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The seder for the second day of Rosh Hashanah:
A. Candle Lighting:
When to light? On the second night of Rosh Hashanah the candles are lit after nightfall. [See next regarding if one is to delay the lighting until close to Kiddush. If the second night of Rosh Hashanah falls on Motzei Shabbos some write that it is best for women to Daven Maariv with Vetodieinu prior to lighting candles and doing Melacha. See Halacha 10 and 26!]
Shehechiyanu by candle lighting: On the second night of Rosh Hashanah a woman should wear a new garment [which she has never yet worn] for candle lighting in order to exempt it with the blessing of Shehechiyanu. Alternatively if she does not have new clothing she is to place a new fruit in front of her before lighting candles [and look at it upon saying the blessing of Shehechiyanu] having it in mind within the blessing. The same new fruit that will be used for Kiddush may be used for this purpose, and certainly another new fruit may be used. [Some Poskim rule that if she will be using a new fruit then she is to delay the lighting of the candles until right before Kiddush and eat the fruit directly after hearing Kiddush. Other Poskim however rule that there is no necessity to do so and she may light candles while seeing the new fruit, with intent to eat the fruit later on, after Kiddush.]
If she does not have new clothing or a new fruit: If she does not have a new fruit or new garment available, then she is nevertheless to say the blessing of Shehechiyanu by candle lighting.
If a man is lighting candles when is he to say the blessing of Shehechiyanu, by the lighting or by Kiddush?
A man always says the blessing of Shehechiyanu by Kiddush. See “The Laws of Erev R”H” Halacha 18 in Q&A for further details on this matter!
Does a woman who will be making Kiddush say Shehechiyanu by candle lighting or by Kiddush?
She is to say the blessing by candle lighting. See “The Laws of Erev R”H” Halacha 18 in Q&A for further details on this matter!
If a man is lighting does he first light the candles and then say the blessing or vice versa?
Many Poskim rule that men are to follow the same order as follow women and hence first light the candles and then say the blessing. See “The Laws of Erev R”H” Halacha 18 in Q&A for further details on this matter!
Tehillim prior to Maariv: Before Maariv on the eve of Rosh Hashanah one is to read Tehillim. [See Introduction of this chapter]
Vetodieinu: When the second night of Rosh Hashanah falls on Motzei Shabbos [i.e. Saturday night], then in the evening prayer of Shemoneh Esrei the paragraph of ותודיענו is added prior to the paragraph of ותתן לנו. See the next Halacha for the full details of this subject!
Shehechiyanu by Kiddush: One who has not said Shehechiyanu by candle lighting [such as all men who had their wives light the candles] is to say Shehechiyanu by Kiddush. On the second night of Rosh Hashanah one is to place before him a new fruit or wear a new garment and intend to exempt it with the blessing of Shehechiyanu. See the previous Halacha and Chapter 2 Halacha 4 for the full details of this subject!
Yaknaha”z: When the first day of Rosh Hashanah falls on Shabbos one says Yaknaha”z in the order of Kiddush of the second night of Rosh Hashanah just as is done by any Holiday that falls on Motzei Shabbos. See Chapter 2 Halacha 4 for the full details of this subject!
D. The Torah Reading:
See Halacha 12 for the full details of this subject!
E. Learning Chassidus towards the end of Rosh Hashanah:
One should learn Chassidus towards the end of Rosh Hashanah until after nightfall in order to fuse the revelations of Rosh Hashanah with the rest of the year through Chassidus.
The Rosh Hashanah Farbrengen:
The Rebbe would customarily hold a Farbrengen on the 2nd day of Rosh Hashanah, towards evening, which would include a Mamar which mentioned all the Rabbeim and was followed by Kos Shel Bracha. Likewise the Niggunim of all the Rabbeim were sung during the Farbrengen. In years that the conclusion of Rosh Hashanah coincided with Shabbos see Halacha 28!
 As one is not to do an action on the 1st day of Yom Tov on behalf of the 2nd day. [Alef Hamagen 625/51]
 Mateh Efraim 599/10
 Elya Raba 600/3; Shaareiy Teshuvah 600/1; Mateh Efraim 581/54; Alef Hamagen 581/126; Kitzur SHU”A 129/23; Kaf Hachaim 600/6; Hiskashrus 898; See previous Halacha for the full details of this matter
Why was Shehechiyanu by candle lighting not mentioned in Admur and other Poskim? As for why the placing of a new fruit or garment by candle lighting is not mentioned by Poskim in chapter 600, this is because in previous times the custom was not widespread for women to bless Shehechiyanu by candle lighting, and thus we do not find this mentioned anywhere in Poskim. [See Sheilas Yaavetz 107]
 However a man, even when he lights the candles, such as a Bochur in Yeshiva, does not say the blessing of Shehechiyanu at that time but rather delays it until Kiddush. [See Q&A]
 Seder 12/4; Ketzos Hashulchan 64/2; See Previous Halacha in Q&A!
 Regarding Kiddush: Siddur; second option in 600/6; M”A 60/1; Mateh Moshe 823; M”B 600/4; M”E 600/8
Must she hold the fruit in his hand when saying the blessing of Shehechiyanu? No. [Poskim ibid] In Admur 600/6 regarding the Shehechiyanu wine he gives two options: a) to hold the cup of grape juice in his hand while saying the blessing; b) To look at the grape juice while saying the blessing. So rules also M”B 600/4; In the Siddur Admur simply mentions to look at the fruit.
 Poskim ibid give both options even by candle lighting, that she can either have new clothing or a new fruit.
Other Poskim: Some Poskim negate the option of using a new fruit for candle lighting. See previous Halacha in Q&A!
 Elya Raba ibid; Shaareiy Teshuvah ibid
 Shaareiy Teshuvah ibid
 Mateh Efraim 599/9 [“Directly before Kiddush in order to eat the fruit right away”]; Alef Hamagen 581/126; See Machatzis Hashekel 600/1; It however does not help to say the blessing over the fruit if Kiddush will not be taking place directly afterwards, as the interval invalidates the blessing of Shehechiyanu said on the fruit. [ibid; Machatzis Hashekel ibid based on M”A 600/3].
 Seemingly in such a case she may not talk until after she eats the fruit after Kiddush, in order not to make an interval.
 Implication of Kaf Hachaim 600/6 [“the blessing is on the seeing and not the eating”] and Setimas Haposkim ibid; See Shevach Hamoadim p. 14
 The reason: As in truth the blessing of Shehechiyanu over a fruit is to be said when one sees the fruit and not upon eating it. [See 225/3; Admur in Seder 11/12]. Now although we don’t rule this way during the year unless one has joy from seeing the fruit [ibid] nevertheless it suffices to remove oneself from the doubt of the 2nd day of R”H. [Kaf Hachaim ibid] Vetzaruch Iyun as by doing so one enters into another doubt regarding if he must repeat Shehechiyanu later on, when eating the fruit, as writes the Machatzis Hashekel ibid. Hence perhaps if one does so they must hear the blessing of Shehechiyanu form another person prior to eating the fruit. Veztaruch Iyun!
 600/6 [regarding Kiddush]
 Sefer Haminhagim P. 118 [English] from a letter of the Rebbe Rayatz
 Sefer Haminhagim p. 121 [English]; Sefer Hasichos 1945 p. 10; 1944 p. 11; Igros Kodesh 4/498; Otzer Minhagei Chabad p. 152
 See Otzer Minhagei Chabad p. 147-149