December 30, 1915] 



NATURE 



495 



tin 



i 



plexion on the question of metallic conduction, for, 

 if the carriers of the current are electrons and not 

 atoms, if the conduction is electronic and not elec- 

 trolytic, there need be no transport of the atoms 

 of the metal by the current; if the electrons, which 

 are of the same kind whatever the metal, can move, 

 there is no need for the atoms to do so. Thus, if 

 metals contain electrons which can move freely under 

 an electric force, they would certainly conduct elec- 

 tricity, and thus physicists investigated the conse- 

 quences of supposing that metallic conduction arose 

 in this way. It is easy to get direct evidence of the 

 existence of electrons in metals, for when the metals 

 are raised to a very high temperature so as to be 

 incandescent, as in the case of the filaments of elec- 

 tric lamps, large quantities of electrons are given 

 off, and though the emission is greatly affected by 

 the presence of gas in the metal, the behaviour o'f 

 Coolidge tubes, in which a tungsten filament con- 

 tinues to give out electrons for months in the highest 

 cuum that can be obtained, shows that the presence 

 gas is not absolutely essential for the emission of 

 ectrons. 



Let us, then, see what the electrical properties 

 a metal would be if it had free electrons 

 isseminated through it, the metal acting as a cage 

 for the electrons, which can move between the atoms 

 of the metal. The assemblage of electrons is sup- 

 posed to have the properties of a gas, and to be in 

 temperature equilibrium with the metal — in other 

 words, the electron temperature is the same 

 as that of the metal. In gases the average 

 kinetic energy of the molecules depends only 

 upon the temperature, and not upon the nature of 

 the gas; thus the average kinetic energy of the 

 electrons will be the same as that of the molecules 

 of air at the same temperature. As the mass of an 

 electron is exceedingly small compared with that of 

 a molecule of air, if the average kinetic energy 

 of the two is to be the same, the average velocity of 

 the electron must be very much greater than that 

 of the air molecule. At'o° C. the velocity of the 

 electron works out at lo^ centimetres per second, 

 or, roughly, sixty miles per second. If there is no 

 electric force acting on the metal, then, though the 

 motion of the electrons produces movement of elec- 

 tricity, there is no flow of electricity through the 

 metal, for whatever is the number of electrons 

 moving in any direction, there are just as manv 

 moving in the opposite. If, however, an external 

 electric force is applied to the metal, the electrons 

 under this force will, since they are negatively elec- 

 trified, drift in the opposite direction to the force. 

 This will cause a current, proportional to the number 

 of electrons which pass in one second across a unit 

 area drawn at right angles to the force, to flow 

 through the metal. Thus, if n is the number of 

 electrons per unit volume, e the charge on an elec- 

 tron, w the velocity of the drift, 



neu' = current through unit area. 

 The velocity of drift w is proportional to the elec- 

 tric force X. Let it equal feX, then the current is 

 kneX, and kne is the specific conductivitv of the 

 metal. Thus the presence of these electrons will 

 make the metal a conductor of electricity. It will 

 also give to the metal specific powers for the con- 

 duction of heat. For if different parts of the metal 

 are at different temperatures, the electrons in those 

 parts will also be at different temperatures, and thus 

 the metal will be in the condition of being filled with 

 a gas which is hotter at one place than it is at 

 another. Confining our attention to the gas, heat will 

 flow from the hot parts to the cold, and, as the 

 kinetic theor\' of gases shows, the conductivity for 

 NO. 2409, VOL. 96] 



heat of the gas will be proportional to nfe. This is 

 proportional to the specific conductivity of the metal 

 for electricity. Thus that part of the conductivity for 

 heat of the metal which arises from the presence of 

 the electrons will be proportional to the electrical 

 conductivity, and if the greater part of the heat 

 conductivity is due to the presence of electrons, the 

 thermal conductivity should bear a constant ratio to 

 the electrical conductivity. Thus good conductors 

 of heat should be good conductors of electricity; in 

 fact, the two conductivities should bear a constant 

 ratio to each other. Now, at any rate at ordinary 

 temperatures, the constancy of this ratio is very 

 remarkable. I will illustrate this in two ways : (i) 

 by a table, and (2) by a diagram. The table, which 

 is due to Jaeger and Diesselhorst, is as follows : — 



Th ermal Conductivity Temperature 

 Electiical Conductivity coefficient of 

 Material At i8° C. this ratio. 



Per cent. 



676X10'° ... — 



665 X 10'* ... 0-39 



671X10"* ... 039 

 6-86x10''' ... 0-37 

 7-27 X 10*° ... 036 



709X10*"' ... 0-37 



6-99X10"' ... 039 



7-05X10**' ... 038 



6-72X10*'' ... 038 



7-06X10*° ... 037 



7- 15x10*° ... 0-40 



7-35X10*° ... 0-34 



6-36X10*° ... 043 



7-76X10*° ... — 



7-53X10*° ... 0-46 



7-54X10*° ... 0-46 



8-02X10*° ... 0-43 



8-38X10*° ... 0-44 



903x10*° ... 0-35 



9-64x10*° ... .0-15 



• 023 



Copper, commercial 



Copper (i), pure ... 



Copper (2), pure ... 



Silver pure 



Gold (i) 



Gold (2), pure 



Nickel 



Zinc (i) 



Zinc (2), pure 



Cadmium, pure ... 



Lead, pure 



Tin, pure 



Aluminium 



Platinum (i) 



Platinum (2), pure 



Palladium 



Iron (i) 



Iron (2) 



Steel 



Bismuth 



Constantan (60 Cu, 4oNi) n-o6xio* 



Manganine (84 Cu, 14 Ni, 



12 Mn) 9-14x10*° ... 0-27 



If we suppose that all the heat is carried by the 



electrons, the kinetic theory of gases (on certain 



assumptions as to the nature of the collisions between 



two electrons and an electron and an atom) leads to 



the equation : — 



Thermal conductivity _4 a^ 

 Electrical conductivity 3 e'-" 



Where e is the charge on an electron, 6 the absolute 

 temperature, and ad the average kinetic energy of a 

 molecule of a gas at this temperature, all these quan- 

 tities are known. Substituting their values in the 

 equation, we find that the ratio of the conductivities 

 is 6-3x10'° and the temperature coefficient 0366 per 

 cent. The close agreement between these numbers 

 and those determined by experiment is very remark- 

 able. 



Fig. I is a diagram which represents the electrical 

 and thermal conductivities of alloys of bismuth and 

 lead in varying proportions. It will be noticed that 

 any sudden change in one conductivity is accompanied 

 by a corresponding change in the other. 



These results point to the conclusion that in metals 

 not only the whole of the current but the greater part 

 of the heat is carried by the electrons. This does not 

 imply that the electrons are the only agents by which 

 heat can be conducted, but merely that in metals most 

 of the heat is carried in this way. In insulators such 

 as glass, though the thermal conductivity is small, its 

 ratio to electrical conductivity is very much greater 

 than for metals. 



