ELECTRICAL PROPERTIES OF CONDUCTORS 595 



Platinum on the other hand must have molecules with very 

 small moment of inertia to account for its large deviations. If 

 the moments are calculated for MnS0 4 and MnS0 4 . 4H0O they 

 are found to be equal to 87 x io~ 41 and 1097 x io -41 respectively. 

 If then the water molecules are arranged symmetrically the 

 distance between the centres of the water molecules and of the 

 sulphate molecule is found to be 44 x io~ 9 cm. This is smaller 

 than the usually assumed radius of the hydrogen molecule 

 (1 x io~ s ), and seems to indicate that there is some inter- 

 penetration of the molecules of salt and water. 



Reference has been made to the quantum theory above for 

 an explanation of electric conductivity, and that the free 

 electrons in their path are continually encountering the atoms 

 of the conductor. The oscillators in the atoms will have 

 motions which will depend on the physical conditions, and 

 if their motion is large and rapid they will oppose more 

 resistance to the passage of the free electrons than if it is 

 small and slow. 



The mean free path of the electrons may be put as inversely 

 proportional to the mean amplitude of the vibrations which 

 disturb them. At the critical value for the super-conductive 

 state the excess of energy of these vibrators above the zero 

 point energy must have fallen to a small value, so that the 

 resistance to the motion of the electrons suddenly becomes 

 nearly zero. 



As indicated the conductivity of mercury, for instance, 

 becomes at this critical condition about io 10 as great as ordinary 

 temperatures. If, then, the assumption is made that the number 

 of electrons per unit volume remains the same, and then the 

 mean free path is calculated in the usual way from the con- 

 ductivity, values are found which are very large. Thus if 

 io~ 7 cm. is taken for the value at ordinary temperatures that at 

 2°45 K. becomes io 2 cm., which is clearly of the order of the 

 length of the conductor. It is not essential to suppose that any 

 particular electron actually travels this distance, if it is possible 

 to suppose that the atoms are touching in the sense that the 

 addition of one free electron at one end of the series would 

 cause a free electron to be projected with the same velocity 

 from the other end of the series, the bound electrons moving up 

 so as to readjust the distribution. This movement has no effect 

 as it is one of the fundamental conceptions of the electron 



