JUST WHEN its nationa rail-passenger network is facing severe cutbacks, Amtrak's business has surged. With gasoline supplies uncertain and air travel snarled by the United Airlines strike, thousands of travelers are rediscovering trains. Amtrak has just assigned more cars to its Los Angeles-San Diego line. Advance bookings for several long-distance routes are mounting fast as nervous families try to tie down their summer plans.

Does this make it shortsighted and ill-timed to eliminate over 40 percent of Amtrak's mileage, as the Carter administration has proposed? In general, no. Outside the Boston-Washington corridor, Amtrak carried only about 8.6 million passengers last fiscal year. That is a tiny fraction of intercity travel, but one that consumes large subsidies. According to the Department of Transportion, eliminating 12,000 miles of sparely used lines would affect just 9 percent of Amtrak's current ridership and save almost $1.4 billion in the next five years. A vast throng of new passengers-far more than anyone anticipates-would be needed to overcome that kind of arithmetic.

Congress seems to agree that future federal investment in Amtrak should be concentrated on the most heavily used lines. Efforts to disapprove the whole DOT cutback plan have not gotten anywhere. Instead, the Senate and House committees are trying to save a few of the 16 threatened routes, including the Washington-Montreal route, and encouraging various states to help sustain others. At the same time, the lawmakers seem willing to provide a fair amount of capital for new equipment and track repairs on the remaining Amtrak lines.

That general approach makes sense. Where enough people do ride the rails consistently, not as a last resort or a one-time trip-of-a-lifetime, there ought to be good service and good trains.