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The Silver Bear was one of the names of the Great Bear in the poem Kortirion among the Trees, written by J.R.R. Tolkien in November 1915 and later revised in many instances until the final version, now titled The Trees of Kortirion was composed, according to Christopher Tolkien, "nearly half a century after the first" (LT1, 39).
The poem was published by C. Tolkien in LT1, 33-43 in three versions, first (= KT1; LT1, 33-36) "in its pre-1937 form, when only slight changes had yet been made" (LT1, 32), second (= KT2; LT1, 36-39) "as [Tolkien] rewrote it in 1937" (LT1, 36), and third (= TK; LT1, 39-43) now renamed and composed in 1960's as explained above.
The Silver Bear appears in the first and the third part of the first version:
KT1 I,30-32: Until the seven lampads of the Silver Bear / Swing slowly in their shrouded hair / And diadem the fallen day. (LT1, 33)
KT1 III,120-121: The seven lampads of the Silver Bear / Are waxen to a wondrous flare / That flames above the fallen year (LT1, 35)
but in the later revisions the Great Bear disappears from the first part of the poem and in the third part it is replaced by the Silver Wain.
Literature: LT1 = The Book of Lost Tales Part One (The History of Middle-earth, vol. 1)