ULTRA-HIGH-FREQUENCY OSCILLATIONS 281 



material forming the resonant system and secondly the losses caused 

 by radiation of energy. These latter are extremely important where 

 the negative resistance is only a few ohms as in the present instance 

 and necessitate the use of nearly closed structures. This again directs 

 attention to the properties of cavities and concentric lines tuned by 

 internal capacitive resonance, the low capacitance being formed by 

 the electrodes between which the electron discharge flows. It was on 

 the basis of these principles that the actual diode models were con- 

 structed. 



The general aspect of these tubes is shown in Fig. 1 which presents 

 a section through the axis of revolution. The cylinders of radii r\ and 

 ^2 respectively constitute the outer and inner conductors of a con- 

 centric line. At one end of the inner conductor a flange partly closes 

 the system thus confining most of the energy within the cavity. At 

 the other end of the inner conductor the flat surface of the inner 

 conductor constitutes an emitting cathode while the opposing surface 

 of the outer conductor constitutes the positively biased anode which 

 also completely closes the end of the cylinder. The system is tuned 

 by the capacitance between cathode and anode and the effective 

 inductance of the coaxial line of length h. The emitter was coated in 

 the experiments with an oxide of the uncombined type and was heated 

 by a filament located within the inner cylinder. The spacers for 

 separating the inner cylinder from the main body of the outer con- 

 ductor were composed of fused quartz in order to obtain low losses and 

 good mechanical rigidity. A water jacket was supplied to assist in 

 cooling the anode. 



In reference to Fig. 1, the tuning relation between the cathode- 

 anode capacitance and the inductance of the resonant circuit connected 

 to it requires the following relation to be satisfied, 



1 2Trh X ... 



7rr2^ lOge — 



Here X stands for the free space wave-length. The other quantities 

 in the formula are illustrated in Fig. 1 and all dimensions are in cen- 

 timeters. The radii ri and r^ refer respectively to the inner surface 

 of the outer cylinder and the outer surface of the inner cylinder. 

 Improved formulas for the resonant frequencies of cavities of this type 

 have recently been published by Hansen.^ 



The formula (1) is based on the approximation that the presence of 

 electrons between cathode and anode does not affect the dielectric 



