The circumflex accent (, also or ) represents a rise in pitch over the first mora of a long vowel followed by a return to standard pitch over the second mora of the same vowel. Thus the whole contonation occurs within a single syllable. The circumflex cannot appear over a short vowel, since a short vowel is too short to allow time for both rise and fall. It may appear on P or U, but never on A. It may appear on P only when U is short, because of the general rule of contonation and mora.
In addition, it is a rule in ancient Greek that an accented long P that is followed by short U must have the circumflex. Conversely, an accented long P that is followed by long U must have the acute.
στρατιῶται – circumflex on long P (only with short U)
δῶρον – circumflex on long P (only with short U)
ἀρχαῖος – circumflex on long P (only with short U)
ὁδοῦ – circumflex on long U
ἀρετῇ – circumflex on long U