650 BELL SYSTEM TECHNICAL JOURNAL 



where D represents the magnitude of d. Below are given some of the 

 values of g^xD/o 



DIa g-'^'« 



0.1 1.875 



0.2 3.514 



0.3 6.587 



0.4 12.35 



0.5 23.17 



0.6 43.39 



0.7 81.34 



0.8 152.5 



0.9 285.5 



1.0 536.0 



This shows that if the magnitude of the cosine term which involves z 

 is to be limited to one per cent of the largest of the three terms consti- 

 tuting the logarithm, then Dja should be greater than 0.84. On the 

 other hand if a ten per cent variation is tolerated, then Dja may be as 

 small as 0.48. 



There is a further consideration that tends to smooth out the 

 corrugations in the potential caused by the grid wires. The relation 

 (53) was derived on the assumption that the cathode and plate were 

 quite distant from the grid. When this is not the case, the fact that 

 both are equipotential surfaces tends to crowd the irregularities in 

 toward the grid, and hence to decrease the area of the pockets. 



The general conclusion to be drawn from this investigation into the 

 potential distribution is that the electronics analysis can be applied 

 with greatest accuracy to tubes where the grid wires are very close 

 together relative to the distance between grid and either cathode or 

 anode. When this is not the case, the analysis may be expected to 

 show the general trend of the performance in most cases but to be 

 unreliable for quantitative computation. In extreme cases, where the 

 grid wires are very far apart, the grid action approximates more nearly 

 to a change in the effective cathode area than a uniform action over 

 the entire surface. The electronics analysis can be adapted to this 

 extreme case when the change in effective cathode area occurs instan- 

 taneously with a change in grid potential, for then the diode analysis 

 applies directly between the effective cathode area and the anode. 

 Means for doing this will become evident when the theory for grids 

 with fine mesh is understood so that the details will not be described. 



The analysis for fine-mesh grids now follows, based on the assump- 



