28 BELL SYSTEM TECHNICAL JOURNAL 



hollow circular tube of varying lengths and electrically by means of 

 an induction coil. The summar\- of the conclusions is as follows:^ 



"(1) The mean frequency of the humming-telephone note is de- 

 termined solely by the receiver diaphragm, and its natural free rate 

 of vibration. (2) The ascending intersections of the frequenc\- 

 zig-zag with the mean frequency line will be formed approximateh' 

 at tube lengths of (3/4+w) v/tJo cm. for one connection, and of (1/4 + 

 m) v/fio cm. for the other connection, of the receiver; where v is the 

 velocity of sound in air, n is the mean frequency in cycles per second, 

 and ni is any positive integer, within the working range of the tube. 

 The constants 3/4 and 1/4 may be modified by the presence of con- 

 densers, and other circumstances. (3) The range of pitch variation, 

 and the breaking positions, are determined by the transmitter, and 

 by the reinforcing capability of the system. For systems that are 

 weak, either electrically or acoustically, the range of pitch, abo\e or 

 below the mean, will be small. (4) The primary current, as measured 

 by a DC instrument, is ordinarily a minimum at the mean frequency, 

 and a maximum at a break. (5) Transmitters may be tested for 

 effectiveness, by measuring their hum-extinguishing resistances in 

 the primary or secondary circuit. The tube length should be such 

 as to produce mean frequency if one connection of receiver only is 

 used, but should favor both connections equally, if both connections 

 of receiver are used." 



They also give a first approximation theory to account for the 

 changes in frequency as the length of the coupling tube is changed. 



In 1917, H. W. Nichols gave the general equations for the 

 special case where the two diaphragms act as pistons closing tiie 

 ends of a tube of air. This case was given as an illustrative example 

 of the "Theory of Variable Dynamical Electrical Systems." ^ 



This paper gives a theoretical treatment of the behavior of a system 

 containing a transmitter and a receiver coupled together acousticalh' 

 and electrically, and with a source of electrical energy feeding the 

 transmitter. Formulae are deduced which give the frequency and 

 intensity of howling in terms of the physical constants of the system. 

 Numerical calculations are given and sufficiently detailed solution 

 of some special cases are given to enable one, who is interested in 

 using the howling telephone as a source of alternating current f)r 

 for other experimental work, to design the set for his particular 

 purpose. 



^ "Huniniing Telephone" hv A. K. Kennell\- and Waller 1.. Ujjson, American 

 Philosophical Society, July 20,' 1908. 

 ^ I'hysical Review, Aug., 1917, p. 191. 



