The narrator waits with Mr. Shaynor while Mr. Cashell attempts to make a connection via radio transmission with someone in another place nearby. At the time, this is a new science. "Marconi" is mentioned - who transmitted the first transatlantic radio transmission in 1901. Cashell can explain how the elements of radio transmissions work but not really why or what they are. Given that this, electricity, and induction are still newly discovered phenomena, they have the appearance and mystery of magic. Consider at the time the propagation of information from one place to another - through space (wireless) - would seem quite magical.
While they wait, the unfortunate Shaynor is fighting tuberculosis and takes an alcoholic drink to calm his symptoms. In his weakened and inebriated state, a trance is induced, and he goes in and out of consciousness. During this state, he is infatuated with a female figure on an advertisement as well as with Fanny, the young girl who he is perhaps in love with. During his trance, he manages to write lines from the poems of John Keats. After waking out of the trance, the narrator discovers Shaynor has no knowledge of Keats, begging the question of how he could come up with Keats' lines word for word.
This clearly parallels the (then) magical connection via radio transmission, information traveling from one place to another through space. The science seems magical; the channeling of Keats seems magical. We see the line between science and spirituality blurred, leading to any number of interpretations as to how Shaynor came up with the lines from Keats: divine inspiration, wild coincidence, a product of the alcohol and sickness, etc.