THE CUT in passenger train service scheduled for Oct. 1 by Amtrak's board of directors is unlikely to please anyone.It is a deeper cut -- six routes totaling 5,000 miles -- than Amtrak's avid supporters believe is justified. But it is not nearly as deep as the cut sought by Amtrak's critics or by the Carter administration early this year.

What will be left of Amtrak, assuming the cuts become effective, will be the framework of a national railroad system with heavy emphasis upon the three urban corridors where the trains have attracted substantial numbers of passengers. What will be missing are five long-haul routes -- one stretching from Chicago to Seattle and another from Chicago to Miami -- whose use has never lived up to the expectations of those who planned the system. They are joined by a shorter route -- from Oakland to Bakersfield -- that may be saved by the state of California.

The disapperance of those trains will be a blow to some of the smaller communities they serve along the way.But the gaps in the transportation network can be filled adequately by the airlines or by bus companies at a saving of millions of dollars to the taxpayers.

It seems safe to conclude that other routes would also be on the Oct. 1 hit list but for the gasoline shortage of early summer. Trains like those from here to Montreal and New Orleans picked up sufficient business at that time to meet the criteria Amtrak is now using to determine which trains can be operated inside the subsidy limits Congress is likely to approve. But the fans of those reprieved routes should not be complacent; those routes are, at best marginal. Unless passengers flock to the trains in times when gasoline is easily available as well as when it is difficult to buy, the other routes put on the endangered list by the Department of Transportation last January may not long survive.

Congress, of course, has not had its say about the elimination of the six routes picked by Amtrak's board. Although these cuts seem to meet the criteria for such action approved by each house before the August recess, a final railraod bill has yet to emerge from the conference committee. Given the history of political meddling with Amtrak's routes, it is always possible that Congress won't react the same way when it is directly confronted with elimination of almost a fifth of Amtrak's total mileage as it did when it was setting criteria without knowing for sure which routes would disappear.

If sense prevails over sentiment, however, Congress will do nothing to interfere with the judgment Amtrak's board has made. There are limits beyond which the federal government should not subsidize passenger trains. Despite their sentimental appeal, these trains can no longer begin to approach economic self-sufficiency, and the six routes in question are clearly beyond those limits.