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The participle is a non-finite form of the verb which has a verbal and an adjectival or an adverbial character.
Participle may have different syntactic functions.
All the forms of Participle I may be used as an adverbial modifier.
a) adverbial modifier of time
Approaching Malta Street, Soho, Soams thought with wonder of those years in Brighton.
Having reached the classroom, she became the object of many questions.
Entering her room that evening, Elfride found a packet for herself on the dressing-table.
Turning slowly she went to the room.
b) adverbial modifier of manner and attendant circumstances
She ran screaming out of room.
She balanced herself on the curbstone and began to walk carefully, setting heel to toe, heel to toe, and counting her steps.
Gwendoline was silent, again looking at her hands.
He has been in three revolutions fighting on the barricades.
Participle II as an adverbial modifier
In this function Participle II is preceded by the conjunctions when, while, as if, as though, though.
a) of time
When questioned Annie had implied vaguely,… but she was anxious about her brother-in-law.
b) of condition
It was a dreadful thing that he now proposed, a break of the law which, if discovered, would bring them into the police court.
c) of comparison
Mr.Kantwise..shook his head as though lost in wonder and admiration.
Participle II of intransitive verbs which denotes passing into a new state may be used attributively, mostly with the verbs to fade, to wither, to retire, to fall, to vanish, e.g. faded leaves, a withered flower, a retired colonel, a fallen star, the vanished jewels.
An attribute expressed by Participle II may be detached; in this case it often has an additional meaning of an adverbial modifier.
The housekeeper had come out of her room, attracted by the violent ringing of the bell.
Accompanied by his father and Steger, he (Cowperwood) ascended to his new room.
Crushed at first by his imprisonment, he had soon found a dull relief in it.
If we have a participle used as an attribute the person denotes by the noun performs the action expressed by the –ing form; e.g. a dancing girl (a girl who dances), a singing child (a child who sings) and in the end in your case a screaming baby (a baby who screams)
If we have a gerund as part of a compound noun, the person or thing denoted by the noun does not perform the action expressed by the ing-form, e.g. a dancing-hall (a hall for dancing), a cooking-stove( a stove for cooking), walking shoes (shoes for walking).