WE WERE well into the Atlantic in about 25 degrees north latitude and somewhere south of Bermuda on a calm and blessed summer evening when the navigator, Massimo, fell down the forehatch without a sound.

He was standing on the foredeck, glued to the sextant, swaying gently against the eternal soft rolling, his broad shoulders and the instrument darkly outlined above the dim horizon on a field of steel stars - and then he was no more.

My first thought, still crystal and horribly clear now, eight months after that evening, was simply, "My God, he's crashed the sextant."

That little black instrument (a crummy sextant by the way, a $69 plastic job) was our only guarantee of finishing up the voyage at Cape Henry - without it, we were sailing for the continent of North America.

Massimo survived the fall with only a sprained ankle and the sextant survived totally, but the subject of celestial navigation, the seagoing mystery show, remains to me what it has always been - a pain.

Those miserable tables! Awful Azimuth, Dread Declination, Greenwich Hour Angle of Woe, Nautical Almanac, pages of figures, Sideral Hour angle. And above them all, and king of all, Kideous Error, with his gray, toothy companion, Gnawing Doubt.

The hours spent with the incomprehensible tomes of Bowditch, the confident prattling of Mary Blewitt, the austere advice of Eric Hiscock. Who has not feared and dreaded those hours, sweated through them? And been afraid to say so?

Navigators - like doctors or lawyers, wrapped in the dignity of their exclusive knowledge - smug and rolling in their mathematical excellences, nodding wisely, scribbling importantly, calculating gravely and then pointing to some empty spot on the chart with a final suck on their pipes, saying, "This, gentlemen, is where we are."

Celestial navigation, far from being an art or a science, has been to me the tax paid for going to sea, the price of freedom, worse than seasickness, worse than the dark and unknown shore on a stormy night.

But amateur navigators of the world, take heart. A new system of celestial navigation is shining like a long sought beacon in your darkness - celestial by calculator.

There is nothing new about the use of calculators in navigation. In fact their use is so well known it has received one of the notable nautical accolades - disapproval by the U.S. Coast Guard, which will not allow advanced calculators to be used by candidates for ships officer licenses.

What is new is a calculator/celestial system developed by two young Washington men who make an astounding claim. Their system, they promise, can give a virtually ignorant person a working knowledge of celestial navigation in a single day.

Jack Buchanek, 41, and Edward J. Bergin, 34, a pair of policy analysts at the Labor Department, have set themselves up as the Calculator Navigation Institute, Alexandria, Va. 22302, and they promise to teach you celestial navigation in a single day.

Now as dubious as the old school navigator may be of a system that depends on a little black box with buttons, quartz watches and transistor technology, you can't be dubious about Buchanek's flat statement: "If we don't teach it, or if you're not satisfied, you get your money back."

Bergin and Buchanek held their first day of instruction Feb. 5 at the well known Annapolis Sailing School with three students in attendance. The all-inclusive fee for the course, to be held Saturdays at the school, is $169.

What about the method? The heart of it is the idea that the calculator solves the mathematical problems of the star of sun sight directly, and so the tables which we have thumbed desperately through so many times, and which, after all, are only lists of solutions to the celestial triangle, can be left to gather dust and leak stains on the cabin shelf. The only traditional tome required is the year's Nautical Almanac, a relatively comfortable, nonhorrifying volume.

"What makes celestial navigation so bad is the rules," says Buchanek."The rules are what you depend on to get around the complex mathematics. But the calculator takes you back to facing the mathematics directly."

But a cautionary word about calculators is necessary. You can't approach a problem that involves sines and cosines and tangents with a simple add, multiply and divide calculator from the drug store. You must have a scientific, or slide-rule calculator. This piece of gear will cost from $55 to $200. The capacities the machine must have are for square roots, exponents and reciprocals, and at least one memory for saving a number until you need it.

In practice, "working down" a sight with the calculator is easy. By the old method, the Gnawing Doubt method, it has taken me as much as three hours. The first one worked with the calculator took four minutes. All I had to do was to follow a sheet of paper which literally told what buttons to punch, and at the end - there was the intercept.

Now you are doubtless saying. "Very well: but the calculator is likely to turn to green cheese in the salt air, or topple into the bilge, or fall overboard, or crash to the cabin sole never to blink its digital eyes again." These objections are perfectly legitimate and Bergin/Buchanek advise their students never to set sail for another continent without a backup system - in fact either the old system of sight reduction tables, or their own choice, the Ageton method, a time-proven tabular approach to solving the celestial triangle that employs Hydrographic Office Volume No. 9 (Bowditch's American Practical Navigator) and of course the Nautical Almanac.

Bergin/Buchanek make another logical departure from standard practice in recommending a quartz crystal watch instead of a $400 chronometer. Many quartz crystal watches now cost under $50, and a super waterproof model should cost about $200. To back that up, you should also have a radio capable of receiving either U.S. or British time signals.

With so many small boats heading for distant horizons these days, the calculator approach is sure to gain a wide following. The method's promoters point to two other advantages.

First, because of the speed of "working down" lines of position, the sextant man is likely to take more frequent sights. Second, and a little more obscure, they've figured out a way to use any visible star at twilight without bothering to identify it. By using the calculator and getting a simple compass bearing on the star, you can go into the Almanac and find out what star it is, without knowing beforehand. That is a terrific advantage on cloudy nights when often as not the "pointers" (the stars that lead you to the one you want to work with) are obscured.

Far from being mathematical whiz-kids, Bergin and Buchanek developed their method from necessity.

Planning an ocean trip, Buchanek tried to teach Bergin the traditional method, but failed. Bergin admits he was a celestial dropout.

"I simple couldn't learn it," he says, and so started fiddling with a calculator in an effort to "crunch the numbers." When the system began to emerge, they put it to the acid test - voyages to Bermuda and the Virgin Islands.

Then Bergin tried it on his 12-year-old daughter, Kinny. She learned it, and now plays a calculator like a piano. But Bergin knew his daughter was a lot smarter than he was, so last December the two policy analysts put a book together on the subject - Piloting/Navigating with the Pocket Calculator, TAB books, $13.95 - and began spreading the gospel of the "new" navigation.

"If I can understand it," says Bergin, "anyone can."