PIERCE, — THEORY OF COUPLED CIRCUITS. 297 



The relation between the height of antenna, //, and the capacity (\ 

 required for resonance was found to be approximately represented by 

 the empirical equation: 



(1) (//- 11.8)(C4 - 84.6) = 88, 



which is the equation of an equilateral hyperbola with axes at TiT = 

 11.8 and C^ = 84.6. The nature of the agreement between the ob- 

 served and the calculated values is shown in Figure 4. Evidently the 

 relation expressed in equation (1), though an interesting approximation, 

 is not exact. 



III. Theoretical Treatment. 



Let us now turn from the experiment to the theory of the oscilla- 

 tion. The problem undertaken is the investigation of the relative 

 current in the detector circuit (Circuit IV of Figure 1) for various 

 adjustments of the constants of Circuit III and Circuit IV. In the 

 theoretical treatment this carries with it (1) a determination of the 

 adjustments that must be made to obtain resonance, (2) a determina- 

 tion of the adjustment for best resonance, (3) a determination of the 

 effect of the resistances on the resonance relations and on the amount 

 of current receivable, (4) a discussion of the resistance that a detector 

 must have for greatest sensitiveness, (.'">) a computation of the amount 

 of disturbing current that will be obtained from an undesired source of 

 waves, and (6) a quantitative judgment as to the sharpest selectivity 

 that can be attained by circuits of the form of Figure 2. 



As stated in the Introduction, in treating these general questions it 

 has been found necessary to depart from strict observance of the actual 

 practical wireless-telegraphic conditions and to assume the capacity of 

 the antenna, which is a distributed capacity in practical wireless teleg- 

 raphy, to be replaceable by a localized capacity C^. This modification 

 of the problem will not completely destroy the validity of the discussion, 

 because the simplified problem enables us to derive certain important 

 conclusions in regard to the problem with the less simple conditions. 



Referring to the localized-capacity circuits of Figure 1, and supposing 

 an electromotive force ^cos wt at e, the differential equations of the 

 current in the two circuits are 



dr f)i/ IP 



(2) ^ ^ + ^/^ + B^x+ -^ xdt = ^cos o)^, 



