Thirteen million years ago the place where we are standing was covered by a warm, shallow sea, paleontologist Tim Collins tells a group of 11-to 13-year-olds who have come to Calvert Cliffs State Park in southern Maryland to hunt fossils with the Audubon Naturalist Society. As we shiver on the beach, we try to imagine whales, porpoises and sharks swimming in the long-ago sea, and rhinos and three-toed horses running along the shore. For unbelievers, there is evidence: fossil remains of the defunct creatures piled up in layers in the cliffs. As marine creatures died, they fell to the bottom of the sea. The remains of land creatures sometimes floated down streams into the sea too. Later, during the ice age, the seas receded, exposing the fossil deposits.

Now the cliffs are being eroded by the waves, Collins explains and fossils often turn up on the beach. It's okay to collect those, but not to dig fossils out of the cliffs. Digging fossils out of the cliffs is impossible now anyway, since it's high tide and there's not enough beach left between the cliffs and the water for safety's sake.

Armed with spades, sifters and magnifying glasses, the kids take off down the part of the beach that isn't overhung by cliffs. Some dig in the sand. Others wade in the water. All run frequently back to Collins for show-and-ask.

"Is this a shark's tooth? someone asks.

"It looks like a rock to me," says Collins.

"That's a Chesapecten," says Collins to another kid. "It's a fossil scallop about 13 million years old."

"Is that a shark's tooth?" asks a little girl.

"No, but it's a piece of a fossil barnacle," says Collins to the finder, who seems disappointed nevertheless.

Rusty Frantz has brought a plastic box of sharks' teeth collected on other trips and brings them out so the other kids can see what sharks' teeth are supposed to look like.

"There are little places where the teeth attach," points out Collins. "That's one of the ways you can tell."

Susan Mead has found one in the bank of a stream that runs into the Bay, and the other kids gather to admire the tiny tooth.

"Sharks have about three hundred teeth," says Audobon Society naturalist Simpson. "That's why there are so many of them."

But to the kids who are digging furiously in the sand near where Susan Mead found her shark's tooth, they seem as scare as hen's teeth. Chesapectens, however, are less elusive.

"That one's been buried in the sand for some time and has undergone some changes in the composition of his shell -- or her shell," says Collins.

The rain that was threatening all along is coming down in earnest now and soon even the most intrepid fossil hunters huddle under a tree to eat lunch.

"I'm sort of confused," confessed a kid. "How can you tell a fossil from whatever it is now?"

"I can tell because I know what they look like," says Collins, chomping on a large carrot. "In the cliffs you can tell by the stratigraphy. Each layer represents a different period of time. When something new comes along, it lands on top. It's frustrating not being able to go right to the cliffs, but what those people are doing is very dangerous."

Another group of fossil-seekers is collecting near the cliffs. Water laps at their heels.

"Sometimes there are slides -- parts of the cliff fall off," Simpson explains.

To get the big picture of life in Miocene times, the group treks through the woods back to the van for a visit to the Calvert Marine Museum.

There are mastodon teeth on display at the museum and peccary jaws and even a rhinoceros tooth. But the kids are most interested in the sharks' teeth. The first collectors, an exhibit tells them, were Patuxent Indians, who turned their sharks' teeth into thumbscrapers or projectile points.

Susan Mead gets out her newly found shark's tooth to compare it with the specimens behind glass, while Rusty Frantz offers some of his specimens which he calls "my portable dentures" to disappointed fossil seekers.

"Oh my gosh, I wouldn't want to meet the guy that goes with that tooth," he says, pointing to a large shark tooth in a case.

One girl has droped a shark's tooth on the brown carpeted floor and other kids crawl around searching until the tooth is found.

" it looks like the tooth of a brown shark," deduces Megan Coss. "Or maybe the thresher shark . . . "

The rain has stopped and the kids aren't ready to give the search, so the van heads for Governor's Run and still more Miocene cliffs. The Governor's Run beach and cliffs are on private property, so we go into a small store at the beach and pay a fee.

"See this?" says the propietor holding a big, mean-looking shark's tooth hung around his neck on a chain. "I found this at the foot of the cliffs about four months ago."

Inspired, we head for the cliffs. they are topped with bungalows that look as if they're about to topple off, but there's a wide stretch of beach to run away from avalanches on.

One kid quickly finds a fossilized oyster, and Jonathan Buchner presents Collins with a lump of clay with prints in it. a

"The actual shell has weathered away, but the print remains in the clay," explains Collins. "Like if you made jello in a mold."

"Is this a shell or a bone?" asks Megan Coss of Collins, who explains that bones usually show more of a honeycomb structure.

Heather Morrow shows a fossil that turned up in her sifter.

"Tim says it's a little animal that drills into shells -- a turatella snail."

One boy entrusts some sharks' teeth he has found to Sheila Simpson, confiding, "My sister would never forgive me if I lost them."

Two other kids decide to conduct another type of scientific experiment. "Let's see if this fluorescent light bulb floats," says one, hurling it into the bay.

Meanwhile, Collins has found a large mound that has fallen from the cliff and he's combing it for fossils. "How many sharks' teeth have you found?" asks a kid.

"I found some nice clams," replied the paleontologist. "I know everybody here is looking for sharks' teeth, but I happen to like mollusks." FOSSIL FINDING Calvert Cliffs State Park is located five miles north of Solomons on Maryland Route 4. Admission is free. To get to the beach and the cliffs, you have to walk about two miles on a wooded trail. Plan your visit at low tide.

Governor's run in located about six miles south of Prince Frederick at the end of Maryland Route 509. The Cliffs Store controls access to the beach and charges 50 cents for children, $1.50 for adults. The parking lot is adjacent to the beach and there is no long walk through the woods.

The Calvert Marine Museum is at Solomons on Maryland Route 4. Adimission is free. A useful publication on sale at the museum for $1.50 is fossils of Calvert Cliffs by Wallace L. Ashby.

For information about future audobon Naturalist Society field trips, call 652-5964.