A story about the attempt by the British to change the tilt of Earth's axis to create a more suitable environment for themselves and how the Americans foil it. The British have been launching incessant payloads of "electrocotton" - mono-layered sheet of cotton molecules - into earth orbit, where it interacts with Earth's magnetic field and gently tugs the planet into a new tilt angle. However, their attempt fails because an American (female) robot adds an extraneous factor of two to the mathematical calculations that go into the project. This change causes the British to launch twice the amount of electrocotton needed for their purposes, with the up-shot that the tilt of the axis is destined to complete a full loop and end up where it started. The subtext of the story is that the robot is able to prove to the male-chauvinist protagonist that mathematical abilities are not inferior in the female gender (I didn't find it convincing and in fact, the story appeared to me to end on a male-chauvinistic note)
It would be a very neat calculation (with some simplifying assumptions) to see how much energy is involved in changing the earth's tilt, the impact on its rotational speed, the time it takes to achieve this and the impact on earth's core temperature as the magnetic field gets drained....I can't see how the time span required to change the tilt is consistent with the story's timeline.
There are a lot of connections that should be addressed. First and foremost, this is clearly an "update" of Verne's Topsy Turvy. However, so far as I know, it has no relation (other than the obvious) to Brian Wilson Aldiss' story of the same name. Additionally, as "William E. Emba" mentions in his review of a novel by Ballantyne elsewhere on this site, the author is a "former maths major/teacher".
Finally, I cannot help but be reminded by this story of the sad but true account of the loss of the Mars Climate Orbiter in 1999 due to the failure of an American contributor to the international project to use metric units.
This story was published in The Mammoth Book of New Jules Verne Stories, ed. Mike Ashley & Eric Brown, Robinson.