Herbert Weir Smyth, A Greek Grammar for Colleges

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Breathings

[*] 9. Every initial vowel or diphthong has either the rough (‘) or the smooth (’) breathing. The rough breathing (spiritus asper) is pronounced as h, which is sounded before the vowel; the smooth breathing (spiritus lenis) is not sounded. Thus, ὅρος hóros boundary, ὄρος óros mountain.

[*] 9 D. The Ionic of Asia Minor lost the rough breathing at an early date. So also before ρ (13). Its occurrence in compounds (124 D.) is a relic of the period when it was still sounded in the simple word. Hom. sometimes has the smooth where Attic has the rough breathing in forms that are not Attic: Ἀΐδης (Ἅ_ιδης), the god Hades, ἆλτο sprang (ἅλλομαι), ἄμυδις together (cp. ἅμα), ἠέλιος sun (ἥλιος), ἠώς dawn (ἕως), ἴ_ρηξ hawk (ἱέρα_ξ), οὖρος boundary (ὅρος). But also in ἄμαξα wagon (Attic ἅμαξα). In Laconian medial ς became ( (h): ἐνί_κα_ἑ ῀ ἐνί_κησε he conquered.

[*] 10. Initial υ (υ^ and υ_) always has the rough breathing.

[*] 10 D. In Aeolic, υ, like all the other vowels (and the diphthongs), always has the smooth breathing. The epic forms ὔμμες you, ὔμμι, ὔμμε (325 D.) are Aeolic.

[*] 11. Diphthongs take the breathing, as the accent (152), over the second vowel: αἱρέω hairéo I seize, αἴρω aíro I lift. But ᾳ, ῃ, ῳ take both the breathing and the accent on the first vowel, even when ι is written in the line (5): ᾁδω ῀ Ἄιδω I sing, ᾄδης ῀ Ἅ_ιδης Hades, but Αἰνεία_ς Aeneas. The writing ἀίδηλος (Ἀίδηλος) destroying shows that αι does not here form a diphthong; and hence is sometimes written αϊ (8).

[*] 12. In compound words (as in προορᾶν to foresee, from πρό ¨ ὁρᾶν) the rough breathing is not written, though it must often have been pronounced: cp. ἐξέδρα_ a hall with seats, Lat. exhedra, exedra, πολυίστωρ very learned, Lat. polyhistor. On Attic inscriptions in the old alphabet (2 a) we find ΕΥΗΟΡΚΟΝ εὐὅρκον faithful to one's oath.

[*] 13. Every initial ρ has the rough breathing: ῥήτωρ orator (Lat. rhetor). Medial ρρ is written ῤῥ in some texts: Πύῤῥος Pyrrhus.

[*] 14. The sign for the rough breathing is derived from H, which in the Old Attic alphabet (2 a) was used to denote h. Thus, HO ὁ the. After H was used to denote η, one half ([rough ]) was used for h (about 300 B.C.), and, later, the other half ([smooth]) for the smooth breathing. From [rough ] and [smooth] come the forms ‘and’.