Governor's Run Beach at Calvert Cliffs, Maryland, is not open to the public. Yesterday's Weekend section contained incorrect information on that point. GO TO THE OTHER BEACH! The last Weekend said that there are two public beach areas at Calvert Cliffs; actually there's only one _ Calvert Cliffs State Park. The other one, Governor's Run Beach, is not open to the too much, you say, and what can you do there, anyway?

This weekend you can journey 25 million years into the past on a few gallons of gas. All it takes is a few hours to reach the Calvert Cliffs, stretching from Fairhaven in Anne Arundel County to Drum Point in Calvert County, snug up against the Chesapeake Bay.

The cliffs are the upthrust bed of a shallow, temperate sea that covered southern Maryland during the Miocene era 10 to 25 million years ago, a time of great volcanic activity and uplift in these parts, when the coast of North America began to assume its present shape.

Now the cliffs stand as a window on that distant past, providing a layered look at the ages of the earth and yielding the fossilized remains of more than 600 plants and animals -- porpoises, sharks, sea cows, mastodons, tapirs, peccaries and even rhinos.

Most of the cliffs are owned privately and trespassing is prohibited. But there are two public areas for viewing the cliffs, scanning them for fossils newly exposed by sea or rain and collecting those that have been washed out onto the beach: the beach at the end of Governor's Run Road and the beach in Calvert Cliffs State Park.

A fee of $1.50 for adults and 50 cents for children at the Governor's Run Beach area is collected at the General Store, which also has a helpful display of the fossils to be found on the beach.

There's no charge at the Calvert Cliffs State Park. Instead, you pay your dues with a 13/4-mile hike to the beach. It's a pleasant toll, though: The easy trail winds through cool woods filled with wildflowers and rich smells.

Park rangers are generally on the beach from 1 to 5 on the weekends to provide information about the cliffs and the fossils. They remind all visitors that it's not permitted to climb on or dig into cliffs anywhere along the Bay.

Should you spot a large, unusual specimen lodged within the cliffs, they ask that you notify them, and they will contact the proper authorities to see that it's removed properly and preserved. Play your cards right and it might go on display, with your name on it as "found by."

Then you would join a list of discoverers headed by Captain John Smith, credited with being the first white man to see the cliffs. Referring to them as "Richard's Cliffes" in his journal of 1608, he makes mention of the sandy soil containing many "curiosities." Local Indians were also frequent visitors to the cliffs, and there's evidence of their using shark teeth as scrapers and spear points.

While you're in the area, you might want to investigate several other areas of interest, such as the Battle Creek Cypress Swamp, the East Coast's northernmost cypress swamp. It offers a pleasant hike on a quarter-mile boardwalk through the swamp and an information center.

On the road toward Solomons Island is the Calvert Marine Museum -- a must stop for information on the fossils at Calvert Cliffs and the ecological and marine history of the area. An entire room is devoted to the paleontology of the cliffs, including many examples of the fossils to be found.

A superb way to end the day is with a sunset dinner in Solomons Island -- a quiet, beautiful town at the mouth of the Patuxent River.

Good fossils, good food, good luck and good hunting. SIFTING THE SANDS OF TIME From the Beltway, take Maryland Route 4 south (exit 11A) through Prince Frederick, approximately 31 miles. BATTLE CREEK CYPRESS SWAMP -- Turn right on Route 506, approximately one mile south of Prince Frederick. GOVERNOR'S RUN BEACH -- Turn left on Governor's Run Road (Route 509), approximately five miles south of Prince Frederick. CALVERT CLIFFS STATE PARK: Continue on Route 4 approximately 15 miles south of Prince Frederick. Park is on the left, three miles south of Calvert Nuclear Plant. CALVERT MARINE MUSEUM: Continue south beyond park. Road signs are plentiful.