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 armature of an electromagnet which receives current impulses from the line circuit.  There is thus one of these driving magnets at each station, each bridged across the line so that when a single impulse of current is sent out from the central office all of the ratchet wheels will be moved one step.  Another impulse will move all of the ratchet wheels another step, and so on throughout any desired number of impulses.  The ratchet wheels, therefore, are all stepped in unison.

Let us further conceive that all of these ratchet wheels are provided with a notch or a hole or a projection, alike in all respects at all stations save in the position which this notch or hole or projection occupies on the wheel.  The thing to get clear in this part of the conception is that all of these notches, holes, or projections are alike on all of the wheels, but they occupy a different position on the wheel for each one of the stations.