Discharge of Electricity . 



395 



Measurement of the Difference of Potential required to produce 

 the same length of Spark at different pressures of a Gaseous 

 Dielectric. 



We took four series of readings for a -5-centimetre spark 

 through air between the parallel disks above mentioned, vary- 

 ing the pressure from 20 millims. of mercury to the atmo- 

 spheric. On diagram 3 I have plotted two of these : the 

 upper curve was first obtained with the capacity of the con- 

 ductor increased by the couple of Leyden jars ; and the lower 

 was obtained immediately afterwards with the jars off. Each 

 of the series gave an experimental curve which coincided with 

 a hyperbola, and more closely than in the case of the former 

 set of curves with variable distance. The results are as fol- 

 lows (where p denotes the pressure, in millimetres of mer- 

 cury):— 



Series. 



Function for V. 



a. 



b. 



I. 



II. 



III. 



IV. 



•04798 </{p 2 + 20o-6p\ 

 •04455 ^{p 2 + 200p\ 

 •04634 V {p 2 + l99p\ 

 •04685 ^{p 2 + 2Qlp\ 



102-8 mm. 

 100-0 „ 

 99-5 „ 

 103-5 „ 



4-668 C.G.S. units. 

 4-455 „ 

 4-611 

 4-851 „ 



Mean 



•04579 ^{p 2 + 202'9p} 



101-5 „ 



4-646 „ 



Here a is the semi- transverse and b the semi- conjugate axis 

 of the hyperbola. The four values of a agree well with one 

 another. To find out how it depended on certain conditions, I 

 took several series of readings with change of a constant. 

 With the length of spark increased to 1 centim. the equation 

 is 



Y = -08062 */{p 2 + 219-8^}, 



giving a= 109-9 millims. and 5 = 8-86 C.G.S. units. The in- 

 crease in the value of a, though small, is so decided that we 

 may infer that the greater the length of the spark the greater 

 is the value of a. 



With hydrogen substituted for air, the curve obtained was 



V= '02is/{p 2 + 600p}, 



which gives a = 300 millims. and 6=7-2 C.G.S. units. Thus, 

 the length of the spark being -5 centim., the value of a for 

 hydrogen is thrice that for air. 



When taking the fourth of the above sets of observations, 

 at the lower pressures we observed not only the reading for 



