﻿858 Prof. J. S. Townsend on the 



the equations for currents between parallel plates and in the 

 method of representing a certain curve obtained experimentally 

 by a mathematical formula. 



The most accurate experiments, namely, those with ultra- 

 violet light, from which all the numbers given in the tables 

 and curves were deduced, are as follows. When ions start 

 from one plate and travel towards another parallel plate at 

 distances a? l9 a? 2 , &c, from the first plate, the numbers n 1} n 2 , &c., 

 that arrive at the second plate are given accurately by the 

 formula n=n Q e* x . This is exactly what would be expected 

 from the theory on the assumption that on an average a 

 negative ion moving under a constant force generates a. ions 

 per centimetre of the gas. As in all experiments in which 

 a mean constant velocity is attained in a resisting medium, 

 the first distance must be sufficiently great to allow the ions 

 to assume that velocity. No experiments were made at short 

 distances, or with small potential differences between the 

 electrodes of the order of 20 or 30 volts. It is not necessary 

 to specify the mean velocity more particularly than to define 

 it as the mean velocity of the ions after those that are 

 initially started have traversed several free paths. In the 

 mean velocity obviously it is necessary to reckon the velocities 

 of ions that have just been generated. Under these conditions 

 the mean velocity of ions traversing planes at distances 

 a?!, # 2 , <fec. from the plane a? = will all be the same, and mathe- 

 matically it is correct to say that the numbers arriving at 

 those distances are given by the equation n — n e ux . 



Mr. Campbell washes for a formula that would apply to 

 distances so short that the final mean velocity would not be 

 attained in it. I cannot see of what use it would be in these 

 experiments. The expression n — n e ax appears to be no 

 more erroneous for the values of x that have been used 

 than the expression M/r 2 for the force outside a spherical 

 distribution of attracting matter, which does not hold w T hen 

 r becomes smaller than the distance of the outer layers from 

 the centre. 



The most important step in establishing the theory is to show 



that the experimental results satisfy the relation =/( — I. 



The theory requires that this formula should hold 

 between the variables, and it has been found to be satisfied 

 accurately. 



Mr. Campbell seems to think that the basis of the theory 

 depends on being able to express the function / accurately 

 by means of a mathematical formula. This is where his 

 criticism is most at fault. In order to obtain any formula 

 to express this function it is necessary to make many 



