148 BELL SYSTEM TECHNICAL JOURNAL 



accumulate down the length of the stream and may exceed in number 

 the negative charges passing along. At the same time, electrons are 

 moving at random outside the stream, producing negative electrifica- 

 tion. There is then a field surrounding the stream which tends to 

 pull the electrons inward. If there were only the mutual repulsion 

 between the electrons to compensate for, this would be done when 

 the number of positive ions in the beam equals the number of electrons. 

 There is in addition an original divergence of the beam which must be 

 overcome. If this divergence is assumed to be one degree from the 

 axis and the electron current 2 x 10~^ amp., then a simple calculation 

 shows that the radial field required to pull the beam to a focus at the 

 usual distance is about one volt per cm. This field strength is pro- 

 duced, with beams of the ordinary intensity, if there are four positive 

 ions for each electron in the stream, a Condition which seems not 

 unreasonable. 



The number of ions per electron in the stream is probably constant 

 as the current in the stream is varied, since the conditions of collision 

 and recombination are not altered. When the current is increased, 

 therefore, the total positive ionization of the beam increases, the field 

 around the beam becomes stronger, and the electrons are brought to 

 a focus in a shorter distance. 



These deductions have been confirmed experimentally. That the 

 focusing of the stream depends upon the current flowing was one of 

 the earliest observations made in developing the tube and this method 

 has been used ever since to obtain a sharp spot. The point of con- 

 vergence can be seen moving in the manner expected when the current 

 is changed, and the effect has been further verified by using a tube with 

 a movable fluorescent screen so that the length of the electron beam 

 could be varied. The presence of the electric field around the beam 

 was shown by the effect of two beams on each other, in a tube in 

 which there were two electron streams crossing each other at right 

 angles at their mid-points, each falling on a fluorescent screen. When 

 one beam was moved away from the other by a field between the 

 deflector plates, the second beam moved as if attracted by the first. 

 The directed electrons in each beam were attracted toward the posi- 

 tive ionization in the other, and for one particular adjustment of the 

 tube the displacement was such as would have been caused by a 

 field ot about 3 volts per cm., a result not far different from that 

 previously calculated. 



Since the beam must produce its own positive ionization some time 

 must elapse before it can produce by collisions the required number 

 of positive ions. Calculation shows this time to be of the order of 



