In another thread, I noticed the use of petered out.

The earliest example of “petered out” I could find was in a poem by Bret Harte, called DOW’S FLAT, published in 1856:

...

Then the bar petered out,
And the boys wouldn’t stay;
And the chills got about,
And his wife fell away;
But Dow in his well kept a peggin’ in his usual ridikilous way.

...

Poetic link.

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I did manage to find some interesting speculation on the etymology of the term:

From The Dial, Vol. 45, November 1, 1908, pp. 284, 285:

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[Edited to add better links]

OED (updated December 2005):

Etymology:  Origin unknown. Perhaps compare peter v.1 1. Alternatively, perhaps compare French péter to explode (1585 in Middle French), to break wind (1380 in Middle French; < pet pet n.1), and the semantic development of fizzle v.; with the mining context of much early use, perhaps also, or alternatively, compare saltpetre n.

orig. U.S.

Here are the 19th-cent. citations:

1. intr. To run out, decrease, or fade; gradually to come to an end or cease to exist. In early use esp. of a vein of ore (U.S. Mining slang). Usu. with out.
1846 Quincy (Illinois) Whig 6 Jan. 1/4 When my mineral petered why they all Petered me. If so be I gets a lead, why I’m Mr. Tiff again.
1854 H. H. Riley Puddleford vi. 84 He ‘hoped this ‘spectable meeting war n’t going to Peter-out’.
1865 S. Bowles Across Continent 133 Humboldt River..runs west and south from three hundred to five hundred miles, and then finds ignominious end in a ‘sink’, or..quietly ‘peters out’.
1877 J. F. Rusling Great West & Pacific Coast 67 He discovered they [sc. the lodes] had only a poor sickly trace or ore, which soon ‘petered out’.
1883 R. L. Stevenson Silverado Squatters ii. i. 60 But the luck had failed, the mines petered out.