132 PFJJ- SySTF.yf TECIISICAL .lOVRXAL 



liaps llie best way to conceive of lliis is, that as the distance between 

 the plates is increased toward tliat critical value of d, the value of 

 .Vo — which is the rate at which we have to supply electrons at the 

 cathode, in order to keep a preassigned current flowing — diminishes 

 continuously and approaches zero; so that e\entually the current 

 will keep itself going (and actually start itself) with the assistance of 

 the occasional ions which are always appearing spontancousK in 

 every gas, even though it be encased in an armor-plated shield. ( )l 

 course, it is rather risky to predict just what is going to happen. 

 when an e(|ualion whicii has been lised u|j to represent a finite physical 

 phenomenon over a certain range exhibits an infinite discontinuity 

 at a point outside of that range. I'sually, of course, the infinite value 

 which the equation rec|uires is modified into a finite one by the influ- 

 ence of some factor which was neglected when the equation was 

 devised. In this case, howe\er, the infinite discontinuity corresponds 

 to a sudden catastrophic change. If an electrometer is shunted 

 across the interspace between anode and cathode, its needle is forci- 

 bly jerked; if a telephone-recei\er is connected in series with the 

 interspace, it makes a clicking or a banging sound; if the gap is wide, 

 so that the voltage just before the disruption is high, there is a brilliant 

 flash, which ma>' bear an uncomfortably strong resemblance to the 

 liglitiiing-bolt which is the cosmical prototype of all electric sparks. 

 What goes on after the critical mcjment of transition or transforma- 

 tion depends on many things; and not only on ob\ious features of the 

 spark-gap, such as the kind and density of gas and the shape and size 

 and material of the electrodes, but also on such things as the resistances 

 and the inductances in series with the discharge, and the qualities of 

 the Sf)urce of elect romoti\e force and its ability to satisfy the demands 

 for current and voltage which the new discharge may make. Some- 

 times these demands are too extravagant for most laboratory sources 

 or jjcrhaps for an\- .source to meet; probably this is why the spark 

 between extended plane surfaces in dense air is as ejihemcral as it is 

 \iolent. But this does not always happen; in a s-ufficienth' rarefied 

 gas, the sc-lf-mainiaining discharge which sets in after the transforma- 

 tion re(|uires only a modest current and a practicable \-oliage, and 

 supports itself with a few thousand \olts ajjplied across its terminals. 

 The same thing occurs in a dense gas, if either of the electrodes is 

 I)ointed or shari)l\- curved, like a needle or a wire; the condition, more 

 exactly, is that the radius of curvature of either electrode should be 

 distinctly less than the least distance between the two. The trans- 

 formation, however, is always very sudden, whether the new dis- 

 charge be transient or |)ermancnt; and there are also sudden transi- 



