,280 | .00124 |Au 90%, Ag 10% | + |Manganese-steel | 67,148 | .00127 |Mn 12%, Fe 78% | + |Nickel-steel | 29,452 | .00201 |Ni 4.35%, remaining| + | | | | percentage | + | | | | chiefly iron, but| + | | | | uncertain | + |German silver | 29,982 | .000273 |Cu5Zn3Ni2 | + |Platinoid[9] | 41,731 | .00031 | | + |Manganin | 46,678 | .0000 |Cu 84%, Mn 12%, | + | | | |Ni 4% | + |Aluminium-silver | 4,641 | .00238 |Al 94%, Ag 6% | + |Aluminium-copper | 2,904 | .00381 |Al 94%, Cu 6% | + |Copper-aluminium | 8,847 | .000897 |Cu 97%, Al 3% | + |Copper-nickel-aluminium| 14,912 | .000643 |Cu 87%, Ni 6.5%, | + | | | | Al 6.5% | + |Titanium-aluminium | 3,887 | .00290 | | + +-----------------------+-----------+-------------+-------------------+ + + Generally speaking, an alloy having high resistivity has poor + mechanical qualities, that is to say, its tensile strength and + ductility are small. It is possible to form alloys having a + resistivity as high as 100 microhms per cubic centimetre; but, on the + other hand, the value of an alloy for electro-technical purposes is + judged not merely by its resistivity, but also by the degree to which + its resistivity varies with temperature, and by its capability of + being easily drawn into fine wire of not very small tensile strength. + Some pure metals when alloyed with a small proportion of another metal + do not suffer much change in resistivity, but in other cases the + resultant alloy has a much higher resistivity. Thus an alloy of pure + copper with 3% of aluminium has a resistivity about 5-1/2 times that of + copper; but if pure aluminium is alloyed with 6% of copper, the + resistivity of the product is not more than 20% greater than that of + pure aluminium. The presence of a very small proportion of a + non-metallic element in a metallic mass, such as oxygen, sulphur or + phosphorus, has a very great effect in increasing the resistivity. + Certain metallic elements also have the same power; thus platinoid has + a resistivity 30% greater than German silver, though it differs from + it merely in containing a trace of tungsten. + +The resistivity of non-metallic conductors is in all cases higher than +that of any pure metal. The resistivity of carbon, for instance, in the +forms of charcoal or carbonized organic material and graphite, varies +from 600 to 6000 microhms per cubic centimetre, as shown in Table VI.:-- + + TABLE VI.--_Electric Volume-Resistivity in Microhms per + Centimetre-cube of Various Forms of Carbon at 15 deg. C._ + + +-----------------------------------------+---------------+ + | Substance. | Resistivity. | + +-----------------------------------------+---------------+ + | Arc lamp carbon rod | 8000 | + | Jablochkoff candle carbon | 4000 | + | Carre carbon | 3400 | + | Carbonized bamboo | 6000 | + | Carbonized parchmentized thread | 4000 to 5000 | + | Ordinary carbon filament from glow-lamp | | + | "treated" or flashed | 2400 to 2500 | + | Deposited or secondary carbon | 600 to 900 | + | Graphite | 400 to 500 | + +-----------------------------------------+---------------+ + +The resistivity of liquids is, generally speaking, much higher than that +of any metals, metallic alloys or non-metallic conductors. Thus fused +lead chloride, one of the best conducting liquids, has a resistivity in +its fused condition of 0.376 ohm per centimetre-cube, or 376,000 +microhms per centimetre-cube, whereas that of metallic alloys only in +few cases exceeds 100 microhms per centimetre-cube. The resistivity of +solutions of metallic salts also varies very largely with the proportion +of the diluent or solvent, and in some instances, as in the aqueous +solutions of mineral acids; there is a maximum conductivity +corresponding to a certain dilution. The resistivity of many liquids, +such as alcohol, ether, benzene and pure water, is so high, in other +words, their conductivity is so small, that they are practically +insulators, and the resistivity can only be appropriately expressed in +megohms per centimetre-cube. + +In Table VII. are given the names of a few of these badly-conducting +liquids, with the values of their volume-resistivity in megohms per +centimetre-cube:-- + + TABLE VII.--_Electric Volume-Resistivity of Various Badly-Conducting + Liquids in Megohms per Centimetre-cube._ + + +---------------------------+----------------+---------------------+ + | | Resistivity | | + | Substance. | in Megohms | Observer. | + | | per c.c. | | + +---------------------------+----------------+---------------------+ + | Ethyl alcohol | 0.5 | Pfeiffer. | + | Ethyl ether | 1.175 to 3.760 | W. Kohlrausch. | + | Benzene | 4.700 | | + | Absolutely pure water | 25.0 at 18 deg.| Value estimated | + | approximates probably to | C. | by F. Kohlrausch | + | | | and A. Heydweiler. | + | All very dilute aqueous | 1.00 at 18 deg.| From results by | + | salt solutions having a | C. | F. Kohlrausch | + | concentration of about | | and others. | + | 0.00001 of an equivalent | | | + | gramme molecule[10] per | | | + | litre approximate to | | | + +---------------------------+----------------+---------------------+ + +The resistivity of all those substances which are generally called +dielectrics or insulators is also so high that it can only be +appropriately expressed in millions of megohms per centimetre-cube, or +in megohms per quadrant-cube, the quadrant being a cube the side of +which is 10^9 cms. (see Table VIII.). + +Effects of Heat.--Temperature affects the resistivity of these different +classes of conductors in different ways. In all cases, so far as is yet +known, the resistivity of a pure metal is increased if its temperature +is raised, and decreased if the temperature is lowered, so that if it +could be brought to the absolute zero of temperature (-273 deg. C.) its +resistivity would be reduced to a very small fraction of its resistance +at ordinary temperatures. With metallic alloys, however, rise of +temperature does not always increase resistivity: it sometimes +diminishes it, so that many alloys are known which have a maximum +resistivity corresponding to a certain temperature, and at or near this +point they vary very little in resistance with temperature. Such alloys +have, therefore, a negative temperature-variation of resistance at and +above fixed temperatures. Prominent amongst these metallic compounds are +alloys of iron, manganese, nickel and copper, some of which were +discovered by Edward Weston, in the United States. One well-known alloy +of copper, manganese and nickel, now called manganin, which was brought +to the notice of electricians by the careful investigations made at the +Berlin Physikalisch-Technische Reichsanstalt, is characterized by having +a zero temperature coefficient at or about a certain temperature in the +neighbourhood of 15 deg. C. Hence within a certain range of temperature +on either side of this critical value the resistivity of manganin is +hardly affected at all by temperature. Similar alloys can be produced +from copper and ferro-manganese. An alloy formed of 80% copper and 20% +manganese in an annealed condition has a nearly zero +temperature-variation of resistance between 20 deg. C. and 100 deg. C. +In the case of non-metals the action of temperature is generally to +diminish the resistivity as temperature rises, though this is not +universally so. The interesting observation has been recorded by J. W. +Howell, that "treated" carbon filaments and graphite are substances +which have a minimum resistance corresponding to a certain temperature +approaching red heat (_Electrician_, vol. xxxviii. p. 835). At and +beyond this temperature increased heating appears to increase their +resistivity; this phenomenon may, however, be accompanied by a molecular +change and not be a true temperature variation. In the case of +dielectric conductors and of electrolytes, the action of rising +temperature is to reduce resistivity. Many of the so-called insulators, +such as mica, ebonite, indiarubber, and the insulating oils, paraffin, +&c., decrease in resistivity with great rapidity as the temperature +rises. With guttapercha a rise in temperature from 0 deg. C. to 24 deg. +C. is sufficient to reduce the resistivity of one-twentieth part of its +value at 0 deg. C., and the resistivity of flint glass at 140 deg. C. is +only one-hundredth of what it is at 60 deg. C. + + TABLE VIII.--_Electric Volume-Resistivity of Dielectrics reckoned in + Millions of Megohms (Mega-megohms) per Centimetre-cube, and in Megohms + per Quadrant-cube, i.e. a Cube whose Side is 10^9 cms._ + + +------------------------+---------------------------+----------+ + | | Resistivity. | | + | +------------+--------------+ Tempera- | + | Substance. |Mega-megohms| Megohms per | tura | + | | per c.c. |Quadrant-cube.| Cent. | + +------------------------+------------+--------------+----------+ + |Bohemian glass | 61 | .061 | 60 deg. | + |Mica | 84 | .084 | 20 deg. | + |Gutta-percha | 450 | .45 | 24 deg. | + |Flint glass | 1,020 | 1.02 | 60 deg. | + |Glover's vulcanized | | | | + | indiarubber | 1,630 | 1.63 | 15 deg. | + |Siemens' ordinary pure | | | | + | vulcanized indiarubber | 2,280 | 2.28 | 15 deg. | + |Shellac | 9,000 | 9.0 | 28 deg. | + |Indiarubber | 10,900 | 10.9 | 24 deg. | + |Siemens' high-insulating| | | | + | fibrous material | 11,900 | 11.9 | 15 deg. | + |Siemens' special | | | | + | high-insulating | | | | + | indiarubber. | 16,170 | 16.17 | 15 deg. | + |Flint glass | 20,000 | 20.0 | 20 deg. | + |Ebonite | 28,000 | 28. | 46 deg. | + |Paraffin | 34,000 | 34. | 46 deg. | + +------------------------+------------+--------------+----------+ + + A definition may here be given of the meaning of the term _Temperature + Coefficient_. If, in the first place, we suppose that the resistivity + ([rho]t) at any temperature (t) is a simple linear function of the + resistivity ([rho]0) at 0 deg. C., then we can write [rho]t = [rho]0(1 + + [alpha]t), or [alpha] = ([rho]t - [rho]0)/[rho]0t. + + The quantity [alpha] is then called the temperature-coefficient, and + its reciprocal is the temperature at which the resistivity would + become zero. By an extension of this notion we can call the quantity + d[rho]/[rho]dt the temperature coefficient corresponding to any + temperature t at which the resistivity is [rho]. In all cases the + relation between the resistivity of a substance and the temperature is + best set out in the form of a curve called a temperature-resistance + curve. If a series of such curves are drawn for various pure metals, + temperature being taken as abscissa and resistance as ordinate, and if + the temperature range extends from the absolute zero of temperature + upwards, then it is found that these temperature-resistance lines are + curved lines having their convexity either upwards or downwards. In + other words, the second differential coefficient of resistance with + respect to temperature is either a positive or negative quantity. An + extensive series of observations concerning the form of the + resistivity curves for various pure metals over a range of temperature + extending from -200 deg. C. to +200 deg. C. was carried out in 1892 + and 1893 by Fleming and Dewar (_Phil. Mag._ Oct. 1892 and Sept. 1893). + The resistance observations were taken with resistance coils + constructed with wires of various metals obtained in a state of great + chemical purity. The lengths and mean diameters of the wires were + carefully measured, and their resistance was then taken at certain + known temperatures obtained by immersing the coils in boiling aniline, + boiling water, melting ice, melting carbonic acid in ether, and + boiling liquid oxygen, the temperatures thus given being +184 deg..5 + C., +100 deg. C., 0 deg. C., -78 deg..2 C. and -182 deg..5 C. The + resistivities of the various metals were then calculated and set out + in terms of the temperature. From these data a chart was prepared + showing the temperature-resistance curves of these metals throughout a + range of 400 degrees. The exact form of these curves through the + region of temperature lying between -200 deg. C. and -273 deg. C. is + not yet known. As shown on the chart, the curves evidently do not + converge to precisely the same point. It is, however, much less + probable that the resistance of any metal should vanish at a + temperature above the absolute zero than at the absolute zero itself, + and the precise path of these curves at their lower ends cannot be + delineated until means are found for fixing independently the + temperature of some regions in which the resistance of metallic wires + can be measured. Sir J. Dewar subsequently showed that for certain + pure metals it is clear that the resistance would not vanish at the + absolute zero but would be reduced to a finite but small value (see + "Electric Resistance Thermometry at the Temperature of Boiling + Hydrogen," _Proc. Roy. Soc._ 1904, 73, p. 244). + + The resistivity curves of the magnetic metals are also remarkable for + the change of curvature they exhibit at the magnetic critical + temperature. Thus J. Hopkinson and D. K. Morris (_Phil. Mag._ + September 1897, p. 213) observed the remarkable alteration that takes + place in the iron resistance temperature curve in the neighbourhood of + 780 deg. C. At that temperature the direction of the curvature of the + curve changes so that it becomes convex upwards instead of convex + downwards, and in addition the value of the temperature coefficient + undergoes a great reduction. The mean temperature coefficient of iron + in the neighbourhood of 0 deg. C. is 0.0057; at 765 deg. C. it rises + to a maximum value 0.0204; but at 1000 deg. C. it falls again to a + lower value, 0.00244. A similar rise to a maximum value and subsequent + fall are also noted in the case of the specific heat of iron. The + changes in the curvature of the resistivity curves are undoubtedly + connected with the molecular changes that occur in the magnetic metals + at their critical temperatures. + + A fact of considerable interest in connexion with resistivity is the + influence exerted by a strong magnetic field in the case of some + metals, notably bismuth. It was discovered by A. Righi and confirmed + by S. A. Leduc (_Journ. de Phys._ 1886, 5, p. 116, and 1887, 6, p. + 189) that if a pure bismuth wire is placed in a magnetic field + transversely to the direction of the magnetic field, its resistance is + considerably increased. This increase is greatly affected by the + temperature of the metal (Dewar and Fleming, _Proc. Roy. Soc._ 1897, + 60, p. 427). The temperature coefficient of pure copper is an + important constant, and its value as determined by Messrs Clark, Forde + and Taylor in terms of Fahrenheit temperature is + + [rho]t = [rho]32 {1 + 0.0023708(t - 32) + 0.0000034548(t - 32)^2}. + +_Time Effects._--In the case of dielectric conductors, commonly called +insulators, such as indiarubber, guttapercha, glass and mica, the +electric resistivity is not only a function of the temperature but also +of the time during which the electromotive force employed to measure it +is imposed. Thus if an indiarubber-covered cable is immersed in water +and the resistance of the dielectric between the copper conductor and +the water measured by ascertaining the current which can be caused to +flow through it by an electromotive force, this current is found to vary +very rapidly with the time during which the electromotive force is +applied. Apart from the small initial effect due to the electrostatic +capacity of the cable, the application of an electromotive force to the +dielectric produces a current through it which rapidly falls in value, +as if the electric resistance of the dielectric were increasing. The +current, however, does not fall continuously but tends to a limiting +value, and it appears that if the electromotive force is kept applied +to the cable for a prolonged time, a small and nearly constant current +will ultimately be found flowing through it. It is customary in +electro-technical work to consider the resistivity of the dielectric as +the value it has after the electromotive force has been applied for one +minute, the standard temperature being 75 deg. F. This, however, is a +purely conventional proceeding, and the number so obtained does not +necessarily represent the true or ohmic resistance of the dielectric. If +the electromotive force is increased, in the case of a large number of +ordinary dielectrics the apparent resistance at the end of one minute's +electrification decreases as the electromotive force increases. + +_Practical Standards._--The practical measurement of resistivity +involves many processes and instruments (see WHEATSTONE'S BRIDGE and +OHMMETER). Broadly speaking, the processes are divided into _Comparison +Methods_ and _Absolute Methods_. In the former a comparison is effected +between the resistance of a material in a known form and some standard +resistance. In the _Absolute Methods_ the resistivity is determined +without reference to any other substance, but with reference only to the +fundamental standards of length, mass and time. Immense labour has been +expended in investigations concerned with the production of a standard +of resistance and its evaluation in absolute measure. In some cases the +absolute standard is constructed by filling a carefully-calibrated tube +of glass with mercury, in order to realize in a material form the +official definition of the ohm; in this manner most of the principal +national physical laboratories have been provided with standard mercury +ohms. (For a full description of the standard mercury ohm of the Berlin +Physikalisch-Technische Reichsanstalt, see the _Electrician_, xxxvii. +569.) For practical purposes it is more convenient to employ a standard +of resistance made of wire. + + Opinion is not yet perfectly settled on the question whether a wire + made of any alloy can be considered to be a perfectly unalterable + standard of resistance, but experience has shown that a platinum + silver alloy (66% silver, 33% platinum), and also the alloy called + manganin, seem to possess the qualities of permanence essential for a + wire-resistance standard. A comparison made in 1892 and 1894 of all + the manganin wire copies of the ohm made at the Reichsanstalt in + Berlin, showed that these standards had remained constant for two + years to within one or two parts in 100,000. It appears, however, that + in order that manganin may remain constant in resistivity when used in + the manufacture of a resistance coil, it is necessary that the alloy + should be _aged_ by heating it to a temperature of 140 deg. C. for ten + hours; and to prevent subsequent changes in resistivity, solders + containing zinc must be avoided, and a silver solder containing 75% of + silver employed in soldering the manganin wire to its connexions. + +The authorities of the Berlin Reichsanstalt have devoted considerable +attention to the question of the best form for a wire standard of +electric resistance. In that now adopted the resistance wire is +carefully insulated and wound on a brass cylinder, being doubled on +itself to annul inductance as much as possible. In the coil two wires +are wound on in parallel, one being much finer than the other, and the +final adjustment of the coil to an exact value is made by shortening the +finer of the two. A standard of resistance for use in a laboratory now +generally consists of a wire of manganin or platinum-silver carefully +insulated and enclosed in a brass case. Thick copper rods are connected +to the terminals of the wire in the interior of the case, and brought to +the outside, being carefully insulated at the same time from one another +and from the case. The coil so constructed can be placed under water or +paraffin oil, the temperature of which can be exactly observed during +the process of taking a resistance measurement. Equalization of the +temperature of the surrounding medium is effected by the employment of a +stirrer, worked by hand or by a small electric motor. The construction +of a standard of electrical resistance consisting of mercury in a glass +tube is an operation requiring considerable precautions, and only to be +undertaken by those experienced in the matter. Opinions are divided on +the question whether greater permanence in resistance can be secured by +mercury-in-glass standards of resistance or by wire standards, but the +latter are at least more portable and less fragile. + + A full description of the construction of a standard wire-resistance + coil on the plan adopted by the Berlin Physikalisch-Technische + Reichsanstalt is given in the Report of the British Association + Committee on Electrical Standards, presented at the Edinburgh Meeting + in 1892. For the design and construction of standards of electric + resistances adapted for employment in the comparison and measurement + of very low or very high resistances, the reader may be referred to + standard treatises on electric measurements. + + BIBLIOGRAPHY.--See also J. A. Fleming, _A Handbook for the Electrical + Laboratory and Testing Room_, vol. i. (London, 1901); _Reports of the + British Association Committee on Electrical Standards_, edited by + Fleeming Jenkin (London, 1873); A. Matthiessen and C. Vogt, "On the + Influence of Temperature on the Conducting Power of Alloys," _Phil. + Trans._, 1864, 154, p. 167, and _Phil. Mag._, 1865, 29, p. 363; A. + Matthiessen and M. Holtzmann, "On the Effect of the Presence of Metals + and Metalloids upon the Electric Conducting Power of Pure Copper," + _Phil. Trans._, 1860, 150, p. 85; T. C. Fitzpatrick, "On the Specific + Resistance of Copper," _Brit. Assoc. Report_, 1890, p. 120, or + _Electrician_, 1890, 25, p. 608; R. Appleyard, _The Conductometer and + Electrical Conductivity_; Clark, Forde and Taylor, _Temperature + Coefficients of Copper_ (London, 1901). (J. A. F.) + + +II. CONDUCTION IN LIQUIDS + +Through liquid metals, such as mercury at ordinary temperatures and +other metals at temperatures above their melting points, the electric +current flows as in solid metals without changing the state of the +conductor, except in so far as heat is developed by the electric +resistance. But another class of liquid conductors exists, and in them +the phenomena are quite different. The conductivity of fused salts, and +of solutions of salts and acids, although less than that of metals, is +very great compared with the traces of conductivity found in so-called +non-conductors. In fused salts and conducting solutions the passage of +the current is always accompanied by definite chemical changes; the +substance of the conductor or electrolyte is decomposed, and the +products of the decomposition appear at the electrodes, i.e. the +metallic plates by means of which the current is led into and out of the +solution. The chemical phenomena are considered in the article +ELECTROLYSIS; we are here concerned solely with the mechanism of this +_electrolytic_ conduction of the current. + +To explain the appearance of the products of decomposition at the +electrodes only, while the intervening solution is unaltered, we suppose +that, under the action of the electric forces, the opposite parts of the +electrolyte move in opposite directions through the liquid. These +opposite parts, named ions by Faraday, must therefore be associated with +electric charges, and it is the convective movement of the opposite +streams of ions carrying their charges with them that, on this view, +constitutes the electric current. + +In metallic conduction it is found that the current is proportional to +the applied electromotive force--a relation known by the name of Ohm's +law. If we place in a circuit with a small electromotive force an +electrolytic cell consisting of two platinum electrodes and a solution, +the initial current soon dies away, and we shall find that a certain +minimum electromotive force must be applied to the circuit before any +considerable permanent current passes. The chemical changes which are +initiated on the surfaces of the electrodes set up a reverse +electromotive force of polarization, and, until this is overcome, only a +minute current, probably due to the slow but steady removal of the +products of decomposition from the electrodes by a process of diffusion, +will pass through the cell. Thus it is evident that, considering the +electrolytic cell as a whole, the passage of the current through it +cannot conform to Ohm's law. But the polarization is due to chemical +changes, which are confined to the surfaces of the electrodes; and it is +necessary to inquire whether, if the polarization at the electrodes be +eliminated, the passage of the current through the bulk of the solution +itself is proportional to the electromotive force actually applied to +that solution. Rough experiment shows that the current is proportional +to the excess of the electromotive force over a constant value, and thus +verifies the law approximately, the constant electromotive force to be +overcome being a measure of the polarization. A more satisfactory +examination of the question was made by F. Kohlrausch in the years 1873 +to 1876. Ohm's law states that the current C is proportional to the +electromotive force E, or C = kR, where k is a constant called the +conductivity of the circuit. The equation may also be written as C = +E/R, where R is a constant, the reciprocal of k, known as the resistance +of the circuit. The essence of the law is the proportionality between C +and E, which means that the ratio E/C is a constant. But E/C = R, and +thus the law may be tested by examining the constancy of the measured +resistance of a conductor when different currents are passing through +it. In this way Ohm's law has been confirmed in the case of metallic +conduction to a very high degree of accuracy. A similar principle was +applied by Kohlrausch to the case of electrolytes, and he was the first +to show that an electrolyte possesses a definite resistance which has a +constant value when measured with different currents and by different +experimental methods. + +_Measurement of the Resistance of Electrolytes._--There are two effects +of the passage of an electric current which prevent the possibility of +measuring electrolytic resistance by the ordinary methods with the +direct currents which are used in the case of metals. The products of +the chemical decomposition of the electrolyte appear at the electrodes +and set up the opposing electromotive force of polarization, and unequal +dilution of the solution may occur in the neighbourhood of the two +electrodes. The chemical and electrolytic aspects of these phenomena are +treated in the article ELECTROLYSIS, but from our present point of view +also it is evident that they are again of fundamental importance. The +polarization at the surface of the electrodes will set up an opposing +electromotive force, and the unequal dilution of the solution will turn +the electrolyte into a concentration cell and produce a subsidiary +electromotive force either in the same direction as that applied or in +the reverse according as the anode or the cathode solution becomes the +more dilute. Both effects thus involve internal electromotive forces, +and prevent the application of Ohm's law to the electrolytic cell as a +whole. But the existence of a definite measurable resistance as a +characteristic property of the system depends on the conformity of the +system to Ohm's law, and it is therefore necessary to eliminate both +these effects before attempting to measure the resistance. + +The usual and most satisfactory method of measuring the resistance of +electrolytes consists in eliminating the effects of polarization by the +use of alternating currents, that is, currents that are reversed in +direction many times a second.[11] The chemical action produced by the +first current is thus reversed by the second current in the opposite +direction, and the polarization caused by the first current on the +surface of the electrodes is destroyed before it rises to an appreciable +value. The polarization is also diminished in another way. The +electromotive force of polarization is due to the deposition of films of +the products of chemical decomposition on the surface of the electrodes, +and only reaches its full value when a continuous film is formed. If the +current be stopped before such a film is completed, the reverse +electromotive force is less than its full value. A given current flowing +for a given time deposits a definite amount of substance on the +electrodes, and therefore the amount per unit area is inversely +proportional to the area of the electrodes--to the area of contact, that +is, between the electrode and the liquid. Thus, by increasing the area +of the electrodes, the polarization due to a given current is decreased. +Now the area of free surface of a platinum plate can be increased +enormously by coating the plate with platinum black, which is metallic +platinum in a spongy state, and with such a plate as electrode the +effects of polarization are diminished to a very marked extent. The +coating is effected by passing an electric current first one way and +then the other between two platinum plates immersed in a 3% solution of +platinum chloride to which a trace of lead acetate is sometimes added. +The platinized plates thus obtained are quite satisfactory for the +investigation of strong solutions. They have the power, however, of +absorbing a certain amount of salt from the solutions and of giving it +up again when water or more dilute solution is placed in contact with +them. The measurement of very dilute solutions is thus made difficult, +but, if the plates be heated to redness after being platinized, a grey +surface is obtained which possesses sufficient area for use with dilute +solutions and yet does not absorb an appreciable quantity of salt. + +Any convenient source of alternating current may be used. The currents +from the secondary circuit of a small induction coil are satisfactory, +or the currents of an alternating electric light supply may be +transformed down to an electromotive force of one or two volts. With +such currents it is necessary to consider the effects of self-induction +in the circuit and of electrostatic capacity. In balancing the +resistance of the electrolyte, resistance coils may be used in which +self-induction and the capacity are reduced to a minimum by winding the +wire of the coil backwards and forwards in alternate layers. + +[Illustration: FIG. 1.] + +With these arrangements the usual method of measuring resistance by +means of Wheatstone's bridge may be adapted to the case of electrolytes. +With alternating currents, however, it is impossible to use a +galvanometer in the usual way. The galvanometer was therefore replaced +by Kohlrausch by a telephone, which gives a sound when an alternating +current passes through it. The most common plan of the apparatus is +shown diagrammatically in fig. 1. The electrolytic cell and a resistance +box form two arms of the bridge, and the sliding contact is moved along +the metre wire which forms the other two arms till no sound is heard in +the telephone. The resistance of the electrolyte is to that of the box +as that of the right-hand end of the wire is to that of the left-hand +end. A more accurate method of using alternating currents, and one more +pleasant to use, gets rid of the telephone (_Phil. Trans._, 1900, 194, +p. 321). The current from one or two voltaic cells is led to an ebonite +drum turned by a motor or a hand-wheel and cord. On the drum are fixed +brass strips with wire brushes touching them in such a manner that the +current from the brushes is reversed several times in each revolution of +the drum. The wires from the brushes are connected with the Wheatstone's +bridge. A moving coil galvanometer is used as indicator, its connexions +being reversed in time with those of the battery by a slightly narrower +set of brass strips fixed on the other end of the ebonite commutator. +Thus any residual current through the galvanometer is direct and not +alternating. The high moment of inertia of the coil makes the period of +swing slow compared with the period of alternation of the current, and +the slight periodic disturbances are thus prevented from affecting the +galvanometer. When the measured resistance is not altered by increasing +the speed of the commutator or changing the ratio of the arms of the +bridge, the disturbing effects may be considered to be eliminated. + +[Illustration: FIG. 2.] + +[Illustration: FIG. 3.] + +The form of vessel chosen to contain the electrolyte depends on the +order of resistance to be measured. For dilute solutions the shape of +cell shown in fig. 2 will be found convenient, while for more +concentrated solutions, that indicated in fig. 3 is suitable. The +absolute resistances of certain solutions have been determined by +Kohlrausch by comparison with mercury, and, by using one of these +solutions in any cell, the constant of that cell may be found once for +all. From the observed resistance of any given solution in the cell the +resistance of a centimetre cube--the so-called specific resistance--may +be calculated. The reciprocal of this, or the conductivity, is a more +generally useful constant; it is conveniently expressed in terms of a +unit equal to the reciprocal of an ohm. Thus Kohlrausch found that a +solution of potassium chloride, containing one-tenth of a gram +equivalent (7.46 grams) per litre, has at 18 deg. C. a specific +resistance of 89.37 ohms per centimetre cube, or a conductivity of 1.119 +X 10^-2 mhos or 1.119 X 10^-11 C.G.S. units. As the temperature +variation of conductivity is large, usually about 2% per degree, it is +necessary to place the resistance cell in a paraffin or water bath, and +to observe its temperature with some accuracy. + +Another way of eliminating the effects of polarization and of dilution +has been used by W. Stroud and J. B. Henderson (_Phil. Mag._, 1897 [5], +43, p. 19). Two of the arms of a Wheatstone's bridge are composed of +narrow tubes filled with the solution, the tubes being of equal diameter +but of different length. The other two arms are made of coils of wire of +equal resistance, and metallic resistance is added to the shorter tube +till the bridge is balanced. Direct currents of somewhat high +electromotive force are used to work the bridge. Equal currents then +flow through the two tubes; the effects of polarization and dilution +must be the same in each, and the resistance added to the shorter tube +must be equal to the resistance of a column of liquid the length of +which is equal to the difference in length of the two tubes. + +A somewhat different principle was adopted by E. Bouty in 1884. If a +current be passed through two resistances in series by means of an +applied electromotive force, the electric potential falls from one end +of the resistances to the other, and, if we apply Ohm's law to each +resistance in succession, we see that, since for each of them E = CR, +and C the current is the same through both, E the electromotive force or +fall of potential between the ends of each resistance must be +proportional to the resistance between them. Thus by measuring the +potential difference between the ends of the two resistances +successively, we may compare their resistances. If, on the other hand, +we can measure the potential difference in some known units, and +similarly measure the current flowing, we can determine the resistance +of a single electrolyte. The details of the apparatus may vary, but its +principle is illustrated in the following description. A narrow glass +tube is fixed horizontally into side openings in two glass vessels, and +an electric current passed through it by means of platinum electrodes +and a battery of considerable electromotive force. In this way a steady +fall of electric potential is set up along the length of the tube. To +measure the potential difference between the ends of the tube, tapping +electrodes are constructed, e.g. by placing zinc rods in vessels with +zinc sulphate solution and connecting these vessels (by means of thin +siphon tubes also filled with solution) with the vessels at the ends of +the long tube which contains the electrolyte to be examined. Whatever be +the contact potential difference between zinc and its solution, it is +the same at both ends, and thus the potential difference between the +zinc rods is equal to that between the liquid at the two ends of the +tube. This potential difference may be measured without passing any +appreciable current through the tapping electrodes, and thus the +resistance of the liquid deduced. + +_Equivalent Conductivity of Solutions._--As is the case in the other +properties of solutions, the phenomena are much more simple when the +concentration is small than when it is great, and a study of dilute +solutions is therefore the best way of getting an insight into the +essential principles of the subject. The foundation of our knowledge was +laid by Kohlrausch when he had developed the method of measuring +electrolyte resistance described above. He expressed his results in +terms of "equivalent conductivity," that is, the conductivity (k) of the +solution divided by the number (m) of gram-equivalents of electrolyte +per litre. He finds that, as the concentration diminishes, the value of +k/m approaches a limit, and eventually becomes constant, that is to say, +at great dilution the conductivity is proportional to the concentration. +Kohlrausch first prepared very pure water by repeated distillation and +found that its resistance continually increased as the process of +purification proceeded. The conductivity of the water, and of the slight +impurities which must always remain, was subtracted from that of the +solution made with it, and the result, divided by m, gave the equivalent +conductivity of the substance dissolved. This procedure appears +justifiable, for as long as conductivity is proportional to +concentration it is evident that each part of the dissolved matter +produces its own independent effect, so that the total conductivity is +the sum of the conductivities of the parts; when this ceases to hold, +the concentration of the solution has in general become so great that +the conductivity of the solvent may be neglected. The general result of +these experiments can be represented graphically by plotting k/m as +ordinates and [root 3]m as abscissae, [root 3]m being a number +proportional to the reciprocal of the average distance between the +molecules, to which it seems likely that the molecular conductivity may +be related. The general types of curve for a simple neutral salt like +potassium or sodium chloride and for a caustic alkali or acid are shown +in fig. 4. The curve for the neutral salt comes to a limiting value; +that for the acid attains a maximum at a certain very small +concentration, and falls again when the dilution is carried farther. It +has usually been considered that this destruction of conductivity is due +to chemical action between the acid and the residual impurities in the +water. At such great dilution these impurities are present in quantities +comparable with the amount of acid which they convert into a less highly +conducting neutral salt. In the case of acids, then, the maximum must be +taken as the limiting value. The decrease in equivalent conductivity at +great dilution is, however, so constant that this explanation seems +insufficient. The true cause of the phenomenon may perhaps be connected +with the fact that the bodies in which it occurs, acids and alkalis, +contain the ions, hydrogen in the one case, hydroxyl in the other, which +are present in the solvent, water, and have, perhaps because of this +relation, velocities higher than those of any other ions. The values of +the molecular conductivities of all neutral salts are, at great +dilution, of the same order of magnitude, while those of acids at their +maxima are about three times as large. The influence of increasing +concentration is greater in the case of salts containing divalent ions, +and greatest of all in such cases as solutions of ammonia and acetic +acid, which are substances of very low conductivity. + +[Illustration: FIG. 4.] + +_Theory of Moving Ions._--Kohlrausch found that, when the polarization +at the electrodes was eliminated, the resistance of a solution was +constant however determined, and thus established Ohm's Law for +electrolytes. The law was confirmed in the case of strong currents by G. +F. Fitzgerald and F. T. Trouton (_B.A. Report_, 1886, p. 312). Now, +Ohm's Law implies that no work is done by the current in overcoming +reversible electromotive forces such as those of polarization. Thus the +molecular interchange of ions, which must occur in order that the +products may be able to work their way through the liquid and appear at +the electrodes, continues throughout the solution whether a current is +flowing or not. The influence of the current on the ions is merely +directive, and, when it flows, streams of electrified ions travel in +opposite directions, and, if the applied electromotive force is enough +to overcome the local polarization, give up their charges to the +electrodes. We may therefore represent the facts by considering the +process of electrolysis to be a kind of convection. Faraday's classical +experiments proved that when a current flows through an electrolyte the +quantity of substance liberated at each electrode is proportional to its +chemical equivalent weight, and to the total amount of electricity +passed. Accurate determinations have since shown that the mass of an ion +deposited by one electromagnetic unit of electricity, i.e. its +electro-chemical equivalent, is 1.036 X 10^-4 X its chemical equivalent +weight. Thus the amount of electricity associated with one +gram-equivalent of any ion is 10^4/1.036 = 9653 units. Each monovalent +ion must therefore be associated with a certain definite charge, which +we may take to be a natural unit of electricity; a divalent ion carries +two such units, and so on. A cation, i.e. an ion giving up its charge at +the cathode, as the electrode at which the current leaves the solution +is called, carries a positive charge of electricity; an anion, +travelling in the opposite direction, carries a negative charge. It will +now be seen that the quantity of electricity flowing per second, i.e. +the current through the solution, depends on (1) the number of the ions +concerned, (2) the charge on each ion, and (3) the velocity with which +the ions travel past each other. Now, the number of ions is given by the +concentration of the solution, for even if all the ions are not actively +engaged in carrying the current at the same instant, they must, on any +dynamical idea of chemical equilibrium, be all active in turn. The +charge on each, as we have seen, can be expressed in absolute units, and +therefore the velocity with which they move past each other can be +calculated. This was first done by Kohlrausch (_Gottingen Nachrichten_, +1876, p. 213, and _Das Leitvermogen der Elektrolyte_, Leipzig, 1898) +about 1879. + + In order to develop Kohlrausch's theory, let us take, as an example, + the case of an aqueous solution of potassium chloride, of + concentration n gram-equivalents per cubic centimetre. There will then + be n gram-equivalents of potassium ions and the same number of + chlorine ions in this volume. Let us suppose that on each + gram-equivalent of potassium there reside +e units of electricity, and + on each gram-equivalent of chlorine ions -e units. If u denotes the + average velocity of the potassium ion, the positive charge carried per + second across unit area normal to the flow is n e u. Similarly, if v + be the average velocity of the chlorine ions, the negative charge + carried in the opposite direction is n e v. But positive electricity + moving in one direction is equivalent to negative electricity moving + in the other, so that, before changes in concentration sensibly + supervene, the total current, C, is ne(u + v). Now let us consider the + amounts of potassium and chlorine liberated at the electrodes by this + current. At the cathode, if the chlorine ions were at rest, the excess + of potassium ions would be simply those arriving in one second, + namely, nu. But since the chlorine ions move also, a further + separation occurs, and nv potassium ions are left without partners. + The total number of gram-equivalents liberated is therefore n(u + v). + By Faraday's law, the number of grams liberated is equal to the + product of the current and the electro-chemical equivalent of the ion; + the number of gram-equivalents therefore must be equal to [eta]C, + where [eta] denotes the electro-chemical equivalent of hydrogen in + C.G.S. units. Thus we get + + n(u + v) = [eta]C = [eta]ne(u + v), + + and it follows that the charge, e, on 1 gram-equivalent of each kind + of ion is equal to 1/[eta]. We know that Ohm's Law holds good for + electrolytes, so that the current C is also given by k.dP/dx, where k + denotes the conductivity of the solution, and dP/dx the potential + gradient, i.e. the change in potential per unit length along the lines + of current flow. Thus + + n + -----(u + v) = kdP/dx; + [eta] + + therefore + + k dP + u + v = [eta] - --. + n dx + + Now [eta] is 1.036 X 10^-4, and the concentration of a solution is + usually expressed in terms of the number, m, of gram-equivalents per + litre instead of per cubic centimetre. Therefore + + k dP + u + v = 1.036 X 10^-1 - -- --. + m dx + + When the potential gradient is one volt (10^8 C.G.S. units) per + centimetre this becomes + + u + v = 1.036 X 10^-7 X k/m. + + Thus by measuring the value of k/m, which is known as the equivalent + conductivity of the solution, we can find u + v, the velocity of the + ions relative to each other. For instance, the equivalent conductivity + of a solution of potassium chloride containing one-tenth of a + gram-equivalent per litre is 1119 X 10^-13 C.G.S. units at 18 deg. C. + Therefore + + u + v = 1.036 X 10^7 X 1119 X 10^-13 + = 1.159 X 10^-3 = 0.001159 cm. per sec. + + In order to obtain the absolute velocities u and v, we must find some + other relation between them. Let us resolve u into 1/2(u + v) in one + direction, say to the right, and 1/2(u - v) to the left. Similarly v + can be resolved into 1/2(v+u) to the left and 1/2(v-u) to the right. + On pairing these velocities we have a combined movement of the ions to + the right, with a speed of 1/2(u - v) and a drift right and left, past + each other, each ion travelling with a speed of 1/2(u + v), + constituting the electrolytic separation. If u is greater than v, the + combined movement involves a concentration of salt at the cathode, and + a corresponding dilution at the anode, and _vice versa_. The rate at + which salt is electrolysed, and thus removed from the solution at each + electrode, is 1/2(u + v). Thus the total loss of salt at the cathode + is 1/2(u + v) - 1/2(u - v) or v, and at the anode, 1/2(v + u) - 1/2(v + - u), or u. Therefore, as is explained in the article ELECTROLYSIS, by + measuring the dilution of the liquid round the electrodes when a + current passed, W. Hittorf (_Pogg. Ann._, 1853-1859, 89, p. 177; 98, + p. 1; 103, p. 1; 106, pp. 337 and 513) was able to deduce the ratio of + the two velocities, for simple salts when no complex ions are present, + and many further experiments have been made on the subject (see _Das + Leitvermogen der Elektrolyte_). + + By combining the results thus obtained with the sum of the velocities, + as determined from the conductivities, Kohlrausch calculated the + absolute velocities of different ions under stated conditions. Thus, + in the case of the solution of potassium chloride considered above, + Hittorf's experiments show us that the ratio of the velocity of the + anion to that of the cation in this solution is .51 : .49. The + absolute velocity of the potassium ion under unit potential gradient + is therefore 0.000567 cm. per sec., and that of the chlorine ion + 0.000592 cm. per sec. Similar calculations can be made for solutions + of other concentrations, and of different substances. + +Table IX. shows Kohlrausch's values for the ionic velocities of three +chlorides of alkali metals at 18 deg. C, calculated for a potential +gradient of 1 volt per cm.; the numbers are in terms of a unit equal to +10^-6 cm. per sec.:-- + + TABLE IX. + + +--------------------------------------------+----------------+ + | | KCl | NaCl | LiCl | + +---------+-----------------+----------------+----------------+ + | m | u + v u v | u + v u v |u + v u v | + +---------+-----------------+----------------+----------------+ + | 0 | 1350 660 690 | 1140 450 690 | 1050 360 690 | + | 0.0001 | 1335 654 681 | 1129 448 681 | 1037 356 681 | + | .001 | 1313 643 670 | 1110 440 670 | 1013 343 670 | + | .01 | 1263 619 644 | 1059 415 644 | 962 318 644 | + | .03 | 1218 597 621 | 1013 390 623 | 917 298 619 | + | .1 | 1153 564 589 | 952 360 592 | 853 259 594 | + | .3 | 1088 531 557 | 876 324 552 | 774 217 557 | + | 1.0 | 1011 491 520 | 765 278 487 | 651 169 482 | + | 3.0 | 911 442 469 | 582 206 376 | 463 115 348 | + | 5.0 | | 438 153 285 | 334 80 254 | + | 10.0 | | | 117 25 92 | + +---------+-----------------+----------------+----------------+ + +These numbers show clearly that there is an increase in ionic velocity +as the dilution proceeds. Moreover, if we compare the values for the +chlorine ion obtained from observations on these three different salts, +we see that as the concentrations diminish the velocity of the chlorine +ion becomes the same in all of them. A similar relation appears in other +cases, and, in general, we may say that at great dilution the velocity +of an ion is independent of the nature of the other ion present. This +introduces the conception of specific ionic velocities, for which some +values at 18 deg. C. are given by Kohlrausch in Table X.:-- + + Table X. + + +------------------------------------+ + | K 66 X 10^-5 cms. per sec. | + | Na 45 " " | + | Li 36 " " | + | NH4 66 " " | + | H 320 " " | + | Ag 57 " " | + | Cl 69 " " | + | I 69 " " | + | NO3 64 " " | + | OH 162 " " | + | C2H3O2 36 " " | + | C3H5O2 33 " " | + +------------------------------------+ + +Having obtained these numbers we can deduce the conductivity of the +dilute solution of any salt, and the comparison of the calculated with +the observed values furnished the first confirmation of Kohlrausch's +theory. Some exceptions, however, are known. Thus acetic acid and +ammonia give solutions of much lower conductivity than is indicated by +the sum of the specific ionic velocities of their ions as determined +from other compounds. An attempt to find in Kohlrausch's theory some +explanation of this discrepancy shows that it could be due to one of two +causes. Either the velocities of the ions must be much less in these +solutions than in others, or else only a fractional part of the number +of molecules present can be actively concerned in conveying the current. +We shall return to this point later. + + _Friction on the Ions._--It is interesting to calculate the magnitude + of the forces required to drive the ions with a certain velocity. If + we have a potential gradient of 1 volt per centimetre the electric + force is 10^8 in C.G.S. units. The charge of electricity on 1 + gram-equivalent of any ion is 1/.0001036 = 9653 units, hence the + mechanical force acting on this mass is 9653 X 10^8 dynes. This, let + us say, produces a velocity u; then the force required to produce unit + velocity is PA = 9.653 X 10^11/u dynes = 9.84 X 10^5/u kilograms-weight. + If the ion have an equivalent weight A, the force producing unit + velocity when acting on 1 gram is P1 = 9.84 X 10^5/Au kilograms-weight. + Thus the aggregate force required to drive 1 gram of potassium ions + with a velocity of 1 centimetre per second through a very dilute + solution must be equal to the weight of 38 million kilograms. + + Table XI. + + +-------------------------------+ + | Kilograms-weight. | + +-------------------------------+ + | PA P1 | + |K 15 X 10^8 38 X 10^6 | + |Na 22 " 95 " | + |Li 27 " 390 " | + |NH4 15 " 83 " | + |H 3.1 " 310 " | + |Ag 17 " 16 " | + |Cl 14 " 40 " | + |I 14 " 11 " | + |NO3 15 " 25 " | + |OH 5.4 " 32 " | + |C2H8O2 27 " 46 " | + |C3H5O2 30 " 41 " | + +------------- -----------------+ + + Since the ions move with uniform velocity, the frictional resistances + brought into play must be equal and opposite to the driving forces, + and therefore these numbers also represent the ionic friction + coefficients in very dilute solutions at 18 deg. C. + +_Direct Measurement of Ionic Velocities._--Sir Oliver Lodge was the +first to directly measure the velocity of an ion (_B.A. Report_, 1886, +p. 389). In a horizontal glass tube connecting two vessels filled with +dilute sulphuric acid he placed a solution of sodium chloride in solid +agar-agar jelly. This solid solution was made alkaline with a trace of +caustic soda in order to bring out the red colour of a little +phenol-phthalein added as indicator. An electric current was then passed +from one vessel to the other. The hydrogen ions from the anode vessel of +acid were thus carried along the tube, and, as they travelled, +decolourized the phenol-phthalein. By this method the velocity of the +hydrogen ion through a jelly solution under a known potential gradient +was observed to about 0.0026 cm. per sec, a number of the same order as +that required by Kohlrausch's theory. Direct determinations of the +velocities of a few other ions have been made by W. C. D. Whetham +(_Phil. Trans._ vol. 184, A, p. 337; vol. 186, A, p. 507; _Phil. Mag._, +October 1894). Two solutions having one ion in common, of equivalent +concentrations, different densities, different colours, and nearly equal +specific resistances, were placed one over the other in a vertical glass +tube. In one case, for example, decinormal solutions of potassium +carbonate and potassium bichromate were used. The colour of the latter +is due to the presence of the bichromate group, Cr2O7. When a current +was passed across the junction, the anions CO3 and Cr2O7 travelled in +the direction opposite to that of the current, and their velocity could +be determined by measuring the rate at which the colour boundary moved. +Similar experiments were made with alcoholic solutions of cobalt salts, +in which the velocities of the ions were found to be much less than in +water. The behaviour of agar jelly was then investigated, and the +velocity of an ion through a solid jelly was shown to be very little +less than in an ordinary liquid solution. The velocities could therefore +be measured by tracing the change in colour of an indicator or the +formation of a precipitate. Thus decinormal jelly solutions of barium +chloride and sodium chloride, the latter containing a trace of sodium +sulphate, were placed in contact. Under the influence of an +electromotive force the barium ions moved up the tube, disclosing their +presence by the trace of insoluble barium sulphate formed. Again, a +measurement of the velocity of the hydrogen ion, when travelling through +the solution of an acetate, showed that its velocity was then only about +the one-fortieth part of that found during its passage through +chlorides. From this, as from the measurements on alcohol solutions, it +is clear that where the equivalent conductivities are very low the +effective velocities of the ions are reduced in the same proportion. + +Another series of direct measurements has been made by Orme Masson +(_Phil. Trans._ vol. 192, A, p. 331). He placed the gelatine solution of +a salt, potassium chloride, for example, in a horizontal glass tube, and +found the rate of migration of the potassium and chlorine ions by +observing the speed at which they were replaced when a coloured anion, +say, the Cr2O7 from a solution of potassium bichromate, entered the tube +at one end, and a coloured cation, say, the Cu from copper sulphate, at +the other. The coloured ions are specifically slower than the colourless +ions which they follow, and in this case it follows that the coloured +solution has a higher resistance than the colourless. For the same +current, therefore, the potential gradient is higher in the coloured +solution and lower in the colourless one. Thus a coloured ion which gets +in front of the advancing boundary finds itself acted on by a smaller +force and falls back into line, while a straggling colourless ion is +pushed forward again. Hence a sharp boundary is preserved. B. D. Steele +has shown that with these sharp boundaries the use of coloured ions is +unnecessary, the junction line being visible owing to the difference in +the optical refractive indices of two colourless solutions. Once the +boundary is formed, too, no gelatine is necessary, and the motion can be +watched through liquid aqueous solutions (see R. B. Denison and B. D. +Steele, _Phil. Trans._, 1906). + +All the direct measurements which have been made on simple binary +electrolytes agree with Kohlrausch's results within the limits of +experimental error. His theory, therefore, probably holds good in such +cases, whatever be the solvent, if the proper values are given to the +ionic velocities, i.e. the values expressing the velocities with which +the ions actually move in the solution of the strength taken, and under +the conditions of the experiment. If we know the specific velocity of +any one ion, we can deduce, from the conductivity of very dilute +solutions, the velocity of any other ion with which it may be +associated, a proceeding which does not involve the difficult task of +determining the migration constant of the compound. Thus, taking the +specific ionic velocity of hydrogen as 0.00032 cm. per second, we can +find, by determining the conductivity of dilute solutions of any acid, +the specific velocity of the acid radicle involved. Or again, since we +know the specific velocity of silver, we can find the velocities of a +series of acid radicles at great dilution by measuring the conductivity +of their silver salts. + + By such methods W. Ostwald, G. Bredig and other observers have found + the specific velocities of many ions both of inorganic and organic + compounds, and examined the relation between constitution and ionic + velocity. The velocity of elementary ions is found to be a periodic + function of the atomic weight, similar elements lying on corresponding + portions of a curve drawn to express the relation between these two + properties. Such a curve much resembles that giving the relation + between atomic weight and viscosity in solution. For complex ions the + velocity is largely an additive property; to a continuous additive + change in the composition of the ion corresponds a continuous but + decreasing change in the velocity. The following table gives Ostwald's + results for the formic acid series:-- + + Table XII. + + +----------------------+----------+---------------------+ + | | Velocity.| Difference for CH2. | + +----------------------+----------+---------------------+ + | Formic acid HCO2 | 51.2 | .. | + | Acetic " H3C2O2 | 38.3 | -12.9 | + | Propionic " H5C3O2 | 34.3 | - 4.0 | + | Butyric " H7C4O2 | 30.8 | - 3.5 | + | Valeric " H9C5O2 | 28.8 | - 2.0 | + | Caprionic " H11C6O2 | 27.4 | - 1.4 | + +----------------------+----------+---------------------+ + +_Nature of Electrolytes._--We have as yet said nothing about the +fundamental cause of electrolytic activity, nor considered why, for +example, a solution of potassium chloride is a good conductor, while a +solution of sugar allows practically no current to pass. + +All the preceding account of the subject is, then, independent of any +view we may take of the nature of electrolytes, and stands on the basis +of direct experiment. Nevertheless, the facts considered point to a very +definite conclusion. The specific velocity of an ion is independent of +the nature of the opposite ion present, and this suggests that the ions +themselves, while travelling through the liquid, are dissociated from +each other. Further evidence, pointing in the same direction, is +furnished by the fact that since the conductivity is proportional to the +concentration at great dilution, the equivalent-conductivity, and +therefore the ionic velocity, is independent of it. The importance of +this relation will be seen by considering the alternative to the +dissociation hypothesis. If the ions are not permanently free from each +other their mobility as parts of the dissolved molecules must be secured +by continual interchanges. The velocity with which they work their way +through the liquid must then increase as such molecular rearrangements +become more frequent, and will therefore depend on the number of solute +molecules, i.e. on the concentration. On this supposition the observed +constancy of velocity would be impossible. We shall therefore adopt as a +wording hypothesis the theory, confirmed by other phenomena (see +ELECTROLYSIS), that an electrolyte consists of dissociated ions. + +It will be noticed that neither the evidence in favour of the +dissociation theory which is here considered, nor that described in the +article ELECTROLYSIS, requires more than the effective dissociation of +the ions from each other. They may well be connected in some way with +solvent molecules, and there are several indications that an ion +consists of an electrified part of the molecule of the dissolved salt +with an attendant atmosphere of solvent round it. The conductivity of a +salt solution depends on two factors--(1) the fraction of the salt +ionized; (2) the velocity with which the ions, when free from each +other, move under the electric forces.[12] When a solution is heated, +both these factors may change. The coefficient of ionization usually, +though not always, decreases; the specific ionic velocities increase. +Now the rate of increase with temperature of these ionic velocities is +very nearly identical with the rate of decrease of the viscosity of the +liquid. If the curves obtained by observations at ordinary temperatures +be carried on they indicate a zero of fluidity and a zero of ionic +velocity about the same point, 38.5 deg. C. below the freezing point of +water (Kohlrausch, _Sitz. preuss. Akad. Wiss._, 1901, 42, p. 1026). Such +relations suggest that the frictional resistance to the motion of an ion +is due to the ordinary viscosity of the liquid, and that the ion is +analogous to a body of some size urged through a viscous medium rather +than to a particle of molecular dimensions finding its way through a +crowd of molecules of similar magnitude. From this point of view W. K. +Bousfield has calculated the sizes of ions on the assumption that +Stokes's theory of the motion of a small sphere through a viscous medium +might be applied (_Zeits. phys. Chem._, 1905, 53, p. 257; _Phil. Trans._ +A, 1906, 206, p. 101). The radius of the potassium or chlorine ion with +its envelope of water appears to be about 1.2 X 10^-8 centimetres. + + For the bibliography of electrolytic conduction see ELECTROLYSIS. The + books which deal more especially with the particular subject of the + present article are _Das Leitvermogen der Elektrolyte_, by F. + Kohlrausch and L. Holborn (Leipzig, 1898), and _The Theory of Solution + and Electrolysis_, by W. C. D. Whetham (Cambridge, 1902). + (W. C. D. W.) + + +III. ELECTRIC CONDUCTION THROUGH GASES + +A gas such as air when it is under normal conditions conducts +electricity to a small but only to a very small extent, however small +the electric force acting on the gas may be. The electrical conductivity +of gases not exposed to special conditions is so small that it was only +definitely established in the early years of the 20th century, although +it had engaged the attention of physicists for more than a hundred +years. It had been known for a long time that a body charged with +electricity slowly lost its charge even when insulated with the greatest +care, and though long ago some physicists believed that part of the leak +of electricity took place through the air, the general view seems to +have been that it was due to almost unavoidable defects in the +insulation or to dust in the air, which after striking the charged body +was repelled from it and went off with some of the charge. C. A. +Coulomb, who made some very careful experiments which were published in +1785 (_Mem. de l'Acad. des Sciences_, 1785, p. 612), came to the +conclusion that after allowing for the leakage along the threads which +supported the charged body there was a balance over, which he attributed +to leakage through the air. His view was that when the molecules of air +come into contact with a charged body some of the electricity goes on to +the molecules, which are then repelled from the body carrying their +charge with them. We shall see later that this explanation is not +tenable. C. Matteucci (_Ann. chim. phys._, 1850, 28, p. 390) in 1850 +also came to the conclusion that the electricity from a charged body +passes through the air; he was the first to prove that the rate at +which electricity escapes is less when the pressure of the gas is low +than when it is high. He found that the rate was the same whether the +charged body was surrounded by air, carbonic acid or hydrogen. +Subsequent investigations have shown that the rate in hydrogen is in +general much less than in air. Thus in 1872 E. G. Warburg (_Pogg. Ann._, +1872, 145, p. 578) found that the leak through hydrogen was only about +one-half of that through air: he confirmed Matteucci's observations on +the effect of pressure on the rate of leak, and also found that it was +the same whether the gas was dry or damp. He was inclined to attribute +the leak to dust in the air, a view which was strengthened by an +experiment of J. W. Hittorf's (_Wied. Ann._, 1879, 7, p. 595), in which +a small carefully insulated electroscope, placed in a small vessel +filled with carefully filtered gas, retained its charge for several +days; we know now that this was due to the smallness of the vessel and +not to the absence of dust, as it has been proved that the rate of leak +in small vessels is less than in large ones. + +Great light was thrown on this subject by some experiments on the rates +of leak from charged bodies in closed vessels made almost simultaneously +by H. Geitel (_Phys. Zeit._, 1900, 2, p. 116) and C. T. R. Wilson +(_Proc. Camb. Phil._ Soc., 1900, 11, p. 32). These observers established +that (1) the rate of escape of electricity in a closed vessel is much +smaller than in the open, and the larger the vessel the greater is the +rate of leak; and (2) the rate of leak does not increase in proportion +to the differences of potential between the charged body and the walls +of the vessel: the rate soon reaches a limit beyond which it does not +increase, however much the potential difference may be increased, +provided, of course, that this is not great enough to cause sparks to +pass from the charged body. On the assumption that the maximum leak is +proportional to the volume, Wilson's experiments, which were made in +vessels less than 1 litre in volume, showed that in dust-free air at +atmospheric pressure the maximum quantity of electricity which can +escape in one second from a charged body in a closed volume of V cubic +centimetres is about 10^-8V electrostatic units. E. Rutherford and S. T. +Allan (_Phys. Zeit._, 1902, 3, p. 225), working in Montreal, obtained +results in close agreement with this. Working between pressures of from +43 to 743 millimetres of mercury, Wilson showed that the maximum rate of +leak is very approximately proportional to the pressure; it is thus +exceedingly small when the pressure is low--a result illustrated in a +striking way by an experiment of Sir W. Crookes (_Proc. Roy. Soc._, +1879, 28, p. 347) in which a pair of gold leaves retained an electric +charge for several months in a very high vacuum. Subsequent experiments +have shown that it is only in very small vessels that the rate of leak +is proportional to the volume and to the pressure; in large vessels the +rate of leak per unit volume is considerably smaller than in small ones. +In small vessels the maximum rate of leak in different gases, is, with +the exception of hydrogen, approximately proportional to the density of +the gas. Wilson's results on this point are shown in the following table +(Proc. Roy. Soc., 1901, 60, p. 277):-- + + +---------+------------------------+-----------------+ + | Gas. | Relative Rate of Leak. | _Rate of Leak._ | + | | | Sp. Gr. | + +---------+------------------------+-----------------+ + | Air | 1.00 | 1 | + | H2 | .184 | 2.7 | + | CO2 | 1.69 | 1.10 | + | SO2 | 2.64 | 1.21 | + | CH3Cl | 4.7 | 1.09 | + | Ni(CO)4 | 5.1 | .867 | + +---------+------------------------+-----------------+ + +The rate of leak of electricity through gas contained in a closed vessel +depends to some extent on the material of which the walls of the vessel +are made; thus it is greater, other circumstances being the same, when +the vessel is made of lead than when it is made of aluminium. It also +varies, as Campbell and Wood (_Phil. Mag._ [6], 13, p. 265) have shown, +with the time of the day, having a well-marked minimum at about 3 +o'clock in the morning: it also varies from month to month. Rutherford +(_Phys. Rev._, 1903, 16, p. 183), Cooke (_Phil. Mag._, 1903 [6], 6, p. +403) and M'Clennan and Burton (_Phys. Rev._, 1903, 16, p. 184) have +shown that the leak in a closed vessel can be reduced by about 30% by +surrounding the vessel with sheets of thick lead, but that the reduction +is not increased beyond this amount, however thick the lead sheets may +be. This result indicates that part of the leak is due to a very +penetrating kind of radiation, which can get through the thin walls of +the vessel but is stopped by the thick lead. A large part of the leak we +are describing is due to the presence of radioactive substances such as +radium and thorium in the earth's crust and in the walls of the vessel, +and to the gaseous radioactive emanations which diffuse from them into +the atmosphere. This explains the very interesting effect discovered by +J. Elster and H. Geitel (_Phys. Zeit._, 1901, 2, p. 560), that the rate +of leak in caves and cellars when the air is stagnant and only renewed +slowly is much greater than in the open air. In some cases the +difference is very marked; thus they found that in the cave called the +Baumannshohle in the Harz mountains the electricity escaped at seven +times the rate it did in the air outside. In caves and cellars the +radioactive emanations from the walls can accumulate and are not blown +away as in the open air. + +The electrical conductivity of gases in the normal state is, as we have +seen, exceedingly small, so small that the investigation of its +properties is a matter of considerable difficulty; there are, however, +many ways by which the electrical conductivity of a gas can be increased +so greatly that the investigation becomes comparatively easy. Among such +methods are raising the temperature of the gas above a certain point. +Gases drawn from the neighbourhood of flames, electric arcs and sparks, +or glowing pieces of metal or carbon are conductors, as are also gases +through which Rontgen or cathode rays or rays of positive electricity +are passing; the rays from the radioactive metals, radium, thorium, +polonium and actinium, produce the same effect, as does also +ultra-violet light of exceedingly short wave-length. The gas, after +being made a conductor of electricity by any of these means, is found to +possess certain properties; thus it retains its conductivity for some +little time after the agent which made it a conductor has ceased to act, +though the conductivity diminishes very rapidly and finally gets too +small to be appreciable. + +[Illustration: FIG. 5.] + +This and several other properties of conducting gas may readily be +proved by the aid of the apparatus represented in fig. 5. V is a testing +vessel in which an electroscope is placed. Two tubes A and C are fitted +into the vessel, A being connected with a water pump, while the far end +of C is in the region where the gas is exposed to the agent which makes +it a conductor of electricity. Let us suppose that the gas is made +conducting by Rontgen rays produced by a vacuum tube which is placed in +a box, covered except for a window at B with lead so as to protect the +electroscope from the direct action of the rays. If a slow current of +air is drawn by the water pump through the testing vessel, the charge on +the electroscope will gradually leak away. The leak, however, ceases +when the current of air is stopped. This result shows that the gas +retains its conductivity during the time taken by it to pass from one +end to the other of the tube C. + +The gas loses its conductivity when filtered through a plug of +glass-wool, or when it is made to bubble through water. This can readily +be proved by inserting in the tube C a plug of glass-wool or a water +trap; then if by working the pump a little harder the same current of +air is produced as before, it will be found that the electroscope will +now retain its charge, showing that the conductivity can, as it were, be +filtered out of the gas. The conductivity can also be removed from the +gas by making the gas traverse a strong electric field. We can show this +by replacing the tube C by a metal tube with an insulated wire passing +down the axis of the tube. If there is no potential difference between +the wire and the tube then the electroscope will leak when a current of +air is drawn through the vessel, but the leak will stop if a +considerable difference of potential is maintained between the wire and +the tube: this shows that a strong electric field removes the +conductivity from the gas. + +The fact that the conductivity of the gas is removed by filtering shows +that it is due to something mixed with the gas which is removed from it +by filtration, and since the conductivity is also removed by an electric +field, the cause of the conductivity must be charged with electricity so +as to be driven to the sides of the tube by the electric force. Since +the gas as a whole is not electrified either positively or negatively, +there must be both negative and positive charges in the gas, the amount +of electricity of one sign being equal to that of the other. We are thus +led to the conclusion that the conductivity of the gas is due to +electrified particles being mixed up with the gas, some of these +particles having charges of positive electricity, others of negative. +These electrified particles are called _ions_, and the process by which +the gas is made a conductor is called the ionization of the gas. We +shall show later that the charges and masses of the ions can be +determined, and that the gaseous ions are not identical with those met +with in the electrolysis of solutions. + +[Illustration: FIG. 6.] + +One very characteristic property of conduction of electricity through a +gas is the relation between the current through the gas and the electric +force which gave rise to it. This relation is not in general that +expressed by Ohm's law, which always, as far as our present knowledge +extends, expresses the relation for conduction through metals and +electrolytes. With gases, on the other hand, it is only when the current +is very small that Ohm's law is true. If we represent graphically by +means of a curve the relation between the current passing between two +parallel metal plates separated by ionized gas and the difference of +potential between the plates, the curve is of the character shown in +fig. 6 when the ordinates represent the current and the abscissae the +difference of potential between the plates. We see that when the +potential difference is very small, i.e. close to the origin, the curve +is approximately straight, but that soon the current increases much less +rapidly than the potential difference, and that a stage is reached when +no appreciable increase of current is produced when the potential +difference is increased; when this stage is reached the current is +constant, and this value of the current is called the "saturation" +value. When the potential difference approaches the value at which +sparks would pass through the gas, the current again increases with the +potential difference; thus the curve representing the relation between +the current and potential difference over very wide ranges of potential +difference has the shape shown in fig. 7; curves of this kind have been +obtained by von Schweidler (_Wien. Ber._, 1899, 108, p. 273), and J. E. +S. Townsend (_Phil. Mag._, 1901 [6], 1, p. 198). We shall discuss later +the causes of the rise in the current with large potential differences, +when we consider ionization by collision. + + The general features of the earlier part of the curve are readily + explained on the ionization hypothesis. On this view the Rontgen rays + or other ionizing agent acting on the gas between the plates, produces + positive and negative ions at a definite rate. Let us suppose that q + positive and q negative ions are by this means produced per second + between the plates; these under the electric force will tend to move, + the positive ones to the negative plate, the negative ones to the + positive. Some of these ions will reach the plate, others before + reaching the plate will get so near one of the opposite sign that the + attraction between them will cause them to unite and form an + electrically neutral system; when they do this they end their + existence as ions. The current between the plates is proportional to + the number of ions which reach the plates per second. Now it is + evident that we cannot go on taking more ions out of the gas than are + produced; thus we cannot, when the current is steady, have more than q + positive ions driven to the negative plate per second, and the same + number of negative ions to the positive. If each of the positive ions + carries a charge of e units of positive electricity, and if there is + an equal and opposite charge on each negative ion, then the maximum + amount of electricity which can be given to the plates per second is + qe, and this is equal to the saturation current. Thus if we measure + the saturation current, we get a direct measure of the ionization, and + this does not require us to know the value of any quantity except the + constant charge on the ion. If we attempted to deduce the amount of + ionization by measurements of the current before it was saturated, we + should require to know in addition the velocity with which the ions + move under a given electric force, the time that elapses between the + liberation of an ion and its combination with one of the opposite + sign, and the potential difference between the plates. Thus if we wish + to measure the amount of ionization in a gas we should be careful to + see that the current is saturated. + + [Illustration: FIG. 7.] + +The difference between conduction through gases and through metals is +shown in a striking way when we use potential differences large enough +to produce the saturation current. Suppose we have got a potential +difference between the plates more than sufficient to produce the +saturation current, and let us increase the distance between the plates. +If the gas were to act like a metallic conductor this would diminish the +current, because the greater length would involve a greater resistance +in the circuit. In the case we are considering the separation of the +plates will _increase_ the current, because now there is a larger volume +of gas exposed to the rays; there are therefore more ions produced, and +as the saturation current is proportional to the number of ions the +saturation current is increased. If the potential difference between the +plates were much less than that required to saturate the current, then +increasing the distance would diminish the current; the gas for such +potential differences obeys Ohm's law and the behaviour of the gaseous +resistance is therefore similar to that of a metallic one. + +In order to produce the saturation current the electric field must be +strong enough to drive each ion to the electrode before it has time to +enter into combination with one of the opposite sign. Thus when the +plates in the preceding example are far apart, it will take a larger +potential difference to produce this current than when the plates are +close together. The potential difference required to saturate the +current will increase as the square of the distance between the plates, +for if the ions are to be delivered in a given time to the plates their +speed must be proportional to the distance between the plates. But the +speed is proportional to the electric force acting on the ion; hence the +electric force must be proportional to the distance between the plates, +and as in a uniform field the potential difference is equal to the +electric force multiplied by the distance between the plates, the +potential difference will vary as the square of this distance. + +The potential difference required to produce saturation will, other +circumstances being the same, increase with the amount of ionization, +for when the number of ions is large and they are crowded together, the +time which will elapse before a positive one combines with a negative +will be smaller than when the number of ions is small. The ions have +therefore to be removed more quickly from the gas when the ionization is +great than when it is small; thus they must move at a higher speed and +must therefore be acted upon by a larger force. + + +When the ions are not removed from the gas, they will increase until the +number of ions of one sign which combine with ions of the opposite sign +in any time is equal to the number produced by the ionizing agent in +that time. We can easily calculate the number of free ions at any time +after the ionizing agent has commenced to act. + + Let q be the number of ions (positive or negative) produced in one + cubic centimetre of the gas per second by the ionizing agent, n1, n2, + the number of free positive and negative ions respectively per cubic + centimetre of the gas. The number of collisions between positive and + negative ions per second in one cubic centimetre of the gas is + proportional to n1n2. If a certain fraction of the collisions between + the positive and negative ions result in the formation of an + electrically neutral system, the number of ions which disappear per + second on a cubic centimetre will be equal to [alpha]n1 n2, where + [alpha] is a quantity which is independent of n1, n2; hence if t is + the time since the ionizing agent was applied to the gas, we have + + dn1/dt = q - [alpha]n1 n2, dn2/dt = q - [alpha]n1 n2. + + Thus n1 - n2 is constant, so if the gas is uncharged to begin with, n1 + will always equal n2. Putting n1 = n2 = n we have + + dn/dt = q - [alpha]n^2 (1), + + the solution of which is, since n = 0 when t = 0, + + k([epsilon]^{2k[alpha]t} - 1) + n = ---------------------------- (2) + [epsilon]^{2k[alpha]t} + 1 + + if k^2 = q/[alpha]. Now the number of ions when the gas has reached a + steady state is got by putting t equal to infinity in the preceding + equation, and is therefore given by the equation + + n0 = k = [root](q/[alpha]). + + We see from equation (1) that the gas will not approximate to its + steady state until 2k[alpha]t is large, that is until t is large + compared with 1/2k[alpha] or with 1/2[root](q[alpha]). We may thus + take 1/2[root](q[alpha]) as a measure of the time taken by the gas to + reach a steady state when exposed to an ionizing agent; as this time + varies inversely as [root]q we see that when the ionization is feeble + it may take a very considerable time for the gas to reach a steady + state. Thus in the case of our atmosphere where the production of ions + is only at the rate of about 30 per cubic centimetre per second, and + where, as we shall see, [alpha] is about 10^-6, it would take some + minutes for the ionization in the air to get into a steady state if + the ionizing agent were suddenly applied. + + We may use equation (1) to determine the rate at which the ions + disappear when the ionizing agent is removed. Putting q=0 in that + equation we get dn/[alpha]t = -[alpha]n^2. + + Hence n = n0/(1 + n0[alpha]t) (3), + + where n0 is the number of ions when t = 0. Thus the number of ions + falls to one-half its initial value in the time 1/n0[alpha]. The + quantity [alpha] is called the _coefficient of recombination_, and its + value for different gases has been determined by Rutherford (_Phil. + Mag._ 1897 [5], 44, p. 422), Townsend (_Phil. Trans._, 1900, 193, p. + 129), McClung (_Phil. Mag._, 1902 [6], 3, p. 283), Langevin (_Ann. + chim. phys._ [7], 28, p. 289), Retschinsky (_Ann. d. Phys._, 1905, 17, + p. 518), Hendred (_Phys. Rev._, 1905, 21, p. 314). The values of + [alpha]/e, e being the charge on an ion in electrostatic measure as + determined by these observers for different gases, is given in the + following table:-- + + +-----+----------+----------+----------+------------+----------+ + | | Townsend.| McClung. | Langevin.|Retschinsky.| Hendred. | + +-----+----------+----------+----------+------------+----------+ + | Air | 3420 | 3380 | 3200 | 4140 | 3500 | + | O2 | 3380 | | | | | + | CO2 | 3500 | 3490 | 3400 | | | + | H2 | 3020 | 2940 | | | | + +-----+----------+----------+----------+------------+----------+ + + The gases in these experiments were carefully dried and free from + dust; the apparent value of [alpha] is much increased when dust or + small drops of water are present in the gas, for then the ions get + caught by the dust particles, the mass of a particle is so great + compared with that of an ion that they are practically immovable under + the action of the electric field, and so the ions clinging to them + escape detection when electrical methods are used. Taking e as 3.5 X + 10^-10, we see that [alpha] is about 1.2 X 10^-6, so that the number + of recombinations in unit time between n positive and n negative ions + in unit volume is 1.2 X 10^-6n^2. The kinetic theory of gases shows + that if we have n molecules of air per cubic centimetre, the number of + collisions per second is 1.2 X 10^-10n^2 at a temperature of 0 deg. C. + Thus we see that the number of recombinations between oppositely + charged ions is enormously greater than the number of collisions + between the same number of neutral molecules. We shall see that the + difference in size between the ion and the molecule is not nearly + sufficient to account for the difference between the collisions in the + two cases; the difference is due to the force between the oppositely + charged ions, which drags ions into collisions which but for this + force would have missed each other. + + Several methods have been used to measure [alpha]. In one method air, + exposed to some ionizing agent at one end of a long tube, is slowly + sucked through the tube and the saturation current measured at + different points along the tube. These currents are proportional to + the values of n at the place of observation: if we know the distance + of this place from the end of the tube when the gas was ionized and + the velocity of the stream of gas, we can find t in equation (3), and + knowing the value of n we can deduce the value of [alpha] from the + equation + + 1/n1 - 1/n2 = [alpha](t1 - t2), + + where n1, n2 are the values of n at the times t1, t2 respectively. In + this method the tubes ought to be so wide that the loss of ions by + diffusion to the sides of the tube is negligible. There are other + methods which involve the knowledge of the speed with which the ions + move under the action of known electric forces; we shall defer the + consideration of these methods until we have discussed the question of + these speeds. + + In measuring the value of [alpha] it should be remembered that the + theory of the methods supposes that the ionization is uniform + throughout the gas. If the total ionization throughout a gas remains + constant, but instead of being uniformly distributed is concentrated + in patches, it is evident that the ions will recombine more quickly in + the second case than in the first, and that the value of [alpha] will + be different in the two cases. This probably explains the large values + of [alpha] obtained by Retschinsky, who ionized the gas by the [alpha] + rays from radium, a method which produces very patchy ionization. + + _Variation of [alpha] with the Pressure of the Gas._--All observers + agree that there is little variation in [alpha] with the pressures for + pressures of between 5 and 1 atmospheres; at lower pressures, however, + the value of [alpha] seems to diminish with the pressure: thus + Langevin (_Ann. chim. phys._, 1903, 28, p. 287) found that at a + pressure of 1/5 of an atmosphere the value of [alpha] was about 1/5 of + its value at atmospheric pressure. + + _Variation of [alpha] with the Temperature._--Erikson (_Phil. Mag._, + Aug. 1909) has shown that the value of [alpha] for air increases as + the temperature diminishes, and that at the temperature of liquid air + -180 deg. C., it is more than twice as great as at +12 deg. C. + + Since, as we have seen, the recombination is due to the coming + together of the positive and negative ions under the influence of the + electrical attraction between them, it follows that a large electric + force sufficient to overcome this attraction would keep the ions apart + and hence diminish the coefficient of recombination. Simple + considerations, however, will show that it would require exceedingly + strong electric fields to produce an appreciable effect. The value of + [alpha] indicates that for two oppositely charged ions to unite they + must come within a distance of about 1.5 X 10^-6 centimetres; at this + distance the attraction between them is e^2 X 10^12/2.25, and if X is + the external electric force, the force tending to pull them apart + cannot be greater than Xe; if this is to be comparable with the + attraction, X must be comparable with e X 10^12/2.25, or putting e = 4 + X 10^-10, with 1.8 X 10^2; this is 54,000 volts per centimetre, a + force which could not be applied to gas at atmospheric pressure + without producing a spark. + + _Diffusion of the Ions._--The ionized gas acts like a mixture of + gases, the ions corresponding to two different gases, the non-ionized + gas to a third. If the concentration of the ions is not uniform, they + will diffuse through the non-ionized gas in such a way as to produce a + more uniform distribution. A very valuable series of determinations of + the coefficient of diffusion of ions through various gases has been + made by Townsend (_Phil. Trans._, 1900, A, 193, p. 129). The method + used was to suck the ionized gas through narrow tubes; by measuring + the loss of both the positive and negative ions after the gases had + passed through a known length of tube, and allowing for the loss by + recombination, the loss by diffusion and hence the coefficient of + diffusion could be determined. The following tables give the values of + the coefficients of diffusion D on the C.G.S. system of units as + determined by Townsend:-- + + Table I.--_Coefficients of Diffusion (D) in Dry Gases._ + + +-----+------------+------------+----------+------------------+ + |Gas. |D for +ions.|D for -ions.|Mean Value| Ratio of D for | + | | | | of D. | - to D for +ions.| + +-----+------------+------------+----------+------------------+ + | Air | .028 | .043 | .0347 | 1.54 | + | O2 | .025 | .0396 | .0323 | 1.58 | + | CO2 | .023 | .026 | .0245 | 1.13 | + | H2 | .123 | .190 | .156 | 1.54 | + +-----+------------+------------+----------+------------------+ + + Table II.--Coefficients of Diffusion in Moist Gases. + + +-----+------------+------------+----------+------------------+ + |Gas. |D for +ions.|D for -ions.|Mean Value| Ratio of D for | + | | | | of D. | - to D for +ions.| + +-----+------------+------------+----------+------------------+ + | Air | .032 | .037 | .0335 | 1.09 | + | O2 | .0288 | .0358 | .0323 | 1.24 | + | CO2 | .0245 | .0255 | .025 | 1.04 | + | H2 | .128 | .142 | .135 | 1.11 | + +-----+------------+------------+----------+------------------+ + + It is interesting to compare with these coefficients the values of D + when various gases diffuse through each other. D for hydrogen through + air is .634, for oxygen through air .177, for the vapour of isobutyl + amide through air .042. We thus see that the velocity of diffusion of + ions through air is much less than that of the simple gas, but that it + is quite comparable with that of the vapours of some complex organic + compounds. + + The preceding tables show that the negative ions diffuse more rapidly + than the positive, especially in dry gases. The superior mobility of + the negative ions was observed first by Zeleny (_Phil. Mag._, 1898 + [5], 46, p. 120), who showed that the velocity of the negative ions + under an electric force is greater than that of the positive. It will + be noticed that the difference between the mobility of the negative + and the positive ions is much more pronounced in dry gases than in + moist. The difference in the rates of diffusion of the positive and + negative ions is the reason why ionized gas, in which, to begin with, + the positive and negative charges were of equal amounts, sometimes + becomes electrified even although the gas is not acted upon by + electric forces. Thus, for example, if such gas be blown through + narrow tubes, it will be positively electrified when it comes out, for + since the negative ions diffuse more rapidly than the positive, the + gas in its passage through the tubes will lose by diffusion more + negative than positive ions and hence will emerge positively + electrified. Zeleny snowed that this effect does not occur when, as in + carbonic acid gas, the positive and negative ions diffuse at the same + rates. Townsend (loc. cit.) showed that the coefficient of diffusion + of the ions is the same whether the ionization is produced by Rontgen + rays, radioactive substances, ultra-violet light, or electric sparks. + The ions produced by chemical reactions and in flames are much less + mobile; thus, for example, Bloch (_Ann. chim. phys._, 1905 [8], 4, p. + 25) found that for the ions produced by drawing air over phosphorus + the value of [alpha]/e was between 1 and 6 instead of over 3000, the + value when the air was ionized by Rontgen rays. + +_Velocity of Ions in an Electric Field._--The velocity of ions in an +electric field, which is of fundamental importance in conduction, is +very closely related to the coefficient of diffusion. Measurements of +this velocity for ions produced by Rontgen rays have been made by +Rutherford (_Phil. Mag._ [5], 44, p. 422), Zeleny (_Phil. Mag._ [5], 46, +p. 120), Langevin (_Ann. Chim. Phys._, 1903, 28, p. 289), Phillips +(_Proc. Roy. Soc._ 78, A, p. 167), and Wellisch (_Phil. Trans._, 1909, +209, p. 249). The ions produced by radioactive substance have been +investigated by Rutherford (_Phil. Mag._ [5], 47, p. 109) and by Franck +and Pohl (_Verh. deutsch. phys. Gesell._, 1907, 9, p. 69), and the +negative ions produced when ultra-violet light falls on a metal plate by +Rutherford (_Proc. Camb. Phil. Soc._ 9, p. 401). H. A. Wilson (_Phil. +Trans._ 192, p. 4O9), Marx (_Ann. de Phys._ 11, p. 765), Moreau (_Journ. +de Phys._ 4, 11, p. 558; _Ann. Chim. Phys._ 7, 30, p. 5) and Gold +(_Proc. Roy. Soc._ 79, p. 43) have investigated the velocities of ions +produced by putting various salts into flames; McClelland (_Phil. Mag._ +46, p. 29) the velocity of the ions in gases sucked from the +neighbourhood of flames and arcs; Townsend (_Proc. Camb. Phil. Soc._ 9, +p. 345) and Bloch (_loc. cit._) the velocity of ions produced by +chemical reaction; and Chattock (_Phil. Mag._ [5], 48, p. 401) the +velocity of the ions produced when electricity escapes from a sharp +needle point into a gas. + +Several methods have been employed to determine these velocities. The +one most frequently employed is to find the electromotive intensity +required to force an ion against the stream of gas moving with a known +velocity parallel to the lines of electric force. Thus, of two +perforated plane electrodes vertically over each other, suppose the +lower to be positively, the upper negatively electrified, and suppose +that the gas is streaming vertically downwards with the velocity V; then +unless the upward velocity of the positive ion is greater than V, no +positive electricity will reach the upper plate. If we increase the +strength of the field between the plates, and hence the upward velocity +of the positive ion, until the positive ions just begin to reach the +upper plate, we know that with this strength of field the velocity of +the positive ion is equal to V. By this method, which has been used by +Rutherford, Zeleny and H. A. Wilson, the velocity of ions in fields of +various strengths has been determined. + + The arrangement used by Zeleny is represented in fig. 8. P and Q are + square brass plates. They are bored through their centres, and to the + openings the tubes R and S are attached, the space between the plates + being covered in so as to form a closed box. K is a piece of wire + gauze completely covering the opening in Q; T is an insulated piece of + wire gauze nearly but not quite filling the opening in the plate P, + and connected with one pair of quadrants of an electrometer E. A plug + of glass wool G filters out the dust from a stream of gas which enters + the vessel by the tube D and leaves it by F; this plug also makes the + velocity of the flow of the gas uniform across the section of the + tube. The Rontgen rays to ionize the gas were produced by a bulb at + O, the bulb and coil being in a lead-covered box, with an aluminium + window through which the rays passed. Q is connected with one pole of + a battery of cells, P and the other pole of the battery are put to + earth. The changes in the potential of T are due to ions giving up + their charges to it. With a given velocity of air-blast the potential + of T was found not to change unless the difference of potential + between P and Q exceeded a critical value. The field corresponding to + this critical value thus made the ions move with the known velocity of + the blast. + + [Illustration: FIG. 8.] + + [Illustration: FIG. 9.] + + Another method which has been employed by Rutherford and McClelland is + based on the action of an electric field in destroying the + conductivity of gas streaming through it. Suppose that BAB, DCD (fig. + 9) are a system of parallel plates boxed in so that a stream of gas, + after flowing between BB, passes between DD without any loss of gas in + the interval. Suppose the plates DD are insulated, and connected with + one pair of quadrants of an electrometer, by charging up C to a + sufficiently high potential we can drive all the positive ions which + enter the system DCD against the plates D; this will cause a deflexion + of the electrometer, which in one second will be proportional to the + number of positive ions which have entered the system in that time. If + we charge A up to a high potential, B being put to earth, we shall + find that the deflexion of the electrometer connected with DD is less + than it was when A and B were at the same potential, because some of + the positive ions in their passage through BAB are driven against the + plates B. If u is the velocity along the lines of force in the uniform + electric field between A and B, and t the time it takes for the gas to + pass through BAB, then all the positive ions within a distance ut of + the plates B will be driven up against these plates, and thus if the + positive ions are equally distributed through the gas, the number of + positive ions which emerge from the system when the electric field is + on will bear to the number which emerge when the field is off the + ratio of 1 - ut/l to unity, where l is the distance between A and B. + This ratio is equal to the ratio of the deflexions in one second of + the electrometer attached to D, hence the observations of this + instrument give 1 - ut/l. If we know the velocity of the gas and the + length of the plates A and B, we can determine t, and since l can be + easily measured, we can find u, the velocity of the positive ion in a + field of given strength. By charging A and C negatively instead of + positively we can arrive at the velocity of the negative ion. In + practice it is more convenient to use cylindrical tubes with coaxial + wires instead of the systems of parallel plates, though in this case + the calculation of the velocity of the ions from the observations is a + little more complicated, inasmuch as the electric field is not uniform + between the tubes. + + [Illustration: FIG. 10.] + + A method which gives very accurate results, though it is only + applicable in certain cases, is the one used by Rutherford to measure + the velocity of the negative ions produced close to a metal plate by + the incidence on the plate of ultra-violet light. The principle of the + method is as follows:--AB (fig. 10) is an insulated horizontal plate + of well-polished zinc, which can be moved vertically up and down by + means of a screw; it is connected with one pair of quadrants of an + electrometer, the other pair of quadrants being put to earth. CD is a + base-plate with a hole EF in it; this hole is covered with fine wire + gauze, through which ultra-violet light passes and falls on the plate + AB. The plate CD is connected with an alternating current dynamo, + which produces a simply-periodic potential difference between AB and + CD, the other pole being put to earth. Suppose that at any instant the + plate CD is at a higher potential than AB, then the negative ions from + AB will move towards CD, and will continue to do so as long as the + potential of CD is higher than that of AB. If, however, the potential + difference changes sign before the negative ions reach CD, these ions + will go back to AB. Thus AB will not lose any negative charge unless + the distance between the plates AB and CD is less than the distance + traversed by the negative ion during the time the potential of CD is + higher than that of AB. By altering the distance between the plates + until CD just begins to lose a negative charge, we find the velocity + of the negative ion under unit electromotive intensity. For suppose + the difference of potential between AB and CD is equal to a sin pt, + then if d is the distance between the plates, the electric intensity + is equal to a sin pt/d; if we suppose the velocity of the ion is + proportional to the electric intensity, and if u is the velocity for + unit electric intensity, the velocity of the negative ion will be ua + sin pt/d. Hence if x represent the distance of the ion from AB + + dx ua + --- = --- sin pt + dT d + + ua + x = ----(1 - cos pt), if x = 0 when t = 0. + pd + + Thus the greatest distance the ion can get from the plate is equal to + 2au/pd, and if the distance between the plates is gradually reduced to + this value, the plate AB will begin to lose a negative charge; hence + when this happens + + d = 2au/pd, or u = pd^2/2a, + + an equation by means of which we can find u. + + In this form the method is not applicable when ions of both signs are + present. Franck and Pohl (_Verh. deutsch. physik. Gesell._ 1907, 9, p. + 69) have by a slight modification removed this restriction. The + modification consists in confining the ionization to a layer of gas + below the gauze EF. If the velocity of the positive ions is to be + determined, these ions are forced through the gauze by applying to the + ionized gas a small constant electric force acting upwards; if + negative ions are required, the constant force is reversed. After + passing through the gauze the ions are acted upon by alternating + forces as in Rutherford's method. + + Langevin (_Ann. chim. phys._, 1903, 28, p. 289) devised a method of + measuring the velocity of the ions which has been extensively used; it + has the advantage of not requiring the rate of ionization to remain + uniform. The general idea is as follows. Suppose that we expose the + gas between two parallel plates A, B to Rontgen rays or some other + ionizing agent, then stop the rays and apply a uniform electric field + to the region between the plates. If the force on the positive ion is + from A to B, the plate B will receive a positive charge of + electricity. After the electric force has acted for a time T reverse + it. B will now begin to receive negative electricity and will go on + doing so until the supply of negative ions is exhausted. Let us + consider how the quantity of positive electricity received by B will + vary with T. To fix our ideas, suppose the positive ions move more + slowly than the negative; let T2 and T1 be respectively the times + taken by the positive and negative ions to move under the electric + field through a distance equal to AB, the distance between the planes. + Then if T is greater than T2 all the ions will have been driven from + between the plates before the field is reversed, and therefore the + positive charge received by B will not depend upon T. Next let T be + less than T2 but greater than T1; then at the time when the field is + reversed all the negative ions will have been driven from between the + plates, so that the positive charge received by B will not be + neutralized by the arrival of fresh ions coming to it after the + reversal of the field. The number of positive ions driven against the + plate B will be proportional to T. Thus if we measure the value of the + positive charge on B for a series of values of T, each value being + less than the preceding, we shall find that until T reaches a certain + value the charge remains constant, but as soon as we reduce the time + below this value the charge diminishes. The value of T when the + diminution in the field begins is T2, the time taken for a positive + ion to cross from A to B under the electric field; thus from T2 we can + calculate the velocity of the positive ion in this field. If we still + further diminish T, we shall find that we reach a value when the + diminution of the positive charge on B with the time suddenly becomes + much more rapid; this change occurs when T falls below T1 the time + taken for the negative ions to go from one plate to the other, for now + when the field is reversed there are still some negative ions left + between the plates, and these will be driven against B and rob it of + some of the positive charge it had acquired before the field was + reversed. By observing the time when the increase in the rate of + diminution of the positive charge with the time suddenly sets in we + can determine T1, and hence the velocity of the negative ions. + + The velocity of the ions produced by the discharge of electricity from + a fine point was determined by Chattock by an entirely different + method. In this case the electric field is so strong and the velocity + of the ion so great that the preceding methods are not applicable. + Suppose P represents a vertical needle discharging electricity into + air, consider the force acting on the ions included between two + horizontal planes A, B. If P is the density of the electrification, + and Z the vertical component of the electric intensity, F the + resultant force on the ions between A and B is vertical and equal to + _ _ _ + / / / + | | | Z[rho]dxdydz. + _/_/_/ + + Let us suppose that the velocity of the ion is proportional to the + electric intensity, so that if w is the vertical velocity of the ions, + which are supposed all to be of one sign, w = RZ. + + Substituting this value of Z, the vertical force on the ions between A + and B is equal to + _ _ _ + 1 / / / + - | | | w[rho]dxdydz. + R _/_/_/ + + But [integral][integral]w[rho]dxdy = [iota], where [iota] is the + current streaming from the point. This current, which can be easily + measured by putting a galvanometer in series with the discharging + point, is independent of z, the vertical distance of a plane between A + and B below the charging point. Hence we have + _ + [iota] / [iota] + F = ------ | dz = ------.z. + R _/ R + + This force must be counterbalanced by the difference of gaseous + pressures over the planes A and B; hence if pB and pA denote + respectively the pressures over B and A, we have + + [iota] + pB - pA = ------ z. + R + + Hence by the measurement of these pressures we can determine R, and + hence the velocity with which an ion moves under a given electric + intensity. + + There are other methods of determining the velocities of the ions, but + as these depend on the theory of the conduction of electricity through + a gas containing charged ions, we shall consider them in our + discussion of that theory. + + By the use of these methods it has been shown that the velocities of + the ions in a given gas are the same whether the ionization is + produced by Rontgen rays, radioactive substances, ultra-violet light, + or by the discharge of electricity from points. When the ionization is + produced by chemical action the ions are very much less mobile, moving + in the same electric field with a velocity less than one-thousandth + part of the velocity of the first kind of ions. On the other hand, as + we shall see later, the velocity of the negative ions in flames is + enormously greater than that of even the first kind of ion under + similar electric fields and at the same pressure. But when these + negative ions get into the cold part of the flame, they move + sluggishly with velocities of the order of those possessed by the + second kind. The results of the various determinations of the + velocities of the ions are given in the following table. The + velocities are in centimetres per second under an electric force of + one volt per centimetre, the pressure of the gas being 1 atmosphere. + V+ denotes the velocity of the positive ion, V- that of the negative. + V is the mean velocity of the positive and negative ions. + + _Velocities of Ions.--Ions produced by Rontgen Rays._ + + +----------------------+------+------+------+-----------------+ + | Gas. | V+. | V-. | V. | Observer. | + +----------------------+------+------+------+-----------------+ + | Air | .. | .. | 1.6 | Rutherford | + | Air (dry) | 1.36 | 1.87 | .. | Zeleny | + | " | 1.60 | 1.70 | .. | Langevin | + | " | 1.39 | 1.78 | .. | Phillips | + | " | 1.54 | 1.78 | .. | Wellisch | + | Air (moist) | 1.37 | 1.81 | .. | Zeleny | + | Oxygen (dry) | 1.36 | 1.80 | .. | " | + | Oxygen (moist) | 1.29 | 1.52 | .. | " | + | Carbonic acid (dry) | 0.76 | 0.81 | .. | " | + | " | 0.86 | 0.90 | .. | Langevin | + | " | 0.81 | 0.85 | .. | Wellisch | + | Carbonic acid (moist)| 0.82 | 0.75 | .. | Zeleny | + | Hydrogen (dry) | 6.70 | 7.95 | .. | " | + | Nitrogen | .. | .. | 1.6 | Rutherford | + | Sulphur dioxide | 0.44 | 0.41 | .. | Wellisch | + | Hydrochloric acid | .. | .. | 1.27 | Rutherford | + | Chlorine | .. | .. | 1.0 | " | + | Helium (dry) | 5.09 | 6.31 | .. | Franck and Pohl | + | Carbon monoxide | 1.10 | 1.14 | .. | Wellisch | + | Nitrous oxide | 0.82 | 0.90 | .. | " | + | Ammonia | 0.74 | 0.80 | .. | " | + | Aldehyde | 0.31 | 0.30 | .. | " | + | Ethyl alcohol | 0.34 | 0.27 | .. | " | + | Acetone | 0.31 | 0.29 | .. | " | + | Ethyl chloride | 0.33 | 0.31 | .. | " | + | Pentane | 0.36 | 0.35 | .. | " | + | Methyl acetate | 0.33 | 0.36 | .. | " | + | Ethyl formate | 0.30 | 0.31 | .. | " | + | Ethyl ether | 0.29 | 0.31 | .. | " | + | Ethyl acetate | 0.31 | 0.28 | .. | " | + | Methyl bromide | 0.29 | 0.28 | .. | " | + | Methyl iodide | 0.21 | 0.22 | .. | " | + | Carbon tetrachloride | 0.30 | 0.31 | .. | " | + | Ethyl iodide | 0.17 | 0.16 | .. | " | + +----------------------+------+------+------+-----------------+ + + _Ions produced by Ultra-Violet Light._ + + Air 1.4 Rutherford + Hydrogen 3.9 Rutherford + Carbonic acid 0.78 Rutherford + + _Ions in Gases sucked from Flames._ + + Velocities varying from .04 to .23 McClelland + + _Ions in Flames containing Salts._ + + Negative ions 12.9 cm./sec. Gold + +ions for salts of Li, Na, + K, Rb, Cs 62 H. A. Wilson + " 200 Marx + " 80 Moreau + + _Ions liberated by Chemical Action._ + + Velocities of the order of 0.0005 cm./sec. Bloch + + _Ions from Point Discharge._ + + +---------------+------+-------+------+----------+ + | Hydrogen | 5.4 | 7.43 | 6.41 | Chattock | + | Carbonic acid | 0.83 | 0.925 | 0.88 | Chattock | + | Air | 1.32 | 1.80 | 1.55 | Chattock | + | Oxygen | 1.30 | 1.85 | 1.57 | Chattock | + +---------------+------+-------+------+----------+ + + It will be seen from this table that the greater mobility of the + negative ions is very much more marked in the case of the lighter and + simpler gases than in that of the heavier and more complicated ones; + with the vapours of organic substances there seems but little + difference between the mobilities of the positive and negative ions, + indeed in one or two cases the positive one seems slightly but very + slightly the more mobile of the two. In the case of the simple gases + the difference is much greater when the gases are dry than when they + are moist. It has been shown by direct experiment that the velocities + are directly proportional to the electric force. + + _Variation of Velocities with Pressure._--Until the pressure gets low + the velocities of the ions, negative as well as positive, vary + inversely as the pressure. Langevin (loc. cit.) was the first to show + that at very low pressures the velocity of the negative ions increases + more rapidly as the pressure is diminished than this law indicates. If + the nature of the ion did not change with the pressure, the kinetic + theory of gases indicates that the velocity would vary inversely as + the pressure, so that Langevin's results indicate a change in the + nature of the negative ion when the pressure is diminished below a + certain value. Langevin's results are given in the following table, + where p represents the pressure measured in centimetres of mercury, V+ + and V- the velocities of the positive and negative ions in air under + unit electrostatic force, i.e. 300 volts per centimetre:-- + + +----------------------+----------------------+ + | Negative Ions. | Positive Ions. | + +-------+------+-------+-------+------+-------+ + | p. | V-. |pV-/76.| p. | V+. |pV+/76.| + +-------+------+-------+-------+------+-------+ + | 7.5 | 6560 | 647 | 7.5 | 4430 | 437 | + | 20.0 | 2204 | 580 | 20.0 | 1634 | 430 | + | 41.5 | 994 | 530 | 41.5 | 782 | 427 | + | 76.0 | 510 | 510 | 76.0 | 480 | 420 | + | 142.0 | 270 | 505 | 142.0 | 225 | 425 | + +-------+------+-------+-------+------+-------+ + + The increase in the case of pV- indicates that the structure of the + negative ion gets simpler as the pressure is reduced. Wallisch in some + experiments made at the Cavendish Laboratory found that the diminution + in the value of pV- at low pressures is much more marked in some gases + than in others, and in some gases he failed to detect it; but it must + be remembered that it is difficult to get measurements at pressures of + only a few millimetres, as the amount of ionization is so exceedingly + small at such pressures that the quantities to be observed are hardly + large enough to admit of accurate measurements by the methods + available at higher pressures. + + _Effect of Temperature on the Velocity of the Ions._--Phillips (_Proc. + Roy. Soc._, 1906, 78, p. 167) investigated, using Langevin's method, + the velocities of the + and - ions through air at atmospheric pressure + at temperatures ranging from that of boiling liquid air to 411 deg. + C.; R1 and R2 are the velocities of the + and - ions respectively when + the + + force is a volt per centimetre. + + +-------+-------+---------------------+ + | R1. | R2. |Temperature Absolute.| + +-------+-------+---------------------+ + | 2.00 | 2.495 | 411 deg. | + | 1.95 | 2.40 | 399 deg. | + | 1.85 | 2.30 | 383 deg. | + | 1.81 | 2.21 | 373 deg. | + | 1.67 | 2.125 | 348 deg. | + | 1.60 | 2.00 | 333 deg. | + | 1.39 | 1.785 | 285 deg. | + | 0.945 | 1.23 | 209 deg. | + | 0.235 | 0.235 | 94 deg. | + +-------+-------+---------------------+ + + We see that except in the case of the lowest temperature, that of + liquid air, where there is a great drop in the velocity, the + velocities of the ions are proportional to the absolute temperature. + On the hypothesis of an ion of constant size we should, from the + kinetic theory of gases, expect the velocity to be proportional to the + square root of the absolute temperature, if the charge on the ion did + not affect the number of collisions between the ion and the molecules + of the gas through which it is moving. If the collisions were brought + about by the electrical attraction between the ions and the molecules, + the velocity would be proportional to the absolute temperature. H. A. + Wilson (_Phil. Trans._ 192, p. 499), in his experiments on the + conduction of flames and hot gases into which salts had been put, + found that the velocity of the positive ions in flames at a + temperature of 2000 deg. C. containing the salts of the alkali metals + was 62 cm./sec. under an electric force of one volt per centimetre, + while the velocity of the positive ions in a stream of hot air at 1000 + deg. C. containing the same salts was only 7 cm./sec. under the same + force. The great effect of temperature is also shown in some + experiments of McClelland (_Phil. Mag._ [5], 46, p. 29) on the + velocities of the ions in gases drawn from Bunsen flames and arcs; he + found that these depended upon the distance the gas had travelled from + the flame. Thus, the velocity of the ions at a distance of 5.5 cm. + from the Bunsen flame when the temperature was 230 deg. C. was .23 + cm./sec. for a volt per centimetre; at a distance of 10 cm. from the + flame when the temperature was 160 deg. C. the velocity was .21 + cm./sec; while at a distance of 14.5 cm. from the flame when the + temperature was 105 deg. C. the velocity was only .04 cm./sec. If the + temperature of the gas at this distance from the flame was raised by + external means, the velocity of the ions increased. + + We can derive some information as to the constitution of the ions by + calculating the velocity with which a molecule of the gas would move + in the electric field if it carried the same charge as the ion. From + the theory of the diffusion of gases, as developed by Maxwell, we know + that if the particles of a gas A are surrounded by a gas B, then, if + the partial pressure of A is small, the velocity u with which its + particles will move when acted upon by a force Xe is given by the + equation + + Xe + u = ------- D, + (p1/N1) + + where D represents the coefficient of inter-diffusion of A into B, and + N1 the number of particles of A per cubic centimetre when the pressure + due to A is p1. Let us calculate by this equation the velocity with + which a molecule of hydrogen would move through hydrogen if it carried + the charge carried by an ion, which we shall prove shortly to be equal + to the charge carried by an atom of hydrogen in the electrolysis of + solutions. Since p1/N1 is independent of the pressure, it is equal to + [Pi]/N, where [Pi] is the atmospheric pressure and N the number of + molecules in a cubic centimetre of gas at atmospheric pressure. Now Ne + = 1.22 X 10^10, if e is measured in electrostatic units; [Pi] = 10^6 + and D in this case is the coefficient of diffusion of hydrogen into + itself, and is equal to 1.7. Substituting these values we find + + u = 1.97 X 10^4X. + + If the potential gradient is 1 volt per centimetre, X = 1/300. + Substituting this value for X, we find u = 66 cm./sec, for the + velocity of a hydrogen molecule. We have seen that the velocity of the + ion in hydrogen is only about 5 cm./sec, so that the ion moves more + slowly than it would if it were a single molecule. One way of + explaining this is to suppose that the ion is bigger than the + molecule, and is in fact an aggregation of molecules, the charged ion + acting as a nucleus around which molecules collect like dust round a + charged body. This view is supported by the effect produced by + moisture in diminishing the velocity of the negative ion, for, as C. + T. R. Wilson (_Phil. Trans._ 193, p. 289) has shown, moisture tends to + collect round the ions, and condenses more easily on the negative than + on the positive ion. In connexion with the velocities of ions in the + gases drawn from flames, we find other instances which suggest that + condensation takes place round the ions. An increase in the size of + the system is not, however, the only way by which the velocity might + fall below that calculated for the hydrogen molecule, for we must + remember that the hydrogen molecule, whose coefficient of diffusion is + 1.7, is not charged, while the ion is. The forces exerted by the ion + on the other molecules of hydrogen are not the same as those which + would be exerted by a molecule of hydrogen, and as the coefficient of + diffusion depends on the forces between the molecules, the coefficient + of diffusion of a charged molecule into hydrogen might be very + different from that of an uncharged one. + + Wellisch (_loc. cit._) has shown that the effect of the charge on the + ion is sufficient in many cases to explain the small velocity of the + ions, even if there were no aggregation. + + _Mixture of Gases._--The ionization of a mixture of gases raises some + very interesting questions. If we ionize a mixture of two very + different gases, say hydrogen and carbonic acid, and investigate the + nature of the ions by measuring their velocities, the question arises, + shall we find two kinds of positive and two kinds of negative ions + moving with different velocities, as we should do if some of the + positive ions were positively charged hydrogen molecules, while others + were positively charged molecules of carbonic acid; or shall we find + only one velocity for the positive ions and one for the negative? Many + experiments have been made on the velocity of ions in mixtures of two + gases, but as yet no evidence has been found of the existence of two + different kinds of either positive or negative ions in such mixtures, + although some of the methods for determining the velocities of the + ions, especially Langevin's, ought to give evidence of this effect, if + it existed. The experiments seem to show that the positive (and the + same is true for the negative) ions in a mixture of gases are all of + the same kind. This conclusion is one of considerable importance, as + it would not be true if the ions consisted of single molecules of the + gas from which they are produced. + + _Recombination._--Several methods enable us to deduce the coefficient + of recombination of the ions when we know their velocities. Perhaps + the simplest of these consists in determining the relation between the + current passing between two parallel plates immersed in ionized gas + and the potential difference between the plates. For let q be the + amount of ionization, i.e. the number of ions produced per second per + unit volume of the gas, A the area of one of the plates, and d the + distance between them; then if the ionization is constant through the + volume, the number of ions of one sign produced per second in the gas + is qAd. Now if i is the current per unit area of the plate, e the + charge on an ion, iA/e ions of each sign are driven out of the gas by + the current per second. In addition to this source of loss of ions + there is the loss due to the recombination; if n is the number of + positive or negative ions per unit volume, then the number which + recombine per second is [alpha]n^2 per cubic centimetre, and if n is + constant through the volume of the gas, as will approximately be the + case if the current through the gas is only a small fraction of the + saturation current, the number of ions which disappear per second + through recombination is [alpha]n^2.Ad. Hence, since when the gas is + in a steady state the number of ions produced must be equal to the + number which disappear, we have + + qAd = iA/e + [alpha]n^2.Ad, + q = i/ed + [alpha]^n2. + + If u1 and u2 are the velocities with which the positive and negative + ions move, nu1e and nu2e are respectively the quantities of positive + electricity passing in one direction through unit area of the gas per + second, and of negative in the opposite direction, hence + + i = nu1e + nu2e. + + If X is the electric force acting on the gas, k1 and k2 the velocities + of the positive and negative ions under unit force, u1 = k1X, u2 = + k2X; hence + + n = i/(k1 + k2)Xe, + + and we have + + i [alpha]i^2 + q = -- + -----------------. + ed (k1 + k2)^2e^2X^2 + + But qed is the saturation current per unit area of the plate; calling + this I, we have + + d[alpha]i^2 + I - i = --------------- + e(k1 + k2)^2X^2 + + or + + i^2.d[alpha] + X^2 = -------------------. + e(I - i)(k1 + k2)^2 + + Hence if we determine corresponding values of X and i we can deduce + the value of [alpha]/e if we also know (k1 + k2). The value of I is + easily determined, as it is the current when X is very large. The + preceding result only applies when i is small compared with I, as it + is only in this case that the values of n and X are uniform throughout + the volume of the gas. Another method which answers the same purpose + is due to Langevin (_Ann. Chim. Phys._, 1903, 28, p. 289); it is as + follows. Let A and B be two parallel planes immersed in a gas, and let + a slab of the gas bounded by the planes a, b parallel to A and B be + ionized by an instantaneous flash of Rontgen rays. If A and B are at + different electric potentials, then all the positive ions produced by + the rays will be attracted by the negative plate and all the negative + ions by the positive, if the electric field were exceedingly large + they would reach these plates before they had time to recombine, so + that each plate would receive N0 ions if the flash of Rontgen rays + produced N0 positive and N0 negative ions. With weaker fields the + number of ions received by the plates will be less as some of them + will recombine before they can reach the plates. We can find the + number of ions which reach the plates in this case in the following + way:--In consequence of the movement of the ions the slab of ionized + gas will broaden out and will consist of three portions, one in which + there are nothing but positive ions,--this is on the side of the + negative plate,--another on the side of the positive plate in which + there are nothing but negative ions, and a portion between these in + which there are both positive and negative ions; it is in this layer + that recombination takes place, and here if n is the number of + positive or negative ions at the time t after the flash of Rontgen + rays, + + n = n0/(1 + [alpha]n0t). + + With the same notation as before, the breadth of either of the outer + layers will in time dt increase by X(k1 + k2)dt, and the number of ions + in it by X(k1 + k2)ndt; these ions will reach the plate, the outer + layers will receive fresh ions until the middle one disappears, which + it will do after a time l/X(k1 + k2), where l is the thickness of the + slab ab of ionized gas; hence N, the number of ions reaching either + plate, is given by the equation + _ + / l/X(k1+k2) n0X(k1 + k2) X(k1 + k2) / n0[alpha]l \ + N = | --------------dt = ---------- log( 1 + ---------- ). + _/ 0 1 + n0[alpha]t [alpha] \ X(k1 + k2) / + + + If Q is the charge received by the plate, + + X / Q0[epsilon]\ + Q = Ne = -------------- log ( 1 + ----------- ), + 4[pi][epsilon] \ 4[pi]X / + + where Q0 = n0le is the charge received by the plate when the electric + force is large enough to prevent recombination, and [epsilon] = + [alpha]4[pi]e(R1 + R2). We can from this result deduce the value of + [epsilon] and hence the value of [alpha] when R1+R2 is known. + + _Distribution of Electric Force when a Current is passing through an + Ionized Gas._--Let the two plates be at right angles to the axis of x; + then we may suppose that between the plates the electric intensity X + is everywhere parallel to the axis of x. The velocities of both the + positive and negative ions are assumed to be proportional to X. Let + k1X, k2X represent these velocities respectively; let n1, n2 be + respectively the number of positive and negative ions per unit volume + at a point fixed by the co-ordinate x; let q be the number of positive + or negative ions produced in unit time per unit volume at this point; + and let the number of ions which recombine in unit volume in unit time + be [alpha]n1n2; then if e is the charge on the ion, the volume density + of the electrification is (n1 - n2)e, hence + + dX + -- = 4[pi](n1 - n2)e (1). + dx + + If I is the current through unit area of the gas and if we neglect any + diffusion except that caused by the electric field, + + n1ek1X + n2ek2X = I (2). + + From equations (1) and (2) we have + + 1 / I k2 dX \ + n1e = ------- ( - + ----- -- ) (3), + k1 + k2 \ X 4[pi] dx / + + 1 / I k1 dX \ + n2e = ------- ( - - ----- -- ) (4), + k1 + k2 \ X 4[pi] dx / + + and from these equations we can, if we know the distribution of + electric intensity between the plates, calculate the number of + positive and negative ions. + + In a steady state the number of positive and negative ions in unit + volume at a given place remains constant, hence neglecting the loss by + diffusion, we have + + d + --(k1n1X) = q - [alpha]n1n2 (5). + dx + + d + - --(k2n2X) = q - [alpha]n1n2 (6). + dx + + If k1 and K2 are constant, we have from (1), (5) and (6) + + d^2X^2 / 1 1 \ + ------ = 8[pi]e(q - [alpha]n1n2)( --- + --- ) (7), + dx^2 \ k1 k2 / + + an equation which is very useful, because it enables us, if we know + the distribution of X^2, to find whether at any point in the gas the + ionization is greater or less than the recombination of the ions. We + see that q - [alpha]n1n2, which is the excess of ionization over + recombination, is proportional to d^2X^2/dx^2. Thus when the ionization + exceeds the recombination, i.e. when q - [alpha]n1n2 is positive, the + curve for X^2 is convex to the axis of x, while when the recombination + exceeds the ionization the curve for X^2 will be concave to the axis of + x. Thus, for example, fig. 11 represents the curve for X^2 observed by + Graham (_Wied. Ann._ 64, p. 49) in a tube through which a steady + current is passing. Interpreting it by equation (7), we infer that + ionization was much in excess of recombination at A and B, slightly so + along C, while along D the recombination exceeded the ionization. + Substituting in equation (7) the values of n1, n2 given in (3), (4), + we get + _ _ + d^2X^2 | [alpha] / k^2 dX^2\ / k2 dX^2\ | / 1 1 \ + ------ = 8[pi]e |q - ----------------- (1 + ----- ---- ) (1 - ----- ---- )| ( --- + --- ) (8). + dx^2 |_ e^2X^2(k1 + k2)^2 \ 8[pi] dx / \ 8[pi] dx /_| \k1 k2 / + + [Illustration: Fig. 11.] + + This equation can be solved (see Thomson, _Phil. Mag._ xlvii. P. 253), + when q is constant and k1 = k2. From the solution it appears that if + X1 be the value of x close to one of the plates, and X0 the value + midway between them, + + 1 + X1/X0 = ------------------- + [beta]^2 - 2/[beta] + + where [beta] = 8[pi]ek1/[alpha]. + + + Since e = 4 X 10^-10, [alpha] = 2X10^-6, and k1 for air at atmospheric + pressure = 450, [beta] is about 2.3 for air at atmospheric pressure + and it becomes much greater at lower pressures. + + Thus X1/X0 is always greater than unity, and the value of the ratio + increases from unity to infinity as [beta] increases from zero to + infinity. As [beta] does not involve either q or I, the ratio of X1 to + X0 is independent of the strength of the current and of the intensity + of the ionization. + + No general solution of equation (8) has been found when k1 is not + equal to k2, but we can get an approximation to the solution when q is + constant. The equations (1), (2), (3), (4) are satisfied by the + values-- + + n1 = n2 = (q / [alpha])^1/2 + + k1 + k1n1Xe = ------- I, + k1 + k2 + + k2 + k2n2Xe = ------- I, + k1 + k2 + + + /[alpha]\^1/2 I + X = ( ------- ) ----------. + \ q / e(k1 + k2) + + These solutions cannot, however, hold right up to the surface of the + plates, for across each unit of area, at a point P, k1I/(k1+k2)e + positive ions pass in unit time, and these must all come from the + region between P and the positive plate. If [lambda] is the distance + of P from this plate, this region cannot furnish more than q[lambda] + positive ions, and only this number if there are no recombinations. + Hence the solution cannot hold when q[lambda] is less than k1I/(k1 + + k2)e, or where [lambda] is less than k1I/(k1 + k2)qe. + + Similarly the solution cannot hold nearer to the negative plate than + the distance k2I/(k1 + k2)qe. + + [Illustration: FIG. 12.] + + The force in these layers will be greater than that in the middle of + the gas, and so the loss of ions by recombination will be smaller in + comparison with the loss due to the removal of the ions by the + current. If we assume that in these layers the loss of ions by + recombination can be neglected, we can by the method of the next + article find an expression for the value of the electric force at any + point in the layer. This, in conjunction with the value + + /[alpha]\^1/2 I + X0 = ( ------- ) ---------- + \ q / e(k1 + k2) + + for the gas outside the layer, will give the value of X at any point + between the plates. It follows from this investigation that if X1 and + X2 are the values of X at the positive and negative plates + respectively, and X0 the value of X outside the layer, + + / k1 I \^1/2 / k2 I \^1/2 + X1 = X0 ( I + -- --------- ) , X2 = X0 ( I + -- --------- ) , + \ k2 [epsilon]/ \ k1 [epsilon]/ + + where [epsilon] = [alpha]/4[pi]e(k1 + k2). Langevin found that for air + at a pressure of 152 mm. [epsilon] = 0.01, at 375 mm. [epsilon] = + 0.06, and at 760 mm. [epsilon] = 0.27. Thus at fairly low pressures + 1/[epsilon] is large, and we have approximately + + /k1\^1/2 I /k2\^1/2 I + X1 = X0 ( -- ) ---------------, X2 = X0 ( -- ) ---------------. + \k2/ [root][epsilon] \k1/ [root][epsilon] + + Therefore X1/X2 = k1/k2, + + or the force at the positive plate is to that at the negative plate as + the velocity of the positive ion is to that of the negative ion. Thus + the force at the negative plate is greater than that at the positive. + The falls of potential V1, V2 at the two layers when 1/[epsilon] is + large can be shown to be given by the equations + + /[epsilon]\^3/2 /k1\^1/2 + V1 = 8[pi]^2( --------- ) k1 ( -- ) i^2, + \q [alpha]/ \k2/ + + /[epsilon]\^3/2 /k2\^1/2 + V2 = 8[pi]^2( --------- ) k2 ( -- ) i^2, + \q [alpha]/ \k1/ + + hence V1/V2 = k1^2/k2^2, + + so that the potential falls at the electrodes are proportional to the + squares of the velocities of the ions. The change in potential across + the layers is proportional to the square of the current, while the + potential change between the layers is proportional to the current, + the total potential difference between the plates is the sum of these + changes, hence the relation between V and i will be of the form + + V = Ai + Bi^2. + + Mie (_Ann. der. Phys._, 1904, 13, P. 857) has by the method of + successive approximations obtained solutions of equation (8) (i.) when + the current is only a small fraction of the saturation current, (ii.) + when the current is nearly saturated. The results of his + investigations are represented in fig. 12, which represents the + distribution of electric force along the path of the current for + various values of the current expressed as fractions of the saturation + current. It will be seen that until the current amounts to about + one-fifth of the maximum current, the type of solution is the one just + indicated, i.e. the electric force is constant except in the + neighbourhood of the electrodes when it increases rapidly. + + Though we are unable to obtain a general solution of the equation (8), + there are some very important special cases in which that equation can + be solved without difficulty. We shall consider two of these, the + first being that when the current is saturated. In this case there is + no loss of ions by recombination, so that using the same notation as + before we have + + d + --(n1k1X) = q, + dx + + d + --(n2k2X) = -q. + dx + + The solutions of which if q is constant are + + n1k1X = qx, + + n2k2X = I/e - qx = q(l - x), + + if l is the distance between the plates, and x = 0 at the positive + electrode. Since + + dX/dx = 4[pi](n1 - n2)e, + + we get + + 1 dX^2 / 1 1 \ l + ----- ---- = qx ( -- + -- ) - q --, + 8[pi] d^2x \k1 k2 / k2 + + or + + X^2 x^2 / 1 1 \ lx + ----- = q --- ( -- + -- ) - q -- + C, + 8[pi] 2 \k1 k2 / k2 + + where C is a quantity to be determined by the condition that + + _ + / l + | Xdx = V, + _/0 + + + where V is the given potential difference between the plates. When the + force is a minimum dX/dx = 0, hence at this point + + lk1 lk2 + x = -------, l - x = -------. + k1 + k2 k1 + k2 + + Hence the ratio of the distances of this point from the positive and + negative plates respectively is equal to the ratio of the velocities + of the positive and negative ions. + + The other case we shall consider is the very important one in which + the velocity of the negative ion is exceedingly large compared with + the positive; this is the case in flames where, as Gold (_Proc. Roy. + Soc._ 97, p. 43) has shown, the velocity of the negative ion is many + thousand times the velocity of the positive; it is also very probably + the case in all gases when the pressure is low. We may get the + solution of this case either by putting k1/k2 = 0 in equation (8), or + independently as follows:--Using the same notation as before, we have + + i = n1k1Xe + n2k2Xe, + + d + --(n2k2X) = q - [alpha]n1n2, + dx + + dX + -- = 4[pi](n1 - n2)e. + dx + + In this case practically all the current is carried by the negative + ions so that i = n2k2Xe, and therefore q = [alpha]n1n2. + + Thus + + n2 = i/k2Xe, n1 = qk2Xe/[alpha]i. + + Thus + + dX 4[pi]e^2k2qX 4[pi]i + -- = ------------ - ------, + dx [alpha]i k2X + + or + + dX^2 8[pi]e^2k2qX^2 8[pi]i + ---- - -------------- = - ------. + dx [alpha]i k2 + + The solution of this equation is + + [alpha] i^2 + X^2 = ------- ------- + C[epsilon]^(8[pi]e^2k2qx/[alpha]i) + q k2^2e^2 + + Here x is measured from the positive electrode; it is more convenient + in this case, however, to measure it from the negative electrode. If x + be the distance from the negative electrode at which the electric + force is X, we have from equation (7) + + [alpha] i^2 + X^2 = ------- ------- + C^1[epsilon]^(8[pi]e^2k2qx/[alpha]i) + q k2^2e^2 + + To find the value of C^1 we see by equation (7) that + + d^2X^2 k1k2 1 + ------ ------- ------ = q - [alpha]n1n2; + dX^2 k1 + k2 8[pi]e + + hence + _ _ _ + | dX^2 k1k2 1 |^x1 / x1 + | ---- ------- ------ | = | (q - [alpha]n1n2)dx. + |_ dX k1 + k2 8[pi]e_| _/0 + + The right hand side of this equation is the excess of ionization over + recombination in the region extending from the cathode to x1; it must + therefore, when things are in a steady state, equal the excess of the + number of negative ions which leave this region over those which enter + it. The number which leave is i/e and the number which enter is i0/e, + if it is the current of negative ions coming from unit area of the + cathode, as hot metal cathodes emit large quantities of negative + electricity i0 may in some cases be considerable, thus the right hand + side of equation is (i - i0)/e. When x1 is large dX^2/dx = 0; hence we + have from equation + + [alpha]i(i - i0) k1 + k2 + C^1 = ---------------- -------, + qk1k2e^2 k2 + + and since k1 is small compared with k2, we have + + [alpha]i^2 / k2 i - i0 \ + X^2 = ---------- (1 + -- ------ [epsilon]^{-8[pi]e^2k2.qx/[alpha].i}). + qk2^2e^2 \ k1 i / + + From the values which have been found for k2 and [alpha], we know that + 8[pi]ek2/[alpha] is a large quantity, hence the second term inside the + bracket will be very small when eqx is equal to or greater than i; + thus this term will be very small outside a layer of gas next the + cathode of such thickness that the number of ions produced on it would + be sufficient, if they were all utilized for the purpose, to carry the + current; in the case of flames this layer is exceedingly thin unless + the current is very large. The value of the electric force in the + uniform part of the field is equal to i/k2e.[root]([alpha]/q), while + when i0 = 0, the force at the cathode itself bears to the uniform + force the ratio of (k1 + k2)^1/2 to k1^1/2. As k1 is many thousand + times k2 the force increases with great rapidity as we approach the + cathode; this is a very characteristic feature of the passage of + electricity through flames and hot gases. Thus in an experiment made + by H. A. Wilson with a flame 18 cm. long, the drop of potential within + 1 centimetre of the cathode was about five times the drop in the other + 17 cm. of the tube. The relation between the current and the potential + difference when the velocity of the negative ion is much greater than + the positive is very easily obtained. Since the force is uniform and + equal to i/k2e.[root]([alpha]/q), until we get close to the cathode + the fall of potential in this part of the discharge will be very + approximately equal to i/k2e.[root]([alpha]l/q), where l is the + distance between the electrodes. Close to the cathode, the electric + force when i0 is not nearly equal to i is approximately given by the + equation + + i /[alpha]\^1/2 + X = --------- (---------) [epsilon]^{-4[pi]e^2k2qx/[alpha]i}, + e(k1k2)^1/2 \ q / , + + and the fall of potential at the cathode is equal approximately to + + _[oo] + / + | X dx, + _/0 + + that is to + + i /[alpha]\^1/2 [alpha]i + --------- (---------) -----------. + e(k1k2)^1/2 \ q / 4[pi]e^2k2q + + The potential difference between the plates is the sum of the fall of + potential in the uniform part of the discharge plus the fall at the + cathode, hence + + /[alpha]\^1/2 i / i[alpha]^2 1 \ + V = (---------) --- ( il + ---------- ------------ ). + \ q / ek2 \ 4[pi]e^2q [root](k1k2)/ + + The fall of potential at the cathode is proportional to the square of + the current, while the fall in the rest of the circuit is directly + proportional to the current. In the case of flames or hot gases, the + fall of potential at the cathode is much greater than that in the rest + of the circuit, so that in such cases the current through the gas + varies nearly as the square root of the potential difference. The + equation we have just obtained is of the form + + V = Ai + Bi^2, + + and H. A. Wilson has shown that a relation of this form represents the + results of his experiments on the conduction of electricity through + flames. + + The expression for the fall of potential at the cathode is inversely + proportional to q^(3/2), q being the number of ions produced per cubic + centimetre per second close to the cathode; thus any increase in the + ionization at the cathode will diminish the potential fall at the + cathode, and as practically the whole potential difference between the + electrodes occurs at the cathode, a diminution in the potential fall + there will be much more important than a diminution in the electric + force in the uniform part of the discharge, when the force is + comparatively insignificant. This consideration explains a very + striking phenomenon discovered many years ago by Hittorf, who found + that if he put a wire carrying a bead of a volatile salt into the + flame, it produced little effect upon the current, unless it were + placed close to the cathode where it gave rise to an enormous increase + in the current, sometimes increasing the current more than a + hundredfold. The introduction of the salt increases very largely the + number of ions produced, so that q is much greater for a salted flame + than for a plain one. Thus Hittorf's result coincides with the + conclusions we have drawn from the theory of this class of conduction. + + The fall of potential at the cathode is proportional to i - i0, where + i0 is the stream of negative electricity which comes from the cathode + itself, thus as i0 increases the fall of potential at the cathode + diminishes and the current sent by a given potential difference + through the gas increases. Now all metals give out negative particles + when heated, at a rate which increases very rapidly with the + temperature, but at the same temperature some metals give out more + than others. If the cathode is made of a metal which emits large + quantities of negative particles, (i - i0) will for a given value of i + be smaller than if the metal only emitted a small number of + particles; thus the cathode fall will be smaller for the metal with + the greater emissitivity, and the relation between the potential + difference and the current will be different in the two cases. These + considerations are confirmed by experience, for it has been found that + the current between electrodes immersed in a flame depends to a great + extent upon the metal of which the electrodes are made. Thus + Pettinelli (_Acc. dei Lincei_ [5], v. p. 118) found that, _ceteris + paribus_, the current between two carbon electrodes was about 500 + times that between two iron ones. If one electrode was carbon and the + other iron, the current when the carbon was cathode and the iron anode + was more than 100 times the current when the electrodes were reversed. + The emission of negative particles by some metallic oxides, notably + those of calcium and barium, has been shown by Wehnelt (_Ann. der + Phys._ 11, p. 425) to be far greater than that of any known metal, and + the increase of current produced by coating the cathodes with these + oxides is exceedingly large; in some cases investigated by Tufts and + Stark (_Physik. Zeits._, 1908, 5, p. 248) the current was increased + many thousand times by coating the cathode with lime. No appreciable + effect is produced by putting lime on the anode. + + _Conduction when all the Ions are of one Sign._--There are many + important cases in which the ions producing the current come from one + electrode or from a thin layer of gas close to the electrode, no + ionization occurring in the body of the gas or at the other electrode. + Among such cases may be mentioned those where one of the electrodes is + raised to incandescence while the other is cold, or when the negative + electrode is exposed to ultra-violet light. In such cases if the + electrode at which the ionization occurs is the positive electrode, + all the ions will be positively charged, while if it is the negative + electrode the ions will all be charged negatively. The theory of this + case is exceedingly simple. Suppose the electrodes are parallel planes + at right angles to the axis of x; let X be the electric force at a + distance x from the electrode where the ionization occurs, n the + number of ions (all of which are of one sign) at this place per cubic + centimetre, k the velocity of the ion under unit electric force, e the + charge on an ion, and i the current per unit area of the electrode. + Then we have dX/dx = 4[pi]ne, and if u is the velocity of the ion neu + = i. But u = kX, hence we have kX/4[pi] . dX/dx = i, and since the + right hand side of this equation does not depend upon x, we get + kX^2/8[pi] = ix + C, where C is a constant to be determined. If l is + the distance between the plates, and V the potential difference + between them, + _ _____ _ _ + / l 1 /8[pi] | | + V = | Xdx = --- / ----- | ( il + C )^3/2 - C^3/2 |. + _/0 i \/ k |_ _| + + We shall show that when the current is far below the saturation value, + C is very small compared with il, so that the preceding equation + becomes + + V^2 = 8[pi]l^3i/k (1). + + To show that for small currents C is small compared with il, consider + the case when the ionization is confined to a thin layer, thickness d + close to the electrode, in that layer let n0 be the value of n, then + we have q = [alpha]n0^2 + i/ed. If X0 be the value of X when x = 0, + kX0n0e = i, and, + + kX0^2 i^2 [alpha] i^2 + C = ----- = ------------ = --------- . -------- (2). + 8[pi] n0^2ke.8[pi] 8[pi]ke^2 q + i/ed + + Since [alpha]/8[pi]ke is, as we have seen, less than unity, C will be + small compared with il, if i/(eq + i/d) is small compared with l. If + I0 is the saturation current, q = I0/ed, so that the former expression + = id/(I0 + i), if i is small compared with I0, this expression is + small compared with d, and therefore _a fortiori_ compared with l, so + that we are justified in this case in using equation (1). + + From equation (2) we see that the current increases as the square of + the potential difference. Here an increase in the potential difference + produces a much greater percentage increase than in conduction through + metals, where the current is proportional to the potential difference. + When the ionization is distributed through the gas, we have seen that + the current is approximately proportional to the square root of the + potential, and so increases more slowly with the potential difference + than currents through metals. From equation (1) the current is + inversely proportional to the cube of the distance between the + electrodes, so that it falls off with great rapidity as this distance + is increased. We may note that for a given potential difference the + expression for the current does not involve q, the rate of production + of the ions at the electrode, in other words, if we vary the + ionization the current will not begin to be affected by the strength + of the ionization until this falls so low that the current is a + considerable fraction of the saturation current. For the same + potential difference the current is proportional to k, the velocity + under unit electric force of the ion which carries the current. As the + velocity of the negative ion is greater than that of the positive, the + current when the ionization is confined to the neighbourhood of one of + the electrodes will be greater when that electrode is made cathode + than when it is anode. Thus the current will appear to pass more + easily in one direction than in the opposite. + + Since the ions which carry the current have to travel all the way from + one electrode to the other, any obstacle which is impervious to these + ions will, if placed between the electrodes, stop the current to the + electrode where there is no ionization. A plate of metal will be as + effectual as one made of a non-conductor, and thus we get the + remarkable result that by interposing a plate of an excellent + conductor like copper or silver between the electrode, we can entirely + stop the current. This experiment can easily be tried by using a hot + plate as the electrode at which the ionization takes place: then if + the other electrode is cold the current which passes when the hot + plate is cathode can be entirely stopped by interposing a cold metal + plate between the electrodes. + +_Methods of counting the Number of Ions._--The detection of the ions and +the estimation of their number in a given volume is much facilitated by +the property they possess of promoting the condensation of water-drops +in dust-free air supersaturated with water vapour. If such air contains +no ions, then it requires about an eightfold supersaturation before any +water-drops are formed; if, however, ions are present C. T. R. Wilson +(_Phil. Trans._ 189, p. 265) has shown that a sixfold supersaturation is +sufficient to cause the water vapour to condense round the ions and to +fall down as raindrops. The absence of the drops when no ions are +present is due to the curvature of the drop combined with the surface +tension causing, as Lord Kelvin showed, the evaporation from a small +drop to be exceeding rapid, so that even if a drop of water were formed +the evaporation would be so great in its early stages that it would +rapidly evaporate and disappear. It has been shown, however (J. J. +Thomson, _Application of Dynamics to Physics and Chemistry_, p. 164; +_Conduction of Electricity through Gases_, 2nd ed. p. 179), that if a +drop of water is charged with electricity the effect of the charge is to +diminish the evaporation; if the drop is below a certain size the effect +the charge has in promoting condensation more than counterbalances the +effect of the surface tension in promoting evaporation. Thus the +electric charge protects the drop in the most critical period of its +growth. The effect is easily shown experimentally by taking a bulb +connected with a piston arranged so as to move with great rapidity. When +the piston moves so as to increase the volume of the air contained in +the bulb the air is cooled by expansion, and if it was saturated with +water vapour before it is supersaturated after the expansion. By +altering the throw of the piston the amount of supersaturation can be +adjusted within very wide limits. Let it be adjusted so that the +expansion produces about a sixfold supersaturation; then if the gas is +not exposed to any ionizing agents very few drops (and these probably +due to the small amount of ionization which we have seen is always +present in gases) are formed. If, however, the bulb is exposed to strong +Rontgen rays expansion produces a dense cloud which gradually falls down +and disappears. If the gas in the bulb at the time of its exposure to +the Rontgen rays is subject to a strong electric field hardly any cloud +is formed when the gas is suddenly expanded. The electric field removes +the charged ions from the gas as soon as they are formed so that the +number of ions present is greatly reduced. This experiment furnishes a +very direct proof that the drops of water which form the cloud are only +formed round the ions. + +This method gives us an exceedingly delicate test for the presence of +ions, for there is no difficulty in detecting ten or so raindrops per +cubic centimetre; we are thus able to detect the presence of this number +of ions. This result illustrates the enormous difference between the +delicacy of the methods of detecting ions and those for detecting +uncharged molecules; we have seen that we can easily detect ten ions per +cubic centimetre, but there is no known method, spectroscopic or +chemical, which would enable us to detect a billion (10^12) times this +number of uncharged molecules. The formation of the water-drops round +the charged ions gives us a means of counting the number of ions present +in a cubic centimetre of gas; we cool the gas by sudden expansion until +the supersaturation produced by the cooling is sufficient to cause a +cloud to be formed round the ions, and the problem of finding the number +of ions per cubic centimetre of gas is thus reduced to that of finding +the number of drops per cubic centimetre in the cloud. Unless the drops +are very few and far between we cannot do this by direct counting; we +can, however, arrive at the result in the following way. From the amount +of expansion of the gas we can calculate the lowering produced in its +temperature and hence the total quantity of water precipitated. The +water is precipitated as drops, and if all the drops are the same size +the number per cubic centimetre will be equal to the volume of water +deposited per cubic centimetre, divided by the volume of one of the +drops. Hence we can calculate the number of drops if we know their size, +and this can be determined by measuring the velocity with which they +fall under gravity through the air. + + The theory of the fall of a heavy drop of water through a viscous + fluid shows that v = (2/9)ga^2/[mu], where a is the radius of the drop, + g the acceleration due to gravity, and [mu] the coefficient of + viscosity of the gas through which the drop falls. Hence if we know v + we can deduce the value of a and hence the volume of each drop and the + number of drops. + + _Charge on Ion._--By this method we can determine the number of ions + per unit volume of an ionized gas. Knowing this number we can proceed + to determine the charge on an ion. To do this let us apply an electric + force so as to send a current of electricity through the gas, taking + care that the current is only a small fraction of the saturating + current. Then if u is the sum of the velocities of the positive and + negative ions produced in the electric field applied to the gas, the + current through unit area of the gas is neu, where n is the number of + positive or negative ions per cubic centimetre, and e the charge on an + ion. We can easily measure the current through the gas and thus + determine neu; we can determine n by the method just described, and u, + the velocity of the ions under the given electric field, is known from + the experiments of Zeleny and others. Thus since the product neu, and + two of the factors n, u are known, we can determine the other factor + e, the charge on the ion. This method was used by J. J. Thomson, and + details of the method will be found in _Phil. Mag._ [5], 46, p. 528; + [5], 48, p. 547; [6], 5, p. 346. The result of these measurements + shows that the charge on the ion is the same whether the ionization is + by Rontgen rays or by the influence of ultra-violet light on a metal + plate. It is the same whether the gas ionized is hydrogen, air or + carbonic acid, and thus is presumably independent of the nature of the + gas. The value of e formed by this method was 3.4 X 10^-10 + electrostatic units. + + H. A. Wilson (_Phil. Mag._ [6], 5, p. 429) used another method. Drops + of water, as we have seen, condense more easily on negative than on + positive ions. It is possible, therefore, to adjust the expansion so + that a cloud is formed on the negative but not on the positive ions. + Wilson arranged the experiments so that such a cloud was formed + between two horizontal plates which could be maintained at different + potentials. The charged drops between the plates were acted upon by a + uniform vertical force which affected their rate of fall. Let X be the + vertical electric force, e the charge on the drop, v1 the rate of fall + of the drop when this force acts, and v the rate of fall due to + gravity alone. Then since the rate of fall is proportionate to the + force on the drop, if a is the radius of the drop, and [rho] its + density, then + + Xe + (4/3)[pi][rho]ga^3 v1 + ---------------------- = ---, + 4/3[pi][rho]ga^3 v + + or Xe = (4/3)[pi][rho]ga^3(v1 - v)/v. + + But v = 2/9ga^2[rho]/[mu], + + so that + + / / [mu]^3 v^(3/2)(v1 - v) + Xe = \/ 2.9[pi] - / ------ . ---------------. + \/ g[rho] v + + Thus if X, v, v1 are known e can be determined. Wilson by this method + found that e was 3.1 X 10^-10 electrostatic units. A few of the ions + carried charges 2e or 3e. + + Townsend has used the following method to compare the charge carried + by a gaseous ion with that carried by an atom of hydrogen in the + electrolysis of solution. We have + + u/D = Ne/[Pi], + + where D is the coefficient of diffusion of the ions through the gas, u + the velocity of the ion in the same gas when acted on by unit electric + force, N the number of molecules in a cubic centimetre of the gas when + the pressure is [Pi] dynes per square centimetre, and e the charge in + electrostatic units. This relation is obtained on the hypothesis that + N ions in a cubic centimetre produce the same pressure as N uncharged + molecules. + + We know the value of D from Townsend's experiments and the values of u + from those of Zeleny. We get the following values for Ne X 10^-10:-- + + +---------------+---------------------+---------------------+ + | | Moist Gas. | Moist Gas. | + +---------------+----------+----------+----------+----------+ + | Gas. | Positive | Negative | Positive | Negative | + | | Ions. | Ions. | Ions. | Ions. | + +---------------+----------+----------+----------+----------+ + | Air | 1.28 | 1.29 | 1.46 | 1.31 | + | Oxygen | 1.34 | 1.27 | 1.63 | 1.36 | + | Carbonic acid | 1.01 | .87 | .99 | .93 | + | Hydrogen | 1.24 | 1.18 | 1.63 | 1.25 | + +---------------+----------+----------+----------+----------+ + | Mean | 1.22 | 1.15 | 1.43 | 1.21 | + +---------------+----------+----------+----------+----------+ + + + Since 1.22 cubic centimetres of hydrogen at the temperature 15 deg. C. + and pressure 760 mm. of mercury are liberated by the passage through + acidulated water of one electromagnetic unit of electricity or 3 X + 10^10 electrostatic units, and since in one cubic centimetre of the + gas there are 2.46 N atoms of hydrogen, we have, if E is the charge in + electrostatic units, on the atom of hydrogen in the electrolysis of + solutions + + 2.46NE = 3 X 10^10, + + or + + NE = 1.22 X 10^10. + + The mean of the values of Ne in the preceding table is 1.24 X 10^10. + Hence we may conclude that the charge of electricity carried by a + gaseous ion is equal to the charge carried by the hydrogen atom in the + electrolysis of solutions. The values of Ne for the different gases + differ more than we should have expected from the probable accuracy of + the determination of D and the velocity of the ions: Townsend (_Proc. + Roy. Soc._ 80, p. 207) has shown that when the ionization is produced + by Rontgen rays some of the positive ions carry a double charge and + that this accounts for the values of Ne being greater for the positive + than for the negative ions. Since we know the value of e, viz. 3.5 X + 10^-10, and, also Ne, = 1.24 X 10^10, we find N the number of + molecules in a cubic centimetre of gas at standard temperature and + pressure to be equal to 3.5 X 10^19. This method of obtaining N is the + only one which does not involve any assumption as to the shape of the + molecules and the forces acting between them. + + Another method of determining the charge carried by an ion has been + employed by Rutherford (_Proc. Roy. Soc._ 81, pp. 141, 162), in which + the positively electrified particles emitted by radium are made use + of. The method consists of: (1) Counting the number of [alpha] + particles emitted by a given quantity of radium in a known time. (2) + Measuring the electric charge emitted by this quantity in the same + time. To count the number of the [alpha] particles the radium was so + arranged that it shot into an ionization chamber a small number of + [alpha] particles per minute; the interval between the emission of + individual particles was several seconds. When an [alpha] particle + passed into the vessel it ionized the gas inside and so greatly + increased its conductivity; thus, if the gas were kept exposed to an + electric field, the current through the gas would suddenly increase + when an [alpha] particle passed into the vessel. Although each [alpha] + particle produces about thirty thousand ions, this is hardly large + enough to produce the conductivity appreciable without the use of very + delicate apparatus; to increase the conductivity Rutherford took + advantage of the fact that ions, especially negative ones, when + exposed to a strong electric field, produce other ions by collision + against the molecules of the gas through which they are moving. By + suitably choosing the electric field and the pressure in the + ionization chamber, the 30,000 ions produced by each [alpha] particle + can be multiplied to such an extent that an appreciable current passes + through the ionization chamber on the arrival of each [alpha] + particle. An electrometer placed in series with this vessel will show + by its deflection when an [alpha] particle enters the chamber, and by + counting the number of deflections per minute we can determine the + number of [alpha] particles given out by the radium in that time. + Another method of counting this number is to let the particles fall on + a phosphorescent screen, and count the number of scintillations on the + screen in a certain time. Rutherford has shown that these two methods + give concordant results. + + The charge of positive electricity given out by the radium was + measured by catching the [alpha] particles in a Faraday cylinder + placed in a very highly exhausted vessel, and measuring the charge per + minute received by this cylinder. In this way Rutherford showed that + the charge on the [alpha] particle was 9.4 X 10^-10 electrostatic + units. Now e/m for the [alpha] particle = 5 X 10^3, and there is + evidence that the [alpha] particle is a charged atom of helium; since + the atomic weight of helium is 4 and e/m for hydrogen is 10^4, it + follows that the charge on the helium atom is twice that on the + hydrogen, so that the charge on the hydrogen atom is 4.7 X 10^-10 + electrostatic units. + +_Calculation of the Mass of the Ions at Low Pressures._--Although at +ordinary pressures the ion seems to have a very complex structure and to +be the aggregate of many molecules, yet we have evidence that at very +low pressures the structure of the ion, and especially of the negative +one, becomes very much simpler. This evidence is afforded by +determination of the mass of the atom. We can measure the ratio of the +mass of an ion to the charge on the ion by observing the deflections +produced by magnetic and electric forces on a moving ion. If an ion +carrying a charge e is moving with a velocity v, at a point where the +magnetic force is H, a mechanical force acts on the ion, whose direction +is at right angles both to the direction of motion of the ion and to the +magnetic force, and whose magnitude is evH sin [theta], where [theta] is +the angle between v and H. Suppose then that we have an ion moving +through a gas whose pressure is so low that the free path of the ion is +long compared with the distance through which it moves whilst we are +experimenting upon it; in this case the motion of the ion will be free, +and will not be affected by the presence of the gas. + + Since the force is always at right angles to the direction of motion + of the ion, the speed of the ion will not be altered by the action of + this force; and if the ion is projected with a velocity v in a + direction at right angles to the magnetic force, and if the magnetic + force is constant in magnitude and direction, the ion will describe a + curve in a plane at right angles to the magnetic force. If [rho] is + the radius of curvature of this curve, m the mass of the ion, + mv^2/[rho] must equal the normal force acting on the ion, i.e. it must + be equal to Hev, or [rho] = mv/He. Thus the radius of curvature is + constant; the path is therefore a circle, and if we can measure the + radius of this circle we know the value of mv/He. In the case of the + rapidly moving negative ions projected from the cathode in a highly + exhausted tube, which are known as _cathode rays_, the path of the + ions can be readily determined since they make many substances + luminous when they impinge against them. Thus by putting a screen of + such a substance in the path of the rays the shape of the path will be + determined. Let us now suppose that the ion is acted upon by a + vertical electric force X and is free from magnetic force, if it be + projected with a horizontal velocity v, the vertical deflection y + after a time t is 1/2 X et^2/m, or if l is the horizontal distance + travelled over by the ion in this time we have since l = vt, + + Xe l^2 + y = 1/2 -- ---. + m v^2 + + Thus if we measure y and l we can deduce e/mv^2. From the effect of the + magnetic force we know e/mv. Combining these results we can find both + e/m and v. + + [Illustration: FIG. 13.] + + The method by which this determination is carried out in practice is + illustrated in fig. 13. The cathode rays start from the electrode C in + a highly exhausted tube, pass through two small holes in the plugs A + and B, the holes being in the same horizontal line. Thus a pencil of + rays emerging from B is horizontal and produces a bright spot at the + far end of the tube. In the course of their journey to the end of the + tube they pass between the horizontal plates E and D, by connecting + these plates with an electric battery a vertical electric field is + produced between E and D and the phosphorescent spot is deflected. By + measuring this deflection we determine e/mv^2. The tube is now placed + in a uniform magnetic field, the lines of magnetic force being + horizontal and at right angles to the plane of the paper. The magnetic + force makes the rays describe a circle in the plane of the paper, and + by measuring the vertical deflection of the phosphorescent patch at + the end of the tube we can determine the radius of this circle, and + hence the value of e/mv. From the two observations the value of e/m + and v can be calculated. + + Another method of finding e/m for the negative ion which is applicable + in many cases to which the preceding one is not suitable, is as + follows: Let us suppose that the ion starts from rest and moves in a + field where the electric and magnetic forces are both uniform, the + electric force X being parallel to the axis of x, and the magnetic + force Z parallel to the axis of z; then if x, y, are the co-ordinates + of the ion at the time t, the equations of motion of the ion are-- + + d^2x dy + m ---- = Xe - He --, + dt^2 dt + + d^2y dx + m ---- = He --. + dt^2 dt + + The solution of these equations, if x, y, dx/dt, dy/dt all vanish when + t = 0, is + + Xm / / e \ \ + x = ---- {1 - cos( -- Ht ) } + eH^2 \ \ m / / + + Xm /e / e \ \ + y = ---- {-- Ht - sin( -- Ht ) }. + eH^2 \m \ m / / + + These equations show that the path of the ion is a cycloid, the + generating circle of which has a diameter equal to 2Xm/eH^2, and rolls + on the line x = 0. + + Suppose now that we have a number of ions starting from the plane x = + 0, and moving towards the plane x = a. The particles starting from x = + 0 describe cycloids, and the greatest distance they can get from the + plane is equal to the diameter of the generating circle of the + cycloid, i.e. to 2Xm/eH^2. (After reaching this distance they begin to + approach the plane.) Hence if a is less than the diameter of the + generating circle, all the particles starting from x = 0 will reach + the plane x = a, if this is unlimited in extent; while if a is greater + than the diameter of the generating circle none of the particles which + start from x = 0 will reach the plane x = a. Thus, if x = 0 is a plane + illuminated by ultra-violet light, and consequently the seat of a + supply of negative ions, and x = a a plane connected with an + electrometer, then if a definite electric intensity is established + between the planes, i.e. if X be fixed, so that the rate of emission + of negative ions from the illuminated plate is given, and if a is less + than 2Xm/eH^2, all the ions which start from x = 0 will reach x = a. + That is, the rate at which this plane receives an electric charge + will be the same whether there is a magnetic field between the plate + or not, but if a is greater than 2Xm/eH^2, then no particle which + starts from the plate x = 0 will reach the plate x = a, and this plate + will receive no charge. Thus the supply of electricity to the plate + has been entirely stopped by the magnetic field. Thus, on this theory, + if the distance between the plates is less than a certain value, the + magnetic force should produce no effect on the rate at which the + electrometer plate receives a charge, while if the distance is greater + than this value the magnetic force would completely stop the supply of + electricity to the plate. The actual phenomena are not so abrupt as + this theory indicates. We find that when the plates are very near + together the magnetic force produces a very slight effect, and this an + increase in the rate of charging of the plate. On increasing the + distance we come to a stage where the magnetic force produces a great + diminution in the rate of charging. It does not, however, stop it + abruptly, there being a considerable range of distance, in which the + magnetic force diminishes but does not destroy the current. At still + greater distances the current to the plate under the magnetic force is + quite inappreciable compared with that when there is no magnetic + force. We should get this gradual instead of abrupt decay of the + current if some of the particles, instead of all starting from rest, + started with a finite velocity; in that case the first particles + stopped would be those which started from rest. This would be when a = + 2Xm/eH^2. Thus if we measure the value of a when the magnetic force + first begins to affect the leak to the electrometer we determine + 2Xm/eH^2, and as we can easily measure X and H, we can deduce the value + of m/e. + +By these methods Thomson determined the value of e/m for the negative +ions produced when ultra-violet light falls on a metal plate, as well as +for the negative ions produced by an incandescent carbon filament in an +atmosphere of hydrogen (_Phil. Mag._ [5], 48, p. 547) as well as for the +cathode rays. It was found that the value of e/m for the negative ions +was the same in all these cases, and that it was a constant quantity +independent of the nature of the gas from which the ions are produced +and the means used to produce them. It was found, too, that this value +was more than a thousand times the value of e/M, where e is the charge +carried by an atom of hydrogen in the electrolysis of solutions, and M +the mass of an atom of hydrogen. We have seen that this charge is the +same as that carried by the negative ion in gases; thus since e/m is +more than a thousand times e/M, it follows that M must be more than a +thousand times m. Thus the mass of the negative ion is exceedingly small +compared with the mass of the atom of hydrogen, the smallest mass +recognized in chemistry. The production of negative ions thus involves +the splitting up of the atom, as from a collection of atoms something is +detached whose mass is less than that of a single atom. It is important +to notice in connexion with this subject that an entirely different line +of argument, based on the Zeeman effect (see MAGNETO-OPTICS), leads to +the recognition of negatively electrified particles for which e/m is of +the same order as that deduced from the consideration of purely +electrical phenomena. These small negatively electrified particles are +called corpuscles. The latest determinations of e/m for corpuscles +available are the following:-- + + Observer. e/m. + + Classen (_Ber. deut. phys. Ges._ 6, p. 700) 1.7728 X 10^7 + Bucherer (_Ann. der Phys._, 28, p. 513) 1.763 X 10^7 + +It follows from electrical theory that when the corpuscles are moving +with a velocity comparable with that of light their masses increase +rapidly with their velocity. This effect has been detected by Kauffmann +(_Gott. Nach._, Nov. 8, 1901), who used the corpuscles shot out from +radium, some of which move with velocities only a few per cent less than +that of light. Other experiments on this point have been made by +Bucherer (_Ann. der Phys._ 28, p. 513). + +_Conductivity Produced by Ultra-Violet Light._--So much use has been +made in recent times of ultra-violet light for producing ions that it is +desirable to give some account of the electrical effects produced by +light. The discovery by Hertz (_Wied. Ann._ 31, p. 983) in 1887, that +the incidence of ultra-violet light on a spark gap facilitates the +passage of a spark, led to a series of investigations by Hallwachs, +Hoor, Righi and Stoletow, on the effect of ultra-violet light on +electrified bodies. These researches have shown that a freshly cleaned +metal surface, charged with negative electricity, rapidly loses its +charge, however small, when exposed to ultra-violet light, and that if +the surface is insulated and without charge initially, it acquires a +positive charge under the influence of the light. The magnitude of this +positive charge may be very much increased by directing a blast of air +on the plate. This, as Zeleny (_Phil. Mag._ [5], 45, p. 272) showed, has +the effect of blowing from the neighbourhood of the plate negatively +electrified gas, which has similar properties to the charged gas +obtained by the separation of ions from a gas exposed to Rontgen rays or +uranium radiation. If the metal plate is positively electrified, there +is no loss of electrification caused by ultra-violet light. This has +been questioned, but a very careful examination of the question by +Elster and Geitel (_Wied. Ann._ 57, p. 24) has shown that the apparent +exceptions are due to the accidental exposure to reflected ultra-violet +light of metal surfaces in the neighbourhood of the plate negatively +electrified by induction, so that the apparent loss of charge is due to +negative electricity coming up to the plate, and not to positive +electricity going away from it. The ultra-violet light may be obtained +from an arc-lamp, the effectiveness of which is increased if one of the +terminals is made of zinc or aluminium, the light from these substances +being very rich in ultra-violet rays; it may also be got very +conveniently by sparking with an induction coil between zinc or cadmium +terminals. Sunlight is not rich in ultra-violet light, and does not +produce anything like so great an effect as the arc light. Elster and +Geitel, who have investigated with great success the effects of light on +electrified bodies, have shown that the more electro-positive metals +lose negative charges when exposed to ordinary light, and do not need +the presence of the ultra-violet rays. Thus they found that amalgams of +sodium or potassium enclosed in a glass vessel lose a negative charge +when exposed to daylight, though the glass stops the small amount of +ultra-violet light left in sunlight after its passage through the +atmosphere. If sodium or potassium be employed, or, what is more +convenient, the mercury-like liquid obtained by mixing sodium and +potassium in the proportion of their combining weights, they found that +negative electricity was discharged by an ordinary petroleum lamp. If +the still more electro-positive metal rubidium is used, the discharge +can be produced by the light from a glass rod just heated to redness; +but there is no discharge till the glass is luminous. Elster and Geitel +arrange the metals in the following order for the facility with which +negative electrification is discharged by light: rubidium, potassium, +alloy of sodium and potassium, sodium, lithium, magnesium, thallium, +zinc. With copper, platinum, lead, iron, cadmium, carbon and mercury the +effects with ordinary light are too small to be appreciable. The order +is the same as that in Volta's electro-chemical series. With +ultra-violet light the different metals show much smaller differences in +their power of discharging negative electricity than they do with +ordinary light. Elster and Geitel found that the ratio of the +photo-electric effects of two metals exposed to approximately +monochromatic light depended upon the wave-length of the light, +different metals showing a maximum sensitiveness in different parts of +the spectrum. This is shown by the following table for the alkaline +metals. The numbers in the table are the rates of emission of negative +electricity under similar circumstances. The rate of emission under the +light from a petroleum lamp was taken as unity:-- + + Blue. Yellow. Orange. Red. + Rb .16 .64 .33 .039 + Na .37 .36 .14 .009 + K .57 .07 .04 .002 + +The table shows that the absorption of light by the metal has great +influence on the photo-electric effect, for while potassium is more +sensitive in blue light than sodium, the strong absorption of yellow +light by sodium makes it more than five times more sensitive to this +light than potassium. Stoletow, at an early period, called attention to +the connexion between strong absorption and photo-electric effects. He +showed that water, which does not absorb to any great extent either the +ultra-violet or visible rays, does not show any photo-electric effect, +while strongly coloured solutions, and especially solutions of +fluorescent substances such as methyl green or methyl violet, do so to a +very considerable extent; indeed, a solution of methyl green is more +sensitive than zinc. Hallwachs (_Wied. Ann._ 37, p. 666) proved that in +liquids showing photo-electric effects there is always strong +absorption; we may, however, have absorption without these effects. +Phosphorescent substances, such as calcium sulphide show this effect, as +also do various specimens of fluor-spar. As phosphorescence and +fluorescence are probably accompanied by a very intense absorption by +the surface layers, the evidence is strong that to get the +photo-electric effects we must have strong absorption of some kind of +light, either visible or ultra-violet. + +[Illustration: FIG. 14.] + +If a conductor A is placed near a conductor B exposed to ultra-violet +light, and if B is made the negative electrode and a difference of +potential established between A and B, a current of electricity will +flow between the conductors. The relation between the magnitude of the +current and the difference of potential when A and B are parallel plates +has been investigated by Stoletow (_Journal de physique_, 1890, 11, p. +469), von Schweidler (_Wien. Ber._, 1899, 108, p. 273) and Varley +(_Phil. Trans. A._, 1904, 202, p. 439). The results of some of Varley's +experiments are represented in the curves shown in fig. 14, in which the +ordinates are the currents and the abscissae the potentials. It will be +seen that when the pressure is exceedingly low the current is +independent of the potential difference and is equal to the negative +charge carried off in unit time by the corpuscles emitted from the +surface exposed to the light. At higher pressures the current rises far +above these values and increases rapidly with the potential difference. +This is due to the corpuscles emitted by the illuminated surface +acquiring under the electric field such high velocities that when they +strike against the molecules of the gas through which they are passing +they ionize them, producing fresh ions which can carry on additional +current. The relation between the current and the potential difference +in this case is in accordance with the results of the theory of +ionization by collision. The corpuscles emitted from a body under the +action of ultra-violet light start from the surface with a finite +velocity. The velocity is not the same for all the corpuscles, nor +indeed could we expect that it should be: for as Ladenburg has shown +(_Ann. der Phys._, 1903, 12, p. 558) the seat of their emission is not +confined to the surface layer of the illuminated metal but extends to a +layer of finite, though small, thickness. Thus the particles which start +deep down will have to force their way through a layer of metal before +they reach the surface, and in doing so will have their velocities +retarded by an amount depending on the thickness of this layer. The +variation in the velocity of the corpuscles is shown in the following +table, due to Lenard (_Ann. der Phys._, 1902, 8, p. 149). + + +------------------------------------+--------+----------+-----------+ + | | Carbon.| Platinum.| Aluminium.| + +------------------------------------+--------+----------+-----------+ + | Corpuscles emitted with velocities | | | | + | between 12 and 8 X 10^7 cm sec. | 0.000 | 0.000 | 0.004 | + | between 8 and 4 X 10^7 cm sec. | 0.049 | 0.155 | 0.151 | + | between 4 and 0 X 10^7 cm sec. | 0.67 | 0.65 | 0.49 | + | | | | | + | Corpuscles only emitted with the | | | | + | help of an external electric | 0.28 | 0.21 | 0.35 | + | field. +--------+----------+-----------| + | | 1.00 | 1.00 | 1.00 | + +------------------------------------+--------+----------+-----------+ + +If the illuminated surface is completely surrounded by an envelope of +the same metal insulated from and completely shielded from the light, +the emission of the negative corpuscles from the illuminated surface +would go on until the potential difference V between this surface and +the envelope became so great that the corpuscles with the greatest +velocity lost their energy before reaching the envelope, i.e. if m is +the mass, e the charge on a corpuscle, v the greatest velocity of +projection, until Ve = 1/2mv^2. The values found for V by different +observers are not very consistent. Lenard found that V for aluminium was +about 3 volts and for platinum 2. Millikan and Winchester (_Phil. Mag._, +July 1907) found for aluminium V = .738. The apparatus used by them was +so complex that the interpretation of their results is difficult. + +An extremely interesting fact discovered by Lenard is that the velocity +with which the corpuscles are emitted from the metal is independent of +the intensity of the incident light. The quantity of corpuscles +increases with the intensity, but the velocity of the individual +corpuscles does not. It is worthy of notice that in other cases when +negative corpuscles are emitted from metals, as for example when the +metals are exposed to cathode rays, Canal-strahlen, or Rontgen rays, the +velocity of the emitted corpuscles is independent of the intensity of +the primary radiation which excites them. The velocity is not, however, +independent of the nature of the primary rays. Thus when light is used +to produce the emission of corpuscles the velocity, as Ladenburg has +shown, depends on the wave length of the light, increasing as the wave +length diminishes. The velocity of corpuscles emitted under the action +of cathode rays is greater than that of those ejected by light, while +the incidence of Rontgen rays produces the emission of corpuscles moving +much more rapidly than those in the cases already mentioned, and the +harder the primary rays the greater is the velocity of the corpuscles. + +The importance of the fact that the velocity and therefore the energy of +the corpuscles emitted from the metal is independent of the intensity of +the incident light can hardly be overestimated. It raises the most +fundamental questions as to the nature of light and the constitution of +the molecules. What is the source of the energy possessed by these +corpuscles? Is it the light, or in the stores of internal energy +possessed by the molecule? Let us follow the consequences of supposing +that the energy comes from the light. Then, since the energy is +independent of the intensity of the light, the electric forces which +liberate the corpuscles must also be independent of that intensity. But +this cannot be the case if, as is usually assumed in the electromagnetic +theory, the wave front consists of a uniform distribution of electric +force without structure, for in this case the magnitude of the electric +force is proportional to the square root of the intensity. On the +emission theory of light a difficulty of this kind would not arise, for +on that theory the energy in a luminiferous particle remains constant as +the particle pursues its flight through space. Thus any process which a +single particle is able to effect by virtue of its energy will be done +just as well a thousand miles away from the source of light as at the +source itself, though of course in a given space there will not be +nearly so many particles to do this process far from the source as there +are close in. Thus, if one of the particles when it struck against a +piece of metal caused the ejection of a corpuscle with a given velocity, +the velocity of emission would not depend on the intensity of the light. +There does not seem any reason for believing that the electromagnetic +theory is inconsistent with the idea that on this theory, as on the +emission theory, the energy in the light wave may instead of being +uniformly distributed through space be concentrated in bundles which +occupy only a small fraction of the volume traversed by the light, and +that as the wave travels out the bundles get farther apart, the energy +in each remaining undiminished. Some such view of the structure of light +seems to be required to account for the fact that when a plate of metal +is struck by a wave of ultra-violet light, it would take years before +the corpuscles emitted from the metal would equal in number the +molecules on the surface of the metal plate, and yet on the ordinary +theory of light each one of these is without interruption exposed to the +action of the light. The fact discovered by E. Ladenburg (_Verh. d. +deutsch. physik. Ges._ 9, p. 504) that the velocity with which the +corpuscles are emitted depends on the wave length of the light suggests +that the energy in each bundle depends upon the wave length and +increases as the wave length diminishes. + +These considerations illustrate the evidence afforded by photo-electric +effects on the nature of light; these effects may also have a deep +significance with regard to the structure of matter. The fact that the +energy of the individual corpuscles is independent of the intensity of +the light might be explained by the hypothesis that the energy of the +corpuscles does not come from the light but from the energy stored up in +the molecules of the metal exposed to the light. We may suppose that +under the action of the light some of the molecules are thrown into an +unstable state and explode, ejecting corpuscles; the light in this case +acts only as a trigger to liberate the energy in the atom, and it is +this energy and not that of the light which goes into the corpuscles. In +this way the velocity of the corpuscles would be independent of the +intensity of the light. But it may be asked, is this view consistent +with the result obtained by Ladenburg that the velocity of the +corpuscles depends upon the nature of the light? If light of a definite +wave length expelled corpuscles with a definite and uniform velocity, it +would be very improbable that the emission of the corpuscles is due to +an explosion of the atoms. The experimental facts as far as they are +known at present do not allow us to say that the connexion between the +velocity of the corpuscles and the wave length of the light is of this +definite character, and a connexion such as a gradual increase of +average velocity as the wave length of the light diminishes, would be +quite consistent with the view that the corpuscles are ejected by the +explosion of the atom. For in a complex thing like an atom there may be +more than one system which becomes unstable when exposed to light. Let +us suppose that there are two such systems, A and B, of which B ejects +the corpuscles with the greater velocity. If B is more sensitive to the +short waves, and A to the long ones, then as the wave length of the +light diminishes the proportion of the corpuscles which come from B will +increase, and as these are the faster, the average velocity of the +corpuscles emitted will also increase. And although the potential +acquired by a perfectly insulated piece of metal when exposed to +ultra-violet light would depend only on the velocity of the fastest +corpuscles and not upon their number, in practice perfect insulation is +unattainable, and the potential actually acquired is determined by the +condition that the gain of negative electricity by the metal through +lack of insulation, is equal to the loss by the emission of negatively +electrified corpuscles. The potential acquired will fall below that +corresponding to perfect insulation by an amount depending on the number +of the faster corpuscles emitted, and the potential will rise if the +proportion of the rapidly moving corpuscles is increased, even though +there is no increase in their velocity. It is interesting to compare +other cases in which corpuscles are emitted with the case of +ultra-violet light. When a metal or gas is bombarded by cathode rays it +emits corpuscles and the velocity of these is found to be independent of +the velocity of the cathode rays which excite them; the velocity is +greater than for corpuscles emitted under ultra-violet light. Again, +when bodies are exposed to Rontgen rays they emit corpuscles moving with +a much greater velocity than those excited by cathode rays, but again +the velocity does not depend upon the intensity of the rays although it +does to some extent on their hardness. In the case of cathode and +Rontgen rays, the velocity with which the corpuscles are emitted seems, +as far as we know at present, to vary slightly, but only slightly, with +the nature of the substance on which the rays fall. May not this +indicate that the first effect of the primary rays is to detach a +neutral doublet, consisting of a positive and negative charge, this +doublet being the same from whatever system it is detached? And that the +doublet is unstable and explodes, expelling the negative charge with a +high velocity, and the positive one, having a much larger charge, with a +much smaller velocity, the momentum of the negative charge being equal +to that of the positive. + +Up to now we have been considering the effects produced when light is +incident on metals. Lenard found (and the result has been confirmed by +the experiments of J. J. Thomson and Lyman) that certain kinds of +ultra-violet light ionize a gas when they pass through. The type of +ultra-violet light which produces this effect is so easily absorbed that +it is stopped by a layer a few millimetres thick of air at atmospheric +pressure. + +_Ionization by Collision._--When the ionization of the gas is produced +by external agents such as Rontgen rays or ultra-violet light, the +electric field produces a current by setting the positive ions moving in +one direction, and the negative ones in the opposite; it makes use of +ions already made and does not itself give rise to ionization. In many +cases, however, such as in electric sparks, there are no external agents +to produce ionization and the electric field has to produce the ions as +well as set them in motion. When the ionization is produced by external +means the smallest electric field is able to produce a current through +the gas; when, however, these external means are absent no current is +produced unless the strength of the electric field exceeds a certain +critical value, which depends not merely upon the nature of the gas but +also upon the pressure and the dimensions of the vessel in which it is +contained. The variation of the electric field required to produce +discharge can be completely explained if we suppose that the ionization +of the gas is produced by the impact with its molecules of corpuscles, +and in certain cases of positive ions, which under the influence of the +electric field have acquired considerable kinetic energy. We have direct +evidence that rapidly moving corpuscles are able to ionize molecules +against which they strike, for the cathode rays consist of such +corpuscles, and these when they pass through a gas produce large amounts +of ionization. Suppose then that we have in a gas exposed to an electric +field a few corpuscles. These will be set in motion by the field and +will acquire an amount of energy in proportion to the product of the +electric force, their charge, and the distance travelled in the +direction of the electric field between two collisions with the +molecules of the gas. If this energy is sufficient to give them the +ionizing property possessed by cathode rays, then when a corpuscle +strikes against a molecule it will detach another corpuscle; this under +the action of the electric field will acquire enough energy to produce +corpuscles on its own account, and so as the corpuscles move through the +gas their number will increase in geometrical progression. Thus, though +there were but few corpuscles to begin with, there may be great +ionization after these have been driven some distance through the gas by +the electric field. + + The number of ions produced by collisions can be calculated by the + following method. Let the electric force be parallel to the axis of x, + and let n be the number of corpuscles per unit volume at a place fixed + by the co-ordinate x; then in unit time these corpuscles will make + nu/[lambda] collisions with the molecules, if u is the velocity of a + corpuscle and [lambda] the mean free path of a corpuscle. When the + corpuscles are moving fast enough to produce ions by collision their + velocities are very much greater than those they would possess at the + same temperature if they were not acted on by electrical force, and so + we may regard the velocities as being parallel to the axis of x and + determined by the electric force and the mean free path of the + corpuscles. We have to consider how many of the nu/[lambda] collisions + which take place per second will produce ions. We should expect that + the ionization of a molecule would require a certain amount of energy, + so that if the energy of the corpuscle fell below this amount no + ionization would take place, while if the energy of the corpuscle were + exceedingly large, every collision would result in ionization. We + shall suppose that a certain fraction of the number of collisions + result in ionization and that this fraction is a function of the + energy possessed by the corpuscle when it collides against the + molecules. This energy is proportional to Xe[lambda] when X is the + electric force, e the charge on the corpuscle, and [lambda] the mean + free path. If the fraction of collisions which produce ionization is + [int](Xe[lambda]), then the number of ions produced per cubic + centimetre per second is [int](Xe[lambda])nu/[lambda]. If the + collisions follow each other with great rapidity so that a molecule + has not had time to recover from one collision before it is struck + again, the effect of collisions might be cumulative, so that a + succession of collisions might give rise to ionization, though none of + the collisions would produce an ion by itself. In this case [int] + would involve the frequency of the collisions as well as the energy of + the corpuscle; in other words, it might depend on the current through + the gas as well as upon the intensity of the electric field. We + shall, however, to begin with, assume that the current is so small + that this cumulative effect may be neglected. + + Let us now consider the rate of increase, dn/dt, in the number of + corpuscles per unit volume. In consequence of the collisions, + [int](Xe[lambda])nu/[lambda] corpuscles are produced per second; in + consequence of the motion of the corpuscles, the number which leave + unit volume per second is greater than those which enter it by + (d/dx)(nu); while in a certain number of collisions a corpuscle will + stick to the molecule and will thus cease to be a free corpuscle. Let + the fraction of the number of collisions in which this occurs be + [beta]. Thus the gain in the number of corpuscles is + [int](Xe[lambda])nu/[lambda], while the loss is (d/dx)(nu) + + [beta](nu)/[lambda]; hence + + dn nu d [beta]nu + -- = [int](Xe[lambda]) -------- - --(nu) - --------. + dt [lambda] dx [lambda] + + When things are in a steady state dn/dt = 0, and we have + + d 1 / \ + --(nu) = --------( [int](Xe[lambda]) - [beta] )nu. + dx [lambda] \ / + + If the current is so small that the electrical charges in the gas are + not able to produce any appreciable variations in the field, X will be + constant and we get nu = C[epsilon]^{[alpha]x}, where [alpha] = + {[int](Xe[lambda]) - [beta]}/[lambda]. If we take the origin from + which we measure x at the cathode, C is the value of nu at the + cathode, i.e. it is the number of corpuscles emitted per unit area of + the cathode per unit time; this is equal to i0/e if i0 is the quantity + of negative electricity coming from unit area of the cathode per + second, and e the electric charge carried by a corpuscle. Hence we + have nue = i0[epsilon]^{[alpha]x}. If l is the distance between the + anode and the cathode, the value of nue, when x = l, is the current + passing through unit area of the gas, if we neglect the electricity + carried by negatively electrified carriers other than corpuscles. + Hence i = i0[epsilon]^{[alpha]l}. Thus the current between the plates + increases in geometrical progression with the distance between the + plates. + + By measuring the variation of the current as the distance between the + plates is increased, Townsend, to whom we owe much of our knowledge on + this subject, determined the values of [alpha] for different values of + X and for different pressures for air, hydrogen and carbonic acid gas + (_Phil. Mag._ [6], 1, p. 198). Since [lambda] varies inversely as the + pressure, we see that [alpha] may be written in the form p[phi](X/p) + or [alpha]/X = F(X/p). The following are some of the values of [alpha] + found by Townsend for air. + + +---------+----------+----------+----------+----------+----------+ + | X Volts | Pressure | Pressure | Pressure | Pressure | Pressure | + | per cm. | .17 mm. | .38 mm. | 1.10 mm. | 2.1 mm. | 4.1 mm. | + +---------+----------+----------+----------+----------+----------+ + | 20 | .24 | | | | | + | 40 | .65 | .34 | | | | + | 80 | 1.35 | 1.3 | .45 | .13 | | + | 120 | 1.8 | 2.0 | 1.1 | .42 | .13 | + | 160 | 2.1 | 2.8 | 2.0 | .9 | .28 | + | 200 | | 3.4 | 2.8 | 1.6 | .5 | + | 240 | 2.45 | 3.8 | 4.0 | 2.35 | .99 | + | 320 | 2.7 | 4.5 | 5.5 | 4.0 | 2.1 | + | 400 | | 5.0 | 6.8 | 6.0 | 3.6 | + | 480 | 3.15 | 5.4 | 8.0 | 7.8 | 5.3 | + | 560 | | 5.8 | 9.3 | 9.4 | 7.1 | + | 640 | 3.25 | 6.2 | 10.6 | 10.8 | 8.9 | + +---------+----------+----------+----------+----------+----------+ + + We see from this table that for a given value of X, [alpha] for small + pressures increases as the pressure increases; it attains a maximum at + a particular pressure, and then diminishes as the pressure increases. + The increase in the pressure increases the number of collisions, but + diminishes the energy acquired by the corpuscle in the electric field, + and thus diminishes the change of any one collision resulting in + ionization. If we suppose the field is so strong that at some + particular pressure the energy acquired by the corpuscle is well above + the value required to ionize at each collision, then it is evident + that increasing the number of collisions will increase the amount of + ionization, and therefore [alpha], and [alpha] cannot begin to + diminish until the pressure has increased to such an extent that the + mean free path of a corpuscle is so small that the energy acquired by + the corpuscle from the electric field falls below the value when each + collision results in ionization. + + The value of p, when X is given, for which [alpha] is a maximum, is + proportional to X; this follows at once from the fact that [alpha] is + of the form X.F(X/p). The value of X/p for which F(X/p) is a maximum is + seen from the preceding table to be about 420, when X is expressed in + volts per centimetre and p in millimetres of mercury. The maximum value + of F(X/p) is about 1/60. Since the current passing between two planes + at a distance l apart is i0[epsilon]^{[alpha]l} or + i0[epsilon]^{XlF(X/p)}, and since the force between the plates is + supposed to be uniform, Xl is equal to V, the potential between the + plates; hence the current between the plates is i0[epsilon]^{VlF(X/p)}, + and the greatest value it can have is i0[epsilon]^{V/60}. Thus the + ratio between the current between the plates when there is ionization + and when there is none cannot be greater than [epsilon]^{V/60}, when V + is measured in volts. This result is based on Townsend's experiments + with very weak currents; we must remember, however, that when the + collisions are so frequent that the effects of collisions can + accumulate, [alpha] may have much larger values than when the current + is small. In some experiments made by J. J. Thomson with intense + currents from cathodes covered with hot lime, the increase in the + current when the potential difference was 60 volts, instead of being e + times the current when there was no ionization, as the preceding theory + indicates, was several hundred times that value, thus indicating a + great increase in [alpha] with the strength of the current. + + Townsend has shown that we can deduce from the values of [alpha] the + mean free path of a corpuscle. For if the ionization is due to the + collisions with the corpuscles, then unless one collision detaches + more than one corpuscle the maximum number of corpuscles produced will + be equal to the number of collisions. When each collision results in + the production of a corpuscle, [alpha] = 1/[lambda] and is independent + of the strength of the electric field. Hence we see that the value of + [alpha], when it is independent of the electric field, is equal to the + reciprocal of the free path. Thus from the table we infer that at a + pressure of 17 mm. the mean free path is 1/325 cm.; hence at 1 mm. the + mean free path of a corpuscle is 1/19 cm. Townsend has shown that this + value of the mean free path agrees well with the value 1/21 cm. + deduced from the kinetic theory of gases for a corpuscle moving + through air. By measuring the values of [alpha] for hydrogen and + carbonic acid gas Townsend and Kirby (_Phil. Mag._ [6], 1, p. 630) + showed that the mean free paths for corpuscles in these gases are + respectively 1/11.5 and 1/29 cm. at a pressure of 1 mm. These results + again agree well with the values given by the kinetic theory of gases. + + If the number of positive ions per unit volume is m and v is the + velocity, we have nue+mve = i, where i is the current through unit + area of the gas. Since nue = i0[epsilon]^nx and i = i0[epsilon]^nl, + when l is the distance between the plates, we see that + + nu / mv = [epsilon]^(nx) / ([epsilon]^(nl) - [epsilon]^(nx)), + + n v [epsilon]^(nx) + -- = -- . -------------------------------. + m u [epsilon]^(ne) - [epsilon]^(nx) + + Since v/u is a very small quantity we see that n will be less than m + except when [epsilon]^nl - [epsilon]^nx is small, i.e. except close to + the anode. Thus there will be an excess of positive electricity from + the cathode almost up to the anode, while close to the anode there + will be an excess of negative. This distribution of electricity will + make the electric force diminish from the cathode to the place where + there is as much positive as negative electricity, where it will have + its minimum value, and then increase up to the anode. + + The expression i = i0[epsilon]^[alpha]l applies to the case when there + is no source of ionization in the gas other than the collisions; if in + addition to this there is a source of uniform ionization producing q + ions per cubic centimetre, we can easily show that + + qe + i = i0[epsilon]^{[alpha]l} + -------(e^{[alpha]l} - 1). + [alpha] + + With regard to the minimum energy which must be possessed by a + corpuscle to enable it to produce ions by collision, Townsend (loc. + cit.) came to the conclusion that to ionize air the corpuscle must + possess an amount of energy equal to that acquired by the fall of its + charge through a potential difference of about 2 volts. This is also + the value arrived at by H. A. Wilson by entirely different + considerations. Stark, however, gives 17 volts as the minimum for + ionization. The energy depends upon the nature of the gas; recent + experiments by Dawes and Gill and Pedduck (_Phil. Mag._, Aug. 1908) + have shown that it is smaller for helium than for air, hydrogen, or + carbonic acid gas. + +If there is no external source of ionization and no emission of +corpuscles from the cathode, then it is evident that even if some +corpuscles happened to be present in the gas when the electric field +were applied, we could not get a permanent current by the aid of +collisions made by these corpuscles. For under the electric field, the +corpuscles would be driven from the cathode to the anode, and in a short +time all the corpuscles originally present in the gas and those produced +by them would be driven from the gas against the anode, and if there was +no source from which fresh corpuscles could be introduced into the gas +the current would cease. The current, however, could be maintained +indefinitely if the positive ions in their journey back to the cathode +also produced ions by collisions, for then we should have a kind of +regenerative process by which the supply of corpuscles could be +continually renewed. To maintain the current it is not necessary that +the ionization resulting from the positive ions should be anything like +as great as that from the negative, as the investigation given below +shows a very small amount of ionization by the positive ions will +suffice to maintain the current. The existence of ionization by +collision with positive ions has been proved by Townsend. Another method +by which the current could be and is maintained is by the anode emitting +corpuscles under the impact of the positive ions driven against it by +the electric field. J. J. Thomson has shown by direct experiment that +positively electrified particles when they strike against a metal plate +cause the metal to emit corpuscles (J. J. Thomson, _Proc. Camb. Phil. +Soc._ 13, p. 212; Austin, _Phys. Rev._ 22, p. 312). If we assume that +the number of corpuscles emitted by the plate in one second is +proportional to the energy in the positive ions which strike the plate +in that second, we can readily find an expression for the difference of +potential which will maintain without any external ionization a current +of electricity through the gas. As this investigation brings into +prominence many of the most important features of the electric +discharge, we shall consider it in some detail. + + Let us suppose that the electrodes are parallel plates of metal at + right angles to the axis of x, and that at the cathode x = 0 and at the + anode x = d, d being thus the distance between the plates. Let us also + suppose that the current of electricity flowing between the plates is + so small that the electrification between the plates due to the + accumulation of ions is not sufficient to disturb appreciably the + electric field, which we regard as uniform between the plates, the + electric force being equal to V/d, where V is the potential difference + between the plates. The number of positive ions produced per second in + a layer of gas between the planes x and x+dx is [alpha]nu.dx. Here n is + the number of corpuscles per unit volume, [alpha] the coefficient of + ionization (for strong electric field [alpha] = 1/[lambda]', where + [lambda]' is the mean free path of a corpuscle), and u the velocity of + a corpuscle parallel to x. We have seen that nu = i0[epsilon]^[alpha]x, + where i0 is the number of corpuscles emitted per second by unit area of + the cathode. Thus the number of positive ions produced in the layer is + [alpha]i0[epsilon]^[alpha]x dx. If these went straight to the cathode + without a collision, each of them would have received an amount of + kinetic energy Vex/d when they struck the cathode, and the energy of + the group of ions would be Vex/d.[alpha]i0[epsilon]^dx dx. The positive + ions will, however, collide with the molecules of the gas through which + they are passing, and this will diminish the energy they possess when + they reach the cathode. + + The diminution in the energy will increase in geometrical proportion + with the length of path travelled by the ion and will thus be + proportional to [epsilon]^-[beta]x, [beta] will be proportional to the + number of collisions and will thus be proportional to the pressure of + the gas. Thus the kinetic energy possessed by the ions when they reach + the cathode will be + + [epsilon]^{-[beta]x} . V(ex/d) . [alpha]i0[epsilon]^{[alpha]x} dx, + + and E, the total amount of energy in the positive ions which reach the + cathode in unit time, will be given by the equation + _ + /d + E = | [epsilon]^{-[beta]x} . V(ex/d) . [alpha]i0[epsilon]^{[alpha]x} dx + _/0 + _ + Ve[alpha]i0 /d + = ----------- | [epsilon]^{-([beta]-[alpha])x}.x.dx + d _/0 + + Ve[alpha]i0 / 1 / 1 d \ \ + = ----------- { ------------------ - [epsilon]^{-([beta]-[alpha])d} { ------------------ + ---------------- } } (1). + d \([beta]-[alpha])^2 \([beta]-[alpha])^2 ([beta]-[alpha])/ / + + + If the number of corpuscles emitted by the cathode in unit time is + proportional to this energy we have i0 = kE, where k is a constant; + hence by equation (1) we have + + ([beta]-[alpha])^2 d + V = ------------------ . --, + ke[alpha] I + + where + + I = 1 - [epsilon]^{-([beta]-[alpha])d} (1 + d([beta] - [alpha])). + + Since both [beta] and [alpha] are proportional to the pressure, I and + ([beta] - [alpha])^2d/[alpha] are both functions of pd, the product of + the pressure and the spark length, hence we see that V is expressed by + an equation of the form + + 1 + V = -- [int](pd) (2), + ke + + where [int](pd) denotes a function of pd, and neither p nor d enter + into the expression for V except in this product. Thus the potential + difference required to produce discharge is constant as long as the + product of the pressure and spark length remains constant; in other + words, the spark potential is constant as long as the mass of the gas + between the electrodes is constant. Thus, for example, if we halve the + pressure the same potential difference will produce a spark of twice + the length. This law, which was discovered by Paschen for fairly long + sparks (_Annalen_, 37, p. 79), and has been shown by Carr (_Phil. + Trans._, 1903) to hold for short ones, is one of the most important + properties of the electric discharge. + + We see from the expression for V that when ([beta] - [alpha])d is very + large + + V = ([beta] - [alpha])^2d/ke[alpha]. + + Thus V becomes infinite when d is infinite. Again when ([beta] - + [alpha])d is very small we find + + V = 1/ke[alpha]d; + + thus V is again infinite when d is nothing. There must therefore be + some value of d intermediate between zero and infinity for which V is + a minimum. This value is got by finding in the usual way the value of + d, which makes the expression for V given in equation (1) a minimum. + We find that d must satisfy the equation + + / \ + 1 = [epsilon]^{-([beta]-[alpha])d} {1 + ([beta] - [alpha])d + ([beta] - [alpha].d)^2}. + \ / + + We find by a process of trial and error that ([beta]-[alpha])d = 1.8 + is approximately a solution of this equation; hence the distance for + minimum potential is 1.8/([beta] - [alpha]). Since [beta] and [alpha] + are both proportional to the pressure, we see that the critical spark + length varies inversely as the pressure. If we substitute this value + in the expression for V we find that [=V], the minimum spark + potential, is given by + + _ [beta] - [alpha] 2.2 + V = ---------------- . ---. + [alpha] ke + + Since [beta] and [alpha] are each proportional to the pressure, the + minimum potential is independent of the pressure of the gas. On this + view the minimum potential depends upon the metal of which the cathode + is made, since k measures the number of corpuscles emitted per unit + time by the cathode when struck by positive ions carrying unit energy, + and unless [beta] bears the same ratio to [alpha] for all gases the + minimum potential will also vary with the gas. The measurements which + have been made of the "cathode fall of potential," which as we shall + see is equal to the minimum potential required to produce a spark, + show that this quantity varies with the material of which the cathode + is made and also with the nature of the gas. Since a metal plate, when + bombarded by positive ions, emits corpuscles, the effect we have been + considering must play a part in the discharge; it is not, however, the + only effect which has to be considered, for as Townsend has shown, + positive ions when moving above a certain speed ionize the gas, and + cause it to emit corpuscles. It is thus necessary to take into account + the ionization of the positive ions. + + Let m be the number of positive ions per unit volume, and w their + velocity, the number of collisions which occur in one second in one + cubic centimetre of the gas will be proportional to mwp, where p is + the pressure of the gas. Let the number of ions which result from + these collisions be [gamma]mw; [gamma] will be a function of p and of + the strength of the electric field. Let as before n be the number of + corpuscles per cubic centimetre, u their velocity, and [alpha]nu the + number of ions which result in one second from the collisions between + the corpuscles and the gas. The number of ions produced per second per + cubic centimetre is equal to [alpha]nu + [gamma]mw; hence when things + are in a steady state + + d + --(nu) = [alpha]nu + [gamma]mw , + dx + + and + + e(nu + mw) = i, + + where e is the charge on the ion and i the current through the gas. + The solution of these equations when the field is uniform between the + plates, is + + enu = C[epsilon]^{([alpha]-[gamma])x} - [gamma]i/([alpha] - [gamma]), + + emw = -C[epsilon]^{([alpha]-[gamma])x} + [alpha]i/([alpha] - [gamma]), + + where C is a constant of integration. If there is no emission of + positive ions from the anode enu = i, when x = d. Determining C from + this condition we find + + i / \ + enu = ----------------- {[alpha][epsilon]^{([alpha]-[gamma])(x-d)} - [gamma] }, + [alpha] - [gamma] \ / + + [alpha]i / \ + emw = ----------------- {1 - [epsilon]^{([alpha]-[gamma])(x-d)} }. + [alpha] - [gamma] \ / + + If the cathode did not emit any corpuscles owing to the bombardment by + positive ions, the condition that the charge should be maintained is + that there should be enough positive ions at the cathode to carry the + current i.e. that emw = i; when x = 0, the condition gives + + i / \ + ----------------- {[alpha][epsilon]^{-([alpha]-[gamma])d} - [gamma] } = 0, + [alpha] - [gamma] \ / + + or + + [epsilon]^{[alpha]d}/[alpha] = [epsilon]^{[gamma]d}/[gamma]. + + Since [alpha] and [gamma] are both of the form pf(X/p) and X = V/d, we + see that V will be a function of pd, in agreement with Paschen's law. + If we take into account both the ionization of the gas and the + emission of corpuscles by the metal we can easily show that + + _ + [alpha]-[gamma][epsilon]^{([alpha]-[gamma])d} k[alpha]Ve | 1 + --------------------------------------------- = ---------- | -------------------------- - + [alpha] - [gamma] d |_ ([beta]+[gamma]-[alpha])^2 + _ + / 1 d \ | + [epsilon]^{-([beta]+[gamma]-[alpha])d} { -------------------------- + ---------------------- } |, + \([beta]+[gamma]-[alpha])^2 [beta]+[gamma]-[alpha]/ _| + + where k and [beta] have the same meaning as in the previous + investigation. When d is large, [epsilon]^{([alpha]-[gamma])d} is also + large; hence in order that the left-hand side of this equation should + not be negative [gamma] must be less than [alpha]/[epsilon]^ + {([alpha]-[gamma])d}; as this diminishes as d increases we see that when + the sparks are very long discharge will take place, practically as soon + as [gamma] has a finite value, i.e. as soon as the positive ions begin + to produce fresh ions by their collisions. + +In the preceding investigation we have supposed that the electric field +between the plates was uniform; if it were not uniform we could get +discharges produced by very much smaller differences of potential than +are necessary in a uniform field. For to maintain the discharge it is +not necessary that the positive ions should act as ionizers all along +their path; it is sufficient that they should do so in the neighbourhood +of cathode. Thus if we have a strong field close to the cathode we might +still get the discharge though the rest of the field were comparatively +weak. Such a distribution of electric force requires, however, a great +accumulation of charged ions near the cathode; until these ions +accumulate the field will be uniform. If the uniform field existing in +the gas before the discharge begins were strong enough to make the +corpuscles produce ions by collision, but not strong enough to make the +positive ions act as ionizers, there would be some accumulation of ions, +and the amount of this accumulation would depend upon the number of free +corpuscles originally present in the gas, and upon the strength of the +electric field. If the accumulation were sufficient to make the field +near the cathode so strong that the positive ions could produce fresh +ions either by collision with the cathode or with the gas, the discharge +would pass though the gas; if not, there will be no continuous +discharge. As the amount of the accumulation depends on the number of +corpuscles present in the gas, we can understand how it is that after a +spark has passed, leaving for a time a supply of corpuscles behind it, +it is easier to get a discharge to pass through the gas than it was +before. + +[Illustration: Fig. 15.] + +The inequality of the electric field in the gas when a continuous +discharge is passing through it is very obvious when the pressure of the +gas is low. In this case the discharge presents a highly differentiated +appearance of which a type is represented in fig. 15. Starting from the +cathode we have a thin velvety luminous glow in contact with the +surface; this glow is often called the "first cathode layer." Next this +we have a comparatively dark space whose thickness increases as the +pressure diminishes; this is called the "Crookes's dark space," or the +"second cathode layer." Next this we have a luminous position called the +"negative glow" or the "third cathode layer." The boundary between the +second and third layers is often very sharply defined. Next to the third +layer we have another dark space called the "Faraday dark space." Next +to this and reaching up to the anode is another region of luminosity, +called the "positive column," sometimes (as in fig. 15, a) continuous, +sometimes (as in fig. 15, b) broken up into light or dark patches called +"striations." The dimensions of the Faraday dark space and the positive +column vary greatly with the current passing through the gas and with +its pressure; sometimes one or other of them is absent. These +differences in appearances are accompanied by great difference in the +strength of the electric field. The magnitude of the electric force at +different parts of the discharge is represented in fig. 16, where the +ordinates represent the electric force at different parts of the tube, +the cathode being on the right. We see that the electric force is very +large indeed between the negative glow and the cathode, much larger than +in any other part of the tube. It is not constant in this region, but +increases as we approach the cathode. The force reaches a minimum either +in the negative glow itself or in the part of the Faraday dark space +just outside, after which it increases towards the positive column. In +the case of a uniform positive column the electric force along it is +constant until we get quite close to the anode, when a sudden change, +called the "anode fall," takes place in the potential. + +[Illustration: + _Discharge in Hydrogen + Pressure 2.25 m.m. Current 0.568.10^-3 ampere_ +FIG. 16.] + +The difference of potential between the cathode and the negative glow is +called the "cathode potential fall" and is found to be constant for wide +variations in the pressure of the gas and the current passing through. +It increases, however, considerably when the current through the gas +exceeds a certain critical value, depending among other things on the +size of the cathode. This cathode fall of potential is shown by +experiment to be very approximately equal to the minimum potential +difference. The following table contains a comparison of the +measurements of the cathode fall of potentials in various gases made by +Warburg (_Wied. Ann._, 1887, 31, p. 545, and 1890, 40, p. 1), Capstick +(_Proc. Roy. Society_, 1898, 63, p. 356), and Strutt (_Phil. Trans._, +1900, 193, p. 377), and the measurements by Strutt of the smallest +difference of potential which will maintain a spark through these gases. + + +---------+-----------------------------------------+-----------------+ + | | Cathode fall in Volts. |Least potential | + | Gas. +-----------------------------+-----------+ difference | + | | Platinum Electrodes. |Aluminium | required to | + | | |Electrodes.|maintain a Spark.| + +---------+-----------+---------+-------+-----------+-----------------+ + | | Warburg. |Capstick.|Strutt.| Warburg. | Strutt. | + +---------+-----------+---------+-------+-----------+-----------------+ + |Air | 340-350 | .. | .. | .. | 341 | + |H2 | about 300 | 298 | .. | 168 | 302-308 | + |O2 | .. | 369 | .. | .. | .. | + |N2 |230 if free| 232 | .. | 207 | 251 | + | |from oxygen| | | | | + |Hg vapour| 340 | .. | .. | .. | .. | + |Helium | .. | .. | 226 | .. | 261-326 | + |H2O | .. | 469 | .. | .. | .. | + |NH3 | .. | 582 | .. | .. | .. | + +---------+-----------+---------+-------+-----------+-----------------+ + +Thus in the cases in which the measurements could be made with the +greatest accuracy the agreement between the cathode fall and the minimum +potential difference is very close. The cathode fall depends on the +material of which the terminals are made, as is shown by the following +table due to Mey (_Verh. deutsch. physik. Gesell._, 1903, 5, p. 72). + + +------+---------------------------------------------+ + | Gas. | Electrode. | + +------+---+---+---+---+---+---+---+---+---+-----+---+ + | | Pt| Hg| Ag| Cu| Fe| Zn| Al| Mg| Na| Na-K| K | + +------+---+---+---+---+---+---+---+---+---+-----+---+ + |O2 |369| ..| ..| ..| ..| ..| ..| ..| ..| .. | ..| + |H2 |300| ..|295|280|230|213|190|168|185|169 |172| + |N2 |232|226| ..| ..| ..| ..| ..|207|178|125 |170| + |He |226| ..| ..| ..| ..| ..| ..| ..| 80| 78.5| 69| + |Argon |167| ..| ..| ..| ..| ..|100| ..| ..| .. | ..| + +------+---+---+---+---+---+---+---+---+---+-----+---+ + +The dependence of the minimum potential required to produce a spark upon +the metal of which the cathode is made has not been clearly established, +some observers being unable to detect any difference between the +potential required to spark between electrodes of aluminium and those of +brass, while others thought they had detected such a difference. It is +only with sparks not much longer than the critical spark length that we +could hope to detect this difference. When the current through the gas +exceeds a certain critical value depending among other things on the +size of the cathode, the cathode fall of potential increases rapidly and +at the same time the thickness of the dark spaces diminishes. We may +regard the part of the discharge between the cathode and the negative +glow as a discharge taking place under minimum potential difference +through a distance equal to the critical spark length. An inspection of +fig. 16 will show that we cannot regard the electric field as constant +even for this small distance; it thus becomes a matter of interest to +know what would be the effect on the minimum potential difference +required to produce a spark if there were sufficient ions present to +produce variations in the electric field analogous to those represented +in fig. 16. If the electric force at a distance x from the cathode were +proportional to [epsilon]^-px we should have a state of things much +resembling the distribution of electric force near the cathode. If we +apply to this distribution the methods used above for the case when the +force was uniform, we shall find that the minimum potential is less and +the critical spark length greater than when the electric force is +uniform. + +_Potential Difference required to produce a Spark of given Length._--We +may regard the region between the cathode and the negative glow as a +place for the production of corpuscles, these corpuscles finding their +way from this region through the negative glow. The parts of this glow +towards the anode we may regard as a cathode, from which, as from a hot +lime cathode, corpuscles are emitted. Let us now consider what will +happen to these corpuscles shot out from the negative glow with a +velocity depending on the cathode fall of potential and independent of +the pressure. These corpuscles will collide with the molecules of the +gas, and unless there is an external electric field to maintain their +velocity they will soon come to rest and accumulate in front of the +negative glow. The electric force exerted by this cloud of corpuscles +will diminish the strength of the electric field in the region between +the cathode and the negative glow, and thus tend to stop the discharge. +To keep up the discharge we must have a sufficiently strong electric +field between the negative glow and the anode to remove the corpuscles +from this region as fast as they are sent into it from the cathode. If, +however, there is no production of ions in the region between the +negative glow and the anode, all the ions in this region will have come +from near the cathode and will be negatively charged; this negative +electrification will diminish the electric force on the cathode side of +it and thus tend to stop the discharge. This back electric field could, +however, be prevented by a little ionization in the region between the +anode and glow, for this would afford a supply of positive ions, and +thus afford an opportunity for the gas in this region to have in it as +many positive as negative ions; in this case it would not give rise to +any back electromotive force. The ionization which produces these +positive ions may, if the field is intense, be due to the collisions of +corpuscles, or it may be due to radiation analogous to ultra-violet, or +soft Rontgen rays, which have been shown by experiment to accompany the +discharge. Thus in the most simple conditions for discharge we should +have sufficient ionization to keep up the supply of positive ions, and +an electric field strong enough to keep the velocity of the negative +corpuscle equal to the value it has when it emerges from the negative +glow. Thus the force must be such as to give a constant velocity to the +corpuscle, and since the force required to move an ion with a given +velocity is proportional to the pressure, this force will be +proportional to the pressure of the gas. Let us call this force ap; then +if l is the distance of the anode from the negative glow the potential +difference between these points will be alp. The potential difference +between the negative glow and the cathode is constant and equals c; +hence if V is the potential difference between the anode and cathode, +then V = c + alp, a relation which expresses the connexion between the +potential difference and spark length for spark lengths greater than the +critical distance. It is to be remembered that the result we have +obtained applies only to such a case as that indicated above, where the +electric force is constant along the positive column. Experiments with +the discharge through gases at low pressure show the discharge may take +other forms. Thus the positive column may be striated when the force +along it is no longer uniform, or the positive column may be absent; +the discharge may be changed from one of these forms to another by +altering the current. The relation between the potential and the +distance between the electrodes varies greatly, as we might expect, with +the current passing through the gas. + +The connexion between the potential difference and the spark length has +been made the subject of a large number of experiments. The first +measurements were made by Lord Kelvin in 1860 (_Collected Papers on +Electrostatics and Magnetism_, p. 247); subsequent experiments have been +made by Baille (_Ann. de chimie et de physique_, 5, 25, p. 486), Liebig +(_Phil. Mag._ [5], 24, p. 106), Paschen (_Wied. Ann._ 37, p. 79), Peace +(_Proc. Roy. Soc._, 1892, 52, p. 99), Orgler (_Ann. der Phys._ 1, p. +159), Strutt (_Phil. Trans._ 193, p. 377), Bouty (_Comptes rendus_, 131, +pp. 469, 503), Earhart (_Phil. Mag._ [6], 1, p. 147), Carr (_Phil. +Trans._, 1903), Russell (_Phil. Mag._ [5], 64, p. 237), Hobbs (_Phil. +Mag._ [6], 10, p. 617), Kinsley (_Phil. Mag._ [6], 9, 692), Ritter +(_Ann. der Phys._ 14, p. 118). The results of their experiments show +that for sparks considerably longer than the critical spark length, the +relation between the potential difference V and the spark length l may +be expressed when the electrodes are large with great accuracy by the +linear relation V = c + blp, where p is the pressure and c and b are +constants depending on the nature of the gas. When the sparks are long +the term blp is the most important and the sparking potential is +proportional to the spark length. Though there are considerable +discrepancies between the results obtained by different observers, these +indicate that the production of a long spark between large electrodes in +air at atmospheric pressure requires a potential difference of 30,000 +volts for each centimetre of spark length. In hydrogen only about half +this potential difference is required, in carbonic acid gas the +potential difference is about the same as in air, while Ritter's +experiments show that in helium only about one-tenth of this potential +difference is required. + +In the case when the electric field is not uniform, as for example when +the discharge takes place between spherical electrodes, Russell's +experiments show that the discharge takes place as soon as the maximum +electric force in the field between the electrodes reaches a definite +value, which he found was for air at atmospheric pressure about 38,000 +volts per centimetre. + +_Very Short Sparks._--Some very interesting experiments on the potential +difference required to produce exceedingly short sparks have been made +by Earhart, Hobbs and Kinsley; the length of these sparks was comparable +with the wave length of sodium light. With sparks of these lengths it +was found that it was possible to get a discharge with less than 330 +volts, the minimum potential difference in air. The results of these +observers show that there is no diminution in the minimum potential +difference required to produce discharge until the spark length gets so +small that the average electric force between the electrodes amounts to +about one million volts per centimetre. When the force rises to this +value a discharge takes place even though the potential difference is +much less than 330 volts; in some of Earhart's experiments it was only +about 2 volts. This kind of discharge is determined not by the condition +that the potential difference should have a given value, but that the +electric force should have a given value. Another point in which this +discharge differs from the ordinary one is that it is influenced +entirely by the nature of the electrodes and not by the nature or +pressure of the gas between them, whereas the ordinary discharge is in +many cases not affected appreciably by changes in the metal of the +electrodes, but is always affected by changes in the pressure and +character of the gas between them. Kinsley found that when one of these +small sparks passed between the electrodes a kind of metallic bridge was +formed between them, so that they were in metallic connexion, and that +the distance between them had to be considerably increased before the +bridge was broken. Almy (_Phil. Mag._, Sept. 1908), who used very small +electrodes, was unable to get a discharge with less than the minimum +spark potential even when the spark length was reduced to one-third of +the wave length of sodium light. He suggests that the discharges +obtained with larger electrodes for smaller voltages are due to the +electrodes being dragged together by the electrostatic attraction +between them. + +_Constitution of the Electric Spark._--Schuster and Hemsalech (_Phil. +Trans._ 193, p. 189), Hemsalech (_Comptes Rendus_, 130, p. 898; 132, p. +917; _Jour. de Phys._ 3. 9, p. 43, and Schenck, _Astrophy. Jour._ 14, p. +116) have by spectroscopic methods obtained very interesting results +about the constitution of the spark. The method employed by Schuster and +Hemsalech was as follows: Suppose we photograph the spectrum of a +horizontal spark on a film which is on the rim of a wheel rotating about +a horizontal axis with great velocity. If the luminosity travelled with +infinite speed from one electrode to the other, the image on the film +would be a horizontal line. If, however, the speed with which the +luminosity travelled between the electrodes was comparable with the +speed of the film, the line would be inclined to the horizontal, and by +measuring the inclinations we could find the speed at which the +luminosity travelled. In this way Schuster and Hemsalech showed that +when an oscillating discharge passed between metallic terminals in air, +the first spark passes through the air alone, no lines of the metal +appearing in its spectrum. This first spark vaporizes some of the metal +and the subsequent sparks passing mainly through the metallic vapour; +the appearance of the lines in the film shows that the velocity of the +luminous part of the vapour was finite. The velocity of the vapour of +metals of low atomic weight was in general greater than that of the +vapour of heavier metals. Thus the velocity of aluminium vapour was 1890 +metres per second, that of zinc and cadmium only about 545. Perhaps the +most interesting point in the investigation was the discovery that the +velocities corresponding to different lines in the spectrum of the same +metal were in some cases different. Thus with bismuth some of the lines +indicated a velocity of 1420 metres per second, others a velocity of +only 550, while one ([lambda] = 3793) showed a still smaller velocity. +These results are in accordance with a view suggested by other phenomena +that many of the lines in a spectrum produced by an electrical discharge +originate from systems formed during the discharge and not from the +normal atom or molecule. Schuster and Hemsalech found that by inserting +a coil with large self induction in the primary circuit they could +obliterate the air lines in the discharge. + +Schenck, by observing the appearance presented when an alternating +current, produced by discharging Leyden jars, was examined in a rapidly +rotating mirror, found it showed the following stages: (1) a thin bright +line, followed in some cases at intervals of half the period of the +discharge by fainter lines; (2) bright curved streamers starting from +the negative terminal, and diminishing rapidly in speed as they receded +from the cathode; (3) a diffused glow lasting for a much longer period +than either of the preceding. These constituents gave out quite +different spectra. + +The structure of the discharge is much more easily studied when the +pressure of the gas is low, as the various parts which make up the +discharge are more widely separated from each other. We have already +described the general appearance of the discharge through gases at low +pressures (see p. 657). There is, however, one form of discharge which +is so striking and beautiful that it deserves more detailed +consideration. In this type of discharge, known as the striated +discharge, the positive column is made up of alternate bright and dark +patches known as _striations_. Some of these are represented in fig. 17, +which is taken from a paper by De la Rue and Muller (_Phil. Trans._, +1878, Pt. 1). This type of discharge only occurs when the current and +the pressure of the gas are between certain limits. It is most +beautifully shown when a Wehnelt cathode is used and the current is +produced by storage cells, as this allows us to use large currents and +to maintain a steady potential difference between the electrodes. The +striations are in consequence very bright and steady. The facts which +have been established about these striations are as follows: The +distance between the bright parts of the striations is greater at low +pressures than at high; it depends also upon the diameter of the tube, +increasing as the diameter of the tube increases. If the discharge tube +is wide at one place and narrow in another the striations will be +closer together in the narrow parts than in the wide. The distance +between the striations depends on the current through the tube. The +relation is not a very simple one, as an increase of current sometimes +increases while under other circumstances it decreases the distance +between the striations (see Willows, _Proc. Camb. Phil. Soc._ 10, p. +302). The electric force is not uniform along the striated discharge, +but is greater in the bright than in the dark parts of the striation. An +example is shown in fig. 16, due to H. A. Wilson, which shows the +distribution of electric force at every place in a striated discharge. +In experiments made by J. J. Thomson (_Phil. Mag._, Oct. 1909), using a +Wehnelt cathode, the variations in the electric force were more +pronounced than those shown in fig. 16. The electric force in this case +changed so greatly that it actually became negative just on the cathode +side of the bright part of the striation. Just inside the striation on +the anode side it rose to a very high value, then continually diminished +towards the bright side of the next striation when it again increased. +This distribution of electric force implies that there is great excess +of negative electricity at the bright head of the striation, and a small +excess of positive everywhere else. The temperature of the gas is higher +in the bright than in the dark parts of the striations. Wood (_Wied. +Ann._ 49, p. 238), who has made a very careful study of the distribution +of temperature in a discharge tube, finds that in those tubes the +temperature varies in the same way as the electric force, but that this +temperature (which it must be remembered is the average temperature of +all the molecules and not merely of those which are taking part in the +discharge) is by no means high; in no part of the discharge did the +temperature in his experiments exceed 100 deg. C. + +[Illustration: FIG. 17.] + +_Theory of the Striations._--We may regard the heaping up of the +negative charges at intervals along the discharge as the fundamental +feature in the striations, and this heaping up may be explained as +follows. Imagine a corpuscle projected with considerable velocity from a +place where the electric field is strong, such as the neighbourhood of +the cathode; as it moves towards the anode through the gas it will +collide with the molecules, ionize them and lose energy and velocity. +Thus unless the corpuscle is acted on by a field strong enough to supply +it with the energy it loses by collision, its speed will gradually +diminish. Further, when its energy falls below a certain value it will +unite with a molecule and become part of a negative ion, instead of a +corpuscle; at this stage there will be a sudden and very large +diminution in its velocity. Let us now follow the course of a stream of +corpuscles starting from the cathode and approaching the anode. If the +speed falls off as the stream proceeds, the corpuscles in the rear will +gain on those in front and the density of the stream in the front will +be increased. If at a certain place the velocity receives a sudden check +by the corpuscles becoming loaded with a molecule, the density of the +negative electricity will increase at this place with great rapidity, +and here there will be a great accumulation of negative electricity, as +at the bright head on the cathode side of a striation. Now this +accumulation of negative electricity will produce a large electric force +on the anode side; this will drive corpuscles forward with great +velocity and ionize the gas. These corpuscles will behave like those +shot from the cathode and will accumulate again at some distance from +their origin, forming the bright head of the next striation, when the +process will be repeated. On this view the bright heads of the +striations act like electrodes, and the discharge passes from one bright +head to the next as by a number of stepping stones, and not directly +from cathode to anode. The luminosity at the head of the striations is +due to the recombination of the ions. These ions have acquired +considerable energy from the electric field, and this energy will be +available for supplying the energy radiated away as light. The +recombination of ions which do not possess considerable amounts of +energy does not seem to give rise to luminosity. Thus, in an ionized gas +not exposed to an electric field, although we have recombination between +the ions, we need not have luminosity. We have at present no exact data +as to the amount of energy which must be given to an ion to make it +luminous on recombination; it also certainly varies with the nature of +the ion; thus even with hot Wehnelt cathodes J. J. Thomson has never +been able to make the discharge through air luminous with a potential +less than from 16 to 17 volts. The mercury lamps, however, in which the +discharge passes through mercury vapour are luminous with a potential +difference of about 12 volts. It follows that if the preceding theory be +right the potential difference between two bright striations must be +great enough to make the corpuscles ionize by collision and also to give +enough energy to the ions to make them luminous when they recombine. The +difference of potential between the bright parts of successive +striations has been measured by Hohn (_Phys. Zeit._ 9, p. 558); it +varies with the pressure and with the gas. The smallest value given by +Hohn is about 15 volts. In some experiments made by J. J. Thomson, when +the pressure of the gas was very low, the difference of potential +between two adjacent dark spaces was as low as 3.75 volts. + +_The Arc Discharge._--The discharges we have hitherto considered have +been characterized by large potential differences and small currents. In +the arc discharge we get very large currents with comparatively small +potential differences. We may get the arc discharge by taking a battery +of cells large enough to give a potential difference of 60 to 80 volts, +and connecting the cells with two carbon terminals, which are put in +contact, so that a current of electricity flows round the circuit. If +the terminals, while the current is on, are drawn apart, a bright +discharge, which may carry a current of many amperes, passes from one to +the other. This arc discharge, as it is called, is characterized by +intense heat and by the brilliant luminosity of the terminals. This +makes it a powerful source of light. The temperature of the positive +terminal is much higher than that of the negative. According to Violle +(_Comptes Rendus_, 115, p. 1273) the temperature of the tip of the +former is about 3500 deg. C, and that of the latter 2700 deg. C. The +temperature of the arc itself he found to be higher than that of either +of its terminals. As the arc passes, the positive terminal gets hollowed +out into a crater-like shape, but the negative terminal remains pointed. +Both terminals lose weight. + + The appearance of the terminals is shown in fig. 18, given by Mrs + Ayrton (_Proc. Inst. Elec. Eng._ 28, p. 400); a, b represent the + terminals when the arc is quiet, and c when it is accompanied by a + hissing sound. The intrinsic brightness of the positive crater does + not increase with an increase in the current; an increased current + produces an increase in the area of the luminous crater, but the + amount of light given out by each unit of area of luminous surface is + unaltered. This indicates that the temperature of the crater is + constant; it is probably that at which carbon volatilizes. W. E. + Wilson (_Proc. Roy. Soc._ 58, p. 174; 60, p. 377) has shown that at + pressures of several atmospheres the intrinsic brightness of the + crater is considerably diminished. + + [Illustration: FIG. 18.] + + [Illustration: FIG. 19.] + + The connexion between V, the potential difference between the + terminals, and l, the length of the arc, is somewhat analogous to that + which holds for the spark discharge. Frohlich (_Electrotech. Zeit._ 4, + p. 150) gives for this connexion the relation V = m + nl, where m and + n are constants. Mrs Ayrton (_The Electric Arc_, chap. iv.) finds that + both m and n depend upon the current passing between the terminals, + and gives as the relation between V and l, V = [alpha] + [beta]/I + + ([gamma] + [delta]/I)l, where [alpha], [beta], [gamma], [delta] are + constants and I the current. The relation between current and + potential difference was made the subject of a series of experiments + by Ayrton (_Electrician_, 1, p. 319; xi. p. 418), some of whose + results are represented in fig. 19. For a quiet arc an increase in + current is accompanied by a fall in potential difference, while for + the hissing arc the potential difference is independent of the + current. The quantities m and n which occur in Frohlich's equation + have been determined by several experimenters. For carbon electrodes + in air at atmospheric pressure m is about 39 volts, varying somewhat + with the size and purity of the carbons; it is diminished by soaking + the terminals in salt solution. The value of n given by different + observers varies considerably, ranging from .76 to 2 volts when l is + measured in millimetres; it depends upon the current, diminishing as + the current increases. When metallic terminals are used instead of + carbons, the value of m depends upon the nature of the metal, m in + general being larger the higher the temperature at which the metal + volatilizes. Thus v. Lang (_Wied. Ann._ 31, p. 384) found the + following values for m in air at atmospheric pressure:--C = 35; Pt = + 27.4; Fe = 25; Ni = 26.18; Cu = 23.86; Ag = 15.23; Zn = 19.86; Cd = + 10.28. Lecher (_Wied. Ann._ 33, p. 609) gives Pt = 28, Fe = 20, Ag = + 8, while Arons (_Wied. Ann._ 31, p. 384) found for Hg the value 12.8; + in this case the fall of potential along the arc itself was abnormally + small. In comparing these values it is important to remember that + Lecher (loc. cit.) has shown that with Fe or Pt terminals the arc + discharge is intermittent. Arons has shown that this is also the case + with Hg terminals, but no intermittence has been detected with + terminals of C, Ag or Cu. The preceding measurements refer to mean + potentials, and no conclusions as to the actual potential differences + at any time can be drawn when the discharge is discontinuous, unless + we know the law of discontinuity. The ease with which an arc is + sustained depends greatly on the nature of the electrodes; when they + are brass, zinc, cadmium, or magnesium it is exceedingly difficult to + get the arc. + + [Illustration: FIG. 20.] + + [Illustration: FIG. 21.] + + The potential difference between the terminals is affected by the + pressure of the gas. The most extensive series of experiments on this + point is that made by Duncan, Rowland, and Tod (_Electrician_, 31, p. + 60), whose results are represented in fig. 20. We see from these + curves that for very short arcs the potential difference increases + continuously with the pressure, but for longer ones there is a + critical pressure at which the potential difference is a minimum, and + that this critical pressure seems to increase with the length of arc. + The nature of the gas also affects the potential difference. The + magnitude of this effect may be gathered from the following values + given by Arons (_Ann. der Phys._ 1, p. 700) for the potential + difference required to produce an arc 1.5 mm. long, carrying a current + of 4.5 amperes, between terminals of different metals in air and pure + nitrogen. + + +-----------+------+-----------+ + | Terminal. | Air. | Nitrogen. | + +-----------+------+-----------+ + | Ag | 21 | ? | + | Zn | 23 | 21 | + | Cd | 25 | 21 | + | Cu | 27 | 30 | + | Fe | 29 | 20 | + | Pt | 36 | 30 | + | Al | 39 | 27 | + | Pb | .. | 18 | + | Mg | .. | 22 | + +-----------+------+-----------+ + + Thus, with the discharge for an arc of given length and current, the + nature of the terminals is the most important factor in determining + the potential difference. The effects produced by the pressure and + nature of the surrounding gas, although quite appreciable, are not of + so much importance, while in the spark discharge the nature of the + terminals is of no importance, everything depending upon the nature + and pressure of the gas. + + The potential gradient in the arc is very far from being uniform. With + carbon terminals Luggin (_Wien. Ber._ 98, p. 1192) found that, with a + current of 15 amperes, there was a fall of potential of 33.7 close to + the anode, and one 8.7 close to the cathode, so that the curve + representing the distribution of potential between the terminals would + be somewhat like that shown in fig. 21. We have seen that a somewhat + analogous distribution of potential holds in the case of conduction + through flames, though in that case the greatest drop of potential is + in general at the cathode and not at the anode. The difference between + the changes of potential at the anode and cathode is not so large with + Fe and Cu terminals as with carbon ones; with mercury terminals, Arons + (_Wied. Ann._ 58, p. 73) found the anode fall to be 7.4 volts, the + cathode fall 5.4 volts. + +The case of the arc when the cathode is a pool of mercury and the anode +a metal wire placed in a vessel from which the air has been exhausted is +one which has attracted much attention, and important investigations on +this point have been made by Hewitt (_Electrician_, 52, p. 447), Wills +(_Electrician_, 54, p. 26), Stark, Retschinsky and Schnaposnikoff (_Ann. +der Phys._ 18, p. 213) and Pollak (_Ann. der Phys._ 19, p. 217). In this +arrangement the mercury is vaporized by the heat, and the discharge +which passes through the mercury vapour gives an exceedingly bright +light, which has been largely used for lighting factories, &c. The +arrangement can also be used as a rectifier, for a current will only +pass through it when the mercury pool is the cathode. Thus if such a +lamp is connected with an alternating current circuit, it lets through +the current in one direction and stops that in the other, thus +furnishing a current which is always in one direction. + +_Theory of the Arc Discharge._--An incandescent body such as a piece of +carbon even when at a temperature far below that of the terminals in an +arc, emits corpuscles at a rate corresponding to a current of the order +of 1 ampere per square centimetre of incandescent surface, and as the +rate of increase of emission with the temperature is very rapid, it is +probably at the rate of many amperes per square centimetre at the +temperature of the negative carbon in the arc. If then a piece of carbon +were maintained at this temperature by some external means, and used as +a cathode, a current could be sent from it to another electrode whether +the second electrode were cold or hot. If, however, these negatively +electrified corpuscles did not produce other ions either by collision +with the gas through which they move or with the anode, the spaces +between cathode and anode would have a negative charge, which would tend +to stop the corpuscles leaving the cathode and would require a large +potential difference between anode and cathode to produce any +considerable current. If, however, there is ionization either in the gas +or at the anode, the positive ions will diffuse into the region of the +discharge until they are sensibly equal in number to the negative ions. +When this is the case the back electromotive force is destroyed and the +same potential difference will carry a much larger current. The arc +discharge may be regarded as analogous to the discharge between +incandescent terminals, the only difference being that in the arc the +terminals are maintained in the state of incandescence by the current +and not by external means. On this view the cathode is bombarded by +positive ions which heat it to such a temperature that negative +corpuscles sufficient to carry the current are emitted by it. These +corpuscles bombard the anode and keep it incandescent. They ionize also, +either directly by collision or indirectly by heating the anode, the gas +and vapour of the metal of which the anode is made, and produce in this +way the supply of positive ions which keep the cathode hot. + +_Discharge from a Point._--A very interesting case of electric discharge +is that between a sharply pointed electrode, such as a needle, and a +metal surface of considerable area. At atmospheric pressures the +luminosity is confined to the immediate neighbourhood of the point. If +the sign of the potential of the point does not change, the discharge is +carried by ions of one sign--that of the charge on the pointed +electrode. The velocity of these ions under a given potential gradient +has been measured by Chattock (_Phil. Mag._ 32, p. 285), and found to +agree with that of the ions produced by Rontgen or uranium radiation, +while Townsend (_Phil. Trans._ 195, p. 259) has shown that the charge on +these ions is the same as that on the ions streaming from the point. If +the pointed electrode be placed at right angles to a metal plane serving +as the other electrode, the discharge takes place when, for a given +distance of the point from the plane, the potential difference between +the electrodes exceeds a definite value depending upon the pressure and +nature of the gas through which the discharge passes; its value also +depends upon whether, beginning with a small potential difference, we +gradually increase it until discharge commences, or, beginning with a +large potential difference, we decrease it until the discharge stops. +The value found by the latter method is less than that by the former. +According to Chattock's measurements the potential difference V for +discharge between the point and the plate is given by the linear +relation V = a + bl, where l is the distance of the point from the plate +and a and b are constants. From v. Obermayer's (_Wien. Ber._ 100, 2, p. +127) experiments, in which the distance l was greater than in +Chattock's, it would seem that the potential for larger distances does +not increase quite so rapidly with l as is indicated by Chattock's +relation. The potential required to produce this discharge is much less +than that required to produce a spark of length l between parallel +plates; thus from Chattock's experiments to produce the point discharge +when l = .5 cm. in air at atmospheric pressure requires a potential +difference of about 3800 volts when the pointed electrode is positive, +while to produce a spark at the same distance between plane electrodes +would require a potential difference of about 15,000 volts. Chattock +showed that with the same pointed electrode the value of the electric +intensity at the point was the same whatever the distance of the point +from the plane. The value of the electric intensity depended upon the +sharpness of the point. When the end of the pointed electrode is a +hemisphere of radius a, Chattock showed that for the same gas at the +same pressure the electric intensity f when discharge takes place is +roughly proportioned to a^-0.8. The value of the electric intensity at +the pointed electrode is much greater than its value at a plane +electrode for long sparks; but we must remember that at a distance from +a pointed electrode equal to a small multiple of the radius of curvature +of its extremity the electric intensity falls very far below that +required to produce discharge in a uniform field, so that the discharge +from a pointed electrode ought to be compared with a spark whose length +is comparable with the radius of curvature of the point. For such short +sparks the electric intensity is very high. The electric intensity +required to produce the discharge from a gas diminishes as the pressure +of the gas diminishes, but not nearly so rapidly as the electric +intensity for long sparks. Here again the discharge from a point is +comparable with short sparks, which, as we have seen, are much less +sensitive to pressure changes than longer ones. The minimum potential at +which the electricity streams from the point does not depend upon the +material of which the point is made; it varies, however, considerably +with the nature of the gas. The following are the results of some +experiments on this point. Those in the first two columns are due to +Rontgen, those in the third and fourth to Precht:-- + + +------+-----------------------------+--------------------+ + | |Discharge Potential. Point +.| Pressure 760. | + | Gas. +--------------+--------------+----------+---------+ + | | Pressure 205.| Pressure 110.| Point +. | Point -.| + +------+--------------+--------------+----------+---------+ + | | Volts. | Volts. | Volts. | Volts. | + | H2 | 1296 | 1174 | 2125 | 1550 | + | O2 | 2402 | 1975 | 2800 | 2350 | + | CO | 2634 | 2100 | .. | .. | + | CH4 | 2777 | 2317 | .. | .. | + | NO | 3188 | 2543 | .. | .. | + | CO2 | 3287 | 2655 | 3475 | 2100 | + | N2 | .. | .. | 2600 | 2000 | + | Air | .. | .. | 2750 | 2050 | + +------+--------------+--------------+----------+---------+ + +We see from this table that in the case of the discharge from a +positively electrified point the greater the molecular weight of the gas +the greater the potential required for discharge. Rontgen concluded from +his experiments that the discharging potential from a positive point in +different gases at the same pressure varies inversely as the mean free +path of the molecules of the gas. In the same gas, however, at different +pressures the discharging potential does not vary so quickly with the +pressure as does the mean free path. In Precht's experiments, in which +different gases were used, the variations in the discharging potential +are not so great as the variations in the mean free path of the gases. + +The current of electrified air flowing from the point when the +electricity is escaping--the well-known "electrical wind"--is +accompanied by a reaction on the point which tends to drive it +backwards. This reaction has been measured by Arrhenius (_Wied. Ann._ +63, p. 305), who finds that when positive electricity is escaping from a +point in air the reaction on the point for a given current varies +inversely as the pressure of the gas, and for different gases (air, +hydrogen and carbonic acid) inversely as the square root of the +molecular weight of the gas. The reaction when negative electricity is +escaping is much less. The proportion between the reactions for positive +and negative currents depends on the pressure of the gas. Thus for equal +positive and negative currents in air at a pressure of 70 cm. the +reaction for a positive point was 1.9 times that of a negative one, at +40 cm. pressure 2.6 times, at 20 cm. pressure 3.2 times, at 10.3 cm. +pressure 7 times, and at 5.1 cm. pressure 15 times the reaction for the +negative point. Investigation shows that the reaction should be +proportional to the quotient of the current by the velocity acquired by +an ion under unit potential gradient. Now this velocity is inversely +proportional to the pressure, so that the reaction should on this view +be directly proportional to the pressure. This agrees with Arrhenius' +results when the point is positive. Again, the velocities of an ion in +hydrogen, air and carbonic acid at the same pressure are approximately +inversely proportional to the square roots of their molecular weights, +so that the reaction should be directly proportional to this quantity. +This also agrees with Arrhenius' results for the discharge from a +positive point. The velocity of the negative ion is greater than that of +a positive one under the same potential gradient, so that the reaction +for the negative point should be less than that for a positive one, but +the excess of the positive reaction over the negative is much greater +than that of the velocity of the negative ion over the velocity of the +positive. There is, however, reason to believe that a considerable +condensation takes place around the negative ion as a nucleus after it +is formed, so that the velocity of the negative ion under a given +potential gradient will be greater immediately after the ion is formed +than when it has existed for some time. The measurements which have been +made of the velocities of the ions relate to those which have been some +time in existence, but a large part of the reaction will be due to the +newly-formed ions moving with a greater velocity, and thus giving a +smaller reaction than that calculated from the observed velocity. + +With a given potential difference between the point and the neighbouring +conductor the current issuing from the point is greater when the point +is negative than when it is positive, except in oxygen, when it is less. +Warburg (_Sitz. Akad. d. Wissensch. zu Berlin_, 1899, 50, p. 770) has +shown that the addition of a small quantity of oxygen to nitrogen +produces a great diminution in the current from a negative point, but +has very little effect on the discharge from a positive point. Thus the +removal of a trace of oxygen made a leak from a negative point 50 times +what it was before. Experiments with hydrogen and helium showed that +impurities in these gases had a great effect on the current when the +point was negative, and but little when it was positive. This suggests +that the impurities, by condensing round the negative ions as nuclei, +seriously diminish their velocity. If a point is charged up to a high +and rapidly alternating potential, such as can be produced by the +electric oscillations started when a Leyden jar is discharged, then in +hydrogen, nitrogen, ammonia and carbonic acid gas a conductor placed in +the neighbourhood of the point gets a negative charge, while in air and +oxygen it gets a positive one. There are two considerations which are of +importance in connexion with this effect. The first is the velocity of +the ions in the electric field, and the second the ease with which the +ions can give up their charges to the metal point. The greater velocity +of the negative ions would, if the potential were rapidly alternating, +cause an excess of negative ions to be left in the surrounding gas. This +is the case in hydrogen. If, however, the metal had a much greater +tendency to unite with negative than with positive ions, such as we +should expect to be the case in oxygen, this would act in the opposite +direction, and tend to leave an excess of positive ions in the gas. + +_The Characteristic Curve for Discharge through Gases._--When a current +of electricity passes through a metallic conductor the relation between +the current and the potential difference is the exceedingly simple one +expressed by Ohm's law; the current is proportional to the potential +difference. When the current passes through a gas there is no such +simple relation. Thus we have already mentioned cases where the current +increased as the potential increased although not in the same +proportion, while as we have seen in certain stages of the arc discharge +the potential difference diminishes as the current increases. Thus the +problem of finding the current which a given battery will produce when +part of the circuit consists of a gas discharge is much more complicated +than when the circuit consists entirely of metallic conductors. If, +however, we measure the potential difference between the electrodes in +the gas when different currents are sent through it, we can plot a +curve, called the "characteristic curve," whose ordinates are the +potential differences between the electrodes in the gas and the +abscissae the corresponding currents. By the aid of this curve we can +calculate the current produced when a given battery is connected up to +the gas by leads of known resistance. + + For let E0 be the electromotive force of the battery, R the resistance + of the leads, i the current, the potential difference between the + terms in the gas will be E0 - Ri. Let ABC (fig. 22) be the + "characteristic curve," the ordinates being the potential difference + between the terminals in the gas, and the abscissae the current. Draw + the line LM whose equation is E = E0 - Ri, then the points where this + line cuts the characteristic curves will give possible values of i and + E, the current through the discharge tube and the potential difference + between the terminals. Some of these points may, however, correspond + to an unstable position and be impossible to realize. The following + method gives us a criterion by which we can distinguish the stable + from the unstable positions. If the current is increased by [delta]i, + the electromotive force which has to be overcome by the battery is + R[delta]i + dE/di . [delta]i. If R + dE/di is positive there will be + an unbalanced electromotive force round the circuit tending to stop + the current. Thus the increase in the current will be stopped and the + condition will be a stable one. If, however, R + dE/di is negative + there will be an unbalanced electromotive force tending to increase + the current still further; thus the current will go on increasing and + the condition will be unstable. Thus for stability R + dE/di must be + positive, a condition first given by Kaufmann (_Ann. der Phys._ 11, p. + 158). The geometrical interpretation of this condition is that the + straight line LM must, at the point where it cuts the characteristic + curve, be steeper than the tangent to characteristic curve. Thus of + the points ABC where the line cuts the curve in fig. 22, A and C + correspond to stable states and B to an unstable one. The state of + things represented by a point P on the characteristic curve when the + slope is downward cannot be stable unless there is in the external + circuit a resistance greater than that represented by the tangent of + the inclination of the tangent to the curve at P to the horizontal + axis. + + [Illustration: FIG. 22.] + + If we keep the external electromotive force the same and gradually + increase the resistance in the leads, the line LM will become steeper + and steeper. C will move to the left so that the current will + diminish; when the line gets so steep that it touches the curve at C', + any further increase in the resistance will produce an abrupt change + in the current; for now the state of things represented by a point + near A' is the only stable state. Thus if the BC part of the curve + corresponded to a luminous discharge and the A part to a dark + discharge, we see that if the electromotive force is kept constant + there is a minimum value of the current for the luminous discharge. If + the current is reduced below this value, the discharge ceases to be + luminous, and there is an abrupt diminution in the current. + +_Cathode Rays._--When the gas in the discharge tube is at a very low +pressure some remarkable phenomena occur in the neighbourhood of the +cathode. These seem to have been first observed by Plucker (_Pogg. Ann._ +107, p. 77; 116, p. 45) who noticed on the walls of the glass tube near +the cathode a greenish phosphorescence, which he regarded as due to rays +proceeding from the cathode, striking against the sides of the tube, and +then travelling back to the cathode. He found that the action of a +magnet on these rays was not the same as the action on the part of the +discharge near the positive electrode. Hittorf (_Pogg. Ann._ 136, p. 8) +showed that the agent producing the phosphorescence was intercepted by a +solid, whether conductor or insulator, placed between the cathode and +the sides of the tube. He regarded the phosphorescence as caused by a +motion starting from the cathode and travelling in straight lines +through the gas. Goldstein (_Monat. der Berl. Akad._, 1876, p. 24) +confirmed this discovery of Hittorf's, and further showed that a +distinct, though not very sharp, shadow is cast by a small object placed +near a large plane cathode. This is a proof that the rays producing the +phosphorescence must be emitted almost normally from the cathode, and +not, like the rays of light from a luminous surface, in all directions, +for such rays would not produce a perceptible shadow if a small body +were placed near the plane. Goldstein regarded the phosphorescence as +due to waves in the ether, for whose propagation the gas was not +necessary. Crookes (_Phil. Trans._, 1879, pt. i. p. 135; pt. ii. pp. +587, 661), who made many remarkable researches in this subject, took a +different view. He regarded the rays as streams of negatively +electrified particles projected normally from the cathode with great +velocity, and, when the pressure is sufficiently low, reaching the sides +of the tube, and by their impact producing phosphorescence and heat. The +rays on this view are deflected by a magnet, because a magnet exerts a +force on a charged moving body. + +These rays striking against glass make it phosphorescent. The colour of +the phosphorescence depends on the kind of glass; thus the light from soda +glass is a yellowish green, and that from lead glass blue. Many other +bodies phosphoresce when exposed to these rays, and in particular the +phosphorescence of some gems, such as rubies and diamonds, is exceedingly +vivid. The spectrum of the phosphorescent light is generally continuous, +but Crookes showed that the phosphorescence of some of the rare earths, +such as yttrium, gives a spectrum of bright bands, and he founded on this +fact a spectroscopic method of great importance. Goldstein (_Wied. Ann._ +54, p. 371) discovered that the haloid salts of the alkali metals change +colour under the rays, sodium chloride, for example, becoming violet. The +coloration is a surface one, and has been traced by E. Wiedemann and +Schmidt (_Wied. Ann._ 54, p. 618) to the formation of a subchloride. +Chlorides of tin, mercury and lead also change colour in the same way. E. +Wiedemann (_Wied. Ann._ 56, p. 201) discovered another remarkable effect, +which he called thermo-luminescence; he found that many bodies after being +exposed to the cathode rays possess for some time the power of becoming +luminous when their temperature is raised to a point far below that at +which they become luminous in the normal state. Substances belonging to +the class called by van 't Hoff solid solutions exhibit this property of +thermo-luminescence to a remarkable extent. They are formed when two +salts, one greatly in excess of the other, are simultaneously precipitated +from a solution. A trace of MnSO4 in CaSO4 shows very brilliant +thermo-luminescence. The impact of cathode rays produces after a time +perceptible changes in the glass. Crookes (_Phil. Trans._ pt. ii. 1879, p. +645) found that after glass has been phosphorescing for some time under +the cathode rays it seems to get tired, and the phosphorescence is not so +bright as it was initially. Thus, for example, when the shadow of a +Maltese cross is thrown on the walls of the tube as in fig. 23, if after +the discharge has been going on for some time the cross is shaken down or +a new cathode used whose line of fire does not cut the cross, the pattern +of the cross will still be seen on the glass, but it will now be brighter +instead of darker than the surrounding portion. The portions shielded by +the cross, not being tired by being made to phosphoresce for a long time, +respond more vigorously to the stimulus than those portions which have not +been protected. Skinner (_Proc. Camb. Phil. Soc._ ix. p. 371) and Thomson +found on the glass which had been exposed to the rays gelatinous +filaments, apparently silica, resulting from the reduction of the glass. A +reducing action was also noticed by Villard (_Journ. de phys._ 3, viii. p. +140) and Wehnelt (_Wied. Ann._ 67, p. 421). It can be well shown by +letting the rays fall on a plate of oxidized copper, when the part struck +by the rays will become bright. The rays heat bodies on which they fall, +and if they are concentrated by using as a cathode a portion of a +spherical surface, the heat at the centre becomes so great that a piece of +platinum wire can be melted or a diamond charred. Measurements of the +heating effects of the rays have been made by Thomson (_Phil. Mag._ [5], +44, p. 293) and Cady (_Ann. der Phys._ 1, p. 678). Crookes (_Phil. +Trans._, 1879, pt. i. p. 152) showed that a vane mounted as in a +radiometer is set in rotation by the rays, the direction of the rotation +being the same as would be produced by a stream of particles proceeding +from the cathode. The movement is not due to the momentum imparted to the +vanes by the rays, but to the difference in temperature between the sides +of the vanes, the rays making the side against which they strike hotter +than the other. + +[Illustration: FIG. 23.] + +_Effect of a Magnet._--The rays are deflected by a magnet, so that the +distribution of phosphorescence over the glass and the shape and +position of the shadows cast by bodies in the tube are altered by the +proximity of a magnet. The laws of magnetic deflection of these rays +have been investigated by Plucker (_Pogg._ _Ann._ 103, p. 88), Hittorf +(_Pogg. Ann._ 136, p. 213), Crookes (_Phil. Trans._, 1879, pt. 1, p. +557), and Schuster (_Proc. Roy. Soc._ 47, p. 526). The deflection is the +same as that of negatively electrified particles travelling along the +path of the rays. Such particles would in a magnetic field be acted on +by a force at right angles to the direction of motion of the particle +and also to the magnetic force, the magnitude of the force being +proportional to the product of the velocity of the particle, the +magnetic force, and the sine of the angle between these vectors. In this +case we have seen that if the particle is not acted on by an +electrostatic field, the path in a uniform magnetic field is a spiral, +which, if the magnetic force is at right angles to the direction of +projection of the particle, becomes a circle in the plane at right +angles to the magnetic force, the radius being mv/He, where m, v, e are +respectively the mass, velocity and charge on the particle, and H is the +magnetic force. The smaller the difference of potential between the +electrodes of the discharge tube the greater the deflection produced by +a magnetic field of given strength, and as the difference of potential +rapidly increases with diminution of pressure, after a certain pressure +has been passed, the higher the exhaustion of the tube the less the +magnetic deflection of the rays. Birkeland (_Comptes rendus_, 1896, p. +492) has shown that when the discharge is from an induction coil the +cathode rays produced in the tube at any one time are not equally +deflected by a magnet, but that a narrow patch of phosphorescence when +deflected by a magnet is split up into several distinct patches, giving +rise to what Birkeland calls the "magnetic spectrum." Strutt (_Phil. +Mag._ 48, p. 478) has shown that this magnetic spectrum does not occur +if the discharge of a large number of cells is employed instead of the +coil. Thomson (_Proc. Camb. Phil. Soc._ 9, p. 243) has shown that if the +potential difference between the electrodes is kept the same the +magnetic deflection is independent of the nature of the gas filling the +discharge tube; this was tested with gases so different as air, +hydrogen, carbonic acid and methyl iodide. + +_Charge of Negative Electricity carried by the Rays._--We have seen that +the rays are deflected by a magnet, as if they were particles charged +with negative electricity. Perrin (_Comptes rendus_, 121, p. 1130) +showed by direct experiment that a stream of negative electricity is +associated with the rays. A modification made by Thomson of Perrin's +experiment is sketched in fig. 24 (_Phil. Mag._ 48, p. 478). + + [Illustration: FIG. 24.] + + The rays start from the cathode A, and pass through a slit in a solid + brass rod B fitting tightly into the neck of the tube. This rod is + connected with earth and used as the anode. The rays after passing + through the slit travel through the vessel C. D and E are two + insulated metal cylinders insulated from each other, and each having a + slit cut in its face so as to enable the rays to pass into the inside + of the inner cylinder, which is connected with an electrometer, the + outer cylinder being connected with the earth. The two cylinders are + placed on the far side of the vessel, but out of the direct line of + fire of the rays. When the rays go straight through the slit there is + only a very small negative charge communicated to the inner cylinder, + but when they are deflected by a magnet so that the phosphorescent + patch falls on the slit in the outer cylinder the inner cylinder + receives a very large negative charge, the increase coinciding very + sharply with the appearance of the phosphorescent patch on the slit. + When the patch is so much deflected by the magnet that it falls below + the slit, the negative charge in the cylinder again disappears. This + experiment shows that the cathode rays are accompanied by a stream of + negative electrification. The same apparatus can be used to show that + the passage of cathode rays through a gas makes it a conductor of + electricity. For if the induction coil is kept running and a stream of + the rays kept steadily going into the inner cylinder, the potential + of the inner cylinder reaches a definite negative value below which it + does not fall, however long the rays may be kept going. The cylinder + reaches a steady state in which the gain of negative electricity from + the cathode rays is equal to the loss by leakage through the + conducting gas, the conductivity being produced by the passage of the + rays through it. If the inner cylinder is charged up initially with a + greater negative charge than corresponds to the steady state, on + turning the rays on to the cylinder the negative charge will decrease + and not increase until it reaches the steady state. The conductivity + produced by the passage of cathode rays through a gas diminishes + rapidly with the pressure. When rays pass through a gas at a low + pressure, they are deflected by an electric field; when the pressure + of the gas is higher the conductivity it acquires when the cathode + rays pass through it is so large that the potential gradient cannot + reach a sufficiently high value to produce an appreciable deflection. + +Thus the cathode rays carry a charge of negative electricity; the +experiment described on page 875 (fig. 13) shows that they are deflected +by an electric field as if they were negatively electrified, and are +acted on by a magnetic force in just the way this force would act on a +negatively electrified body moving along the path of the rays. There is +therefore every reason for believing that they are charges of negative +electricity in rapid motion. By measuring the deflection produced by +magnetic and electric fields we can determine the velocity with which +these particles moved and the ratio of the mass of the particle to the +charge carried by it. + +We may conclude from the experiments that the value of m/e for the +particles constituting the cathode rays is of the order 1/1.7 X 10^7, +and we have seen that m/e has the same value in all the other cases of +negative ions in a gas at low pressure for which it has been +measured--viz. for the ions produced when ultra-violet light falls on a +metal plate, or when an incandescent carbon filament is surrounded by a +gas at a low pressure, and for the [beta] particles given out by +radio-active bodies. We have also seen that the value of the charge on +the gaseous ion, in all cases in which it has been measured--viz. the +ions produced by Rontgen and uranium radiation, by ultra-violet light, +and by the discharge of electrification from a point--is the same in +magnitude as the charge carried by the hydrogen atom in the electrolysis +of solutions. The mass of the hydrogen alone is, however, 10^-4 times +this charge, while the mass of the carriers of negative electrification +is only 1/1.7 X 10^7 times the charge; hence the mass of the carriers of +the negative electrification is only 1/1700 of the mass of the hydrogen +atom. We are thus, by the study of the electric discharge, forced to +recognize the existence of masses very much smaller than the smallest +mass hitherto recognized. + + Direct determinations of the velocity of the cathode rays have been + made by J. J. Thomson (_Phil. Mag._ 38, p. 358), who measured the + interval between the appearance of phosphorescence on two pieces of + glass placed at a known distance apart, and by Maiorana (_Nuovo + Cimento_, 4, 6, p. 336) and Battelli and Stefanini (_Phys. Zeit._ 1, + p. 51), who measured the interval between the arrival of the negative + charge carried by the rays at two places separated by a known + distance. The values of the velocity got in this way are much smaller + than the values got by the indirect methods previously described: thus + J. J. Thomson at a fairly high pressure found the velocity to be 2 X + 10^7 cm./sec. Maiorana found values ranging between 10^7 and 6 X 10^7 + cm./sec, and Battelli and Stefanini values ranging from 6 X 10^6 to + 1.2 X 10^7. In these methods it is very difficult to eliminate the + effect of the interval which elapses between the arrival of the rays + and the attainment by the means of detection, such as the + phosphorescence of the glass or the deflection of the electrometer, of + sufficient intensity to affect the senses. + +[Illustration: FIG. 25.] + +_Transmission of Cathode Rays through Solids--Lenard Rays._--It was for +a long time believed that all solids were absolutely opaque to these +rays, as Crookes and Goldstein had proved that very thin glass, and even +a film of collodion, cast intensely black shadows. Hertz (_Wied. Ann._ +45, p. 28), however, showed that behind a piece of gold-leaf or +aluminium foil an appreciable amount of phosphorescence occurred on the +glass, and that the phosphorescence moved when a magnet was brought +near. A most important advance was next made by Lenard (_Wied. Ann._ 51, +p. 225), who got the cathode rays to pass from the inside of a discharge +tube to the air outside. For this purpose he used a tube like that shown +in fig. 25. The cathode K is an aluminium disc 1.2 cm. in diameter +fastened to a stiff wire, which is surrounded by a glass tube. The anode +A is a brass strip partly surrounding the cathode. The end of the tube +in front of the cathode is closed by a strong metal cap, fastened in +with marine glue, in the middle of which a hole 1.7 mm. in diameter is +bored, and covered with a piece of very thin aluminium foil about .0026 +mm. in thickness. The aluminium window is in metallic contact with the +cap, and this and the anode are connected with the earth. The tube is +then exhausted until the cathode rays strike against the window. Diffuse +light spreads from the window into the air outside the tube, and can be +traced in a dark room for a distance of several centimetres. From the +window, too, proceed rays which, like the cathode rays, can produce +phosphorescence, for certain bodies phosphoresce when placed in the +neighbourhood of the window. This effect is conveniently observed by the +platino-cryanide screens used to detect Rontgen radiation. The +properties of the rays outside the tube resemble in all respects those +of cathode rays; they are deflected by a magnet and by an electric +field, they ionize the gas through which they pass and make it a +conductor of electricity, and they affect a photographic plate and +change the colour of the haloid salts of the alkali metals. As, however, +it is convenient to distinguish between cathode rays outside and inside +the tube, we shall call the former Lenard rays. In air at atmospheric +pressure the Lenard rays spread out very diffusely. If the aluminium +window, instead of opening into the air, opens into another tube which +can be exhausted, it is found that the lower the pressure of the gas in +this tube the farther the rays travel and the less diffuse they are. By +filling the tube with different gases Lenard showed that the greater the +density of the gas the greater is the absorption of these rays. Thus +they travel farther in hydrogen than in any other gas at the same +pressure. Lenard showed, too, that if he adjusted the pressure so that +the density of the gas in this tube was the same--if, for example, the +pressure when the tube was filled with oxygen was 1/16 of the pressure +when it was filled with hydrogen--the absorption was constant whatever +the nature of the gas. Becker (_Ann. der Phys._ 17, p. 381) has shown +that this law is only approximately true, the absorption by hydrogen +being abnormally large, and by the inert monatomic gases, such as helium +and argon, abnormally small. The distance to which the Lenard rays +penetrate into this tube depends upon the pressure in the discharge +tube; if the exhaustion in the latter is very high, so that there is a +large potential difference between the cathode and the anode, and +therefore a high velocity for the cathode rays, the Lenard rays will +penetrate farther than when the pressure in the discharge tube is higher +and the velocity of the cathode rays smaller. Lenard showed that the +greater the penetrating power of his rays the smaller was their magnetic +deflection, and therefore the greater their velocity; thus the greater +the velocity of the cathode rays the greater is the velocity of the +Lenard rays to which they give rise. For very slow cathode rays the +absorption by different gases departs altogether from the density law, +so much so that the absorption of these rays by hydrogen is greater than +that by air (Lenard, _Ann. der Phys._ 12, p. 732). Lenard (_Wied. Ann._ +56, p. 255) studied the passage of his rays through solids as well as +through gases, and arrived at the very interesting result that the +absorption of a substance depends only upon its density, and not upon +its chemical composition or physical state; in other words, the amount +of absorption of the rays when they traverse a given distance depends +only on the quantity of matter they cut through in the distance. +McClelland (_Proc. Roy. Soc._ 61, p. 227) showed that the rays carry a +charge of negative electricity, and M'Lennan measured the amount of +ionization rays of given intensity produced in different gases, finding +that if the pressure is adjusted so that the density of the different +gases is the same the number of ions per cubic centimetre is also the +same. In this case, as Lenard has shown, the absorption is the same, so +that with the Lenard rays, as with uranium and probably with Rontgen +rays, equal absorption corresponds to equal ionization. A convenient +method for producing Lenard rays of great intensity has been described +by Des Coudres (_Wied. Ann._ 62, p. 134). + +_Diffuse Reflection of Cathode Rays._--When cathode rays fall upon a +surface, whether of an insulator or a conductor, cathode rays start from +the surface in all directions. This phenomenon, which was discovered by +Goldstein (_Wied. Ann._ 62, p. 134), has been investigated by Starke +(_Wied. Ann._ 66, p. 49; _Ann. der Phys._ 111, p. 75), Austin and Starke +(_Ann. der Phys._ 9, p. 271), Campbell-Swinton (_Proc. Roy. Soc._ 64, p. +377), Merritt (_Phys. Rev._ 7, p. 217) and Gehrcke (_Ann. der Phys._ 8, +p. 81); it is often regarded as analogous to the diffuse reflection of +light from such a surface as gypsum, and is spoken of as the diffuse +reflection of the cathode rays. According to Merritt and Austin and +Starke the deviation in a magnetic field of these reflected rays is the +same as that of the incident rays. The experiments, however, were +confined to rays reflected so that the angle of reflection was nearly +equal to that of incidence. Gehrcke showed that among the reflected rays +there were a large number which had a much smaller velocity than the +incident ones. According to Campbell-Swinton the "diffuse" reflection is +accompanied by a certain amount of "specular" reflection. Lenard, who +used slower cathode rays than Austin and Starke, could not detect in the +scattered rays any with velocities comparable with that of the incident +rays; he obtained copious supplies of slow rays whose speed did not +depend on the angle of incidence of the primary rays (_Ann. der Phys._ +15, p. 485). When the angle of incidence is very oblique the surface +struck by the rays gets positively charged, showing that the secondary +rays are more numerous than the primary. + +_Repulsion of two Cathode Streams._--Goldstein discovered that if in a +tube there are two cathodes connected together, the cathodic rays from +one cathode are deflected when they pass near the other. Experiments +bearing on this subject have been made by Crookes and Wiedemann and +Ebert. The phenomena may be described by saying that the repulsion of +the rays from a cathode A by a cathode B is only appreciable when the +rays from A pass through the Crookes dark space round B. This is what we +should expect if we remember that the electric field in the dark space +is far stronger than in the rest of the discharge, and that the gas in +the other parts of the tube is rendered a conductor by the passage +through it of the cathode rays, and therefore incapable of transmitting +electrostatic repulsion. + +Scattering of the Negative Electrodes.--In addition to the cathode rays, +portions of metal start normally from the cathode and form a metallic +deposit on the walls of the tube. The amount of this deposit varies very +much with the metal. Crookes (_Proc. Roy. Soc._ 50, p. 88) found that +the quantities of metal torn from electrodes of the same size, in equal +times, by the same current, are in the order Pd, Au, Ag, Pb, Sn, Pt, Cu, +Cd, Ni, In, Fe.... In air there is very little deposit from an Al +cathode, but it is abundant in tubes filled with the monatomic gases, +mercury vapour, argon or helium. The scattering increases as the density +of the gas diminishes. The particles of metal are at low pressures +deflected by a magnet, though not nearly to the same extent as the +cathode rays. According to Grandquist, the loss of weight of the cathode +in a given time is proportional to the square of the current; it is +therefore not, like the loss of the cathode in ordinary electrolysis, +proportional to the quantity of current which passes through it. + +[Illustration: FIG. 26.] + +_Positive Rays or "Canalstrahlen."_--Goldstein (_Berl. Sitzungsb._ 39, +p. 691) found that with a perforated cathode certain rays occurred +behind the cathode which were not appreciably deflected by a magnet; +these he called Canalstrahlen, but we shall, for reasons which will +appear later, call them "positive rays." + +Their appearance is well shown in fig. 26, taken from a paper by Wehnelt +(_Wied. Ann._ 67, p. 421) in which they are represented at B. Goldstein +found that their colour depends on the gas in which they are formed, +being gold-colour in air and nitrogen, rose-colour in hydrogen, +yellowish rose in oxygen, and greenish gray in carbonic acid. + +The colour of the luminosity due to positive rays is not in general the +same as that due to anode rays; the difference is exceptionally well +marked in helium, where the cathode ray luminosity is blue while that +due to the positive rays is red. The luminosity produced when the rays +strike against solids is also quite distinct. The cathode rays make the +body emit a continuous spectrum, while the spectrum produced by the +positive rays often shows bright lines. Thus lithium chloride under +cathode rays gives out a steely blue light and the spectrum is +continuous, while under the positive rays the salt gives out a brilliant +red light and the spectrum shows the red helium line. It is remarkable +that the lines on the spectra of the alkali metals are much more easily +produced when the positive rays fall on the oxide of the metal than when +they fall on the metal itself. Thus when the positive rays fall on a +pool of the liquid alloy of sodium and potassium the specks of oxide on +the surface shine with a bright yellow light while the untarnished part +of the surface is quite dark. + +W. Wien (_Wied. Ann._ 65, p. 445) measured the values of e/m for the +particles forming the positive rays. Other measurements have been made +by Ewers (_Wied. Ann._ 69, p. 167) and J. J. Thomson (_Phil. Mag._ 13, +p. 561). The differences between the values of e/m for the cathode and +positive rays are very remarkable. For cathode rays whose velocity does +not approach that of light, e/m is always equal to 1.7 X 10^8, while for +the positive rays the greatest value of this quantity yet observed is +10^4, which is also the value of e/m for the hydrogen ions in the +electrolysis of dilute solutions. In some experiments made by J. J. +Thomson (_Phil. Mag._, 14, p. 359) it was found that when the pressure +of the gas was not too low the bright spot produced by the impact of a +pencil of these rays on a phosphorescent screen is deflected by electric +and magnetic forces into a continuous band extending on both sides of +the undeflected position. The portion on one side is in general much +fainter than that on the other. The direction of this deflection shows +that it is produced by particles charged with negative electricity, +while the brighter band is due to particles charged with positive +electricity. The negatively electrified particles which produce the band +c.c are not corpuscles, for from the electric and magnetic deflections +we can find the value of e/m. As this proves to be equal to 10^4, we see +that the mass of the carrier of the negative charge is comparable with +that of an atom, and so very much greater than that of a corpuscle. At +very low pressures part of the phosphorescence disappears, while the +upper portion breaks up into two patches (fig. 27). For one of these the +maximum value of e/m is 10^4 and for the other 5 X 10^3. At low pressures +the appearance of the patches and the values of e/m are the same whether +the tube is filled originally with air, hydrogen or helium. In some of +the experiments the tube was exhausted until the pressure was too low to +allow the discharge to pass. A very small quantity of the gas under +investigation was then admitted into the tube, just sufficient to allow +the discharge to pass, and the deflection of the phosphorescent patch +measured. The following gases were admitted into the tube, air, carbonic +oxide, oxygen, hydrogen, helium, argon and neon, but whatever the gas +the appearance of the phosphorescence was the same; in every case there +were two patches, for one of which e/m = 10^4 and for the other e/m = +5 X 10^3. In helium at higher pressures another patch was observed, for +which e/m = 2.5 X 10^8. The continuous band into which the +phosphorescent spot is drawn out when the pressure is not exceedingly +low, which involves the existence of particles for which the mean value +of e/m varies from zero to 10^4, can be explained as follows. The rays +on their way to the phosphorescent screen have to pass through gas which +is ionized by the passage through it of the positive rays; this gas will +therefore contain free corpuscles. The particles which constitute the +rays start with a charge of positive electricity. Some of these +particles in their journey through the gas attract a corpuscle whose +negative charge neutralizes the positive charge on the particle. The +particles when in this neutral state may be ionized by collision and +reacquire a positive charge, or by attracting another particle may +become negatively charged, and this process may be repeated several +times on their journey to the phosphorescent screen. Thus some of the +particles, instead of being positively charged for the whole of the time +they are exposed to the electric and magnetic forces, may be for a part +of that time without a charge or even have a negative charge. The +deflection of a particle is proportional to the average value of its +charge whilst under the influence of the deflecting forces. Thus if a +particle is without a charge for a part of the time, its deflection will +be less than that of a particle which has retained its positive charge +for the whole of its journey, while the few particles which have a +negative charge for a longer time than they have a positive will be +deflected in the opposite direction to the main portion and will produce +the tail (fig. 27). + +[Illustration: Fig. 27.] + +A similar explanation will apply to the positive rays discovered by +Villard (_Comptes rendus_, 143, p. 674) and J. J. Thomson (_Phil. Mag._ +13, p. 359), which travel in the opposite direction to the rays we have +been considering, i.e. they travel away from the cathode and in the +direction of the cathode's rays; these rays are sometimes called +"retrograde" rays. These as far as has been observed have always the +same maximum value of e/m, i.e. 10^4, and there are a considerable +number of negative ones always mixed with them. The maximum velocity of +both the positive and retrograde rays is about 2 X 10^8 cm./sec. and +varies very little with the potential difference between the electrodes +in the tube in which they are produced (J. J. Thomson, _Phil. Mag._, +Dec. 1909). + +The positive rays show, when the pressure is not very low, the line +spectrum of the gas through which they pass. An exceedingly valuable set +of observations on this point have been made by Stark and his pupils +(_Physik. Zeit._ 6, p. 892; _Ann. der Phys._ 21, pp. 40, 457). Stark has +shown that in many gases, notably hydrogen, the spectrum shows the +Doppler effect, and he has been able to calculate in this way the +velocity of the positive rays. + +_Anode Rays._--Gehrcke and Reichenhein (_Ann. der Phys._ 25, p. 861) +have found that when the anode consists of a mixture of sodium and +lithium chloride raised to a high temperature either by the discharge +itself or by an independent heating circuit, very conspicuous rays come +from the anode when the pressure of the gas in the discharge tube is +very low, and a large coil is used to produce the discharge. The +determination of e/m for these rays showed that they are positively +charged atoms of sodium or lithium, moving with very considerable +velocity; in some of Gehrcke's experiments the maximum velocity was as +great as 1.8 X 10^7 cm./sec. though the average was about 10^7 cm./sec. +These velocities are less than those of the positive rays whose maximum +velocity is about 2 X 10^8 cm./sec. (J. J. T.) + + +FOOTNOTES: + + [1] The values for nickel and bismuth given in the table are much + higher than later values obtained with pure electrolytic nickel and + bismuth. + + [2] The value here given, namely 12.885, for the electric + mass-resistivity of liquid mercury as determined by Matthiessen is + now known to be too high by nearly 1%. The value at present accepted + is 12.789 ohms per metre-gramme at 0 deg. C. + + [3] The value (1630) here given for hard-drawn copper is about 1/4% + higher than the value now adopted, namely, 1626. The difference is + due to the fact that either Jenkin or Matthiessen did not employ + precisely the value at present employed for the density of hard-drawn + and annealed copper in calculating the volume-resistivities from the + mass-resistivities. + + [4] Matthiessen's value for nickel is much greater than that obtained + in more recent researches. (See Matthiessen and Vogt, _Phil. Trans._, + 1863, and J. A. Fleming, _Proc. Roy. Soc._, December 1899.) + + [5] Matthiessen's value for mercury is nearly 1% greater than the + value adopted at present as the mean of the best results, namely + 94,070. + + [6] The samples of silver, copper and nickel employed for these tests + were prepared electrolytically by Sir J. W. Swan, and were + exceedingly pure and soft. The value for volume-resistivity of nickel + as given in the above table (from experiments by J. A. Fleming, + _Proc. Roy. Soc._, December 1899) is much less (nearly 40%) than the + value given by Matthiessen's researches. + + [7] The electrolytic bismuth here used was prepared by Hartmann and + Braun, and the resistivity taken by J. A. Fleming. The value is + nearly 20% less than that given by Matthiessen. + + [8] In 1899 a committee was formed of representatives from eight of + the leading manufacturers of insulated copper cables with delegates + from the Post Office and Institution of Electrical Engineers, to + consider the question of the values to be assigned to the resistivity + of hard-drawn and annealed copper. The sittings of the committee were + held in London, the secretary being A. H. Howard. The values given in + the above paragraphs are in accordance with the decision of this + committee, and its recommendations have been accepted by the General + Post Office and the leading manufacturers of insulated copper wire + and cables. + + [9] Platinoid is an alloy introduced by Martino, said to be similar + in composition to German silver, but with a little tungsten added. It + varies a good deal in composition according to manufacture, and the + resistivity of different specimens is not identical. Its electric + properties were first made known by J. T. Bottomley, in a paper read + at the Royal Society, May 5, 1885. + + [10] An equivalent gramme molecule is a weight in grammes equal + numerically to the chemical equivalent of the salt. For instance, one + equivalent gramme molecule of sodium chloride is a mass of 58.5 + grammes. NaCl = 58.5. + + [11] F. Kohlrausch and L. Holborn, _Das Leitvermogen der Elektrolyte_ + (Leipzig, 1898). + + [12] It should be noticed that the velocities calculated in + Kohlrausch's theory and observed experimentally are the average + velocities, and involve both the factors mentioned above; they + include the time wasted by the ions in combination with each other, + and, except at great dilution, are less than the velocity with which + the ions move when free from each other. + + + + + +End of the Project Gutenberg EBook of Encyclopaedia Britannica, 11th +Edition, Volume 6, Slice 8, by Various + +*** END OF THIS PROJECT GUTENBERG EBOOK ENCYC. 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