"P.C.B."—"(1)What is the possessive form of the expression 'some one else'? (2) I learned a rule, 'the possessive is formed by adding s, except to plural nouns ending in s, to which the apostrophe only should be added.' Does not this rule apply to proper nouns like 'Jones', 'James,' etc.?"

(1) " Some one else's " is good usage, but many prefer to treat such expressions simply as elliptical, as, the umbrella is somebody's else (i.e., other than the person previously mentioned). The subject is covered by the Standard Dictionary on p. 588, under "else."
(2) "Some words ending in a sibilant omit the s of the possessive to avoid the disagreeable repetition of a hissing sound. The rules for the possessive followed by the Standard Dictionary are: (a) To singular monosyllablic nouns ending in a sibilant sound, as s, .x, ce, se, or dental ge, add the apostrophe and s, except when the following word begins with a sibilant sound; as, "James's reign" ; "Jones's hat"; "a fox' skin." (b) Singular dissyllabic nouns ending in a sibilant sound add the apostrophe and s, unless the sibilant is preceded by another sibilant or the last syllable is unaccented ; as, "Porus ' defeat" ; "Moses' face"; "Jesus' disciples"; "Hortense's fate." (c) Singular polysyllabic nouns ending in a sibilant sound add the apostrophe and s only when a principal or secondary accent falls on the last syllable as "Boniface's mistake"; "Quackenbos's Rhetoric," etc.