394 Prof. lownsend on the Conductivity produced 



found by finding the number of molecules that a single ion 

 encounters in going through a centimetre of gas at a given 

 pressure ; this will be the maximum value to which a ap- 

 proaches as the electric force increases. A simple investiga- 

 tion of the curves obtained for ultra-violet light will be 

 sufficient for this purpose. 



Let an ion be travelling in a gas under an electric force X. 

 The velocity with which it encounters a molecule depends on 

 the free path which it traverses previous to the collision. 

 Let it be supposed that two new ions are formed whenever 

 the velocity at collision exceeds a certain value, so that an 

 ion will acquire the requisite velocity under a force X, if it 

 travels along a path x such that X# = or> V, where V de- 

 notes a constant difference of potential. Let the gas be at a 

 pressure of one millimetre, and let N be the number of en- 

 counters that an ion makes with molecules of the gas when 

 it travels through a distance of one centimetre. The mean 



free path will be ^, and the number of paths which exceed 



the distance x will be Ne -:Nx . When Xa? = V new ions will be 

 produced, so that the number of ions which a single ion 



generates in going through one centimetre will be Ne K ■ 

 This is the value of a corresponding to X when p = l. 

 Hence the equations of the curves should be of the form 



NV 



a = Ne x , where N and Y are constants to be determined 

 by any two points on the curves. This simple formula gives 

 the values of a fairly accurately for the larger forces, and 

 the following tables show how it may be applied to the gases 

 which have been examined. 



Thus for air when IS T = 15*2 and V = 25 we obtain the 

 following values of a (Table III.) . The values of a, taken from 

 the curves (in the former paper) are given in the same table, 

 the pressure^ being one millimetre. 



The values of a corresponding to the larger forces are thus 

 seen to agree with the numbers obtained from the simple 



_ NT 



formula N = e ~x , so that N represents the maximum value 

 of a 9 or the number of collisions which an ion makes in going- 

 through one centimetre at one millimetre pressure. 



Since the formula is not in agreement with the experi- 

 mental results for the smaller forces, it is necessary to modify 

 the original hypothesis in order to obtain an explanation of 

 the results over the whole range of forces. 



