In other words, do not use periods for commas.
I met them on a Cunard liner several years ago. Coming home from Liverpool to New York.
He was an interesting talker. A man who had traveled all over the world and lived in half a dozen countries.
In both these examples, the first period should be replaced by a comma, and the following word begun with a small letter.
It is permissible to make an emphatic word or expression serve the purpose of a sentence and to punctuate it accordingly:
Again and again he called out. No reply.
The writer must, however, be certain that the emphasis is warranted, and that he will not be suspected of a mere blunder in syntax or in punctuation.
Rules 3, 4, 5, and 6 cover the most important principles in the punctuation of ordinary sentences; they should be so thoroughly mastered that their application becomes second nature.
Walking slowly down the road, he saw a woman accompanied by two children.
The word walking refers to the subject of the sentence, not to the woman. If the writer wishes to make it refer to the woman, he must recast the sentence:
He saw a woman accompanied by two children, walking slowly down the road.