These unambitious sign-offs (styled ""homilies"") from 15 years of This Week with David Brinkley never pretend to much--and they surely don't presume to anything as weighty as a raison d'etre. Which makes for a graceful exercise but not for a discernible imperative, even for the author's following. The venerable Brinkley, who gave us his more substantive (if still characteristically anecdotal) Memoirs last year, takes on the usual Establishment targets, but his potshots are throwaways--180 pieces in 192 scant pages. In the aggregate, they constitute time-capsule commentary on the culture of the past decade and a half, however slight: The fastest-growing job in government (as of April 23, 1988) was that of prison guard; the IRS will be set up within one month after nuclear attack to collect taxes (this per some government memo); daylight saving time was moved up to the first Sunday in April due to lobbying by the Barbecue Industry Association. Brinkley ranges well beyond the Washington bureaucracy, sometimes pithily (""The Constitution calls for electing a president every four years, but it does not say we have to spend the whole four years doing it""), more often lamely (on why the Arabs need Israel: ""What would they find to do with themselves? What would. . . Arafat do for excitement?""). While Brinkley's authoritative weariness informs every one of the program-closing snippets, his stubbornly clipped sentences fail to resonate on the page as they do on the air. Clearly, his gift is lodged in the delivery--at least when it comes to afterthoughts.