The sentences of a good expository paragraph reflect a clear, rational analysis of the topic. Here is a brief example, this one by Bertrand Russell. (The sentences have been numbered for convenience.)
 The intellectual life of the nineteenth century was more complex than that of any previous age.  This was due to several causes.  First: the area concerned was larger than ever before; America and Russia made important contributions, and Europe became more aware than formerly of Indian philosophies, both ancient and modern.  Second: science, which had been a chief source of novelty since the seventeenth century, made new conquests, especially in geology, biology, and organic chemistry.
 Third: machine production profoundly altered the social structure, and gave men a new conception of their powers in relation to the physical environment.  Fourth: a profound revolt, both philosophical and political, against traditional systems of thought, in politics and in economics, gave rise to attacks upon many beliefs and institutions that had hitherto been regarded as unassailable.  This revolt had two very different forms, one romantic, the other rationalistic.  (I am using these words in a liberal sense.)  The romantic revolt passes from Byron, Schopenhauer, and Nietzsche to Mussolini and Hitler; the rationalistic revolt begins with the French philosophers of the Revolution, passes on, somewhat softened, to the philosophical radicals in England, then acquires a deeper form in Marx and issues in Soviet Russia.
Russell's nine sentences correspond to his steps in analyzing his topic:
Topic: increasing intellectual complexity Plan: list several causes First cause: larger area Second cause: science Third cause: machine production Fourth cause: intellectual revolt two forms qualification specification of the two forms
Examining whether the sentences of a paragraph correspond with its ideas is a good test of the coherence of the paragraph. The correspondence need not be as exact as in Russell's paragraph (and usually will not be). But if you cannot outline a generally clear relationship, the paragraph is probably confused and confusing.
The fact that a paragraph like Russell's reveals a coherent logical structure does not imply that the writer worked from an outline. One can proceed in this way, but in writing of any length an outline is tedious and time-consuming. Experienced writers adjust sentences to thought intuitively, without constantly thinking about when to begin a new sentence. Those with less experience must remain more conscious of the problem. Working up paragraphs from outlines provides good practice. But whether it is consciously thought out or intuitive, a well-made paragraph uses sentences to analyze the subject.
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