A: The parenthetical note in Acts 1:18 speaks of Judas purchasing the property in an indirect, somewhat metonymical sense: the money was actually in the hands of the chief priests at the time (well, /actually/ odds are that it would have been in a bag, held by one of them, not distributed into the hands of each one of them) but as Matthew 27:6 relates, the chief priests did not consider the money to be their property. Although Judas had thrown down the silver-pieces in the temple, the chief priests scrupulously refused to place the money in the treasury, since it was blood-money.
The early Christians, aware that the silver-pieces that were used for the transaction were the same silver-pieces used to purchase Akeldama, regarded the money as Judas money. In this sense, Judas was the one who purchased the field.
When one considers the contents of Matthew and Acts, the following step-by-step scenario about the death of Judas may be reconstructed:
(1) Judas throws the 30 pieces of silver in the temple and proceeds, at some point, to hang himself.
(2) Judas corpse swells up, and his intestines splurt out, falling upon the ground below.
(3) The chief priests, using Judas money, purchase the very plot of ground situated where Judas hanged himself (to be used as a place to bury strangers).
(4) Because it became known in Jerusalem that the money used to purchase this plot of ground was the money which Judas had received to betray Jesus (i.e., to betray innocent blood), it became known as Akeldama -- Field of Blood.
Yours in Christ,
Waterrock
