Coscinomancy

Meaning: Divination by the sieve and shears. It's difficult to explain, but Brewer claims that:

The points of the shears were stuck in the rim of a sieve, and two persons supported them with their finger-tips. Then a verse of the Bible was read aloud, and St. Peter and St. Paul were asked if it was A, B, or C (naming the persons suspected). When the right person was named, the sieve would suddenly turn round. 

The first image here will give you an idea of the fragility of the arrangement on which someone's guilt might rest.

Usefulness: 2 (Mainly as a synonym for a pointless, arcane ritual that confirms what everyone suspects. Elections, perhaps?)

Logofascination: 3 (I'm more fascinated by the weird and wonderful ways humans have sought for truth.)

In the wild: Not really, but I found a word cloud for it on a stock photo website, and I'm dying to know where the market for such things is.

Degrees: 1

Connections: n/a

Which is used in: G&P, Le Tiers-Livre, XXV: In which Panurge consulteth Herr Trippa.  The -mancy chapter, of course.

By coscinomancy, most religiously observed of old amidst the ceremonies of the ancient Romans. Let us have a sieve and shears, and thou shalt see devils.

It's the devils making the sieve spin, of course.