Names 37 to 45 open the second half. The first, אני, is the one Rashi works out on Sukkah 45a: the Alef of "meachareihem," the Nun of "heanan" counted backwards, the Yod of "ruach kadim." The Mishnah reports that Rabbi Yehudah said around the altar "Ani vaho, hoshia na," joining this name to the first. Then the first letter returns to the second "vayissa" of the first verse, the second passes through "Yisrael vayehi heanan," the third through "kadim azah kol halaylah," "a strong east wind all night."
37. אני (Alef, Nun, Yod). Psalm 94:18: "When I say: my foot slips, Your kindness, Lord, holds me up."
38. חעם (Chet, Ayin, Mem). Psalm 91:9: "For You, Lord, are my refuge; you have made the Most High your dwelling."
39. רהע (Resh, Heh, Ayin). Psalm 118:16: "The right hand of the Lord is exalted, the right hand of the Lord does valiantly."
40. ייז (Yod, Yod, Zayin). Psalm 115:11: "You who fear the Lord, trust in the Lord: He is their help and their shield."
41. ההה (Heh, Heh, Heh). Psalm 120:2: "Lord, rescue my soul from the lying lip, from the deceitful tongue."
42. מיך (Mem, Yod, Kaf). Psalm 121:7: "The Lord will guard you from all evil, He will guard your soul."
43. וול (Vav, Vav, Lamed). Psalm 121:8: "The Lord will guard your going out and your coming in, from now and forever."
44. ילה (Yod, Lamed, Heh). Psalm 106:2: "Who can tell the mighty acts of the Lord, or make heard all His praise?"
45. סאל (Samekh, Alef, Lamed). Psalm 33:22: "May Your kindness, Lord, be upon us, as we have hoped in You."
Names 42 and 43 receive two consecutive verses of Psalm 121, the psalm of the guardian of Israel. Sha'arei Tziyon gives no reason for these choices; simply keep in mind that each verse contains the letters of the name it accompanies. Name 39 receives "The right hand of the Lord," a verse of Psalm 118, which is also said in Hallel.