Discharge of Electricity from Cylinders and Points. 793 



surface of the inner cylinder is V/alogA/a ; and with the 

 second pair the force is Y/ka log A/a. 



Hence aX t is constant when ap is constant for pairs of 

 cylinders which are geometrically similar. Now Gaugain* 

 found that the force at the surface of a given wire, necessary 

 to produce a discharge, was independent of the radius of the 

 outer cylinder. In all his experiments, however, the radius 

 of the outer cylinder was large compared with that of the 

 inner, the pressure being atmospheric, and Baillef found 

 later that if the difference between the radii was small enough 

 the force at the inner surface was affected by the radius of 

 the outer cylinder, the force increasing when this radius 

 was decreased beyond a certain point. 



The ionization due to collision outside the cylindrical 

 surface at which X/p = 40 is too small to affect materially 

 the sparking potential, and the condition that the force X x 

 should be independent of the radius of the outer cylinder is 

 that X /p should be less than 40, X being the force at the 

 outer cylinder. 



5. In the results used in the following discussion X /p 

 was always less than 40. Hence the theory gives the simple 

 result that aKi should be the same for all wires for the same 

 value of ap. To test this a curve, giving the relation between 

 the sparking potential and the pressure, was drawn for each 

 wire; these curves were found to be quite regular and that 

 obtained with a wire 2*38 millimetres radius in a cylinder 

 7"45 cm. radius is shown as an example (fig. 2, p. 799). It 

 will be noticed that the curves for negative and positive wires 

 cross at about four millimetres pressure. 



Between the pressures p = 3 and p = 7 the negative 

 sparking potential changes from 800 volts to 1700 volts. 

 Between these pressures the sparking potential was very 

 irregular. 



Similar remarks apply to some of the values obtained 

 from the cylinders II., where the radii were *063 and 1*98 cm. 

 respectively. For this reason some of the figures in the 

 following tables are enclosed in square brackets and are not 

 considered in finding the mean values. This irregularity 

 did not occur with the smaller wires. 



The following tables give the values of aX x corresponding 

 to a series of values of ap. The numbers in the different 

 columns are obtained from the sparking potential curves for 

 cylinders of different radii. 



* J. M. Gaugain, Ann. de Chim. et de Phys. (4) viii. (1866). 

 t Bailie, Ann. de Chim. et de Phys. (5 ) xxv. (1882). 



