1. “Students write a third essay regarding the impact of geography on history and culture.”
The implication of this sentence is that students produce three essays on the topic in question. But if the preceding text refers to differing topics for the first two essays, the sentence suffers from insufficient differentiation. This revision specifies that the third essay’s topic differs from those of the others: “Students write a third essay, this one regarding the impact of geography on history and culture.”
2. “Students participate in a workshop on learning to research effectively and refine their search with a professional researcher.”
The relationship between the verb phrases in this sentence is unclear: Do students first participate in a workshop and then refine their research, or do they participate in a workshop about researching effectively, during which they also refine their search? Either way, the sentence, because of the ambiguity, is erroneously organized.
If the former meaning is intended, the sentence should read, “Students participate in a workshop in which they first learn to research effectively and then refine their search with a professional researcher.” If the latter meaning is the correct interpretation, it should read, “Students participate in a workshop on learning to research effectively, and then refine their search with a professional researcher.”
3. “He invoked the dreaded comparison with Mary Smith, only Jones has been more successful in her sport than Smith.”
Because of the paucity of punctuation in this sentence, the sentence could be read as containing a comma splice, an error in which a comma is incorrectly employed in place of a more substantial punctuation mark. But if a semicolon or a period separates the two clauses, and the second element (depending on which punctuation mark is used, an independent clause or a separate sentence) seems to imply that no one other than Jones has been more successful than Smith, a non sequitur results.
It’s much more likely that only serves as a less formal synonym for however. However, just as when that word is used, the sentence still requires stronger punctuation to clarify its function: “He invoked the dreaded comparison with Mary Smith; only, Jones has been more successful in her sport than Smith.” The semicolon seems too formal for the casual only, though; a dash seems more appropriate. Either way, however, only must be set off from the following statement by a comma: “He invoked the dreaded comparison with Mary Smith — only, Jones has been more successful in her sport than Smith.”
4. “She also uses a Geiger counter, which measures radiation; motion detectors; barometric-pressure monitors; and thermometers.”
This sentence, containing four listed elements — only one of which, the first, is modified — is hampered by the notion that because of that extra phrase, the usual commas must be promoted to semicolons to bear the burden of supporting the sentence’s structure. When used with such short phrases, however, the semicolons seem overbearing.
The simple insertion of the conjunction plus, which serves to provide more distance between sentence elements than the standard and, obviates the complicating semicolon solution: “She also uses a Geiger counter, which measures radiation, plus thermometers, motion detectors, and barometric pressure monitors.” (Notice that, for euphony, I’ve reordered the additional list items according to the number of syllables in each item.)
5. “The majority has upheld the act in whole, not by relying on an expansive reading of the commerce clause, but on Congress’s firmly rooted power to tax.”
The initial proposition in this sentence, “The majority has upheld the act in whole not by relying on an expansive reading of the commerce clause . . .,” is a continuous thought, and there is no reason to include punctuation within it.
But there’s a larger problem: The sentence is not parallel. Relying should be repositioned to serve both propositions (those beginning “not on” and “but on”), because the structure of the two phrases, in the original sentence respectively headed by “not by” and “but on,” is discordant. The solution, which (like “not only . . . but also” constructions), requires no internal punctuation: “The majority has upheld the act in whole by relying not on an expansive reading of the commerce clause but on Congress’s firmly rooted power to tax.”