Thomas Wright Hill is generally credited with inventing STV in the early 19th century. A statement of his voting rule appears in the Laws of the Society for Literary and Scientific Improvement; established in Birmingham, October the 19th, 1819.

Brian Wichmann has kindly provided a scan of this document, downloadable as a 5MB PDF. The original is available for inspection in the Birmingham Central Library (reference 62702).

The rule itself appears in section X of the bylaws:

X. At the first meeting in April, and also in October, a Committee shall be elected, which shall consist of at least one fifth of the members of the society. The mode of election shall be as follows. A ticket shall be delivered to each member present, with his own name at the head of it, immediately under which he shall write the name of the member whom he may wish to represent him in the Committee. The votes thus given shall be delivered to the president, who, after having assorted them, shall report to the meeting the number of votes given for each nominee. Every one who has five votes shall be declared a member of the committee; if there are more than five votes given to any one person, the surplus votes, (to be selected by lot) shall be returned to the electors whose naames they bear, for the purpose of making other nominations, and this process shall be repeated till no surplus votes remain, when all the inefficient votes shall be returned to the respective electors, and the same routine shall be gone through a second time, and also a third time if necessary; when if a number is elected, equal in all to one half of the number of which the committee shoud consist, they shall be a committee; and if at the close of the meeing the number is not filled up, by unanimous votes of five for each member of the committee, given by those persons whose votes were returned to them at the end of the third election, then this committee shall have the power, and shall be required, to choose persons to fill up their number; and the constituents of each member so elected shall, if necessary, be determined by lot. …

You'll notice that Hill's method differs somewhat from our present idea of STV. In particular, he uses successive balloting instead of a single ranked ballot, and all non-winning candidates in each round remain eligible for subsequent rounds (indeed, apparently, additional candidates could be added). Nonetheless, the key elements of the single transferable vote are present, and for a small group meeting in face-to-face, it seems an eminently practical system—and quite easy to grasp.