(2) The adverbial use, modifying the predicate, instances of which were seen in Sec. 352, 3. In these the participial phrases connect closely with the verb, and there is no difficulty in seeing that they modify.
These need close watching.
There are other participial phrases which are used adverbially, but require somewhat closer attention; thus, "The letter of introduction, containing no matters of business, was speedily run through."
In this sentence, the expression containing no matters of business does not describe letter, but it is equivalent to because it contained no matters of business, and hence is adverbial, modifying was speedily run through.
Notice these additional examples:—
Being a great collector of everything relating to Milton [reason, "Because I was," etc.], I had naturally possessed myself of Richardson the painter's thick octavo volumes.
Neither the one nor the other writer was valued by the public, both having [since they had] a long warfare to accomplish of contumely and ridicule.
Wilt thou, therefore, being now wiser [as thou art] in thy thoughts, suffer God to give by seeming to refuse?
(3) Wholly independent in meaning and grammar. See Sec. 355, (5), and these additional examples:—
Assuming the specific heat to be the same as that of water, the entire mass of the sun would cool down to 15,000° Fahrenheit in five thousand years.