Is the rate 2 cents or 3 cents? It appears to depend on the carrier. Here's, apparently, a page from the 37th congress session III, chapter 71, page 705, 1863.
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http://memory.loc.gov/ll/llsl/012/0700/07370705.tif
From this page, sections 22 and 23:
Quote:
Sec. 22. And be it further enacted, That the rate of postage on all domestic letters transmitted in the mails of the United States, and not exceeding one half ounce in weight, shall be uniform at three cents; and for each half ounce, or fraction thereof of additional weight, there shall be charged an additional rate of three cents, to be in all cases prepaid by postage stamps plainly affixed to such letter.
Sec. 23. And be it further enacted, That the rate of postage on all letters not transmitted through the mails of the United States, but delivered through the post-office or its carriers, commonly described as local or drop letters, and not exceeding one half ounce in weight, shall be uniform at two cents, and and additional rate for each half ounce or fraction thereof of additional weight, to be in all cases prepaid by postage stamps affixed to the envelope of such letter, but no extra postage or carrier's fee shall hereafter be charged or collected upon letters delivered by carriers, nor upon letters collected by them for mailing or for delivery. [Emphasis mine.]
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Partial page attached for your convenient viewing pleasure.
Jay Scott.