Here, dear reader, for your instruction and edification are two passages from the Acts of the Apostles.
And laid their hands on the apostles, and put them in the common prison. But the angel of the Lord by night opened the prison doors, and brought them forth, and said, Go, stand and speak in the temple to the people all the words of this life. And when they heard that, they entered into the temple early in the morning, and taught. But the high priest came, and they that were with him, and called the council together, and all the senate of the children of Israel, and sent to the prison to have them brought. But when the officers came, and found them not in the prison, they returned and told, Saying, The prison truly found we shut with all safety, and the keepers standing without before the doors: but when we had opened, we found no man within.
- Acts 5v18-23
And when he had apprehended him, he put him in prison, and delivered him to four quaternions of soldiers to keep him; intending after Easter to bring him forth to the people. Peter therefore was kept in prison: but prayer was made without ceasing of the church unto God for him. And when Herod would have brought him forth, the same night Peter was sleeping between two soldiers, bound with two chains: and the keepers before the door kept the prison. And, behold, the angel of the Lord came upon him, and a light shined in the prison: and he smote Peter on the side, and raised him up, saying, Arise up quickly. And his chains fell off from his hands. And the angel said unto him, Gird thyself, and bind on thy sandals. And so he did. And he saith unto him, Cast thy garment about thee, and follow me. And he went out, and followed him; and wist not that it was true which was done by the angel; but thought he saw a vision. When they were past the first and the second ward, they came unto the iron gate that leadeth unto the city; which opened to them of his own accord: and they went out, and passed on through one street; and forthwith the angel departed from him.
- Acts 12v4-10
The phrase peter out goes back to Michigan in 1854 and a book called Puddleford Papers or Humors of the West, which contains the line:
He hoped this 'spectable meeting warn't going to Peter-out.
Without the out you can get back another nine years to the Wild West of Wisconsin. An old prospector is complaining of how his luck has disappeared:
When my mineral petered why they all Petered me. Now it is dig, dig, dig, drill, drill for nothing. My luck is clean gone - tapered down to nothing.
Nobody knows why the phrase peter out should mean mysteriously disappear. There are four speculative theories.
1) It's to do with St Peter denying Jesus three times.
2) It's to do with a seam of rock in mining having been exhausted, because St Peter was the rock upon which Jesus would build his church.
3) It's to do with the French word péter meaning fart, because péter dans la main is a French phrase meaning fart in the hand or come to nothing.
4) It's to do with a seam of rock in mining having been exhausted, because it's all been blown away with explosive saltpeter, otherwise known as potassium nitrate.
I don't think any of these work. Peter's denials seem irrelevant and his rockiness doesn't have anything to do with disappearance. The French word is pronounce pay-tay and is an odd intrusion into Midwestern English. Saltpetre, which is usually considered the most convincing, doesn't work because it implies explosion, whereas petering is always about quiet and inexplicable disappearance.
However, anybody who knows the New Testament knows that St Peter is forever mysteriously disappearing. In a faintly Christian country, the twelfth chapter of Acts is all you need to explain Peter as a slang term for enigmatic escape, or silently slipping away.
UPDATE I've just come across the verb to peter in a dictionary of London slang from 1860 where it means "to run short, to give out". As the earliest American version is only 1846, that means that well... I'm no longer convinced of the US origin.
Can't a chap get some sleep?