Основы теории английского языка. Листунова Е.И. - 93 стр.

     It’s grand up there with the gorge all round... and now and then
a young hawk overhead (Galsworthy) (adverbial modifier). He... gave
up wine and cigars, drank a special kind of coffee with no coffee in it
(Galsworthy) (attribute).

                           Nominative Absolute

      1. The subjects of the action denoted by the partici ple is usually
expressed by some noun or pronoun in the sentence.
      He strolled along the streets looking in the shop windows (Mazo
de la Roche). She heard a voice calling her (Lawrence).
      But sometimes the participle has asubject of its own expressed by a
noun (in the common case) or a pronoun (a personal pronoun in the
nominative case). Such a construction is called the «Nominative Absolute».
      The rain having rained my hat, I had to buy a new one. Here the
noun rain is not the subject of the predicate had to buy; it stands
independently (it is absolute, i. e. independent) and denotes the sub-
ject of the action expressed by the perfect partici ple having ruined.
Thus the relation between the noun and the partici ple is that of
secondary subject and secondary predicate.
      Although the «Nominative Absolute» is formally independent of the
sentence, it is logically connected with it, serving as an adverbial modifier
to the predicate: the rain having ruined my hat (adverbial modifier of cause
= as the rain had ruined my hat), /had to buy a new one,
      The «Nominative Absolute» is chiefly used in literary style.
      The «Nominative Absolute» usually expresses a d verbial relations
(time, cause, condition, manner or attending circum stanñes):
      a) Time:
      A private sitting room having been engaged, bed rooms inspect-
ed, and dinner ordered, the party walked out to view the city (Dick-
ens). This being done, they set off with light hearts (Irving).
      b) Cause:
      Fleur having declared that it was simply impossible to stay in-
doors, they all went out (Galsworthy). ...It being found impossible to
awaken Mr. Pickwick from his torpore, some discussion took place...
(Dickens). Martin had to carry his water from the kitchen, there
being no tap in the room (London).
      c) Condition (rare):
      Weather permitting, we shall start tomorrow.

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