In Patronymics used in narrower sense (counting first from the grand-child), which are formed the affixes aṇ and iñ , the feminine is formed by substituting ya (ṣyaṅ) for the a and i of those affixes and adding the long ā under -- yaṅaścāp [[4.1.74]], provided that they do not denote ṛṣi clans and have prosodially long syllable preceding the last syllable.,
The wording of this aphorism requires a little analysis. It consists of five words: (1) अणिञोः 'of अण् and इञ्' (2) अनार्षयोः 'of non-rishi' (3) गुरूपोत्तमयोः 'having a heavy vowel as upottama i. e. last but one,' (4) ष्यङ 'the substitute is shyan' (5) गोत्रे 'in denoting gotra.' That is to say, the gotra affixes अण् and इञ् are replaced by ष्यङ् before the feminine affix चाप्, in those words which denoting non-rishi gotras, have a heavy vowel as last but one. The word uttama meaning last letter, being formed by the superlative affix tamap, implies that the word must be of at least three syllables. Therefore, the present sutra does not apply to forms like दाक्षि &c.
Of the substitute ष्यङ् the letter ष् and ङ् are indicatory, the real affix is य, the letter ष् differentiating this affix from ञ्यङ् and the letter ङ् affording a common hold for both. In forming the feminine we shall have to add चाप् by 4.1.74. Thus करीषगन्धि 'having the smell of dung-cake', is the name of a person. In forming a patronymic from this word, we add the affix अण् ॥ Thus करीषगन्धि + अण् 4.1.92 Replace this affix by ष्य and we have कारीषगन्ध्या ॥ कुमुदगन्धि gives us कौमुदगन्ध्या ॥ Similarly with words taking the affix इञ् (as taught in sutra अतइञ् 4.1.75: as वाराहिः gives us वाराह्या, so also बालाक्या ॥
Why do we say 'of अण् and इञ् ॥ Witness आर्तभागा from ऋतभाग ॥ Here the word ऋतभाग belongs to बिदादि gana, and therefore by 4.1.104, it would take the affix अञ् in forming gotra patronymic: this affix अञ् is not replaced by ष्यङ्, and the feminine is by long ई 4.1.15; for though, its last vowel but one is heavy, it is a non-rishi gotra word, yet it does not fulfil the other condition of taking the affix अण् or इञ् ॥
Why do we say 'of non- rishi gotras'? Witness वासिष्ठी and वैश्वामित्री ॥ Why do we say 'whose last vowel but one is heavy'? Observe औपगवी and कापटवी ॥ Why do we say 'denoting Gotra?' Witness आहिच्छत्री 'born in Ahichhatra', कान्यकुब्जी 'born in Kanyakubja'.,