Emphasis.
(2) It is more emphatic than the simple possessive, especially when used with this or that, for it brings out the modified word in strong relief.
Clearness.
(3) It prevents ambiguity. For example, in such a sentence as, "This introduction of Atterbury's has all these advantages" (Dr. Blair), the statement clearly means only one thing,—the introduction which Atterbury made. If, however, we use the phrase of Atterbury, the sentence might be understood as just explained, or it might mean this act of introducing Atterbury. (See also Sec. 87.)
The following are some instances of double possessives:—
This Hall of Tinville's is dark, ill-lighted except where she stands.—Carlyle.
Those lectures of Lowell's had a great influence with me, and I used to like whatever they bade me like.—Howells
Niebuhr remarks that no pointed sentences of Cæsar's can have come down to us.—Froude.
Besides these famous books of Scott's and Johnson's, there is a copious "Life" by Thomas Sheridan.—Thackeray
Always afterwards on occasions of ceremony, he wore that quaint old French sword of the Commodore's.—E. E. Hale.