32 Mr. J. A. McClelland on the Conductivity of 



Ohm's law, but that the current tends to a maximum value 

 which is not increased when the E.M.F. is further increased. 

 This is the form of curve we should expect to get if we 

 regard the conductivity of the gas as due to its ionization 

 in the flame, so that we have a number of positively and 

 negatively charged ions in the gas passing the electrode B. 

 If the terminal B be positive, then the negatively charged 

 carriers are deflected to it and give up their charge, causing 

 the observed leakage of the charge from B. If we suppose 

 that one of these carriers of electricity moves with a velocity 

 of v centimetres per second under an electromotive force of 

 1 volt per centimetre, and that the stream of carriers takes a 

 time t to pass along the length of the electrode B, the carriers 

 inside a radius p will be discharged to B, where p is given by 



vY t to r 



(■?*! = radius of tube A; r =radius of B; V= potential of B), 

 and 



v 



[1 = length of B; v' = velocity of the stream of gas up the 

 tube A). 



Therefore if q be the charge carried by the carriers of one 

 sign in unit volume in the tube at B, the amount of electricity 

 given up to B in unit time is 



2 , ZirqlvY 



!<>« ? 

 'o 



The current is therefore proportional to the E.M.F. until 

 p = i\ (the radius of A), when all the carriers are discharged 

 toB. 



We have neglected in this calculation the rate at which 

 the positive and negative carriers are recombining ; as we go 

 up the tube the recombination diminishes the conductivity, so 

 that a large E.M.F. by discharging the carriers sooner to B 

 increases slightly the current, so that the curves do not 

 become perfectly flat at the point where the E.M.F. is 

 sufficient to discharge all the carriers before they pass the 

 electrode. 



In curve II. the maximum current is reached for a smaller 

 E.M.F. than in I., because the velocity of the stream is less 

 and the carriers take a longer time to pass the electrode. 



In the following table (III.) the numbers are given for an 



