498 



NATURE 



[December 30, 191 5 



without the application of any further electromotive 

 force, and he estimates that it would take four days 

 to fall to half its value ; we have here a somewhat 

 close approach to a perfect conductor. We saw that 

 much smaller increases in conductivity at low tem- 

 peratures were a difficulty in the way of the free 

 electron theory, the enormous increases in the con- 

 ductivity discovered by Kamerlingh Onnes make these 

 difficulties much more formidable. These increases, 

 however, admit of a very simple explanation on a 

 theory which I suggested some time ago — in fact, the 

 main" features of the theory are the same as one I 

 gave in my "Applications of Dynamics to Physics 

 and Chemistry, 1888," except that as at that time 

 the electron had not been discovered, I had to suppose 

 that the electricity was carried by atoms ; this in- 

 volved the transport of the metal by the current, a 

 difficulty which disappeared on the discovery of the 

 electron. 



Perhaps the clearest way of introducing the theory 

 is to direct your attention to a theory with which many 

 of you are doubtless familiar, that of the magnetisation 

 of iron, which has many analogies with our theory. 

 This theory of magnetisation supposes that a piece of 

 iron is a collection of an immense number of little 

 magnets, called molecular magnets ; when the iron 

 is not magnetised these molecular magnets are all 

 higgledy-piggledy, so that they completely neutralise 

 each other's effects, and the iron shows no sign of 

 magnetisation. When, however, the iron is acted on 

 by a magnetic force, the force acting on the magnet 

 tends to make them swing round, so as to point in 

 the direction of the force ; the result is that more 

 point in this direction than in any other. As some 

 order is brought into their arrangement, they no 

 longer neutralise each other, and the iron as a whole 

 behaves like a magnet. The intensity of magnetisa- 

 tion will be measured by the excess of the number of 

 those which point in the direction of the magnetic 

 force over those which point in any other directions. 

 Now, when the magnetic force acts on the iron, why 

 do not all the magnets swing round and point in the 

 direction of the force? It is because there are other 

 causes at work tending to knock them out of line as 

 fast as the magnetic force pulls them back. One of 

 these causes is the knocking about they get in conse- 

 quence of the movement of the molecules arising from 

 their temperature. This is more violent at high tem- 

 peratures than at low, and so more will be pulled into 

 line by the same force at low temperatures than they 

 would at high. There seems to be evidence that this 

 is the cause that is most efficacious in preventing the 

 complete set of the atoms ; and Langevin has shown 

 that, neglecting other effects and supposing the colli- 

 sions are like those in a gas, the intensity of mag- 

 netisation can be represented by the expression 



I = NM 



where 



\^^^-x\ 



HIM 



RT 



N is the number of magnets per unit volume, M 

 the moment of a little magnet, T the absolute tem- 

 perature, R the gas constant, and H^ the force acting 

 on a little magnet. H^ will consist of two parts, one 

 the external magnetic force, the other due to the action 

 of the magnets in its neighbourhood. This will be 

 proportional to I ; let it equal fel. 



^=(H+/&I)^^. 



The graph representing the relation between x and 

 I is thus a straight line, and to find the value of I 



NO. 2409, VOL. 96] 



corresponding to any value of H, we draw this line 

 and find where it intersects the curve U, the equation 

 of which is 



I = NM 



\t^-(' 



and the graph of which is represented in Fig. 2. 



Let us now turn to the problem of the metal. We 

 will suppose that each atom of the metal contains an 

 electrical dipole — the electrical analogue of a molecular 

 magnet. The molecular magnet consists of equal and 

 opposite magnetic poles separated by a short distance. 

 The electrical dipole consists of equal and opposite 

 electrical charges at a short distance apart, the nega- 

 tive charge being an electron. These dipoles if acted 

 on by an electrical force will set themselves along the 

 lines of electric force, in the same fashion as the 

 magnets~along the lines of magnetic force ; the result 

 will be the same as if a certain fraction pointed in the 

 direction of the electric force, while the remainder 

 pointed indifferently in all directions. We thus shall 

 have in the substance a number of chains of atoms 

 j^rranged as in Fig. 3. So far there is nothing in the 

 behaviour of these atoms which depends on the differ- 

 ence between a non-metal and a metal. The exist- 

 ence of these chains will produce what is called specific 

 inductive capacity in the medium. But you will see 

 that the doublets in the atoms will produce intense 

 electric forces in their neighbourhood, and these forces 

 will tend to drag the electrons out of one atom into 

 the other. Now, on this theory, the difference be- 

 tween an insulator and a metal is that the electrons 

 in an atom of an insulator are able to resist this pull 

 and remain within the atom. In a metal, on the other 

 hand, the electrons are much more easily detached, 

 and yield to the pull, and electrons pass from one atom 

 to another along the chain. Let us suppose that in 

 con sequence o f this action ^ electrons pass along the 



B A 



e© 0©0©0©G© e© 



Fig. 3. 



chain per second. The force which drags the electrons 

 out is due to the pull exerted by the atoms in its 

 neighbourhood, and so does not depend on the mag- 

 nitude of the electric force. Since p electrons pass 

 along each chain per second, the quantity of electricity 

 which passes through unit area per second is N/)f, 

 where N is the .number of chains through unit area, 

 hence 



i = 'Npe. 



Now, if I is the number of doublets per unit volume 

 which point in the direction of the electric force, and 



