312 PROCEEDINGS OF THE AMERICAN ACADEMY. 



employs any of the ordinary detectors, because the resistance of the 

 detectors is a function of the received current. This is a complex 

 phenomenon and will enter into the consideration of sharpness of 

 resonance, which is discussed below. 



VII. On the Sharpness of Resonance and on the Possibility 

 OF Preventing Interference. 



By reference to the previous pages it is seen that in order to obtain 

 the best resonance, which gives a maximum of current in Circuit IV, 

 it is necessary to adjust the period of both Circuit III and Circuit IV. 

 We have given an expression for the value of the maximum current 

 (that at best resonance) in equation (23), and we have also obtained 

 a general expression for the current in Circuit IV (equation (16)), so 

 that it is now possible to plot the current as best resonance is ap- 

 proached, and to form an estimate of the sharpness of resonance, 

 whenever the constants of the circuits are known. This may conven- 

 iently be done in either of two ways, — which I shall classify as Case I 

 and Case II, as follows: 



Case I. Let us assume that the Circuit III is put at its best value 

 (equation (21)), and let us compute the current in Circuit IV as the 

 wave length of Circuit IV is varied. This corresponds to fixing the 

 antenna circuit and tuning with the detector circuit. 



Case II. Assume Circuit IV to be set at its best value (equa- 

 tion (22)) and compute the current in Circuit IV as the wave length of 

 Circuit III is varied. This corresponds to fixing the constants of the 

 detector circuit and tuning with the antenna circuit. 



In either case we must know certain constants of the circuits, and I 

 shall carry through the computation for both cases with several sets of 

 constants. First it is necessary to transform the equations into suitable 

 forms for making the computations. 



Development of Equations for computing Case I. — The general 

 expression for the amplitude of current in Circuit IV is given in equa- 

 tion (10) ; namely, 



(16) Y= ^'^ 



Let us combine with this the condition that U shall have its opti- 

 mum value, equation (22), 



(22) Uo,n = ± |/^(iJ/V-7?3//4), 



