Let us suppose that Mr Kennedy threw that splendid book together as a break from the boring details of the Washington Naval Treaties and was astonished by its world-wide success.

The question then arises, what does he do next? How are you going to keep them down on the farm, now that they've seen Paree? asked the old song, and Mr Kennedy has seen Paree.

He has been lionised, interviewed, guest lectured, televisioned, and celebrated. He is worth several thousand dollars a pop on the speaking circuit. He reviews for publications like The New York Times which unlike the Transactions of the Royal HistoricalSociety are read by real people.

For such a man the correspondence of Metternich no longer beckons. The finer points of who did what to the Ems telegram have lost their allure.

It may be going too far to say that Mr Kennedy has sold his soul. But when a historian starts writing pop mega-books about the future, something has been sold to someone.

Having made a conspicuous success of predicting the End of the American Era, how do you follow it? Clearly there is a temptation to go on to the End of the World and Mr Kennedy has not entirely escaped it.

Mr Kennedy has also succumbed to that occupational hazard of the more commercially acceptable Renaissance painters, the temptation to sprout a large studio of assistants who can do repetitive things like crowd scenes and foliage in the master's style, leaving him to concentrate on overall design and the interesting bits.

In Mr Kennedy's case the studio takes the form of five graduate students (generously acknowledged in the foreword) who did much of the spadework.

I did not succeed as some reviewers claim to have done, in producing a separate grade for each of the five sub-authors. I did notice that there were some unresolved contradictions (is bio-technology a boon to consumers or a bane to peasant farmers?) which could be attributed to the many hands working behind the scenes.

Actually, Mr Kennedy is too intelligent and sensible to write a good book about the future.

Herman Kahn who was intelligent, but not sensible, used to utter outrageous predictions preceded with the usefully vague warning that they would occur in the next ''10-20-50-100 years''. Malthus, who was perhaps sensible but not intelligent, simply assumed that what was happening in his own time would continue, but worse.

At least Kahn and Malthus did say something about the future. Mr Kennedy outlines the problems comfortably enough - population, the global economy, food, automation, the environment - and nobody is going to be surprised by them.

When it comes to what happens next, the book hedges. If this, then maybe that, or possibly the other.

Here, for example is a typically timid summary, from the section on Chinese agriculture: ''This is not to say that Chinese agricultural policy has entered a cul-de-sac, but it is difficult to see how it can keep increasing crop output to match populationgrowth - unless technology provides another form of agricultural revolution. As things now stand, however, the structural obstacles to such a revolution appear daunting.'' One is reminded of the editor who advertised for a one-handed editorial writer. He wanted to avoid the phrase ''on the other hand. . .'' which crops up in this book with depressing frequency.

Mr Kennedy would make a good two-handed editorial writer. The book is rather like an editorial from The Economist - a journal which is often quoted - which has overflowed its usual bed and sprawled over 350 or so pages.

There is some well-crafted writing here, some interesting statistics, and a wealth of odd titbits of information which will send questions scurrying through any lively mind. Why is the UN Potato Research Centre in Peru? Why is Mongolia the only country where the education of women has not produced lower birth rates? Do three-quarters of Americans really not know where the Persian Gulf is? But in the last analysis the book is better at posing questions than giving answers. Perhaps that should not be surprising. After all, that is the difference between the past and the future. We know what happened in the past; we don't know what will happen in the future.

Readers may feel that they already knew we live on a ''troubled. . . planet whose problems deserve the serious attention of politicians and public alike.'' And they have not been much helped by the resounding conclusion that ''. . . the pace and complexity of the forces for change are daunting; yet it may still be possible for intelligent men and women to lead their societies through the complex task of preparing for the century ahead.'' Yet, if, however, on both hands and taking the medium to long-term view, Mr Kennedy might have been better advised to return to the Congress of Vienna.

History, as students are carefully warned by all honest teachers of this subject, does not predict the future. Historians should follow this example.