So wait, does a gallon of water weight more or less in frozen vs liquid form............................................................................
OK ... not sure if serious. Yes, a gallon of water weighs substantially more than a gallon of ice (at typical atmospheric pressures):
And, of course, melting doesn't change the weight. If it is a ballerina affect (solid ice from the poles flows towards the equator - or at least redistributes equally) ....
"The continental crust contains 0.374 % of the Earth's mass" of which only 1.4% is water by weight (
https://en.wikipedia.org/wiki/Earth) ... so if all of Earth's (crust) water migrated to the equater, it would be like 0.005% of the Earth's mass.
A more useful ref: "'70% of the Earth's surface is water. Of this 70%, 98% is salt water, leaving 2% as fresh water. Of the 2% that is fresh, about 90% is frozen. This frozen water is locked up in the Antarctic ice sheets and glaciers on the Alps, etc.'" (
http://www.funtrivia.com/askft/Question37603.html)
So, 0.374% * 1.4% * 2% * 90% = ~0.00009% of Earth's mass that could potentially make run for the equator. It might redistribute somewhat equally over the oceans so that number could be cut in half (and perhaps cut further by all the ice that is already somewhat distanced from the poles).
Having skimmed the article (Yahoo version) looking for the extent quoted - which I didn't find - they say the actual mechanism is the Earth becoming more round as weight is relieved from the crust of the ice-covered regions (and then that crust rises). Somehow ... I find that mechanism less plausible but can't say.
The numbers are so tiny not unlike
random mass shootings as a percentage of murders as a percentage of deaths.
As to the contradictory headlines, it could be due to differing mechanisms:
Business Insider:
"Because glaciers are at high latitudes, when they melt they redistribute water from these high latitudes towards lower latitudes, and like a figure skater who moves his or her arms away from their body, this acts to slow the rotation rate of the Earth," Harvard University geophysicist Jerry Mitrovica said.
Yahoo!:
When polar ice caps melt, they remove weight off underlying rock, which then rebounds upward. This makes the poles less flat and the planet more round overall. This should in turn cause Earth to tilt a bit and spin more quickly.
Interesting ... but par for the course from the chicken little crowd.