Encyclopedia of Judaism (Wigoder)
"Shemini Atseret ('Eighth Day of Solemn Assembly'). Festival observed immediately after SUKKOT (Tabernacles), i.e., on 22 Tishri, as laid down in the Pentateuch: 'On the eighth day you shall observe a holy occasion ... it is a solemn gathering (Atseret); you shall not work at your occupations' (Lev. 23:36; cf. Num. 29:35). The term Atseret (lit. 'concluding festival') is also applied to the last day of PASSOVER (Deut. 16:8) and, by the rabbis, to SHAVUOT (RH 1:2; Shev. 1:1). A parallel function may thus have been served, in biblical times, by the Atseret of Passover (Shavu'ot) and the Atseret of Sukkot (Shemini Atseret). The rabbis treated the eighth day as a festival in its own right, and the liturgy indicates this independent status through appropriate references in the AMIDAH and the KIDDUSH. Shemini Atseret is distinguished from Sukkot also in that the FOUR SPECIES are no longer utilized after HOSHANA RABBAH and Kiddush on the eighth day is followed by the special SHE-HE-HEYANU benediction, which can only be recited for a new festival and not merely for the conclusion of Sukkot.
By rabbinic decree, the annual cycle of Pentateuch readings is completed and begun anew on Shemini Atseret. For this reason, the festival is known also as SIMCHAT TORAH, the Rejoicing of the Law."
"SHEMINI ATSERET--EIGHTH DAY OF SOLEMN ASSEMBLY
Other names: Yom ha-Shemini
Hag ha Atseret (Eighth Day Concluding Festival)
Torah & Prophetical Readings (in Diaspora):
Deut. 14:22-16:17; Num. 29:35-30:1 (Maftir); 1 Kings 8:54-9:1 (Ashkenazi Haftarah); 1 Kings 8:54-66 (Sephardi Haftarah)
Scroll: Ecclesiastes (if there is no Intermediate Sabbath on Sukkot)"
The Oxford Dictionary of the Jewish Religion:
"SHEMINI 'ATSERET....The striking difference between the number of sacrifices offered during the previous seven days, which total seventy in all (Nm. 29.12-32) and the solitary 'one ram, one bullock' of this festival (Nm. 36), is the basis of a midrash to the effect that they seventy sacrifices correspond to the 'seventy nations' (i.e., humankind), while Shemini 'Atseret symbolizes the special relationship between God and Israel."