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I thought that I should always use "the" in front of noun + "of" since the noun is specified. But, I see some exceptions like:

A leaf can reach a diameter of 15 feet.

What is the rule of using an indefinite articled nounce in front of "of". I appreciate your insight and help.

  • You thought wrong. – Hot Licks Oct 21 '18 at 15:28
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As a matter of fact, the article of choice is context-dependent.

One can have a cup of tea while debating the subtleties of grammar.

Which article is chosen depends on the intent of the speaker, not on any preposition of the sentence.

Examples from ODO:

  • ‘the sleeve of his coat’
  • ‘the days of the week’
  • ‘a boy of 15’
  • ‘a former colleague of John's’
  • In fact, “Wednesday is a day of the week” and “Wednesday is the day of the week they collect trash” are both right. – Jim Oct 21 '18 at 2:14
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I asked essentially that same question some time ago, here: “Has a value of” vs. “has the value of”. What I've learned since then is approximately the following.

There is one unfortunate truth to keep in mind whenever English articles are discussed, and it is this: there is no completely general and reliable algorithm for figuring out which article (if any) is needed. On the contrary, it seems that the English system of articles has quite a bit of instability. In particular, there are many instances of article use that do not seem to be deducible from any general principles—something that becomes especially obvious in cases when there is a difference between British and American usage. So for example, when we want to say that someone has been hospitalized, in British English you'd say he's in hospital, whereas in American English you'd say he's in the hospital, even though you don't have a particular hospital in mind (see here). And there is no general principle that would explain why it's OK to say she has the flu even though we don't have any particular kind of flu in mind, but under the same conditions, it's not OK to say *she has the influenza (you must say she has influenza instead). As Janus Bahs Jacquet said in a comment to this question, 'Articles are a fairly random part of any language that has them: they pop up in places where you’d never expect them, and they’re conspicuous in their absence in places where you’d never dream of not seeing them. Their use is, to a certain extent, outside the normal logic of the grammar of a language, and their idiosyncracies must be learnt by rote.'

Now, as far as the particular construction you're asking about. It's a special case of the following construction: [measurable quantity] + of + [numerical quantity]. Other examples would be speed of, value of, price of, … And it is just a fact of English that before such a construction, you use the indefinite article:

The electric field within the capacitor has a value of 170 N/C.
The Commodore PET was also released in 1977 with a price of $800.
The front of the train has a speed of 23 m/s.

There does not seem to be a general principle that would allow you to deduce this rule. But it is a rule of English all the same.

So striving for completely general rules is probably hopeless. Nevertheless, there are some more restricted situations where some rules (or at least strong tendencies) may be discerend. Concerning preposition phrases with of, two such strong tendencies are described in the following section of Collins COBUILD English Guides: Articles (pp. 30-31):

4.10 Nouns qualified by an 'of'-phrase

There are two cases where an 'of'-phrase after a noun suggests a unique interpretation and so normally requires the definite article.

Firstly, where the noun involved refers to an action, event, or state and the 'of'-phrase indicates the performer of the action or the thing affected:

..following the closure of a Courtaulds factory.
Orders should not be cashed after the death of the person.
...the elimination of low pay.

Here the first nouns refer to (possible) actions or events, and can be related to verbs: a factory was closed, the person died, low pay was or will be eliminated.

Secondly, certain nouns which refer to a part or characteristic of something are followed by an 'of'-phrase very frequently, and have unique reference.

...after the beginning of the tax year.
The price of copper fell spectacularly.
...Picture 5 at the top of page 43.
...at the end of 1980.

The tax year has only one beginning, copper has only one price, page 43 has only one top, 1980 has only one end. Here are some nouns like this.

back              end         middle    top
beginning    front       price       weight
bottom         height     size
edge              length     title

Note that you can also use the definite article before these nouns even when they are not qualified because they are often found in association with other nouns which have been mentioned before.

A generalization of the above is given in another section of the same book (p. 30):

4.9 Nouns with qualification

The definite article is also used with nouns when it is the phrase or clause following the noun (rather than a previous word or the general situation) which indicates which thing the noun refers to. Nouns with phrases or clauses after them are said to be qualified.

It is the title of the chapter
...haunted by the fear that no one would turn up.

Nouns can be qualified in a number of ways:

• by prepositional phrases:

The only way to learn the price of something is to pay for it.
The reason for this selection is obvious.
...on the basis of the data in Table 7.l.
Of course he knew the answer to that one.

The preposition most commonly used in these phrases is 'of': see section 4.10 [above!].

• by relative clauses:

What about the argument that reality isn't like that?
the amount it cost to build the house.
…to get back to the hotel where he was staying.
the success which has been achieved.

• by clauses with non-finite verbs (that is, infinitives or participles):

Power at work is the power to get decisions implemented.
the interest paid on overdrafts and credit cards.

• by apposition (using one noun group to qualify another)

And he wrote a book with the title 'The Summing Up'.

Note that when uncount nouns referring to qualities or feelings are used with the, it is usually because they are qualified.

I tried to concentrate on the beauty of the scenery.
I share the anger that many of you must feel.

This leaves us with a practical question for non-native speakers: how does one figure out which article (if any) to use in any particular instance one is unsure of? There is only one answer: look at patterns of usage by native speakers. These days this can be done very effectively with the help of google books. Try googling the exact phrase you need, in all variations, and see if any patterns emerge. The patterns I'm talking about include the context in which the phrase appears. Play with the phrasing, modify a bit if need be.

And if no clear pattern emerges, this may well be because different native speakers would make different choices on that issue. In that case, it probably makes no difference (as far as acceptability) what choice you make.

  • Thank you for the answer to my question and some suggestions of using "google books". It is very clear. I really appreciate your help. – Sun J Oct 24 '18 at 10:22

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