426 Dr. A. M. Tyndall on the Spread of the 



is different from- that generally accepted, there would be 

 strong indirect evidence that the assumption of one-way 

 flow is not justified. The method is as follows : — 



Consider a given charged point opposite an earthed plate. 

 When no discharge is occurring the distribution of lines of 

 force between them is settled by the potential of the point. 

 When discharge is occurring, the distribution is changed 

 owing to presence of free ions in the space between the 

 electrodes, the amount of change depending upon the current 

 passing from point to plate. Suppose that without altering 

 the geometrical conditions it were possible to double the 

 electrical density at every point on the electrodes. It seems 

 to follow as a necessary consequence that in doing this the 

 volume density of the ions at every point would also be 

 doubled, assuming that the magnetic effect of the moving- 

 ions has no appreciable influence on the general ionic distri- 

 bution. (A simple calculation shows that this assumption 

 is quite justified even close by the point where the ionic 

 velocities must be high.) 



A given ion under these conditions will still travel along 

 the same path as before, but owing to the change of density of 

 charge, the potential gradient at every point will be doubled, 

 and the ion will move at double the rate, thus contributing 

 double the current to the plate. Since, also, the volume 

 density of the ions is doubled, the current at any point on the 

 plate will be in all increased four times. In other words, for 

 a constant relative distribution of the field — referred to in 

 future as a "constant spread," the current C at any point 

 on the plate is given by 



™ == constant, 



where V is the difference of potential between point and 

 plate. This formula only applies for given ions under constant 

 physical conditions, If by varying the conditions the specific 

 ionic velocity of the ions " v " is changed* then 



C 



To test this expression the following apparatus was set 

 tip . — .The plate, 15 cm, in diameter, consisted of a central 

 brass disk A surrounded by concentric brass rings B, 0, and 

 D, all insulated from one another and supported on ebonite 

 pillars fixed to a large disk forming the lid of a bell-jar. 

 Through the neck of this bell-jar was the sliding point 

 P, backed by a plate, also adjustable in position. A 



