Charles Finger, in Sailor Chanties and Cowboy Songs (1923) provides the following:
In the sealing outfits in the Antarctic, there was a chantie which was more properly a fo'c'sle song known as the "Dirty Cook". I have heard eight or ten men sing it for an hour or more with keenest delight, each adding his line, each mind busy with a couplet to follow while roaring the chorus. It was a song peculiar to the Chilean seaboard I think...
The ship's cook of course would join in heartily, quite unconscious of any incongruity between conduct and profession.
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Our cook he is a very dirty man. Ch:Sail away for the Rio Grande He cooks the food as dirty as he can. Ch:Sail away for the Rio Grande.
He stirred the tea with the end of a rope. And in the bread we found a big piece of soap.
Every sailor got his fair peck of dirt. He boiled the cap'nes puddin in the tail of his shirt.