नातः परस्य

When the first vowel of the second member preceded by अर्ध and denoting mass is short अ before a तद्धित affix having an indicatory ञ् , ण् or क् and optionally so for the first vowel of the first member (i.e. अर्ध).
Thus अर्धप्रस्थिकः or आर्धप्रस्थिकः 5.1.18 ॥ अर्धकंसिकः or आर्धकंसिकः ॥ Why do we say 'when it is a short अ'? Observe आर्धकौडविकः ॥ Why 'short अ' ? Observe अर्ध खार्याम् भवः = अर्धखारी ॥ Here Vriddhi is substituted for the आ of खारी, and though the form remains the same, the power of this word is changed. For अर्धखारी being formed by a Taddhita affix causing Vriddhi, in forming a Bahuvrihi compound, this word will retain its feminine form and will not be changed into masculine under 6.3.39 as अर्धखारीभार्यः (= अर्धखारीभार्यायस्य) (वृद्धिनिमित्तस्य च तद्धितस्य &c.) Whereever Vriddhi is prohibited with regard to a Taddhita affix, that affix cannot be called वृद्धिनिमित्त, and a word formed with such an affix will become masculine in a Bahuvrihi compound referring to a male person, वैयाकरणी भार्या अस्य = वैयाकरणभार्यः ॥ The word वैयाकरण is formed by prohibition of Vriddhi. See 7.3.3.