Sparking Voltages in small gaps. 463 



(2) the time for which the voltage must continue to act 

 after it reaches a certain value, and (3) the initial ionization 

 of the gap. When the voltage rises rapidly, variation of 

 any one of these will affect the sparking voltage. By con- 

 sidering these conditions together an explanation of the 

 variations found in impulsive sparking voltages in a constant 

 gap can be given in a direct and simple manner. 



Let it be supposed that the sparks are to be produced in 

 a small gap between, say, small spherical electrodes, by 

 means of an induction-coil. Assuming first that the gap is 

 removed from connexion with the coil, and that the high 

 tension terminals of the coil are so far apart that no spark 

 can pass when the primary current is interrupted, then the 

 maximum voltage which can be attained in the secondary of 

 the coil is variable in a regular manner by varying the 

 primary current (? ) at break. Disregarding, for the sake of 

 simplicity, the double oscillation which occurs in the secon- 

 dary, the rise of voltage can be represented by a sine curve, 

 its period being constant, and its amplitude proportional to 

 the primary current at break. The rate of rise of voltage 

 from zero will vary with ? . In figure 1 a number of sine 

 curves are drawn corresponding to the arbitrary current 

 values noted in the graph. The ordinates represent Volts 

 and the abscissae Time. A small gap is now connected to the 

 coil and adjusted so that with i — l in the primary, sparking 

 just occurs. It will be supposed that the spark appears 

 when V reaches the crest of the curve i =l. It will also 

 be supposed that the static sparking voltage for the same 

 gap is a slightly smaller value V such as is represented by 

 the horizontal line. Assuming that there is ample initial 

 ionization in the gap between the electrodes, then the time 

 interval after the intersection of the curve ?' =1 and the line 

 V is that required for the voltage to act before sparking 

 can occur. During that time the voltage rises to Y 1 . As 

 it is supposed that i — l is the smallest primary current by 

 which sparking can be obtained, the effect of variation in 

 the initial ionization is to alter the regularity of occurrence 

 of the spark. 



From the crest of i =l, draw any straight line as shown 

 at an inclination to the horizontal. The inclination of this 

 line will be different for different gaps. Thus for a gap 

 between large spheres it will be small, but for a gap between 

 points it will be relatively large. The horizontal distance 

 or time between the intersection of this line on any curve 

 and that of the line V on the same curve decreases regu- 

 larly from curve to curve. This may be taken to represent 



