Remember that the objective of this level is not to have the students learn the various verbals. It is to teach them how to know when these verbs should not be underlined twice.
 
1. On they rushed, sweeping and flapping, {like eagles} {after a hare}. |

"They sweeping and flapping" fails the sentence test. ["Sweeping" and "flapping" are verbals -- gerundives that modify "they."]

"To ask" fails both the "to" test and the sentence test -- "Me to ask the way" is not a sentence. [There are two valid explanations here. "Me" can be considered the direct object. That makes "to ask" a verbal (infinitive) that functions as an adverb answering the question "Why?" Or "me" can be consider the subject of the infinitive "to ask." This view makes the infinitive phrase the direct object of "have sent." In either case, "way" is the direct object of "to ask."]

"This girl to die" fails both the "to" and the sentence test. [Here again there are two possible explanations of the verbal. "Girl" can be seen as the direct object of "left" and the infinitive "to die" can be considered an adverb (How?) to "left." Or "girl can be seen as the subject of "to die" and the infinitive phrase then becomes the direct object of "left."]

     and {through the men's rooms, and the women's rooms}, and so {through

      all the house}. |

"He grinding his teeth" fails the sentence test. ["Grinding" is a gerundive that modifies "he." "Teeth" is the direct object of "grinding."]

"Them come howling" fails the sentence test. ["Them" is the subject of the infinitive "come." The infinitive phrase functions as the direct object of "saw."]
     "Them howling" also fails the sentence test. ["Howling" can be explained in two ways. For one, it can be seen as a gerundive that modifies "He." Second, it can be seen as a gerund (a verb that functions as a noun) that here functions as a Noun Used as an Adverb to "come."]

     the Immortals. |

Although "the people build alters to Father Zeus" passes the sentence test, it won't if we substitute a pronoun -- "(Let) them build altars." ["People is the subject of the infinitive "build," and "altars" is its direct object. The infinitive phrase functions as the direct object of "Let." The same holds for "worship" -- the "and" joins the two infinitives. "Immortals" is the direct object of "worship."]

     as he rolled along, dripping and glistening {in the beams} {of the morning sun}]. |

"He dripping and glistening" fails the sentence test. ["Dripping" and "glistening" are gerundives that modify "He," or, as above, gerunds that function as Nouns Used as Adverbs.]

"He watching the rich men" fails the sentence test. (It also violates the meaning--if we ask what saddened him, the answer is "Watching." Thus "Watching" also fails the noun test.) ["Watching" is a verbal, a gerund that functions as the subject of "saddened."
     Although "the men go in" passes the sentence test, it does not if we substitute a pronoun -- "them go in." ["Men" is the subject of the infinitive "go." The infinitive phrase functions as the direct object of "Watching."]

      force}], cast about {in his wicked heart} {*for* [OP how he might get 

     it (DO) {by cunning} ] } . |

"Polydectes" not being able" fails the sentence test. ["Being" is a gerundive that modifies "Polydectes."]
     "To get" fails the "to" test. [It is an infinitive that functions as an adverb to "able," which is a predicate adjective after "being."
     Grammarians will probably have a variety of explanations for the "how" clause, but the easiest is probably to consider it the object of the ellipsed preposition "for."
     "Cunning" will probably not cause students much of a problem because it is used more as a noun than as a verb. Technically, it is a gerund that functions here as the object of the preposition "by."

     day ^[NuA] long to see the blue Mediterranean sparkling, [Adv. (purpose) to

      "hoping"  that he might fly {across it} {to his home}]. |

"Perseus hoping" fails the sentence test. ["Hoping" is a gerundive that modifies "Perseus."]
   "To see" fails the "to test." [It is an infinitive that functions as the direct object of "hoping."]
    "The Mediterranean sparkling" fails the sentence test. ["Sparkling" can be explained in several ways. For one, it can be seen as a gerundive that modifies "Mediterranean," the direct object of "to see." At KISS Level 5.8, many people may prefer to see "Mediterranean sparkling" as a noun absolute that functions as the direct object of "to see."]