The affix yat comes in the chandas (Vedas) after a prātipadika (Nominal Stem) in the Nominative 1st-Case in construction, ending with the affix matup when the sense is 'this is their mantra of putting up' provided that the things put are bricks and the affix matup is luk elided.,
This sutra requires analysis. तद्वान् is formed by adding मतुप् to तद् meaning 'having that', and refers to a noun formed by the affix मतुप् ॥ The word आसाम् is genitive plural fem. of इदं meaning 'of them'; the pronoun refers to the word इष्टका ॥ The word उपधान means 'putting up', and technically means 'used as a Mantra in the putting up of sacrificial bricks, pots &c'. मन्त्र \sacred hymn\ इष्टका 'bricks'. The whole sutra means \the affix 'yat' is used with the force of a genitive (asam), after a word which ends with matup (tadvan), and denotes a mantra used in putting up of sacrificial objects; when such mantra refers to bricks : and when this affix yat is added, the affix matup is elided\. Thus वर्चस्वान् is a Mantra containing the word वर्चस् ॥ The bricks put up or collected (उपधीयते) with the recitation of वर्चस्वान् Mantra, will be called वर्चस्या (वर्चस्वत् + यत् = वर्चस् + यत् the affix वत् (मतुप्) being elided = वर्चस्य, fem वर्चस्या) ॥ Thus वर्चस्या उपदधाति 'he collects Varchasya bricks i. e. on which Varchasvan mantra has been pronounced'. So तेजस्या उपदधाति ॥ So पयस्याः, रेतस्याः ॥
Why do we say तद्वान् ? The affix is not to be added to the whole Mantra. Why do we say, उपधान 'putting up'? The affix is not to be added to other Mantras such as those used in praying etc. e. g. वर्चस्वानुपस्थान मन्त्र आसामिष्टकानाम्, here there will be no affix. Why do we say Mantra? Observe अंगुलिमानुपधानो हस्त आसाम् 'these bricks are collected with hand having fingers', here there will be no affix. Why do we say इष्टकासु ? Observe वर्चस्वानुपधानो मन्त्र एषां कपालानाम्, here there will be no affix, the thing collected being potsherds and not bricks.,