Transmission of Electric Disturbances. 135 



diminishes the mean distances between the atoms increase, 

 and therefore T, the time required for recombination, will 

 increase ; but as on the above view the distance between two 

 striae is VT, where V is the velocity of light, the diminution of 

 the pressure will cause a separation of the striae. Again, the 

 distance between two striae increases as the diameter of the 

 tube in which the discharge takes place increases ; since in the 

 wider parts of the tube we have the same number of mole- 

 cules split up as in the narrower, the average distance between 

 the atoms will be greater in the wide part of the tube than 

 in the narrow, so that the time required for recombination, 

 and therefore the distance between two striae, will be greater 

 in the wide part of the tube than in the narrow. 



We have not the requisite data for calculating the time 

 required for the recombination of the atoms, but we may 

 perhaps suppose it is of the same order as the time required 

 for a particle moving with the average molecular velocity to 

 travel over half the average distance between the molecules : 

 this time for air at the pressure of 1 millim. of mercury is 

 about 2 x 10 -11 seconds, which would correspond to a distance 

 between the striae of 6 millimetres, which is a length quite of 

 the same order as the actual one. 



An interesting point arises when the electrodes are separated 

 by a distance less than VT. In this case the discharge cannot 

 be propagated from one electrode to the other with the velocity 

 V unless the velocity of the atoms is very much increased. 

 This increase in the energy which has to be communicated to 

 the gas to allow the spark to pass will increase the resistance 

 which the gas opposes to the passage of electricity along the 

 line joining the electrodes ; that is, it will require a greater 

 electromotive intensity to produce the discharge. If, how- 

 ever, instead of taking the straight line of force between the 

 electrodes, we consider one of the longer curved lines, and 

 choose one whose length is VT, or a multiple of it, then along 

 this line a Grotthus chain could be formed, which would convey 

 the discharge with the velocity V; and since in this case it is 

 not necessary to increase the velocity of the atoms in order 

 to attain the requisite velocity of propagation, the resistance 

 opposed by the curvilinear path per unit length will be less 

 than that offered by the straight path. Thus, when the elec- 

 trodes are separated by a shorter distance than VT, the shortest 

 distance between them need not be the path of least resistance, 

 and we might expect to find the discharge taking place along 

 curvilinear paths of such length as would enable the discharge 

 to travel at a rate V without increasing the kinetic energy 

 of the molecules. 



