Jeremías 31:1 Halajá: Shulchan Arukh, Yoreh De'ah & Shulchan Arukh, Orach Chayim

Some⁴Kol Bo s. 115. Thus also R. Amram; Tanya s. 68; Abudraham, Laws of Benedictions. Cf. the prayer נחם recited on the ninth day of Ab. add in the third benediction,⁵ Oẓar Hat. ibid. ['and rebuild Jerusalem, the Holy City speedily in our days,' — the words], 'Comfort, O Lord our God, the mourners of Jerusalem and the mourners who are observing this mourning. Comfort them from this mourning and make them rejoice from their sorrow,⁶Cf. Jer. XXXI, 1 as it is said, one whom his mother comforteth, so will I comfort you and ye shall be comforted in Jerusalem.⁷Is. LXVI, 13. Blessed art Thou, O God, who comfortest Zion in the rebuilding of Jerusalem.'⁸One should not say, ‘Blessed art thou … who comfortest mourners and rebuildest Jerusalem,’ for the closing formula must never contain two subjects. One may, however, say, ‘Blessed art Thou … who comfortest Zion and rebuildest Jerusalem, for both these subjects relate to the same idea. This latter closing formula is said at the Minḥa service on the ninth day of Ab in the נחם prayer — Shak.

The order of the 2nd day of Rosh HaShana and in it is 2 paragraphs
On the 2nd day (we pray like the 1st day) (Tur) and we read from "And God tested Abraham" (Bereshis 22:1) until the end of the portion (Bereshis 22:24). The Maftir reading is the same as yesterday. And the Haftarah is in Yirmiyah (Jeremiah) "Thus Spoke Hashem: (the Nation) found favor in the desert" (Jeremiah 31:2) until "The son, precious to me, is Efrayim" (Jeremiah 31:20). On Motzei Rosh HaShana, we make Havdala like on Motzei Shabbos; however, we do not make a blessing on the spices or on the flame.