Absolute Elements

Most of the elements of a sentence have a clear grammatical relation to one another. But there are pieces of structure which have no evident relationship to anything else.

Noun absolute:He lay down, his heart heavy with sorrow.
Hat in hand, he came down stairs.

The participle absolute is more frequent.

Participle absolute:This said, he sat down.
One of them having fallen, the rest ran away.
The teacher absenting himself, there was no school.