Oscillations in the Discharge of a Leyden-jar. 107 



Suppose spark-gap =1 cm., 



then V = 10 4 x<± volts, 



and C = 25 x 10 2 E.S. units for one jar ; 



~ 25xl0 2 x4xl0 4 1 1A6 ™ Q 

 •'■ Q= 300 =3X10* E.S. umts. 



Now the charge on an ion has been found by J. J. Thomson 

 to be equal to 6 x 10~ 10 E.S. units, and the energy required 

 to produce an ion (by E. Rutherford and R. K. McClung, 

 Proc. Roy. Soc. vol. lxvii.) to be =1*9 x 10~ 10 ergs; 

 therefore energy required for the dissociation of 1 E.S. unit 



_ 1-9 xlO- 10 _ 



~ 6xl0" 10 -' der £' 



therefore energy required to carry across a quantity Q 



= |xl0 6 x ~=10 6 ergs. 



Now the total E.S. energy of the charge 

 _ i pv 2 



therefore 



= 22 x 10 6 ergs. 



Ratio of energy required to dissociate sufficient no. of ions 

 total energy of charge 



10 5 1 



~ 22 x 10 6 ~ 220 ' 



a damping of about 1-2 per cent. 



If V = 10,000, t. e. for a spark-gap of -^ inch, the ratio is 

 1 : 55, a damping of about 2 per cent. 



Thus we see that the expenditure of energy required to 

 produce a sufficient number of ions to carry the discharge 

 across is not enough to account for the damping. We are 

 therefore driven to the conclusion that a much greater 

 number of ions are produced than are sufficient to convey the 

 discharge. The path of the discharge is very narrow and 

 confined, and the ions so numerous and close together that 

 recombination is very rapid. To these recombinations is 



