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.
Participial phrases preceded by a conjunction or by a preposition, nouns in apposition, adjectives, and adjective phrases come under the same rule if they begin the sentence.
On arriving in Chicago, his friends met him at the station.
When he arrived (or, On his arrival) in Chicago, his friends met him at the station.
A soldier of proved valor, they entrusted him with the defence of the city.
A soldier of proved valor, he was entrusted with the defence of the city.
Young and inexperienced, the task seemed easy to me.
Young and inexperienced, I thought the task easy.
Without a friend to counsel him, the temptation proved irresistible.
Without a friend to counsel him, he found the temptation irresistible.
Sentences violating this rule are often ludicrous.
Being in a dilapidated condition, I was able to buy the house very cheap.
Wondering irresolutely what to do next, the clock struck twelve.
III. ELEMENTARY PRINCIPLES OF COMPOSITION
8. Make the paragraph the unit of composition: one paragraph to each topic.
If the subject on which you are writing is of slight extent, or if you intend to treat it very briefly, there may be no need of subdividing it into topics. Thus a brief description, a brief summary of a literary work, a brief account of a single incident, a narrative merely outlining an action, the setting forth of a single idea, any one of these is best written in a single paragraph. After the paragraph has been written, examine it to see whether subdivision will not improve it.
Ordinarily, however, a subject requires subdivision into topics, each of which should be made the subject of a paragraph. The object of treating each topic in a paragraph by itself is, of course, to aid the reader. The beginning of each paragraph is a signal to him that a new step in the development of the subject has been reached.
The extent of subdivision will vary with the length of the composition. For example, a short notice of a book or poem might consist of a single paragraph. One slightly longer might consist of two paragraphs:
A. Account of the work. B. Critical discussion.
A report on a poem, written for a class in literature, might consist of seven paragraphs:
A. Facts of composition and publication. B. Kind of poem; metrical form. C. Subject. D. Treatment of subject. E. For what chiefly remarkable. F. Wherein characteristic of the writer. G. Relationship to other works.
The contents of paragraphs C and D would vary with the poem. Usually, paragraph C would indicate the actual or imagined circumstances of the poem (the situation), if these call for explanation, and would then state the subject and outline its development. If the poem is a narrative in the third person throughout, paragraph C need contain no more than a concise summary of the action. Paragraph D would indicate the leading ideas and show how they are made prominent, or would indicate what points in the narrative are chiefly emphasized.
A novel might be discussed under the heads:
A. Setting. B. Plot. C. Characters. D. Purpose.
An historical event might be discussed under the heads:
A. What led up to the event. B. Account of the event. C. What the event led up to.
The Elements of Style · The Wunder Library — complete classics, free to read, with narration.