Demai

Demai (Mishnaic Hebrew: ) is a Halakhic term meaning "doubtful"; something which may still contain the elements of "things holy" when referring to agricultural produce, the owner of which was not trusted with regard to the correct separation of tithes, although the "terumah" (the part designated to priests) was believed to have been separated from such fruits. In such "dubious" cases, all that was necessary was to separate the one-tenth portion due to the priests from the First Tithe given to the Levites, being the 1/100th part of the whole. The Second Tithe is also removed (redeemed) from the fruit in such cases of doubt.
The laws pertaining to "Demai"-produce only apply to produce grown in the Land of Israel, and to adjacent territories immediately outside the Land of Israel where produce grown in Israel was thought to have been taken. The law of separating the "Demai"-tithe was enacted by John Hyrcanus, in whose days the commoners of the people of Israel were considered faithful in separating the "Terumah" (heave-offering) from all agricultural produce, but were thought to have neglected the First tithe and the Second tithe.
The Sages of Israel have mentioned certain fruits as being mostly exempt from tithing as "Demai" produce, owing to their nature of being taken generally from trees that grow in the wild, such as wild figs ("Ficus carica"), jujubes ("Ziziphus spina-christi"), hawthorns ("Crataegus aronia"), sycamore figs ("Ficus sycomorus"), windfall dates, capers ("Capparis spinosa"), and, in Judea, the sumach ("Rhus coriaria").
The tribe of Levi, having been excluded from participating in the division of the land, obtained as compensation a share in its produce. As the tribe included two elements, priests and Levites, the compensation was given in two forms: ""terumah" (heave-offering) for the priests and "ma'aser" (tithes) for the Levites; and the Levites gave the tenth part of the tithe to the priests as "terumat ma'aser" (heave-offering of the tithe). In addition, a second tithe had to be separated from the produce in the first, second, fourth, and fifth years of the shemitah cycle. This tithe had to be taken to Jerusalem and consumed there, in accordance with certain regulations; while in the third and sixth years it was given to the poor. In the former case it was called "ma'aser sheni" (second tithe); in the latter "ma'asar 'ani"" (the tithe for the poor). The produce of the seventh year was free from all these dues.
Etymology.
There are several opinions concerning the word's etymology. According to Maimonides and Rabbi Obadiah ben Abraham, the word originates from a contraction of the two Aramaic words meaning "doubtful" (literally, "what is this?"). Another possibility is that the word originates from a corruption of the Hebrew word , "things holy", in this case referring to something which may still contain the elements of "things holy".
"Terumah" and "ma'aser".
The heave-offerings, both "terumah" and "terumat ma'aser", could not be eaten by non-priests; the second tithe, unless redeemed with "silver," which was to be spent on food in Jerusalem, could not be eaten outside that city; while the first tithe and the tithe for the poor were not subject to any restrictions. Conscientious Jews would not partake of the produce of the land unless they had first satisfied themselves that the heave-offering and tithes had been duly separated. The owners of land in the Land of Israel were divided into three classes; (1) non-Jews, to whom the Jewish laws about tithes did not apply; (2) the trustworthy Jews ("ne'emanim" or "chaberim"), who were sure to separate from the produce all that was due according to the Law; and (3) the am ha'aretz, who was suspected of neglecting these laws. Produce bought of any person of the first class was considered as unprepared—i.e., as produce from which heave-offering and tithes had not been separated; that bought of the second class was ""metukkan" (prepared); and that bought of the third class was "demai"" (doubtful, or suspected).
"Ma'aser sheni".
The conscientious never partook of demai without first separating the tithes due thereon. It was not necessary, however, to separate all the dues enumerated above, as no one was suspected with regard to the heave-offering, for two reasons: first, it was not burdensome, as the minimum quantity satisfied the Law, and, secondly, the offense of neglecting it was considered very serious. It was therefore only necessary to mark out the first tithe and the second. Of the former, one-tenth was separated as "the heave-offering of the tithe," and the remaining nine-tenths were retained by the owner, as the Levite was unable to prove his claim. The second tithe could be redeemed without the addition of one-fifth of its value. These regulations concerning "demai" are ascribed to the high priest John Hyrcanus, who inquired into the matter and discovered the fact that most people only separated the heave-offering and neglected the tithes.
References.
 It has the following bibliography: