718 



Dr. S. R. Milner on the Current -Potential 



from a capacity of *0055 mf. with gradually diminishing in- 

 ductances, are shown, which exhibit these effects. They are 

 easily explained qualitatively in terms of the above theory. 

 The brightness of the core may be taken as proportional to 

 the amount of ionization per c.c. of the air produced by the 

 initial sparking p.d., the more slowly the initial p.d. falls to 

 the arc value the greater will be the final ionization produced, 

 and we have seen that the slowness of this fall will increase 

 as the inductance in the discharge circuit is diminished. The 

 fact that after a certain point the thickness of the core begins 

 to increase suggests that at this point the ionization of the 

 air is approaching completion, and that any further increase 

 in the discharge current then necessitates an increase in the 

 cross-section of the region in which ionization takes place. 

 This is confirmed by the following table, in which the diameter 

 of the core and the calculated value of the density of the 

 average spark current, assuming that it is concentrated into 

 the core, are given for a series of sparks with different 

 inductances similar to those of tig. 9. The average current 

 is taken as charge of jars-hhalf period = 30,000 /K/7T ^LK, 

 where 1 = spark-length, *335 cm., K= capacity of jars, 

 *0055 mf., L = inductance. 



Inductance. 



Average Current. 



Thickness of 

 Core. 



Current Density. 



mcrli. 



amp. 



cm. 



amp./sq. cm. 



320 



13 



0-03 



18600 



170 



18 



003 



26000 



95 



24 



03 



34500 



40 



38 



03 



54000 



15-6 



60 



04 



47500 



100 



75 



0045 



48000 



5-0 



106 



0-05 



54000 



2-7 



140 



06 



50000 



Conn, wires o 



lly. — 



0095 







It will be seen that the average current density reaches a 

 limiting value of 50,000 as the inductance is diminished *. 

 The maximum current density would be 7r/2 times as great as 

 this. A rough calculation shows that the limiting density 

 is of the same order as that which would occur in completely 

 dissociated air. This would be 



where N is the number of molecules per c.c. of the air in the 



* In another set of sparks *G8 cm. long the limiting current density 

 «>j,000 was obtained, in a third set "1 cm. long the value was only 20,000. 



