This Guitarphone zither by Oscar Schmidt, from 1917 is an instrument sometimes referred to as a "fretless zither." Several features distinguish the "fretless" ones from the European "concert/alpine zithers," which are more familiar and what most people tend to visualize when they hear the word "zither." One obvious difference between the two kinds is that the concert/alpine zithers include a fretboard on part of the instrument and the fretless ones don't. Another important distinction is that the concert/alpine zithers were expensive handcrafted instruments intended for use by highly trained professional musicians, whereas the fretless zithers were mass-produced, low-cost instruments and specifically marketed as easy-to-play instruments, providing the opportunity for music making to people of all ages having no innate musical skill or special training.
This massive industry was spawned in America following the great Panic of 1893. Following that depression, people having less financial resources welcomed the new music-made-easy paradigm being offered to them, both because the instruments were inexpensive and the investment of time and money previously required for learning how to play music was no longer a necessity.
Thus the instruments were designed and marketed as a music-made-easy package which typically included a set of interchangeable play-by-number music charts, which simply slid under the strings. The player would begin by finding the number "1" on the chart, pluck whichever particular string was over it, and then continue by following each number in succession to the end of the tune. In addition, most instruments also came with a wire "music stand" one could use for holding the music charts if they preferred.