A preceding Vocative is considered as non-existent (for the purposes of the accent of the following word and the enclitic forms of yuṣmad and asmad).,
Such a Vocative is treated as if not at all existing, it is simply ignored. The operation which its presence otherwise would have caused does not take place, and that operation takes place which would have taken place had it not existed. What are the particular purposes served by considering it as non-existent? They are (1) the absence of the accent-less-ness of the subsequent vocative, which the first, taken as a पद, would have caused under 8.1.19. As देव꣡दत्त ! य꣡ज्ञदत्त ! Here the first Vocative देवदत्त does not cause the second Vocative to lose its accent, but it remains first acute by 6.1.198. (2) The accentless-ness of the verb required by (VIII. I. 28) is prevented: as, दे꣡वदत्त प꣡चसि ॥ (3) The substitution of the shorter forms of युष्मद् and अस्मद्, required by 8.1.20 — 8.1.23 is prevented, as देवदत्त तव (not ते) ग्रामः स्वम्, देवदत्त मम (not मे) ग्रामः स्वम् ॥ (4) The application of 8.1.37 takes place, in spite of the intervention of the Vocative between the Particle and the verb; such intervention is not considered as taking away anything from the immediateness (अनन्तरम्) of the Particle from the verb: as, यावद् देवदत्त प॒॒च॒॒सि॒॒ ॥ (5) For the purposes of (VIII. I. 47), though a Vocative may precede जातु, the latter is still considered as अविद्यमानपूर्वं and 8.1.47 applies, as देवदत्त जातु प꣡चसि ॥ (6) So also in the case of 8.1.49, as आहो देवदत्त प꣡चसि, उताहो देवदत्त पचसि, no option is allowed here by 8.1.50.
Why do we use the word 'as if' or यत् in the sutra, instead of saying 'altogether'? In other words, why do we say \it is considered as if non-existent\, instead of saying \it is considered altogether non-existent\? The vocative does produce its own particular effect. Thus in आम् भो देवदत्त ! the vocative भो is considered as one word (एकान्तर) for the purposes of separating आम् from the vocative देवदत्त under 8.1.55. This is the opinion of Patanjali; but the opinion of the author of Kasika is that भो would have been considered as अविद्यमानवत् but for 8.1.73.
Why do we say 'a Vocative'? Observe देवदत्तः प॒॒च॒॒ति॒॒ ॥ Why do we say पूर्वं 'with regard to the subsequent word'? The vocative itself will not be considered as non-existent, for the application of rules that would apply to vocative as such. Thus in देव꣡दत्त य꣡ज्ञदत्त, the vocative देवदत्त gets its accent by 6.1.193 also. In fact, the word पूर्वं connotes its correlative पर 'subsequent'; and the vocative is considered as non-existent, for the purposes of the operations to be performed on such subsequent term, whether such operation be caused by the vocative itself, or by any other cause; but it is not to be considered non-existent for the purposes of operations to be performed upon itself. Therefore in दे꣡वदत्त प꣡चसि, Devadatta does get the accent of the vocative. In इमं मे गङ्गे यमुने सरस्वति शतुद्रि the first vocative गङ्गे is considered as non-existent with regard to यमुने, and, therefore, यमुने is considered as following immediately after the pada मे and thus यमुने becomes anudatta, not because of गङ्गे, but because of मे; similarly सरस्वति and शतुद्रि are anudatta, not because of the preceding Vocative, but because of मे ॥ In other words, the intervention of the vocatives does not stop the action of मे ॥,
