The general rule is to use the apostrophe-s for the possessive form of proper nouns and generic names of living or tangible entities, as in “Alicia’s dilemma,” “Manila’s nightlife,” “the planet’s survival,” “Jupiter’s 66 confirmed moons,” “the monkey’s back,” and “the beetle’s lifespan.” Awkward-sounding possessives often result when the apostrophe-s is used for the possessive of inanimate things or abstract concepts, as in “table’s edge” (better: “edge of the table”), “fairy’s tales” (better: “fairy tales”), “democracy’s enemies” (better: “enemies of democracy”), and “sin’s wages” (better: “wages of sin”); such constructions should be routinely avoided. Of course, there are some exceptions to the rule against using the apostrophe-s for the possessive of inanimate things, such as “the razor’s edge” and “a doorknob’s function.”
Based on the above guidelines, both the possessive forms “essay introduction” and “essay’s introduction” fail the euphony test; the better form is “introduction to the essay.” “Bank card” sounds better than “bank’s card,” and “student card” sounds better than “student’s card.”
When in doubt, use the possessive form that doesn’t sound dissonant or jarring to the ear. I would say that the ultimate criterion for using or not using the apostrophe is how badly the construction sounds when said aloud.
