A hospitalized President Reagan did not wait for the tragic sinking April 10 of a Japanese trawler by a missile-firing Polaris submarine to bring the admirals to heel by ordering full speed ahead on a vital submarine communications system they wanted stopped.

From the White House last week, an undated memorandum ordered Secretary of Defense Casper Weinberger to countermand the Navy's decision to cancel its extremely low frequency (ELF) communications system. The memo bore only Reagan's name, not his signature, but it had been orally approved from the hospital bed of the invalided commander in chief. b

"There shall be no funding reductions," Reagan said. "You should advise the Navy that I am not inclined to terrminate this much-needed program without compelling evidence to do so."

That presumably scuttled the effort by the admirals to play the familiar old Navy game: put aside currently needed projects at the expense of funding futuristic systems. Surprisingly, the Pentagon civilians did not bring the Navy brass up short; the decision on a piece of hardware had to go all the way to the president's hospital bed.

The Navy leaked the first news of this to the public via no champion of the Pentagon: Sen. Carl Levin of Michigan, a liberal Democratic and all-out environmentalist foe of ELF, a system destined for his home state. When Levin passed the word to the Detroit News, it exploded with the force of a Polaris missile among defense leaders on Capitol Hill.

For 20 years, the Navy and a few brave politicians willing to take on the environmentalist lobby had preached the soundness and safety of ELF. Without it, the president cannot communicate with submerged U.s. submarines; they must come close to the surface and trial their antennas.

That is probably what happened, Navy submarines told us, in the East China Sea tragedy April 10. The U.S.S. George Washington, a Polaris missile sub, was almost certainly surfacing to pick up new orders. That maneuver would be unnecessary with ELF.

In an international emergency, the president could not order U.S. strategic submarines to prepare for possible missile firings, or to rush to a new location, without risking their destruction by an enemy as they expose their surface antennas. ELF is "the critical linchpin" to wartime deployment of the subs, wrote Sen. John Tower, chairman of the Senate Armed Services Committee, in an angry note to Weinberger when he first heard about the Navy's decision.

Why, then, did the Navy risk congressional wrath and the commander in chief's personal affront by canceling ELF? The full reason is shrouded in Pentagon mists, but defense specialists -- including many submariners -- say the reason was simple greed for defense appropriations.

The Navy brass decidede the $34 million earmarked for ELF in the coming fiscal year could be used to develop a futuristic aircraft for communicating with submarines called TACAMO. Then in another year or two, it could return to ELF, knowing that growing congressional support of the ELF system would still guarantee delivery of the funds.

In so doing the Navy betrayed its friends who, on April 7, had won a referendum over the governmentalists in Ashland County, Wis., where the first part to ELF is being built. Supporting ELF in the name of national Security, veterans groups have spent thousands of dollars to argue there is nothing to fear from the underground antennas. The VFW had wired Adm. Thomas Hayward, chief of naval operations, two weeks earlier that cancellation would destroy Navy credibility.

The decision reversing the admirals was made by the White House on two grounds: First, ELF is the only foreseeable system to give the president command-and-control access to missile-firing submarines, which are a vital part of the strategic triad; second credibility of the entire defense establishment, not just the Navy, was on the line at a time the new administration is trying to restore American defenses.

Pentagon civilians, in distinction to this White House posture, did little to bring the admirals to heel. Entirely exempted WAS secretary of the Navy John Lehman, who pleaded conflict of interest stemming from his activities as a Washington-based defense consultant. Although Weinberger quietly informed White House aides of his own doubts about the Navy's decision, he did nothing publicly to force a reversal.

That left it up to the commander in chief. The display of a decisive president able to make a quick political decision from his hospital in the one dividend to emerge from the ELF affair. What Reagan should now do is transfer some of that spirit to the Pentagon.