ἐν δὲ μηνὸς πρῶτον τύχεν ἆμαρ → it chanced to be on the first of the month, that day fell on the first of the month
οῦσα, όν :part. prés. de ἔπειμι².
see ἔπειμ Od. 9.2.
ἐπιών: οῦσα, όν part. к ἔπειμι II.