98 BELL SYSTEM TECHNICAL JOURNAL 



tive starting point rather than as a completed structure. Of the funda- 

 mental correctness of the method of attack there can be Httle doubt. 

 The various simpHfying assumptions, however, require careful scru- 

 tiny and doubtless some of them will be revised as time goes on and 

 additional experience is acquired. Experimental guidance will be in- 

 valuable, and indeed certain data already have been obtained which 

 are helpful in analysis of the assumptions. Although these data are in 

 general qualitative agreement with the theory as outlined, the ex- 

 perimental technique must be refined before quantitative comparison 

 can be made. It is hoped that the results can be made available at an 

 early date. 



Among the various assumptions which were made in the develop- 

 ment of the theory, there are three which lead particularly to far- 

 reaching consequences. These three may be enumerated as follows: 



1. Plane-parallel tube structures 



2. Current flow in straight lines 



3. Small alternating-current amplitudes. 



There are grounds for the belief that the assumption of plane- 

 parallel tube structures does not exclude the application of the alter- 

 nating-current results to cylindrical structures as completely as might 

 be supposed. In the first place, the approximation of cylindrical 

 arrangements to the plane-parallel structure becomes better as the 

 cathode diameter is made large. Many tubes contain special cathode 

 structures where this is the case. Furthermore, Benham ^ has obtained 

 an approximate solution for the alternating-current velocity in cylin- 

 drical diodes where the cathode diameter is vanishingly small, and the 

 transit angle is less than 5 radians. The resulting curves of alternating- 

 current velocity versus transit angle have the same shape as the curves 

 for the planar structures, and when the cylindrical transit angle is 

 arbitrarily increased by about 20 per cent, the quantitative agreement 

 is fair for transit angles less than 4 radians. It follows that until 

 accurate solutions for cylindrical triodes can be obtained, the planar 

 solutions may be expected to give correct qualitative results, and fair 

 quantitative results when appropriate modifications of the transit 

 angle are made. In fact, good agreement is obtained if calculations of 

 the cylindrical transit angle are made as though the structure were 

 planar. 



The assumption of current flow in straight lines is open to some 

 question when a grid mesh is interposed in the current path. For the 

 positive grid triode, the objection to the assumption has been over- 

 come by postulating a special case where an ideal choke coil prevents 



