196 Dr. B. Hodgson on Heating Effects at 



that clusters and multiple-charged atoms both exist. H. A. 

 Wilson found that the mobility of ions in flames changed 

 suddenly at a certain temperature, suggesting a change in 

 the clustering of the ions. Todd * has proved, from measure- 

 ments of the mobility of the positive ion at fairly low 

 pressures, the existence of clusters up to cluster 6 in 

 Kleeman' s notation f, and also % that the negative ion 

 consists of a cluster which becomes less complex at lower 

 pressures. 



Lattey and Tizard § have obtained evidence of the exist- 

 ence of a cluster of 25 molecules round a positive charge. 



Kleeman || has shown from theoretical considerations that 

 there probably exists in ionized gases a continual forming 

 and breaking up of clusters of different orders so that a state 

 of equilibrium is finally reached, in which the number of 

 clusters of different orders depends on the electric field and 

 the gas pressure. 



Now it can be shown that the formation of clusters 

 permits the "accumulation" of energy. Consider a cluster 

 n, i. e. n molecules aggregated round one charge, colliding 

 with another molecule and forming a cluster n+1. the 

 collision being direct. Let the mass, energy of motion, and 

 velocity of cluster n just before collision be respectively 



n??i, E ;i and v n j 

 and let these quantities for cluster n + 1 immediately after 



collision be 



n + 1 



m, B n „ and v H „ 



Then 





nm v = n + 1 m v n , 



or 





n 

 n+ I 



Hence 





/ n 



T? 1 i 1 1 





E„, = ln + lm^ +1 



Now 





E n = \ n, m. v 2 m 



therefore 





E, = ^E, 



That is the energy of motion of the cluster just after 



* Todd, Phil. Mag. xxv. p. 165 (1913). 



t Kleeman, Proc. Camb. Phil. Soc. xvi. p. 285 (1912). 



t Todd, Proc. Camb. Phil. Soc. xvi. p. 21 (1912). 



§ Lattey & Tizard, Proc. Roy. Soc. lxxxvi. A. p. 356 (1912). 



II Kleeman, Proc. Camb. Phil. Soc. xvi. p. 285 (1912). 



