the Anode in Vacuum-Tubes. 197 



n 

 collision is - - „ o£ its energy immediately before, and the 

 n + 1 &,; J 



larger the colliding cluster the smaller the fraction of energy 



not appearing as energy of motion. The latter fraction, 



— p E„, probably appears as internal energy of the cluster. 



In some such way as above indicated, the energy is absorbed 

 by the cluster till such amount is accumulated as to render it 

 unstable. Now if it be assumed that the energy acquired per 

 mean free path is the same for all clusters, an approximate 

 value of the energy of cluster n after the nth collision can be 



n 4- 1 

 shown by induction to be E„= — — — Ej where E 1 is the 



energy gained per mean free path. Now in the case con- 

 sidered above, a 15-volt energy has to be u accumulated," 

 that is, all the energy available in a path 1 cm. long. As 

 this would involve at least 100 collisions, and imply the 

 formation of a cluster 100, it is improbable that the ex- 

 planation of the phenomena is as simple as above described. 

 It is clear that, in addition to collisions between clusters and 

 molecules, there will be collisions among the clusters them- 

 selves. Once a cluster is formed, its acceleration in the electric 

 field is less than that of the simple ion. So that it is possible 

 for an ion or small cluster to overtake a larger one. In this 

 case combination may take place resulting in a neavier 

 cluster with increased energy, or two clusters if the resulting 

 combination happened to be unstable. The accumulation of 

 energy by the clusters will then reach some limit whicii 

 depends on the number of complex ions of different orders 

 in equilibrium under the conditions of the experiment. In 

 addition to the energy of motion, some fraction of the energy 

 absorbed by the clusters will also be given up to the electrode 

 as heat. 



Another explanation of the " accumulation " of energy 

 suggests itself. The charged ion moving towards the 

 anode gains energy in its mean free path, so that after 

 collision with a neutral molecule, the latter rebounds with a 

 greater momentum than it would possess if no current were 

 flowing. This would be repeated after the ion had moved 

 again in the electric field, so that there would be a trans- 

 ference of momentum along the tube towards the anode. 

 This would mean that both a pressure and temperature 

 gradient would exist in the positive column, and on this ex- 

 planation the excess energy given to the anode would be 

 accounted for by a transference of energy to the anode from 

 a hotter gas surrounding it. 



