The Magazine of the Week is the August 1941 issue of Amazing Stories, with an Edgar Rice Burroughs cover story and great BEM cover art by J. Allen St. John.
As discussed in an earlier BOTW (seen here), Amazing Stories was the first of the science fiction pulp magazines. This issue's cover story, "Yellow Men of Mars," is by Edgar Rice Burroughs, probably the most successful of all the pulp writers. Burroughs is best known outside science fiction circles as the creator of Tarzan of the Apes, but most fondly remembered among SF fans for his tales of John Carter of Mars. "Yellow Men of Mars" is a John Carter story, later incorporated into the novel Llana of Gathol, tenth in the John Carter series.
The St. John illustration on the Magazine of the Week is one of my favorite examples of pulp era BEM cover art. Like any specialized community, science fiction fandom has its own peculiar jargon. (You are an SF geek, for example, if you can translate the statement, "I can't decide whether to go check out the filk or just gafiate.") Any serious SF fan will instantly recognize the creature on the cover of the Magazine of the Week as a traditional skiffy BEM, or "bug-eyed monster."