CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL 

 LABORATORY, HARVARD UNIVERSITY. 



THEORY OF COUPLED CIRCUITS, UNDER THE ACTION OF 



AN IMPRESSED ELECTROMOTIVE FORCE, WITH 



APPLICATIONS TO RADIOTELEGRAPHY. 



By George W. Pierce. 



Presented October 12, 1910. Received October 20, 1910. 



I. Introduction. 



Persistent, or sustained, electric oscillations have recently come into 

 extensive use in wireless telegraphy. With these oscillations, which 

 are produced continuously while the transmitting key is depressed, 

 tens of thousands of waves arrive at the receiving station during even 

 the production of a single dot of the Morse code. This permits the 

 establishment of a practically steady state at the receiving station, so 

 that by the use of these persistent oscillations the mathematical treat- 

 ment of the problem of the resonance conditions at the receiving station 

 reduces to a problem of forced vibration. 



The exact solution for the radiotelegraphic circuits, however, still 

 presents considerable difficulty on account of the effect of the distrib- 

 uted capacity of the antennae. An approximation to a solution of the 

 practical problem can be obtained by supposing that the antenna of 

 the receiving station of the practical case can be replaced by a localized 

 capacity so that the circuits become those represented in Figure 1. 

 While this simplified system is a considerable departure from the actual 

 practical circuits, calculations made from the simplified circuits seem 

 nevertheless to be of importance, because the resonance in the simpli- 

 fied system is sharper than in the actual circuits, and the simplified 

 computations thus aff"ord a means of assigning certain theoretical 

 limits to practical attainments. 



It is the purpose of the present communication to give a solution of 

 the equations representing the flow of electricity in a system of circuits 

 of the form of Figure 1, under the action of a sinusoidal impressed 

 electromotive force at e, and to make from this solution deductions in 



