Louis Agassiz relied on ice-polished rocks near his home in Switzerland concluding that an Ice Age had occurred far more recently than previously thought.
Compare the two sentences:
Tim ran a mile in four minutes, finishing before the others.
Tim ran a mile in four minutes finishing before the others.
The first sentence is correct, because the dependent clause, “finishing…others”, must refer to the subject of the sentence. Otherwise, you are implying that “four minutes” finished before the others (that four minutes is awfully fast).
To show you how important a comma is when dealing with clause that starts with a gerund take a look at the following:
The dog lay down next to the man talking to his mother on the phone.
The dog lay down next to the man, talking to his mother on the phone.
The man sat down next to dog, talking to his mother on the phone.
Remember, it’s all about the comma. In the first sentence everything is fine, since if there is no comma, then the phrase beginning with gerund (“talking to his…phone”) should refer to the noun that comes right before it.
And that’s exactly what we want, unless we have a cartoon about talking dogs, which the second example implies. In other words, the comma between man and talking “breaks” them apart. Now, “talking” refers to the subject of the sentence, “dog” (like everyone these days, he’s probably got an iPhone).
The final sentence correctly uses the phrase, “talking to his…phone”, to describe the man (notice the comma).
Okay, now let’s up the difficulty of the material (let the sleeping dogs lie!).