The genitive case. The formation of the genitive

The apostrophe is added only to regular plural nouns (boys', sol­diers') and to Greek names in -s of more than one syllable: Archimedes' [a:kimi:di:z] Law, Sophocles' tragedies, Euripides' plays.
With other proper names ending in -s there is vacillation both in pronunciation and spelling, but most commonly the spelling is the apostrophe only while the pronunciation is [iz]. Thus, Burns' (or less commonly, Burns's) is pronounced [-ziz]. Cf. also Dickens' novels, Jones' house etc. where the pronunciation is [ziz].
With compounds, the inflection -'s is added to the final element: my brother-in-law's children, my brothers-in-law's children.

The Use of the Genitive
The genitive case is used to express a variety of ideas: possession, relationship, physical features and characteristics, non-physical qualities and measurements.
The -'s genitive mainly occurs with animate nouns denoting personal names (Jane's brother, Mr Wilson's library, George Washington's statue), personal nouns (the student's answer, the girl's letter) and animals with personal gender characteristics mostly domestic, or those that are credited with some intelligence (the dog's tail, the cat's paw, the elephant's trunk).

The -'s genitive is not normally used with inanimate nouns. In­stead, the noun is modified by an of-phrase:
the colour of the dress, the leg of the chair, etc. However, some nouns denoting lifeless objects regularly occur with the -'s genitive and there is tendency to use the -'s forms even more extensively.

The -'s genitive is optional with collective nouns that refer to a group of people: the government's policy, the team's victory, the committee's meeting, the nation's social security, etc.; with geographical and institutional names: Africa's future, Moscow's traffic, America's resources, the school's history, the university's buildings etc.; with nouns considered to be of special interest to human activity: the earth's surface, the sun's rays, science's influence, the mind's general development, etc.

The -'s genitive tends to be obligatory with temporal nouns that refer to the length of duration of an event, and some substantivized adverbs:
a moment's thought, a week's holiday, a day's rest, a year's work, today's business, yesterday's news, an hour and a half's drive, a month or two's time.

Note the parallel structures: -
I've got three weeks' holiday in August.
I've got a three week holiday in August.
I need eight hours' sleep every night.
I need an eight hour sleep every night.

The -'s genitive is also common with nouns denoting distance and measure and also some miscellaneous nouns: a mile's distance, a shilling's worth, a room's interior, a book's title, the work's popularity, the engine's overhaul life, etc.
Some freely formed phrases seem to prove that it is not absolutely necessary for a noun to denote a living being in order to be capable of having an -'s form. There is a considerable number of fixed expressions in which all kinds of nouns occur in the -'s genitive: the ship's crew, the ship's doctor, a needle's point, keep someone at arm's length, keep out of harm's way, do something to one's heart's content, be only a stone's throw away, be at one's wit's end, for goodness' sake, etc.

With some nouns, both the -'s genitive and the of-phrase are used to express possession:
the Earth's gravity - the gravity of the Earth
the Queen's arrival - the arrival of the Queen
the plan's importance - the importance of the plan
Syria's history - the history of Syria.

The -'s genitive is generally used to talk about parts of people's or animals' bodies: a man's hand, a cat's tail. But to talk about parts of non-living things, the noun + noun structure or the of-phrase is used: the car door, a table leg, the roof of the house. Note that for words like top, bottom, front, back, side, edge, inside, outside, beginning, middle, end, part, the of-structure is usually preferred: the top of the hill, the end of the book, the bottom of the glass. There are, however, a number of common exceptions: the water's edge, the mountain top, etc.
The of-structure can refer to something that is used by a person or animal; the first noun refers to the user: children's clothes, women's magazines, a bird's nest. British and American English sometimes differ. Cf.:

British English:
a baby's bottle
a doll's house
a baby's pram
American English: a baby bottle,
a doll house
a baby carriage

The -'s genitive is also used for products from living animals: cow's milk, lamb's wool, sheep's wool, a bird's egg (but: camel hair).
Note that when the animal is killed to provide something, the noun + noun structure is generally used: calf skin, fox fir, chicken soup, tortoise shell.

The noun + noun structure is normally used to describe what objects are made of:
a silk scarf,
a stone bridge,
an iron rod,
a gold ring.

The Group Genitive
The inflection -'s may be added not only to a single noun but also to a whole group of words if it forms a close semantic unit. Various patterns can be found in this construction. Thus, in Smith and Brown's office not only Brown, whose name is immediately connected with the -'s, but also Smith is included into the possessive relation. Cf. also: Jack and Jill's wedding, Mr and Mrs Carter's house, Mary and John's children.