242 Mr. A. T. Waterman on the Positive 



equation (1) equal to the potential Y at the middle of the 

 strip, no matter what the fall of potential due to the heating 

 current or what the distribution of emission of the ions 

 along the strip may be. This may be shown by the foilowing 

 argument, for which I am indebted to Professor Richardson: — 

 Imagine the strip to be represented by a vertical line AB 

 and the deflexion caused by the magnetic field to occur in a 

 horizontal direction. For given values of z, H, and e/m } the 

 magnetic deflexion x is determined at each point by the 

 value of the potential difference V between that point and 

 the plates. Suppose that the strip lies along the y-axis and 

 the intensity of emission between y and y + dy is denoted by 

 f(y)dy. Let the actual balance position for a given value of 

 H be x x . Corresponding to x x there will, from equation 

 (1), be a particular value V of the potential difference which 

 will belong to a point C of the strip when the electric 

 current is flowing in one direction, and in general, let us 

 suppose, to some other point D when the current is flowing 

 in the opposite direction. The condition for a balance is 

 clearly 



f "Ay) dy + i B /Q/) dy= P/(</) dy + P f(y) dy 



Ja Jd J a Jc 



or r*c 



\ f(y)dy=0 (2) 



t, n 



As f(y) is necessarily positive, it follows that C and D are 

 coincident, and as they have to have the same potential they 

 must coincide with the only point whose potential V is 

 independent of the direction of the heating current. For 

 this theory to hold the potentials at every point must be 

 sufficient to saturate the emission current. 



The alternating current actually used was obtained from 

 a direct current by means of a rotating commutator with a 

 frequency of about 20 cycles per second. This frequencv 

 was high enough for the electrometer readings to be 

 sufficiently steady. It was not found possible to get readings 

 actually in the break with this arrangement, as the moly- 

 bdenite strip could not be induced to stay in the break. 

 The measurements which follow were taken with very little 

 preliminary heating, — only the amount necessary to take a 

 series of readings of the resistance up to the start of the 

 emission. 



