Can a which-clause be used with another which in this sentence?

Question

Apologies for the unclear title, but I wasn't sure how to phrase it.

Situation
Assume a table, on which lies an object, occupying half of the table. A hat is placed on the table.

Question
Which of the following sentences is correct?

1. The hat was placed on the table, half of which was occupied by an object
2. The hat was placed on the table, which half of which was occupied by an object

The second sentence feels so unnatural to me, but isn't the first one not quite right either? Though not ungrammatical, it has a ring of offering a rather parenthetical, separate clause rather than a clause describing the previous one (that is, reading the first sentence, I get an impression of "and by the way, half of the table was occupied by an object". Indeed, I feel a semi-colon rather than a comma would be preferable in that case).

Also consider the sentences

3. The hat was placed on the table, which was occupied by an object
4. The hat was placed on the table, which was partly occupied by an object

Any input on the matter would be appreciated.

Answer 1

The problem with using which in either of your example sentences (between the two, the first sounds more natural) is that it's not entirely clear if which refers to the hat or to the table. We can assume it refers to the table, but it's possible that it doesn't.

One way of rephrasing the sentence is to remove the comma and use an adjectival phrase:

The hat was placed on the table which was half-occupied by an object.

Without the comma, which is now easily parsed as applying to the table specifically.

---

But there is now another problem. Without the comma, the sentence implies that there is more than a single table and that, of all of the tables, the hat was placed on the one that was half-occupied by some object.

(If that actually is the intended meaning, then there is no problem.)

You mention using a semicolon. That would certainly be one way of removing this particular ambiguity:

The hat was placed on the table; half of the table was occupied by an object.

This works but it's a bit long-winded.

---

Perhaps the most appropriate method of saying this is to reuse an earlier suggestion but simply change the definite article in front of table to the indefinite article:

The hat was placed on a table which was half-occupied by an object.

This is concise, presents no ambiguity, and also doesn't convey the implication that there is necessarily more than a single table.