er, and the only difference between the harmonic-ringing telephone
and the ordinary telephone is in the ringer itself. The absence of all
relays and other mechanism and also the absence of the necessity for
ground connections at the telephone are all points in favor of the
harmonic system.

[Illustration: Fig. 185. Circuits of Kellogg Harmonic System]

_Limitations_. As already stated, the harmonic systems of the various
companies, with one exception, are limited to four frequencies. The
exception is in the case of the North Electric Company, which sometimes
employs four and sometimes five frequencies and thus gets a selection
between five stations. In the four-party North system, the frequencies,
unlike those in the Dean and Kellogg systems, wherein the higher
frequencies are multiples of the lower, are arranged so as to be
proportional to the whole numbers 5, 7, 9, and 11, which, of course,
have no common denominator. The frequencies thus employed in the North
system are, in cycles per second, 30.3, 42.4, 54.5, and 66.7. In the
five-party system, the frequency of 16.7 is arbitrarily added.

While all of the commercial harmonic systems on the market are
limited to four or five frequencies, it does not follow that a greater
number than four or five stations may not be selectively rung. Double
these numbers may be placed on a party line and selectively actuated,
if the first set of four or five is bridged across the line and the
second set of four or five is connected between one limb of the line
and ground. The first set of these is selectively rung, as already
described, by sending the ringing currents over the metallic circuit,
while the second set may be likewise selectively rung by sending the
ringing currents over one limb of the line with a ground return. This
method is frequently employed with success on country lines, where it
is desired to place a greater number of instruments on a line than
four or five.

Step-by-Step Method. A very large number of step-by-step systems
have been proposed and reduced to practice, but as yet they have not
met with great success in commercial telephone work, and are nowhere
near as commonly used as are the polarity and harmonic systems.

_Principles_. An idea of the general features of the step-by-step
systems may be had by conceiving at each station on the line a ratchet
wheel, having a pawl adapted to drive it one step at a time, this pawl
being associated with the armatur