Wheat and Chessboard Problem/19th Century Version

Wheat and Chessboard Problem: 19th Century Version
It is calculated that $200$ pins go to the ounce.

Suppose that for the $52$ weeks in the year:
 * one pin were dropped into the hold during the first week
 * two in the second
 * four in the third

and so on.

By the end of the year the weight of the whole would be no less than $628 \, 292\, 358$ tons of pins.

As the Great Eastern steamship was built to carry $22 \, 500$ tons only, it follows that to carry all the pins there would be required $27 \, 924$ ships of the size of the Great Eastern.