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Punctuation and Logic of Compound Main Clauses
Lassie, Come Home, by Eric Knight 
Analysis Key

1. Their clothes were coated (P) {with muck}, | and {in the men's hands} or {on 

their heads} were lanterns. |

The two clauses are joined by ", and" because they both are physical descriptions of the men.
2. But this {at last} was her solution (PN) | -- she must walk {among men}. |
The dash suggests that the second main clause equals the "solution."
3. She stared {at him} | and then she clasped her hands (DO) together. |
The "and" implies two equally important actions. [Note the absence of a comma.]
4. The rain streamed {from her coat}; | the mud splashed up {over her legs}. |
Does the semicolon reflect the contrast between the downward action of the rain and the upward splashing of the mud? She's getting it from top and bottom.
5. Lassie got up again and went back {to the sun}; | but that was not the answer (PN). |
The "; but" suggests a contrast between the possibility stated in the first clause and its negation in the second. The "but," in the sense of "except," excepts this "answer" from the remaining possible answers.
6. She tried to lift her head [#1] | but it would not move. |
"But" here probably introduces an exception to what one would expect.  [Note the absence of a comma.]
7. The conclusion to draw [#2] is this (PN): | *You* Never trust a dog (DO)! |
The colon indicates that what follows will in some way equal or explain what follows. In this case, the second clause equals the "this," which, as a predicate noun, is equal to the "conclusion."
8. And the heart was gallant (PA) | and the instinct was true (PA). |
The "and" joins two equally important characterizations.  [Note the absence of a comma.]
9. Freeth began to laugh [#3], | but McBane's tone halted him (DO). |
The ", but" reflects McBane's opposition (exception) to Freeth's laughing.
10. "Well [Inj], I'll tell you (IO) the truth (DO) | -- it escaped." |
The dash implies that what follows will amplify (clarify) something that was just said. In this case, the second clause equals the "truth."

Notes
1. "Head" is the direct object of the verbal (infinitive) "to lift." The infinitive phrase functions as the direct object of "tried."
2. The verbal (infinitive) "to draw" functions as an adjective to "conclusion."
3. "Began to" can be considered a helping verb, thereby  making "began to laugh" a finite verb phrase, or "to laugh" can be explained as a verbal (infinitive) that functions as the direct object of "began."