Auchincloss turns to Louis XIV; The Cat and the King, by Louis Auchincloss. Boston: Houghton Mifflin Co. $10. 95.

"He reigned, indeed, in little things; the great he could never reach. . . ." When France's spectacular Louis XIV is summed up in this way by a lesser member of his court, it seems clear that a cat may not only look at a king but look down on him. The quoted words are by Louis de Rouvroy, duc de Saint-Simon, in the monumental posthumous "Memoirs" that gave him more fame than could his courtly career.

Now, in a small novel echoing Saint-Simon's observant prose, Louis Auchincloss imagines the duc writing about himself after the 'Memoirs" have been completed -- a man dwelling on the coarseness and corruption in the midst of royal splendor even as he quests for order and "virtue."

The niceties of rank and lineage loom large to Saint-Simon, making him congenial company in the Auchincloss body of fiction set in more recent times.

It all adds up to an interesting literacy exercise for readers with a taste for palace gossip; a succinct evocation of a tawdry-elegant time; and, in the words of Saint-Simon's wife, a clue to how those "Memoirs" came about: "I've read all your notes, your memoranda, even your journal! I've read every scrap of paper in our whole house. And I know what you are at last. What you really are. You're not really a duke or a soldier or even a courtier. Your're a writer!"

Which Auchincloss's Saint-Simon proceeds to prove by noting that he's not sure his wife thought this was an honorable t hing to be.

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