Then said Boaz unto his servant that was set over the reapers, Whose damsel is this?

And Booz said to the young man that was set over the reapers: Whose maid is this?

And Boaz said to his servant that was set over the reapers, Whose maiden is this?

Then said Boaz unto his servant that was set over the reapers, Whose damsel is this? r

And Boaz saith to his young man who is set over the reapers, 'Whose is this young person?'

Then Boaz said to his servant who was in authority over the cutters, Whose girl is this?

And Boaz said to the young man who was in charge of the reapers, "Whose young woman is this?"

His servant that was set over the reapers - This was a kind of steward or hind who had the under management of the estate. Some think that an officer of this kind is intended in the description given by Homer of the labors of a harvest field, as represented by Vulcan on one compartment of the shield which he made for Achilles: -
Εν δ' ετιθει τεμενος βαθυληΐον· ενθα δ εριθοι
Ἡμων, οξειας δρεπανας εν χερσιν εχοντες·
Δραγματα δ' αλλα μετ' ογμον επμον επητριμα πιπτον εραζε,
Αλλα δ' αμαλλοδετηρες εν ελλεδανοισι δεοντο.
Τρεις δ' αρ' αμαλλοδετηρες εφεστασαν· αυταρ οπισθε
Παιδες δραγμευοντες, εν αγκαλιδεσσι φεροντες,
Ασπερχες παρεχον· βασιλευς δ' εν τοισι σιωπῃ
Σκηπτρον εχων ἑστηκει επ' ογμου γηθοσυνος κηρ.
Κηρυκες δ' απανευθεν ὑπο δρυΐ δαιτα πενοντο·
Βουν δ' ἱερευσαντες μεγαν, αμφεπον· αἱ δε γυναικες
Δειπνον εριθοισιν, λευκ' αλφιτα πολλα παλυνον.
Iliad xviii., v. 550.
There too he form'd the likeness of a field
Crowded with corn, in which the reapers toil'd,
Each with a sharp-tooth'd sickle in his hand.
Along the furrow here, the harvest fell
In frequent handfuls; there, they bound the sheaves.
Three binders of the sheaves their sultry task
All plied industrious, and behind them boys
Attended, filling with the corn their arms,
And offering still their bundles to be bound.
Amid them, staff in hand, the master stood,
Enjoying, mute the order of the field:
While, shaded by an oak, apart his train
Prepared the banquet - a well thriven ox
New slain, and the attendant maidens mix'd
Large supper for the hinds, of whitest flour.
Cowper.
This scene is well described; and the person who acts as overseer is here called βασιλευς, king, and his staff is called σκηπτρον, a scepter; and he stands in mute dignity, merely to see that the work is well done, and that each person performs his task; and there appear to me to be gleaners in the description, viz., the boys who gather the handfuls after the three binders. See the Greek.

Then said Boaz unto his servant that was set over the reapers,.... To direct them their work, what part each was to do, and to see that they did it well; to take care for provisions for them, and to pay them their wages when their work was done. Josephus (t) calls him that had the care of the field, and all things relative to it; the Jews (u) say, he was set over two and forty persons, whom he had the command of:
whose damsel is this? to whom does she belong? of what family is she? whose daughter is she? or whose wife? for he thought, as Aben Ezra notes, that she was another man's wife; the Targum is, of what nation is she? perhaps her dress might be somewhat different from that of the Israelitish women.
(t) Antiqu. l. 5. c. 9. sect. 2. (u) Midrash Ruth, fol. 32. 1.

his servant that was set over the reapers--an overseer whose special duty was to superintend the operations in the field, to supply provision to the reapers, and pay them for their labor in the evening.