A wire signal is a brevity code used by telegraphers to save time and cost when sending long messages. The most well-known of these was the 92 Code adopted by Western Union in 1859. The reason for this adoption was to reduce bandwidth usage over the telegraph lines and speed transmissions by utilizing a numerical code system for various frequently used phrases. 
In the above list, the numbers 19 and 31 refer to train order operations, whereby messages from the dispatcher about changes in railroad routing and scheduling were written on paper forms. Form 19 was designed to be passed to the train as it went through a station at speed; Form 31 required hand delivery for confirmation.
Today, amateur radio operators still use codes 73 and 88 profusely, and -30- is used in journalism, as it was shorthand for "No more - the end". The Young Ladies Radio League uses code 33 to mean "love sealed with friendship and mutual respect between one YL [young lady] and another YL." The other codes have mostly fallen into disuse.
The following code was taken from 1873 telegraph rulebook of the Lakeshore and Tuscarawas Valley Railway Company of Cleveland, Ohio.